bj frac manual v1.0 june 2005(a4)

8/17/2019 BJ Frac Manual v1.0 June 2005(A4)

http://slidepdf.com/reader/full/bj-frac-manual-v10-june-2005a4 1/265

BJ Services’ Frac ManualContents

Page i Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

BBJJ SSEERRVVIICCEESS CCOOMMPPAANNYY

HHYYDDRRAAUULLIICC FFRRAACCTTUURRIINNGGMMAANNUUAALL

TToonnyy MMaarrttiinnRReeggiioonn EEnnggiinneeeerr

SSiinnggaappoorree

VVeerrssiioonn 11..00((AA44--SSiizzeedd))

JJuunnee 22000055




Page ii Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

Contents

Contents .....................................................................................................................................ii

List of Figures ............................................................................................................................ v

1. Introduction................................................................................................................... 1

2. Basics of Hydraulic Fracturing...................................................................................... 4

2.1 The Basic Process ......................................................................................................................42.2 Pressure .....................................................................................................................................52.3 Basic Fracture Characteristics.....................................................................................................62.4 Fluid Leakoff ...............................................................................................................................82.5 Near Wellbore Damage and Skin Factor ....................................................................................9

3. Types of Fracturing.....................................................................................................12

3.1 Low Permeability Fracturing ......................................................................................................123.2 High Permeability Fracturing .....................................................................................................12

3.3 Frac and Pack Treatments ........................................................................................................133.4 Skin Bypass Fracturing .............................................................................................................153.5 Coal Bed Methane Fracturing....................................................................................................163.6 Fracturing Through Coiled Tubing.............................................................................................16

4. Fluid Mechanics..........................................................................................................19

4.1 Fundamental Fluid Properties ...................................................................................................194.2 Shear Stress and Shear Rate....................................................................................................194.3 Types of Fluid ...........................................................................................................................204.4 Measuring Viscosity ..................................................................................................................234.5 Apparent Viscosity ....................................................................................................................254.6 Flow Regimes and Reynold’s Number.......................................................................................264.7 Friction Pressure.......................................................................................................................27

5. Fluid Systems............................................................................................................. 29

5.1 Water-Based Linear Systems....................................................................................................295.2 Water-Based Crosslinked Systems ...........................................................................................305.3 Oil-Based Systems....................................................................................................................335.4 Emulsions .................................................................................................................................355.5 Energised Fracturing Fluids.......................................................................................................355.6 Visco-Elastic Surfactant Fluids ..................................................................................................365.7 Additives...................................................................................................................................40

6. Proppants ................................................................................................................... 45

6.1 Proppant Pack Permeability and Fracture Conductivity .............................................................456.2 Proppant Selection....................................................................................................................486.3 BJ Services FlexSand and LiteProp .........................................................................................50

7. Rock Mechanics .........................................................................................................53

7.1 Stress........................................................................................................................................537.2 Strain ........................................................................................................................................537.3 Young’s Modulus.......................................................................................................................547.4 Poisson’s Ratio .........................................................................................................................557.5 Other Rock Mechanical Properties ............................................................................................567.6 In-Situ Stresses.........................................................................................................................587.7 Stresses Around a Wellbore......................................................................................................597.8 Fracture Orientation ..................................................................................................................607.9 Breakdown Pressure and Frac Gradient....................................................................................617.10 Rock Mechanical Properties from Wireline Logs........................................................................63

8. 2-D Fracture Models................................................................................................... 68

8.1 Radial or Penny-Shaped ...........................................................................................................688.2 Kristianovich and Zheltov - Daneshy (KZD) ...............................................................................698.3 Perkins and Kern – Nordgren (PKN)..........................................................................................70




Page iii Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

9. Fracture Mechanics .................................................................................................... 72

9.1 LEFM and Fracture Toughness.................................................................................................729.2 Non-Linear and Non-Elastic Effects...........................................................................................759.3 The Energy Balance..................................................................................................................77

10. Advanced Concepts....................................................................................................80

10.1 Tortuosity..................................................................................................................................8010.2 Nolte Analysis ...........................................................................................................................8210.3 Dimensionless Fracture Conductivity.........................................................................................8210.4 Tip Screen Out..........................................................................................................................8310.5 Multiple Fractures and Limited Entry .........................................................................................8410.6 Proppant Convection and Settling .............................................................................................8510.7 Proppant Flowback ...................................................................................................................8610.8 Forced Closure..........................................................................................................................8810.9 Non-Darcy Flow ........................................................................................................................88

11. 3-D Fracture Simulators .............................................................................................91

11.1 RES’s FracPro and Pinnacle Technology’s FracproPT ..............................................................91

11.2 Meyers & Associates’ MFrac .....................................................................................................9211.3 Other Simulators .......................................................................................................................93

12. Predicting Production Increase................................................................................... 95

12.1 Steady State Production Increase .............................................................................................9512.2 Pseudo-Steady State Production Increase ................................................................................9612.3 Nodal Analysis ..........................................................................................................................99

13. Candidate Selection..................................................................................................101

13.1 Economic Justification for Fracturing.......................................................................................10113.2 Completion Limitations............................................................................................................10413.3 Things to Look For ..................................................................................................................106

14. Perforating for Fracturing..........................................................................................109

14.1 Controlling Fracture Initiation...................................................................................................10914.2 Controlling Tortuosity ..............................................................................................................11114.3 Perforating for Skin Bypass Fracturing ....................................................................................112

15. The Step Rate Test ..................................................................................................115

15.1 The Step Up Test....................................................................................................................11515.2 The Step Down Test ...............................................................................................................11615.3 Step Rate Test Example – Step Up/Step Down Test...............................................................117

16. The Minifrac.............................................................................................................. 121

16.1 Planning and Execution...........................................................................................................12116.2 Anatomy of a Minifrac..............................................................................................................12416.3 Decline Curve Analysis ...........................................................................................................12516.4 Pressure Matching ..................................................................................................................13116.5 Near Wellbore Effects and Multiple Fractures..........................................................................13216.6 Minifrac Example 1 - 2D Minifrac Analysis...............................................................................13416.7 Minifrac Example 2 - 3D Pressure Matching with FracProPT ...................................................13916.8 Minifrac Example 3 – Problems with Tortuosity .......................................................................14716.9 Minifrac Example 4 – Perforation Problems.............................................................................153

17. Designing the Treatment ..........................................................................................164

17.1 General...................................................................................................................................16417.2 Designing for Skin Bypass.......................................................................................................16517.3 Designing for Tip Screen Out ..................................................................................................16617.4 Designing for Frac and Pack...................................................................................................167

17.5 Designing for Tight Formations ...............................................................................................16817.6 Designing for Injection Wells ...................................................................................................17017.7 Designing for CBM Treatments ...............................................................................................170




Page iv Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

17.8 Designing for Coiled Tubing Fracturing ...................................................................................17217.9 Unified Fracture Theory and Proppant Number .......................................................................17317.10 Net Present Value Analysis.....................................................................................................174

18. Real-Time Monitoring and On-Site Re-Design......................................................... 176

18.1 Real-Time Data Gathering.......................................................................................................176

18.2 On-Site Redesign....................................................................................................................18118.3 Real-Time Fracture Modeling..................................................................................................183

19. Post Treatment Evaluation .......................................................................................186

19.1 Pressure Matching ..................................................................................................................18619.2 Well Testing for Fracture Evaluation........................................................................................19319.3 Other Diagnostic Techniques .................................................................................................205

20. Equipment.................................................................................................................209

20.1 Horsepower Requirements......................................................................................................20920.2 Flow Lines...............................................................................................................................21020.3 High Pressure Pumps .............................................................................................................21120.4 Intensifiers...............................................................................................................................214

20.5 Blenders, Gel Hydration and Liquid Additives..........................................................................21620.6 Proppant Storage and Handling ..............................................................................................21820.7 Treatment Monitoring..............................................................................................................22020.8 Wellhead Isolation Tool...........................................................................................................22120.9 The Frac Spread – How it Fits Together..................................................................................224

21. Designing Wells for Fracturing .................................................................................228

21.1 How Many Wells do I Need to Drill? ........................................................................................22821.2 The Best Wells are the Best Candidates for Fracturing ...........................................................22921.3 Designing Wells for Fracturing ................................................................................................229

22. The Fracture Treatment: From Start to Finish..........................................................232

22.1 Frac Job Flow Chart................................................................................................................232

22.2 Example Treatment Schedules ...............................................................................................238

Nomenclature ........................................................................................................................241

Index ..................................................................................................................................245



BJ Services’ Frac ManualList of Figures

Page v Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

List of Figures

Section 2

2.1a Typical hydraulic fracture treatment job plot.2.3a Diagram showing fracture half Length x f , fracture height H , and fracture width W .2.5a Illustration of the reduction in permeability around the wellbore.

Section 3

3.3a Diagram illustrating the components of the frac-pack completion.3.3b Diagram illustrating two of the four positions in which a standard gravel pack or frac

pack tool can be set. The left hand side shows the squeeze position, in which fluidsflow down the tubing, through the crossover, out into the annulus below the GPpacker and into the formation. The right hand side shows the lower circulatingposition. Fluid flows down to the perforations, as for the squeeze position. However,

because the setting tool has been shifted upwards, the fluid can flow either into theformation, or back through the screens, up the washpipe (inside the screens) throughthe crossover, and out into the annulus above the tubing (shown in blue). By closingthe annulus at surface, the fluid can be squeezed into the formation, whilstmaintaining a dead string on the annulus, to monitor BHP.

3.4a Diagram illustrating how the skin bypass fracture penetrates the skin to allowundamaged communication between the reservoir and the wellbore.

Section 4

4.2a Graph illustrating Newton’s law of fluids4.3a Relationship between shear rate and shear stress for a Bingham plastic fluid.4.3b Relationship between shear rate and shear stress for a power law fluid. Note that the

graph shows the relationship in its most common form. However, in certain fluids the

line can also curve upwards.4.3c Power law fluid log-log plot.4.4a Chandler 35 viscometer. The position of the rotor is indicated (A), whilst the bob is

hidden inside this. The cup (B) holds the test fluid, and is mounted on a support (C)that can move up and down as required.

4.4b Cross-section through the rotor and bob on a model 35 viscometer.4.4c Schematic diagram showing the model 35 viscometer bob assembly.4.4d Fann 50 high pressure, high temperature rheometer. This model is fully computer

controlled, whereas earlier models had manual controls and were twice the size of themodel shown.

4.5a Graph illustrating the change in apparent viscosity for a power law fluid at twodifferent shear rates.

4.6a Diagram illustrating the three flow regimes.

Section 5

5.1a Hydration of polymer gels in water. A shows a polymer molecule before hydration inwater, whilst B shows a polymer molecule after hydration in water.

5.2a A crosslinked polymer. A shows the hydrated polymer prior to addition of thecrosslinker. B shows the crosslink chemical bonds between the polymer molecules.

5.2b pH ranges for crosslinkers (after SPE 37359).5.2c Temperature range for crosslinkers (after SPE 37359).5.3a Aluminium phosphate association polymer.5.6a Proppant transport as a function of foam quality. This graph is a combination of the

work performed by several individuals and organisations. It is intended as aqualitative illustration of the effect foam quality has on the ability of the fracturing

foam to transport and suspend proppant.




Page vi Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

Section 6

6.1a The effect of uniform and natural grain size distribution on porosity.6.1b Diagram illustrating how larger grains have larger pore spaces and hence greater

permeability.6.1c Diagram illustrating the difference between a proppant with good sphericity and

roundness (left), and a proppant with poor sphericity and roundness (right).6.1d Three SEM micrographs showing the effects of frac fluid residue. The micrograph on

the left shows undamaged proppant before the addition of the frac fluid. The centermicrograph shows the residue left by a poorly designed crosslinked system. The finalmicrograph shows the same proppant pack after an enzyme breaker has been used.

6.3a SEM micrograph of FlexSand grain clearly showing the indentations caused by theclosure of the surrounding proppant grains.

Section 7

7.1a A block of material subjected to a force F .7.2a Strain produced by the application of force F.7.4a Application of force F also produces a deformation in the y direction.7.5a Force F applied to produce a shear stress.

7.5b Volume changes from V 1 to V 2 as pressure increases from P 1 to P 2.7.7a Three dimensional stresses around a wellbore.7.8a Changes in stress regime due to erosion.

Section 8

8.1a Propagation of a radial or penny-shaped fracture.8.2a Schematic showing the general shape of the KZD fracture.8.3a The Perkins and Kern - Nordgren fracture.

Section 9

9.1a The Griff ith crack.9.1b Failure modes in Linear Elastic Fracture Mechanics.

9.1c Coordinate system for stress intensity factor.9.2a The Cleary et al approach.9.2b Crack tip diameter and the plastic zone. Note that r p is the radius of the plastic zone.9.2c The shape of the plastic zone, for a Poisson’s ratio of 0.25.9.3a Sources of Energy Gains and Losses for the fracturing fluid. Energy Gains + Energy

Losses = 0.

Section 10

10.1a. Diagram illustrating the effects of horizontal stress contrast on tortuosity (after GRI-AST 1996).

10.2a The Nolte plot.10.4a The Tip Screen Out.

10.6a Proppant convection. As the heavier slurry enters the fracture it sinks and displacesthe lighter slurry upwards.10.7a Illustration of the “Pipelining” effect.

Section 12

12.2a Transient production. The red lines illustrate the variation of pressure with distancefrom the wellbore, as time increases. The radius of the disturbed formation iscontinually increasing.

12.2b Pseudo-steady state production. The radius of the disturbed formation has reachedthe reservoir boundary, r e, and now the reservoir pressure is decreasing.

12.2c The McGuire-Sikora Curves.12.3a Nodal analysis IPR curves for a gas well with a fracture of varying propped fracture

width.




Page vii Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

Section 13

13.3a The effect of skin factor upon production rate. Note that this Figure is based purely onskin factor effects. No fracture stimulation is included.

Section 14

14.1a The Effect of perforations on fracture initiation.14.1b Perforating for zonal coverage.14.2a Perforation strategy for vertical wells.14.2b Perforation strategy for horizontal wells.14.3a The Effect of fracture initiation point on skin bypass fracs.14.3b Multiple skin bypass fracs over a long interval.

Section 15

15.1a The step up test.15.2a The step down test.15.3a Step up pressure-rate crossplot using the example data. This plot shows the fracture

extension pressure to be at +/- 6570 psi.15.3b Step down pressure-rate crossplot for the example data. The convex shape of the

curve indicates near wellbore friction dominated by tortuosity.15.3c Step down pressure-rate crossplot for the example data, using surface treating

pressure (STP). This graph illustrates the danger of using STP for step rate testanalysis, as in this case, the near wellbore friction would have been incorrectlydiagnosed as being perforation dominated.

Section 16

16.2a Typical minifrac job plot, showing BHTP, STP and rate.16.2b Expanded plot showing BHTP.16.3a Typical minifrac pressure decline curve.16.3b Use of a square root time plot to determine closure pressure.16.3c Typical minifrac pressure decline Horner plot.

16.3d Graph showing the variation of g (∆t D) with ∆t D.16.4e Typical Nolte G time pressure decline plot.16.4f Example derivative plot based on a Horner Plot.16.6a Minifrac example 1 job plot.16.6b BH gauge pressure decline against elapsed time. Possible closure pressure at +/-

2770 psi (where the two red lines cross, marking a change in gradient). Note thesudden drop of about 50 psi as the pumps shut down at t = +/- 13 mins.

16.6c BH gauge pressure decline against the square root of elapsed time. Possible closurepressure at +/- 2790 psi (where the two red lines cross, marking a change fromstraight line to curve).

16.6d G function plot. The “true” ISIP is at +/- 3150 psi, whilst the closure pressure appearsto be at +/- 2780 psi (where the two red lines cross). This gives a G c of 1.30.

16.6e Horner plot. The results from this plot are ambiguous and do not help in the analysis.

16.7a Minifrac example 2 step rate test job plot.16.7b Step rate test crossplot for minifrac example 2, step rate test, showing fracture

extension at +/- 8700 psi.16.7c Minifrac example 2 job plot.16.7d Comparison between gauge and calculated BHTP for minifrac example 2. Note that

whilst the calculated BHTP follows the same general trend as the gauge BHTP, theactual value is quite different. Short term variations in the trend of the calculatedBHTP are caused by the variations in rate. The general offset of the data is probablycaused by incorrect input data in the fracture monitoring package (in this caseFracRT).

16.7e Minifrac example 2 pressure decline with derivative.16.7f Minifrac example 2 pressure decline square root time plot, with derivative.16.7g Initial pressure match for minifrac example 2.

16.7h Interim pressure match after the stresses have had a first approximate adjustment. Inthis case, the stress gradient for the sandstone was increased from 0.62 to 0.68 psi/ft,




Page viii Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

and then 1300 psi was added to each stress. Note that the pressures are on a largervertical scale than in Figure 16.7g.

16.7i Minifrac example 2 final pressure match.16.7j FracProPT estimated fracture dimensions for minifrac example 2.16.8a Minifrac example 3 treatment plot.16.8b Minifrac example 3, detail of post-treatment pressure decline.

16.8c Minifrac example 3, square root time pressure decline plot.16.8d Horner plot for minifrac example 3. Note that several lines may be fitted to the final

slope on the LHS of this plot. In fact, the reservoir pressure is substantially lower thanthat indicated on the plot (as the well is produced by ESP’s), so all of these lines maybe unreliable.

16.8e G Function plot for minifrac example 3. Note the true ISIP of +/- 2730 psi, and theclosure pressure of +/- 2320. These values are in agreement with the value obtainedfrom other plots, such as the pressure decline and the square root time plots.

16.8f MFrac output showing the initial pressure match before any adjustments were made.There is very little agreement between the predicted and actual BHTP’s.

16.8g Final MFrac output, after the model has been adjusted.16.9a Job plot for Minifrac Example 4, Step Rate Test 116.9b Step up crossplot for Step Rate Test 1. Fracture extension seems to be at

approximately 9100 psi.16.9c Step down crossplot. Note the concave shape of the best fit curve, indicating that the

near wellbore friction is dominated by the perforations.16.9d Minifrac Example 4 job plot.16.9e Detail of job plot showing bottom hole proppant concentration, gauge BHTP and

slurry rate, as the proppant slug enters the formation. Note the +/- 400 psi rise inpressure.

16.9f Minifrac pressure decline, showing +/- 650 psi near wellbore friction and a closurepressure of +/- 8350 psi.

16.9g Square root of time plot for the minifrac pressure decline. This gives a slightly lowerclosure pressure than Figure 16.9f, at +/- 8230 psi.

16.9h Job plot for second step rate test.16.9i Step down crossplot for the second step rate test.

16.9j Minifrac Example 4 BHTP plot before pressure matching.16.9k Minifrac Example 4 pressure match using MFrac .16.9l Job plot for the main treatment for Minifrac Example 4. Note the proppant

concentration is measured at the surface.16.9m Detail of the main treatment for Minifrac Example 4, showing the formation’s response

to the proppant slugs. Proppant concentration is bottom hole.

Section 17

17.4a The diagram on the LHS illustrates the position of the slurry and the ‘pack’ atscreenout – with the top of the ‘packed’ proppant at the top of perforations, and theannular space between the completion and the wellbore full of slurry, up until thecrossover ports. The RHS shows the position of the pack after all the proppant has

been allowed to settle.17.9a Optimum dimensionless fracture conductivity against dimensionless proppant number(after Economides et al , 2002).

Section 18

18.1a Process loop for real-time fracture modeling and redesign.18.1b Inside of a typical frac control van, showing the numerical display and some of the

displays being run by JobMaster .18.1c Remote data transmission schematic.18.2a On-site redesign process flowchart.

Section 19

19.1a Pressure matching. The variables in the simulator are adjusted to make thecalculated net pressure match the actual net pressure.19.2a Anatomy of a drawdown / build-up well test (after Agarwal, 1980)




Page ix Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

19.2b Graphs illustrating the deviation from transient flow caused by a reservoir boundary(i.e. pseudo-steady state flow).

19.2c Constant rate drawdown semi-log plot. The straight line section can be used toevaluate the permeability. The deviation from the straight line at late time, is due toboundary effects of the reservoir, as the transient flow changes to pseudo-steadystate flow.

19.2d Example Horner plot, showing the extrapolation of the straight line portion to obtainthe reservoir pressure, P i. Once again, deviation from the straight line is caused by achange from transient flow to pseudo-steady state flow.

19.2e Log-log diagnostic plot with derivative for the pressure build-up of an infinite-actingreservoir (i.e. no boundaries and no pseudo-steady state flow).

19.2f Log-log diagnostic plot with derivative for the pressure build-up of reservoir with apartial boundary (e.g. a sealing fault).

19.2g Log-log diagnostic plot with derivative for the pressure build-up of an infiniteconductivity fracture.

19.2h Log-log diagnostic plot with derivative for the pressure build-up of a finite conductivityfracture.

19.2i Type curves for a single well in an infinite reservoir, with wellbore storage and skindamage (after Agarwal, Al-Hussainy and Ramey, 1970).

19.2j Example of a log-log plot of ∆t against ∆P , used for type curve matching.19.2k Post-treatment log-log plot of well test data for a gas well.19.2l Type curves for a well with a finite conductivity, vertical fracture (after Agarwal et al ,

1979 and Economides et al , 1987).19.3a The principle of tiltmeter fracture diagnostics (after Cipolla and Wright, 2000).19.3b Generic temperature log illustrating that the treating fluid has entered only a small

portion of the perforated interval. The fracture will have initiated in the smaller interval.However, this does not necessarily mean that this is the center of the fracture.

Section 20

20.1a Typical pump curves. This set is for a 30-16-6 frac skid, with a 16V92TA engine, aCLBT8962 transmission and a pacemaker pump with a 4.5 inch fluid end. Nominal

rating of the pump skid is 700 HHP.20.2a Chart showing fluid velocity against fluid rate for various nominal diameters of Figure1502 high pressure iron.

20.3a Schematic diagram of a generic frac pump.20.3b Generic frac pump, suction stroke.20.3c Generic frac pump, discharge stroke.20.3d Skid mounted 16V 92T pump unit (700 HHP). Skid splits into two parts.20.3e Two views of a trailer-mounted Gorilla pump unit (2700 HHP).20.3f Body-load Kodiak pump unit (2200 HHP).20.3g Skid-mounted 1300 HHP pump unit.20.4a Schematic diagram of a generic intensifier.20.4b Schematic diagram of the intensifier hook-up.20.4c Intensifier worksite. Each intensifier (A) is hooked up to three frac pumpers (B), which

are pumping the power fluid. Power fluid is handled by the power fluid unit (C).Intensifiers are rigged into a manifold (D). Note that whilst there are three intensifiersand 9 power fluid pumpers on location, there are also an additional two frac pumpers(E) rigged up to the downhole line to provide extra horsepower.

20.4d Detail of an intensifier. In the foreground, on the RHS, is the downhole fluid end. Inthe background, on the LHS, is the power end, complete with high pressure ironrigging it to the frac pumpers.

20.5a Generic flow diagram for a frac blender. Note that on a blender fitted with a Condortub (such as BJ’s Cyclone blenders), the functions of the blender tub and thedischarge pump are combined.

20.5b 125D Frac blender, capable of 125 bpm and 35,000 lbs/min proppant rate.20.5c Body-load mounted Cyclone II blender, capable of 25 bpm.20.5d Skid mounted Cyclone blender.

20.5e LFC hydration unit.




Page x Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

20.6a Frac sand being delivered from a Sand King to the hopper of a blender. Note thatthere are two blenders in this picture – one is on standby as a backup in case ofequipment failure.

20.6b Vertically mounted, gravity feed proppant bins.20.6c Trailer mounted sand dumper.20.6d BJ Services Sand King.

20.6e Sand belt conveyor.20.7a External view of BJ’s Stimulation Van 1800.20.7b External view of a treatment monitoring container.20.7c Two internal views of a treatment monitoring van.20.8a Generic wellhead isolation tool rigged up to wellhead. The WIT is connected to the

wellhead via the wellhead’s top flange. At this point the wellhead master valve andsub master valves are closed, maintaining control of the well and allowing the fraclines and WIT to be pressure tested.

20.8b+c Once the WIT has been connected to the wellhead and pressure tested (Fig 20.8a),the next stage is to close the valves of the frac lines (not shown – note that someWIT’s have their own master valves) and open the master and sub master valves onthe wellhead. One the wellhead is open, the stinger is stroked down into the top of thetubing by pumping hydraulic fluid into the master cylinder.

20.8d Wellhead isolation tool rigged up on location. Note the two 3” frac lines connected toeither side, plus the remote actuated 4” plug valve.

20.9a Schematic diagram of a frac spread.20.9b Large scale treatment, carried out on several low permeability zones simultaneously.

Note the number of Sand Kings and frac tanks on location, as well as the use of twoblenders (one for backup in case of equipment failure). This frac spread features aseparate mobile field lab (bottom left) and a third blender, just for gelling up the tanksand for pumping fluid from the tanks that are located a significant distance from theblender (located just above the bottom left hand row of frac tanks).

20.9c The MV Blue Ray , a Gulf of Mexico frac boat, designed primarily for highpermeability, frac and pack treatments.

20.9d Skin Bypass Frac spread, using the “batch” frac method. The two frac pumps arepositioned opposite each other, just below the wireline mast (the small read and

yellow derrick). A third pump (with “BJ” painted on its roof) is being used as anannulus pump. The two vertical stainless steel tanks on the RHS are for fluid storage.The two batch mixers (each with two round batch tanks - the blue batch mixer is 2 x50 bbls, whilst the red one is 2 x 40 bbls), used to batch mix the proppant into the gel,are located at the bottom of the picture.

20.9e Coiled tubing frac spread. The wellhead is positioned directly below the CT injector(center of picture), with the reel on the RHS. On the LHS are two nitrogen tankers.The main part of the frac spread is positioned behind the injector, with the sand dumptruck being the most prominent feature.

20.9f The MV Thanh Long . This was a boat put together for a single fracturing treatment,for a customer operating offshore Vietnam. The aft deck holds the followingequipment:- 4 x 1200 HHP frac pumps, Cyclone II blender, 2 x 640 cu ft proppantbins, treatment monitoring container c/w field lab, 4 x 165 bbls tanks and a 100 bbl

vertical tank.

Section 22

22.1a Frac job process flow diagram.



BJ Services’ Frac Manual1. Introduction

Page 1 Version 1.0 June 2005 Uncontrolled Copy – DO NOT DISTRIBUTE

1. Introduction

History

The first attempts at fracturing formations were not hydraulic in nature – they involved the useof high explosives to break the formation apart and provide “flow channels” from the reservoirto the wellbore. There are records indicating that this took place as early as 1890. Indeed,one of the predecessor companies of BJ Services, the Independent Torpedo Company(founded in 1905), used nitroglycerine to explosively stimulate formations in Ohio. This type ofreservoir stimulation reached its ultimate conclusion with the experimental use of nucleardevices to fracture relatively shallow, low permeability formations in the late 1950’s and early1960’s.

In the late 1930’s, acidising had become an accepted well development technique. Severalpractitioners observed that above a certain “breakdown” pressure, injectivity would increasedramatically. It is probable that many of these early acid treatments were in fact acidfractures.

In 1940, Torrey recognized the pressure-induced fracturing of formations for what it was.His observations were based on squeezecementing operations. He presented data toshow that the pressures generated during theseoperations could part the rocks along beddingplanes or other lines of “sedimentaryweakness”. Similar observations were made forwater injection wells by Yuster and Calhoun in1945.

The first intentional hydraulic fracturing process for stimulation was performed in the Hugoton

gas field in western Kansas, in 1947. The Klepper No 1 well was completed with 4 gasproducing limestone intervals, one of which had been previously treated with acid. Fourseparate treatments were pumped, one for each zone, with a primitive packer beingemployed for isolation. The fluid used for the treatment was war-surplus napalm, surely anextremely hazardous operation. However, 3000 gals of fluid were pumped into eachformation.

Although post treatment tests showed that the gas injectivity of some zones had beenincreased relative to others, the overall deliverability from the well was not increased. It wastherefore concluded that fracturing would not replace acidising for limestone formations.However, by the mid-1960’s, propped hydraulic fracturing had replaced acidising as thepreferred stimulation method in the Hugoton field. Early treatments were pumped at 1 to 2bpm with sand concentrations of 1 to 2 ppa.

Today, thousands of these treatments arepumped every year, ranging from small skinbypass fracs at $20,000, to massive fracturingtreatments that end up costing well over $1million. Many fields only produce because ofthe hydraulic fracturing process. In spite of this,many industry practitioners remain ignorant ofthe processes involved and of what can beachieved.





The Process

Hydraulic fracturing occurs as a result of the phenomenon described by Darcy’s law for radialflow:-

q =kh ∆P

µ ln(r e /r

w ) ...................................................................... (1.1)

Where q is the flow rate, k the formation permeability, h the net height, ∆P the pressuredifferential (or drawdown), µ the fluid viscosity, r e the drainage radius and r w the wellboreradius. This Equation describes the flow rate for a given reservoir-wellbore configuration, foran applied pressure differential. Re-arranging this Equation gives a different emphasis:

∆P =q µ ln(r e / r w )

kh ................................................................... (1.2)

This Equation describes the pressure differential produced by a given flow rate.Remembering that Darcy’s Equation applies equally to injection and to production, Equation

1.2 tells us the pressure differential needed to pump a fluid of viscosity µ into a given

formation at a given rate q .

As the flow rate increases, the pressure differential also increases. Pressure and stress areessentially the same thing (see Section 2.2), so that as the fluid flow generates a pressuredifferential, it also creates a stress in the formation. As flow rate (or viscosity) increases, sodoes the stress. If we are able to keep increasing the rate, eventually a point will be reachedwere the stress becomes greater than maximum stress that can be sustained by theformation – and the rock physically splits apart.

This is how we frac, by pumping a fluid into a formation at high rate and – consequently – high pressure. However, it is important to remember that it is pressure – not rate – thatcreates fractures (although we often use rate to create the pressure).

Pressure – and stress – is stored energy, or moreaccurately stored energy per unit volume. Energyis what hydraulic fracturing is all about. In order tocreate and propagate a fracture to usefulproportions, we have to transfer energy to theformation. Producing width and physically tearingthe rock apart both require energy. Overcoming theoften highly viscous frac fluid’s resistance to beingpumped also takes energy. So the key tounderstanding the hydraulic fracturing process is tounderstand the sources of energy gain, such as the

frac pumps and the well’s hydrostatic head, and the sources of energy loss and use. The sumof these is always equal to zero.

As pressure is energy, a great deal can be learned about a formation by studying thepressures produced by a treatment. The product of the pressure and the flow rate gives usthe rate at which energy is being used, i.e. work. This is usually expressed as hydraulichorsepower. The analysis of the behaviour of fracturing pressures is probably the mostcomplex aspect of the process that most Frac Engineers will become involved in.

Once a fracture has been created, proppant is placed inside it. If the treatment has beendesigned effectively and pumped without any problems, then this proppant should form ahighly conductive path from the reservoir to the wellbore. This is what makes the well producemore.





Using this Manual

This manual is not intended as an all-inclusive work onthe science of hydraulic fracturing. Instead, it is intendedto be a practical introduction to the science and artinvolved in these processes. It is intended to be used by junior Engineers who wish to gain some knowledge ofthe fracturing process, and by experienced Engineerswho wish to gain a deeper insight into specific areas.This manual has been written with the intent that anyonewith a technical background can come to understandfracturing.

Readers are invited to consult the references at the end of each section for more detailedinformation on any specific subject.

The author of this manual welcomes any comments that the reader may have – whether it isabout something which is unclear, an omission or something that is just simply incorrect. Iwelcome any constructive comments that the reader may have.

Throughout this manual, the author has used United Kingdom English, rather than AmericanEnglish. Consequently, some readers may find the occasional word that seems to be spelledin a manner somewhat different from that which they are used to. Examples includeprogramme (instead of program), acidise (instead of acidize), grey (instead of gray),aluminium (instead of aluminum) and sulphate (instead of sulfate). The author makes noapologies for this.

AcknowledgementsThis manual has taken five years to complete, on and off (two to write and three to get proofread.....). Over this period, I have received assistance from a number of persons who deserve

my thanks. Todd Gilmore, for continually reviewing each section as it was written; AntonioMoreira for correcting the mistakes and omissions in the equipment section; Phil Rae for hiscontinuing help, support and encouragement; and finally Dave Cramer, Ron Matson, HaroldHudson and Kieran O’Driscoll, for the vital but tedious and time consuming process of proofreading. Thanks to you all.

Tony Martin, Singapore, June 2005.

References

Torrey, P.D.: “Progress in Squeeze Cementing Applications and Technique”, Oil Weekly , July

29, 1940.

Yuster, S.T. and Calhoun, J.C., Jr.: “Pressure Parting of Formations in Water FloodOperations – Part I”, Oil Weekly , March 12, 1945.

Yuster, S.T. and Calhoun, J.C., Jr.: “Pressure Parting of Formations in Water FloodOperations – Part II”, Oil Weekly , March 19, 1945.

Farris, R.F. : “Hydraulic fracturing, a method for increasing well productivity by fracturing theproducing formation and thus increasing the well drainage area”, US Patent reissued Nov 10,1953. Re. 23733.

Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,

Texas, USA (1970).



BJ Services’ Frac Manual2. Basics of Hydraulic Fracturing


2. Basics of Hydraulic Fracturing

Hydraulic fracturing is the process of providing a conductive path from the reservoir to thewellbore. How this is achieved depends upon the objectives, the reservoir and the well.

2.1 The Basic Process

As fluid is pumped into a permeable formation, a pressure differential is generated that isproportional to the permeability of the formation, kf . As the rate increases, this pressuredifferential between the wellbore pressure and the original reservoir pressure also increases.This pressure differential causes additional stress around the wellbore. Eventually, as the rateis increased, this pressure differential will cause stresses that will exceed the stress neededto break the rock apart, and a fracture is formed. At this point, if the pumps are shut down orthe pressure is bleed off, the fracture will close again. Eventually, depending on how hard therock is and the magnitude of the force acting to close the fracture, it will be as if the rock hadnever been fractured. By itself, this would not necessarily produce any increase in production.

However, if we pump some propping agent, or proppant , into the fracture and then releasethe pressure, the fracture will stay propped open, providing the proppant is stronger than theforces trying to close the fracture. If this proppant also has significant porosity, then under theright circumstances a path of increased permeability has been created from the reservoir tothe wellbore. If the treatment has been designed correctly, this will produce an increase inproduction.

Generally, the process requires that a highly viscous fluid is pumped into the well at high rateand pressure, although this is not always the case (see Skin Bypass Fracturing, below). Highrate and high pressure mean horsepower, and this is why the process generally involveslarge trucks or skids with huge diesel engines and massive pumps. A typical frac pump will berated at 700 to 2700 hydraulic horsepower (HHP) – to put this in perspective, the average car

engine (outside North America, that is) has a maximum power output of 80 to 100 HP.

In order to create the fracture, a fluid stage known as the pad is generally pumped first. Thisis then followed by several stages of proppant-laden fluid, which actually caries the proppantinto the fracture. Finally, the whole treatment is displaced to the perforations. These stagesare pumped consecutively, without any pauses. Once the displacement has finished, thepumps are shut down and the fracture is allowed to close on the proppant. The Frac Engineercan vary the pad size, proppant stage sizes, number of proppant stages, proppantconcentration within the stages, the overall pump rate and the fluid type in order to producethe required fracture characteristics. Typically, the treatment will look like Figure 2.1a:-

Figure 2.1a – Typical hydraulic fracture treatment job plot

P r e s s u r e , R a t e , P r o p p a n t C o n c e n t r a t i o

n

Time

BHTP

STP

Rate

Prop Conc





2.2 Pressure

Everybody understands what pressure is. Or at least, everyone thinks they understand whatpressure is. If you ask someone to define pressure, then they will usually say “force dividedby area”, or something similar. This is not what pressure is - it is merely how we measure,create and use pressure.

The simple fact is that pressure is stored energy, and we use that energy to perform work onthe formation during the fracturing process. Everything we do in fracturing can be thought ofin terms of energy. For instance, when we pump a fluid into a fracture we start out withchemical energy – in the form of diesel fuel. This is converted to mechanical energy by thediesel engine. The high pressure pump then transfers this mechanical energy into pressure inthe fracturing fluid. As the fluid moves into the formation, the pressure is transformed intostress in the formation (see below), which is another form of stored energy, and so the wallsof the fracture are pushed back, creating fracture width and forcing the fracture to propagate.

Work is defined as the rate at which energy is used – in the SI system, one watt is defined asa joule per second. Therefore, by observing the way the pressure is changing, or notchanging, with respect to time, we can tell how much work we are performing on theformation (see Section 10.2 – Nolte Analysis).

Pressure and stress are essentially the same thing. The only difference is that stresses act insolids and pressures act in liquids and gases. Because liquids and gases easily deform awayfrom any applied force, pressures tend to act equally in all directions. Stresses, however, tendto act along planes, so that a solid experiencing a stress will always have a plane where thestresses are a maximum, and a plane perpendicular to this where the stresses are at aminimum.

In fracturing, we refer to several different pressures. These names merely refer to where andwhen we are measuring (or calculating) the pressure;

Surface Treating Pressure, STP – also referred to as wellhead pressure, injection pressure,tubing pressure (if we are pumping down the tubing), P STP, P wellhead, P tubing and so on. Thename speaks for itself – it is the pressure that the pumps have to act against at the surface.

Hydrostatic Pressure – also referred to as hydrostatic head, P H, HH and P hydro. This is thepressure downhole due to the weight of the column of fluid in the well. This pressure is afunction of the density of the fluid and the vertical depth:

HH = 0.433 γ TVD.................................................................. (2.1)

where HH is the hydrostatic head in psi, γ is the specific gravity of the fluid and TVD is thetrue vertical depth at which the pressure is acting. This looks relatively easy to calculate, but

can get quite complicated in a dynamic system in a deviated well with fluids of severaldifferent densities actually in the well – which is the usual situation during a frac job. We usecomputers to keep track of this.

Tubing Friction Pressure – also known simply as friction pressure, P frict or ∆P frict . Thispressure will be covered in more detail in later sections of this manual (see Section 4). Fornow, we can define it qualitatively as the pressure caused by the resistance of the fluid to flowdown the tubing. Friction pressure decreases with increasing tubular diameter and increaseswith rate.

Bottom Hole Treating Pressure – BHTP or P BHT . This is the pressure inside the well, by theformation being treated. Generally, at is calculated at the center of the perforated interval. Atthis point, the fluid has not passed through the perforations or into the fracture. Unless there

are gauges in the well, or there is a static column, this pressure is usually calculated:-





BHTP = STP + HH - ∆P frict ........................................................ (2.2)

As there are always uncertainties with the calculation of ∆P frict (unless fluid rate is zero), therewill always be uncertainties in calculated BHTP .

Perforation Friction Pressure – also known as perforation friction or ∆P perf . This is the

pressure drop experienced by the fluid as it passes through narrow restrictions generallyreferred to as perforations:-

∆P perf =2.93 SG (q / n )

2

d 4 .............................................................. (2.3)

where ∆P perf is in psi, SG is the specific gravity of the fluid, q is the slurry rate in bpm, d is theperforation diameter in inches and n is the number of perforations.

Near Wellbore Friction Pressure – a.k.a. near wellbore friction or ∆P nwb . This is the sum ofthe perforation friction and any pressure losses caused by tortuosity, which will be covered ingreater detail in Section 10.

Closure Pressure – P c or P closure . This is the force acting to close the fracture. Below thispressure the fracture is closed, above this pressure the fracture is open. This value is veryimportant in fracturing and is usually determined from a minifrac, by careful examination of thepressure decline after the pumps have been shut down.

Extension Pressure – or P ext . This is the pressure required in the frac fluid in the fracture inorder to make the fracture propagate. It is usually 100 to 200 psi greater than the closurepressure, and this pressure differential represents the energy required to actually make thefracture propagate, as opposed to merely keeping it open (i.e. P closure ). In hard formations,fracture extension pressure is close to the closure pressure. In softer formations, wheresignificant quantities of energy can be absorbed by plastic deformation at the fracture tip,extension pressure can be significantly higher than closure pressure (see Section 9). Thefracture extension pressure can be obtained from a step rate test.

Net Pressure – or P net . This is a fundamental value used in fracturing and the analysis of thisvariable forms a whole branch of frac theory by itself. This will be discussed in detail later onin this manual. For now, P net is the difference between the fluid pressure in the fracture andthe closure pressure, such that:-

P net = BHTP – ∆P nwb - P closure .................................................. (2.4)

= STP + HH – ∆P frcit – ∆P nwb - P closure ............................... (2.5)

P net is a measure of how much work is being performed on the formation. By analysing thetrends in P net a great deal can be determined about how the fracture is growing – or shrinking.

Instantaneous Shut in Pressure – or ISIP or ISDP . This is the pressure, which can bedetermined either at surface or bottom hole, which is obtained just after the pumps are shutdown, at the start of a pressure decline. If measured at bottom hole, the ISIP should be equalto the BHTP , provided P nwb is zero. One of the methods for determining if the P nwb issignificant is to compare the ISIP and the BHTP from a minifrac (provided the BHTP isreliable).

2.3 Basic Fracture Characteristics

Every fracture, regardless of how it was pumped or what it is designed to achieve, has certainbasic characteristics, as shown in Figure 2.3a (below).





All fracture modeling is designed around determining these three characteristics, height H ,half length x f and width W . Once these three characteristics have been determined, otherquantities such as proppant volume, fracture conductivity and ultimately production increasecan be determined. It is usually assumed that the two wings of the fracture are identical and180 º apart (i.e. on opposite sides of the wellbore. This is not necessarily the case. It is alsonormal to model the fracture wings as being elipitcal in shape - however, the reality is that the

geometry is probably quite a bit more complex. However, based on the three characteristicsof width, half length and height, we can define a few simple parameters, which will be usedfrequently in this manual:-

Figure 2.3a – Diagram showing fracture half Length x f , fracture height H , and fracture width W .

Aspect ratio;

AR =H x f

.................................................................................. (2.6)

So a radial frac, which is perfectly circular and has a height equal to twice the fracture halflength, has an AR of 0.5

Fracture conductivity;

F c = w ¯ .k p .............................................................................. (2.7)

where w ¯ is the average fracture width and k p is the permeability of the proppant pack.

Remember that the width in Equation 2.7 is the propped width, which is usually less than thewidth actually created during the treatment. The propped width is a function of the volume ofproppant pumped into the fracture, expressed in terms of the mass of proppant per unit areaof the fracture face. This areal proppant concentration is expressed in terms of lbs/sq ft, andis not to be confused with the slurry proppant concentration, that is expressed in lbs/gal (orppg). This is a measure of how much proppant is added by the surface mixing equipment to agallon of frac fluid. Another way of expressing slurry proppant concentration, which is usedless often but is clearer and easier to understand, is ppa, or lbs of proppant added. Thisclearly illustrates the quantity of proppant being added to a gallon of clean fluid.

H x f

W





2.4 Fluid Leakoff

Hydraulic fracture treatments are pumped into permeable formations – there is little point incarrying out the process in a formation with zero permeability. This means that as thefracturing fluid is being pumped into the formation, a certain proportion of this fluid is beinglost into the formation as fluid leakoff .

The leakoff coefficient is a function of the formation permeability k f , the fracture area A, thepressure differential between the fracturing fluid and the formation ∆P , the formationcompressibility, viscosity and the fluid characteristics. Often, this coefficient is set as aconstant throughout the treatment, which means that the fluid loss rate varies with time andfracture area only, and does not vary with pressure differential or fluid type. The effect of theformation permeability and the fluid characteristics are often combined together into a singleleakoff coefficient, variously called C T , C L or C eff . We shall use C eff . This coefficient defines thevolume of fluid leaked off into the formation V L, as follows:-

V L = π C eff A t ................................................................... (2.8)

where t is the time that the fracture has been open. The units of C eff are generally ft/min

½

, soin Equation 2.8 if the area is in square feet, the leakoff volume is in cubic feet. Remember thatthe area A is the surface area of the whole fracture, including both sides of both wings of thefracture. A fracture geometry model must be used to determine the value for A. In a multi-layer reservoir, with different values of C eff for each zone, the total leakoff will be the sum ofthe leakoff for each zone.

The leakoff coefficient is usually determined from minifrac tests and from analysis of previoustreatments.

A more accurate method for calculating fluid loss is to use a dynamic leakoff model, in whichvariations in the pressure differential and the fluid composition are taken into account. Indynamic leakoff, the overall leakoff coefficient is generally assumed to have three

components; the viscosity controlled coefficient C V or C I , the compressibility controlledcoefficient C C or C II and the wall-building coefficient C w or C III .

The viscosity controlled coefficient is the effect of the fracture fluid filtrate moving into theformation under Darcy linear flow conditions, and is defined as (in field units):-

C I = 0.0469k f φ ∆P

2 µ f ...................................................... (2.9)

where k f is the permeability of the formation to the frac fluid filtrate, φ is the formation porosityand µ f is the frac fluid filtrate viscosity in cp.

The compressibility controlled coefficient defines the leakoff which is due to the formationcompressing, and allowing volume into which the frac fluid filtrate can move. It is defined, infield units, as:-

C II = 0.0374 ∆Pk r c f φ

µ r ................................................. (2.10)

where k r is the permeability of the formation to the reservoir fluid, c f is the compressibility of

the formation in psi-1

and µ r is the reservoir fluid viscosity in cp.

The wall building coefficient is usually determined experimentally using a standard fluid losstest. The volume of filtrate is plotted against the square root of time, to give a slope m . Thewall building coefficient is then defined as (in field units):-





C III =0.0164 m

Af .................................................................... (2.11)

where Af is the area of the filter cake in the fluid loss cell. Generally, modern fracturesimulator will have wall-building coefficients for a wide range of fracturing fluids, so that all theEngineer has to do is select the fluid type.

The three components can then be combined to produce C eff as follows:-

C eff =2 C l C lI C llI

1 + (C l C lll )2 + ( )4 C II

2 ( C I

2 + C III

2)

............................ (2.12)

This is for dynamic fluid leakoff. The components can be arranged in a different form forharmonic fluid leakoff:-

C eff =(C l C ll C lll )

(C l C ll + C ll C lll + C l C lll ) .................................................. (2.13)

This process of deducing the theoretical leakoff coefficient looks to be rather intimidating, andin practice is only used in fracture simulators. During minifrac analysis, the permeability of theformation and the wall building coefficient are varied to produce the required leakoff rate.

Generally, the dynamic model is better than the harmonic, although under mostcircumstances there will not be much difference between the two. This is especially true for anon-wall-building fluid, or for gas reservoirs.

Another form of fluid loss into the formation is called spurt loss. This is the fluid loss whichoccurs on “new” parts of the fracture, before the fluid has a chance to build up a filter cake.Usually, the fracture models take a simplistic approach to spurt loss and use a spurt losscoefficient, S p , such that:-

V s = A S p ............................................................................. (2.14)

where V s is the volume of fluid lost due to spurt loss and A is the total area of the fracture(both wings). A more detailed approach to spurt loss (and fluid loss in general) can be foundin SPE Monograph Volume 12, Recent Advances in Hydraulic Fracturing , Chapter 8 (seereferences).

2.5 Near Wellbore Damage and Skin Factor

Darcy’s Equation for radial flow defines the rate at which oil is produced from the reservoirinto the wellbore, under steady state flow conditions. In field units for an oil well, Darcy’sEquation becomes:-

q =0.00708 k h ∆P

µ ln (r e /r w ) .......................................................... (2.15)

where q is the downhole flow rate in bbls/day. We can see that the wellbore radius, r w has ahuge impact on the flow rate. This is easily visualised, as the closer the fluid comes to thewellbore, the more congested the flow paths become and the faster the fluid has to move.Therefore, the final few inches by the wellbore are the most critical part of the reservoir.

Unfortunately, this is also the part of the reservoir most susceptible to damage. This damagecan come from a variety of sources, but most often comes from the process of drilling the wellin the first place.

A full discussion on sources of formation damage is beyond the scope of this manual.However, the major sources are; particulates in the drilling fluid (barite, calcium carbonate





etc), filtrate invasion, whole fluid invasion, pH of drilling fluid and surfactants in the drillingfluid.

What this results in, is a region around the wellbore of reduced permeability, as illustrated inFigure 2.5a.

This reduction in permeability around the wellbore is generally referred to as the Skin, whichwas first rationalised by van Everdingen and Hurst (1949). The skin factor, S , is a variablethat is used to describe the difference between the ideal production given in Equation 2.15,and the actual production through the damaged area. Generally, the skin is measured using apressure build up test. The API has defined the skin factor for an oil well as follows (seeSection 19):-

S = 1.151

P 1hr - P wf

m - log10

k

φµ cr w 2 + 3.23 ....................... (2.16)

where P wf is the bottom hole stabilised flowing pressure (psi), P 1hr is the bottom hole pressureafter one hour of static pressure build up (psi), k is the formation permeability, m is the slope

of the graph of P against log10[(t + ∆t )/ ∆t ] (in psi per log10 cycle), φ is the porosity (fraction), µ

is the fluid viscosity (cp), c is the average reservoir compressibility (psi-1) and r w is thewellbore radius (feet).

Figure 2.5a – Illustration of the reduction in permeability around the wellbore

To help matters, m can be found from the following (in field units):-

m =162.6 q µ

k h .................................................................... (2.17)

Note that both q and µ are at bottom hole conditions. A completely undamaged reservoir willhave a skin factor of zero. Damaged reservoirs will have skins in the ranging from 0 to 50 oreven higher. Under certain circumstances, stimulation can result in a negative skin factor,which means that the well is producing more than predicted by ideal Darcy flow.

Once the skin factor has been obtained, it can be used in Darcy’s Equation to give themodified flow from a skin damaged reservoir:-

q = 0.00708 k h ∆P µ [ln (r e / r w ) + S ]

......................................................... (2.18)

Permeability

high low

DamageWellbore





This means that as S increases, flow rate decreases, and vice versa.

Another way of employing the skin factor is to use an effective wellbore radius, as given inEquation 2.19:-

r w ’ = r w e-S

............................................................................ (2.19)

This means that in a damaged wellbore, the well is behaving as if it had a smaller wellboreradius, whilst a stimulated reservoir behaves as if it had a larger wellbore radius.

References

Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,Texas (1970).

Gidley , J.L., et al .: Recent Advances in Hydraulic Fracturing , Monograph Series Vol 12, SPE,Richardson, Texas (1989).

Archer, J.S. and Wall, C.G.: Petroleum Engineering – Principles and Practices , Graham andTrotman, London (1986).

van Everdingen, A.F. and Hurst, W.: “The Application of the Laplace Transformation to FlowProblems in Reservoirs”, 1949, Trans., AIME, 186, 305-324.

Meyer and Associates, MFrac version 5.10 on-line Help section, 2003.



BJ Services’ Frac Manual3. Types of Hydraulic Fracturing


3. Types of Hydraulic Fracturing

There are various different types of hydraulic fracturing, which have evolved around the basicprocess of creating a fracture and then propping it open. The type of treatment selected

depends upon the formation characteristics (permeability, skin damage, fluid sensitivity,formation strength), the objectives of the treatment (stimulation, sand control, skin bypass or acombination) and the constraints we have to work within (cost, logistics, equipment etc).

3.1 Low Permeability Fracturing

There are various different types of hydraulic fracturing, which have evolved around the basicprocess of creating a fracture and then propping it open. The type of treatment selecteddepends upon the formation characteristics (permeability, skin damage, fluid sensitivity,formation strength), the objectives of the treatment (stimulation, sand control, skin bypass or acombination) and the constraints we have to work within (cost, logistics, equipment etc).

This type of fracturing is often carried out in tight gas formations, found in areas such as theRocky Mountains, Algeria, Western Germany, parts of Australia and many other places world-

wide. Permeabilities for such formations range 1 md right down to 1 µd and less. This type oftreatment is also applicable to low permeability oil formations, although permeabilities tend tobe 1 or 2 orders of magnitude greater.

In order for hydrocarbons to flow down the fracture, rather than through the adjacentformation, the fracture must be more conductive than the formation. Given that the kp for20/40 Colorado Silica frac sand is 275 darcies (provided closure pressure is below 3,000 psi),we can see that even a very narrow fracture will have a much higher conductivity than theformation itself. This does not allow for the effects of non-Darcy flow (see Section 10).

Therefore, the limiting factor defining how much the reservoir production has increased is not

how conductive the fracture is (as any propped fracture will be significantly more conductivethan the formation), but instead is how fast the formation can get the hydrocarbon to thefracture. Therefore, when treating low permeability reservoirs, fractures should be designedwith a specific minimum fracture conductivity, but a large surface area - which means,because formations are usually limited in height, designing for maximum fracture half length,x f. See Section 17.9 for a detailed discussion of how to determine the required fractureconductivity.

Because formation permeability is low, fluid leakoff also tends to be low. This has twoconsequences. First, pad volumes tend to be very low, relative to the rest of the job volumes.In some cases, a pad is hardly needed at all – the proppant-laden fluid can be used to createthe fracture. The second consequence is that fracture closure time – the length of time takenfor the fracture to close on the proppant after the treatment has finished – tends to be long.This means that the fracturing fluid has to suspend the proppant for a relatively long period oftime at bottom hole temperature.

Therefore, hydraulic fracture treatments in low permeability formations tend to have fairlylarge fluid and proppant volumes, although the overall proppant concentration in the fluid isrelatively low. Pad volumes are small. Treatment fluids are usually fairly robust, capable ofmaintaining viscosity for extended periods of time. The process of designing for lowpermeability formations is discussed in greater detail in Section 17.5.





3.2 High Permeability Fracturing

High permeability fracturing is, not unexpectedly, the opposite of low permeability fracturing.

In high permeability formations, moving the fluid through the rock to the fracture is easy. Thehardest part is creating a fracture that is more conductive than the formation in the nearwellbore region.

In Equation 2.7, the concept of fracture conductivity was introduced. The next step is to definerelative or dimensionless conductivity, C fD (often referred to as F cD in many previouspublications):

C fD =F c

x f k f ................................................................................. (3.1)

where x f is the fracture half length and k f is the permeability of the formation. C fD is a measure

of how conductive a fracture is compared to the formation and compares the ability of thefracture to deliver fluids to the wellbore with the ability of the formation to deliver fluids to thefracture. A C fD of greater than one means that the fracture is more conductive than theformation, whereas a C fD of less than one means that the fracture is less conductive than theformation and the reservoir fluids flow more easily through the formation. This does notaccount for the effects of the skin factor – in reality all the fracture needs to be in order toincrease production, is more conductive than the skin (see Section 3.4 – Skin BypassFracturing).

From Equation 2.7, which stated that F c = w̄ .k p, we can see that two parts of the definition ofC fD are fixed; k f and k p (although k p can be increased to a certain extent by using a betterquality proppant). Therefore, in order to increase dimensionless conductivity, we have tomaximise w̄ and minimise x f. This means that we need a very short, wide fracture. In order to

achieve this, a technique known as the Tip Screen Out (TSO) is often used. This will bediscussed in more detail in Section 17.3.

Because the formations have high permeability, fluid leakoff tends to be very high. Therefore,pad volumes tend to be a significant part of the treatment. This high leakoff is used by thetechnique of TSO fracturing. Young’s modulus tends to be very low, which means thatcreating fracture width is relatively easy.

Formations with very high permeability also tend to have two other characteristics. First, theyare often weak or unconsolidated, so that the fracturing process is often combined with gravelpacking techniques to produce a frac pack treatment (see below, Section 3.3). Second, theformations also tend to have large skin factors, so that a significant production increase canbe obtained simply by providing a conductive path through the skin (see Section 3.4, below).

The processes involved in designing treatments for high permeability are discussed in greaterdetail in Section 17.3

3.3 Frac and Pack Treatments

The frac and pack (or simply frac-pack) treatment is a combination of a high permeabilityfracture treatment and a gravel pack treatment. Technically, the process of designing theactual treatment is the same as for a high permeability frac. Operationally, however, theprocess is much more complex, due the presence in the wellbore of the gravel packcompletion. Figure 3.3a illustrates this.





Figure 3.3a – Diagram illustrating the components of the frac-pack completion. Setting tool isshown in the squeeze position.

Figure 3.3b – Diagram illustrating two of the three positions in which a standard gravel pack orfrac pack tool can be set. The left hand side shows the squeeze position, in which fluids flow

down the tubing, through the crossover, out into the annulus below the GP packer and into theformation. The right hand side shows the lower circulating position. Fluid flows down to theperforations, as for the squeeze position. However, because the setting tool has been shifted

upwards, the fluid can flow either into the formation, or back through the screens, up thewashpipe (inside the screens) through the crossover, and out into the annulus above the tubing(shown in blue). By closing the annulus at surface, the fluid can be squeezed into the formation,

whilst maintaining a dead string on the annulus, to monitor BHP.

Sump Packer

Screen

GP/Prod. Packer

Blank Pipe

Fluid Control Valve





The treatment is normally pumped with the setting tool in the squeeze position, althoughsometimes the tool is in the lower circulating position (see Figure 3.3b). In either case,fracturing fluids are pumped down the tubing, through the setting tools, through the crossover,out into the annulus and into the perforations.

As stated before, the pumping schedule is designed as if the completion did not exist, and anormal high permeability fracture treatment was being performed. With one exception – extraproppant (or gravel) is pumped on the final stage, in order to fill the annulus space betweenthe screen and the casing, producing the gravel pack. The process of designing a frac andpack treatment will be discussed in more detail in Sections 17.3 and 17.4.

3.4 Skin Bypass Treatments

Skin bypass treatments are designed to do exactly what the name describes – bypass skindamage. These treatments are not necessarily designed to be the absolute optimumstimulation treatment for the well. Instead, these treatments are designed to be small, costeffective and easy to run operationally. Often these treatments are pumped in places wherespace or equipment weight is a limiting factor – such as offshore. In many cases, if the fracengineer was given a technical free hand to design the optimum treatment, the job itselfwould be much larger. However, given the restraints of cost and space that are often placedupon frac engineers, the skin bypass frac is an attempt (often highly successful) to produceeffective stimulation.

The skin bypass frac can also be considered as a more effective alternative to matrixacidising, when factors such as mineralogy, temperature, logistics and cost prevent the use ofacid.

Figure 3.4a – Diagram illustrating how the skin bypass fracture penetrates the skin to allowundamaged communication between the reservoir and the wellbore.

Figure 3.4a shows the basic concept behind the skin bypass frac. Although the formation hasconsiderable damage (dark-shaded area), this is effectively bypassed by the more conductive

path created by the fracture. In order for the fracture to produce a production increase, it doesnot have to be more conductive than the formation (i.e. C fD > 1.0). It merely has to be moreconductive than the damaged area. Of course, usually we are usually aiming for considerably





more than just the production increase due to skin bypass. Given that Skin Bypass Fracs arenormally carried out on marginal wells (wells that cannot justify the expense of a majorstimulation treatment), often the economics dictates that significant production increase mustbe obtained. Equation 3.1 gave the definition of dimensionless conductivity, which has to begreater than 1.0 for the fracture to provide stimulation of the formation. Equation 3.2 showsthe condition, for a fracture which has H D ≤ 1.0, under which the skin bypass fracture is more

conductive than the formation:

F c

H k f >

ln (r e / r w )

ln(r e / r w + S ) .................................................. (3.2)

Where F c is the fracture conductivity (mdft), H is the fracture height (ft), r e is the radial extent(ft), r w is the wellbore radius and S is the skin factor. So if S = 0, the RHS of Equation 3.2goes to 1, so that then F c has to be greater than H .k f , which is another way of saying that theC fD has to be greater than one. This Equation takes into account the fact that the fracturedoes not cover the entire zone vertically. However, it is an approximation, as it does notaccount for vertical flow or non-Darcy effects (Section 10).

H D is the dimensionless height and is equal to the fracture height divided by the formationheight.

3.5 Coal Bed Methane Fracturing

It is estimated that for every tonne of coal that is generated underground - by the process ofcoalification - up to 45 mscf of gas (mostly methane) is generated. In areas such as theSouthern North Sea, this gas migrates upwards until it reaches an impermeable layer, so thatthe coal itself contains very little gas. In other cases, nearly all the gas remains in place,waiting to be produced.

Coal itself usually has very low matrix permeability, with the gas being produced throughnatural fractures (called cleats) and through desorption from the coal itself. The objective ofcoal bed methane fracturing is to connect up the cleats with a propped fracture, allowing thegas to be produced both from the cleats and from the coal

CBM fracturing is more of an art than a science. Because of the unusual characteristics of theformations, most fracture simulators are unable to accurately model these treatments.Engineers usually have to rely on experience and trial and error.

These treatments usually consist of large volumes of proppant, pumped at lowconcentrations, at high rates. Various fluid systems have been used, but recent work hasdemonstrated that crosslinked fluids, especially guar-based gels, can be very damaging to theformation. The trend has been towards HEC, foams and even just water as the carrier fluid.

Proppant concentrations tend to be in the 3 to 4 ppg range. Because wells are relatively lowrate, large fracture conductivities are not required – what is needed is a conductive path fromcleat to cleat. As formations are usually shallow, sand is generally selected as the proppant.

CBM wells often tend to be marginal. They will not produce economically without a fractreatment, but even after a frac can be very low rate. Therefore, fracturing treatments tend tobe fairly low tech, no frills operations, using minimal fluids technology and often eliminatingthe need for modern, sophisticated, computerised blending and pumping equipment. CBMfracturing will be covered in more detail in Section 17.7.

Gas production from a CBM reservoir relies on different mechanisms than production fromconventional reservoirs. The main production mechanism is not expansion of gas in pore

spaces - coals generally have little or no primary porosity. Instead, as stated above, the gas isadsorbed into the coal itself. In order to produce the gas, the pressure has to be reducedbelow a specific critical pressure, at which point the gas starts to desorb. Some CBM





reservoirs are naturally below this critical pressure. Most, however, are significantly above thispressure. In such cases, considerable quantities of water have to be rapidly produced in orderto get the reservoir pressure low enough to initiate gas desorption. Often, a propped fractureplays a critical role in this de-watering process.

3.6 Fracturing Through Coiled Tubing

Fracturing through coiled tubing has been around since the early 1990’s, and was first carriedout through a string of coiled tubing that was left in the well after the treatment, becoming theproduction tubing. However, as the industry began to perceive the advantages of this process – and as Engineers began to leave their preconceived coiled tubing ideas behind – theconcept has become more widely accepted.

The advantage of coiled tubing fracturing does not lie with the design or type of fracture that isplaced in the ground, as most types of fracture can be performed this way. The benefits of CTfracturing lie in the operational aspects of how the treatments are placed.

The obvious limitation for coiled tubing fracturing is the diameter of the coil and the maximumpressure it can be taken to. However, this restriction is not nearly as bad as it initially seems.With modern fluid systems, friction pressure down the coiled tubing can be dramaticallyreduced, allowing treatments to be pumped at quite high rates. Also, as the coiled tubing isstatic during the treatment (i.e. the tubing is not being plastically deformed on a continuousbasis), the maximum allowable pressure is far higher than is normal for CT operations.

Advantages

1. The coiled tubing can be used to isolate the completion from the fracturing process.By setting a squeeze packer at the end of the tubing, the hole tubing string isprotected from the pressure and temperature changes normally experienced by thecompletion. This means that completions that are pressure-limited (due to slidingsleeves, packer ratings, poor quality tubing, wellhead size etc) can be fractured.

Completions which cannot be cooled down too much (due to risk of stinging thetubing out if the PBR on the packer), can also be fractured.

2. Coiled tubing fracturing is particularly effective when working on monoborecompletions, or on wells that have not yet been completed. By using an opposing cuptool, the coiled tubing can be used to easily isolate one zone from another. Anextension of this, is that the tool can be very easily moved from one zone to another,allowing multiple fracs to be performed in rapid succession.

3. If required, the coiled tubing can be used to gas lift the well on to production after thetreatment(s).

4. Coiled tubing can often be used as an alternative to a workover. This can meansignificant cost saving, especially offshore.

Disadvantages

1. The extra cost of the coiled tubing unit, over and above the cost of the frac spread.However, often this extra cost can produce savings in other areas (rig time, frac crewtime etc). The operating company must also be prepared to pay for some or all of thecost of the coiled tubing string.

2. The extra space needed, due to the extra equipment required as compared to thefrac spread by itself. Of course, if the CT unit is being used as an alternative to aworkover rig, this may not be as significant.

3. Rate limitations. In general, for a given fluid system, higher rates can be achievedthrough completions than through coiled tubing. However, it should be rememberedthat it is usually possible to take the static coiled tubing to higher pressures than thecompletion/wellhead assembly.

4. Although it is possible to frac through coiled tubing with standard fluid systems, as the

depth increases and/or the coiled tubing diameter decreases, it may be necessary touse more exotic and expensive fluid systems.





References

Product Catalogue, Colorado Silica Sand, 1994

Economides, M.J., and Nolte, K.G.: Reservoir Stimulation , Schlumberger EducationalServices, 1987.

Gidley, J.L., et al : Recent Advances in Hydraulic Fracturing , Monograph Series Vol 12, SPE,Richardson, Texas (1989).

Bradley, H.B. (Ed): Petroleum Engineers Handbook , SPE, Richardson, Texas (1987)

Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,SPE 56473, presented at the SPE Annual Technical Conference and Exhibition, Houston,October 1999.

O’Driscoll, K.: Middle-East Region Coal Bed Methane Fracturing Manual , BJ Services, 1995.

Gavin, W.G.: “Fracturing Through Coiled Tubing – Recent Developments and CaseHistories”, SPE 60690, presented at the 2000 SPE/ICoTA Coiled Tubing Roundtable,Houston, April 2000.

Wong, G.K., Fors, R.R., Casassa, J.S., Hite, R.H., and Shlyapobersky, J.: “Design, Executionand Evaluation of Frac and Pack (F and P) Treatments in Unconsolidated Sand Formations inthe Gulf of Mexico”, SPE 26563, presented at the SPE Annual Technical Conference andExhibition, Houston TX, Oct 1993.

Tiner, R.L., Ely, J.W. and Schraufnagel, R.: “Frac Packs – State of the Art”, SPE 36456,presented at the SPE Annual Technical Conference and Exhibition, Denver CO, Oct 1996.



BJ Services’ Frac Manual4. Fluid Mechanics


4. Fluid Mechanics

Fluid Mechanics is the study of the behaviour of fluids. In the oil field, this means that fluidmechanics is used to predict fluid friction pressures and the forces due to the dynamics of

fluid flow. Rheology is the study of the deformation and flow of matter, and in the oil field isused to predict the resistance of a fluid to the application of a force or pressure.

4.1 Fundamental Fluid Properties

Density ( ρ ) - A measure of how much matter a material contains within a unit ofvolume. The denser a material is, the heavier a given volume.Provided the liquid composition remains constant, we can think offluid density (especially for water-based fluid systems) as a constant – although it will actually decrease slightly with increasingtemperature and increase slightly with increasing pressure.Hydrocarbon-based fluid systems are significantly morecompressible, and assuming a constant density can result in

inaccuracies (see references for diesel data).

Viscosity ( µ ) - Viscosity is a measure of how much a fluid resists deformation as aresult of an applied force or pressure. It is a measure of how “thick”the fluid is. Viscosity is only very rarely a constant value, as it canchange dramatically with temperature, applied shear stress and fluidcomposition. Viscosity is defined as the relationship between shearstress and shear rate.

Temperature (T ) - A measure of how much energy a material contains – the hotter thematerial, the more energy. Although strictly speaking temperature isnot a fundamental property, in the oil field it an important parameterthat needs to quantified. Most fluid properties are affected to agreater or lesser extent by temperature.

4.2 Shear Stress and Shear Rate

Shear Rate (γ ). In fluid mechanics, shear rate is a measure of how fast a fluid is flowing pasta fixed surface. Shear rate can be thought of as a measure of how much agitation a fluid isreceiving.

Causes of Shear Rate:-- Spinning centrifugal pump- Flow through a pipe- Fann 35 Test

- Jet mixer- Tank agitators

Shear Stress (τ ). Shear stress is the resistance the fluid produces to an applied shear rate.For instance, it requires more force (pressure) to pump water at 20 bpm than at 10 bpm.

Viscosity ( µ ). The fluid property that defines how much shear stress is produced by a shearrate, is called viscosity. The greater the viscosity, the greater the resistance of a fluid to shearagitation.

Newton’s Law of Fluids

µ = τ

γ........................................................................................... (4.1)





This is known as Newton’s law of fluids, and is illustrated in Figure 4.2a:-

Figure 4.2a – Graph illustrating Newton’s law of fluids

In oil field units, Newton’s law can be expressed as follows:-

µ = 47,879 τ

γ.............................................................................. (4.2)

with µ measured in cp (centipoise), τ in lbf/ft2 and γ in sec

-1. Newton was the first to realise the

relationship in fluids between an applied force and the resistance to that force. Hisexperiments were carried out on simple fluids such as water and brine, and not on morecomplex fluids, such as those used in stimulation activities.

4.3 Types of Fluid

In the oil field, we generally deal with three different types of fluids, according to how therelationship between shear stress and shear rate develops. These fluid types are definedbelow.

Newtonian Fluids

As illustrated in Figure 4.2a, these are fluids for which Newton’s law is valid. Newtonian fluidshave a straight line (linear) relationship between shear rate and shear stress until turbulenceoccurs. Equations 4.1 and 4.2 are valid. Examples of Newtonian fluids include:-

Fresh WaterSea WaterMost Acids (ungelled)DieselAlcoholsGases

Bingham Plastic Fluids

Bingham plastic fluids require an initial shear stress to be induced before they will deform. Putanother way, they have a yield point or gel strength that must be broken before the fluid canmove (although some fluids have a gel strength that is nothing to do with yielding). This typeof fluid is not Newtonian, although they usually have a constant viscosity once the initial gelstrength has been overcome.

Slope = µµµµ

S h e a r S t r e s s , τ ττ τ

Shear Rate, γ γγ γ 0

0





τ = Y p + P v γ ......................................................................... (4.3)

Y p is the yield point, and in the oil field has units of lbf/100 ft2 (note that in the oil field, τ has

the units lbf/ft2, so the value for Y p has to be converted before it is used), whilst P v is theplastic viscosity, with cp as its units.

Figure 4.3a illustrates the behaviour of a Bingham plastic fluid Examples of Bingham plasticfluids include some cement slurries and some drilling muds.

Figure 4.3a – Relationship between shear rate and shear stress for a Bingham plastic fluid.

Power Law Fluids

The third group of fluids is generally referred to as power law fluids, although there are othernames which have been used to describe them. In general, there is no linear relationshipbetween shear rate and shear stress, so that apparent viscosity (the viscosity which the fluidappears to have, at a specific shear rate) changes with shear rate. The following Equationdescribes the behaviour of the power law fluid, and this is illustrated in Figure 4.3b.

τ = K ’γn ’ .............................................................................. (4.4)

Figure 4.3b – Relationship between shear rate and shear stress for a power law fluid. Note that

the graph shows the relationship in its most common form - “shear thinning”. However, incertain fluids the line can also curve upward - “shear thickening”.

Slope = P v

S h e a r S t r e s s , τ ττ τ


0

Y p

S h e a r S t r e

s s , τ ττ τ


0





K’ is referred to as the power law consistency index, and in order to be coherent has therather awkward units of lbf sec

n’ /ft

2. n’ is the power law index and is dimensionless.

In order to determine n’ and K’ , the log of Equation 4.4 is taken;

log τ = log K’ + n’ log γ .......................................................... (4.5)

On a plot of logτ against logγ , the intercept of the vertical axis is log K’ and the gradient of theline is n’ , as shown in Figure 4.3c;

Figure 4.3c – Power law fluid log-log plot

Power law fluids can be divided into 3 major categories;

Shear-thinning fluids. In these fluids, n’ is less than 1, so that the fluids experience adecrease in apparent viscosity as the shear rate increases. Most of the fluids used forfracturing fall within this category.

Newtonian fluids. Newtonian fluids are a special case of power law fluids in which n’ isequal to one, i.e. the viscosity is constant and equal to K’ .

Shear-thickening fluids. These fluids have an n’ greater than one, and so exhibit anincrease in apparent viscosity as shear rate increases. Extreme examples of these fluids canbehave as it they were solids when exposed to even moderate shear forces.

Another example of a power law fluid is the Herschel-Buckley fluid, which is often used tomodel the flow behaviour of foams;

τ = τ ’o + K’’ γ n’’

.................................................................... (4.6)

where τ ’o is the threshold shear stress, K’’ is the Herschel-Buckley consistency index and n’’ the Herschel-Buckley exponent.

Herschel-Buckley fluids are basically a combination of the Bingham plastic fluid and thepower law fluid. An initial threshold shear stress has to be overcome before the fluid will flow.Once this has happened, the viscosity is not constant, and will vary according to the shearrate.

Slope = n’

l o g τ ττ τ

log γ γγ γ 0

0

log K’





4.4 Measuring Viscosity

In order to measure viscosity, two variables need to be determined. First, the shear rate ofsome moving device within the fluid, needs to be determined. Second, the resistance to thisshear rate needs to be evaluated. This can be done either by measuring the amount of forcerequired to move the source of shear rate, or by measuring the deflection on an object placedin the fluid, close to the source of shear rate.

If the fluid being analysed is not Newtonian, then the apparatus will have to perform thesetasks at several different shear rates.

Once the resistance to the shear rate (i.e. the shear stress) has been determined at one ormore known shear rates, the viscosity (or the components required to determine the apparentviscosity) can be derived.

Model 35 Viscometer

The model 35 viscometer, produced either by Fann or Chandler , is the most common deviceused in the oil industry for determining viscosity and rheological properties. It is robust, easyto use and reliable. It can also be fairly easily calibrated, provided the user is familiar with theprocess. Figure 4.4a shows a photograph of a model 35 viscometer, whilst Figures 4.4b and4.4c illustrate how it works;

TorsionSpring

Bob

BobShaft

Figure 4.4b – Cross-section through the rotorand bob on a model 35 viscometer

Figure 4.4c – Schematic diagram showingthe model 35 viscometer bob assembly

Figure 4.4a – Chandler 35 viscometer.The position of the rotor is indicated(A), whilst the bob is hidden insidethis. The cup (B) holds the test fluid,

and is mounted on a support (C) thatcan move up and down as required.

A

B

C

Rotor

Fluid

Bob

Bob Shaft





The model 35 viscometer works by rotating the rotor (see Figure 4.4b) around the bob. Thefluid is positioned in a narrow gap between the rotor and the bob. As the rotor spins, itproduces a shear on the fluid, which in turn produces a drag force on the bob. The bob ismounted on a spring loaded bob shaft (see Figure 4.4c), so that as it experiences a dragforce, it will rotate slightly. The greater the drag force, then more the bob rotates. Attached tothe top end of the bob shaft is a dial indicator, allowing the operator to read how much the

bob has rotated. As the bob deflection is directly related to the shear stress beingexperienced by the fluid, it is possible to use the dial reading as a measure of viscosity.

Generally, the model 35 viscometer can spin the rotor at the following speeds, although thesevary slightly from model to model. The speeds are 1, 2, 3, 6, 12, 20, 30, 60, 100, 200, 300and 600 rpm.

By plotting the rpm’s of the rotor (shear rate) against the dial reading (shear stress) it ispossible to determine what type of fluid is being measured, by analysing the shape of thecurve.

τ = 0.01066 N θ .................................................................. (4.7)

γ = 1.703 ω ......................................................................... (4.8)

where N is the spring factor of the torsion spring fitted to the model 35 viscometer (usually

equal to 1), θ is the dial reading and ω is the speed of the rotor in rpm’s. It should be notedthat Equation 4.8 is valid only for the R1 rotor and B1 bob combination – for othercombinations refer to the manufacturer’s manual.

By using Equations 4.7 and 4.8, a plot of shear rate against shear stress can be produced, orif necessary, a log-log plot. From these, the viscosity defining parameters can be derived.

Other Methods for Measuring Viscosity

Various other methods for measuring viscosity are available;

i) Helical Screw Rheometer. Uses a helical screw inside a sleeve. The screw rotatesand fluid flows up the inside of the sleeve and out of the top. The amount of forcetaken to rotate the screw is measured to produce the shear stress. The shear rate isderived from the speed of the screw. Used by some service companies for in-linereal-time viscosity measurement during frac jobs.

ii) Fann 50 HPHT Viscometer. Works on the same principle as the model 35viscometer, but is designed so that the analysis can be carried out at hightemperature and pressure. These viscometers are also usually remote controlled by aPC, allowing shear rate and temperature schedules to be used, as well as therecording of all data. Although quite expensive, these machines are commonly used

for designing frac fluid systems. Figure 4.4d shows a Fann 50.

Figure 4.4d – Fann 50 highpressure, high temperaturerheometer. This model is fullycomputer controlled, whereasearlier models had manualcontrols and were twice thesize of the model shown.





iii) Brookfield In-Line Viscometer. Viscometer designed to provide real time viscositymeasurement for fluids flowing down a process line. This viscometer works on asimilar principle to the model 35, although the rotor and bob are of a different size andshape.

iv) Funnel Viscometer. A simple device for determining apparent viscosity. It consists ofa funnel with a hole in the end. A specific volume of the fluid is placed in the funnel,and the time taken for it to drain out of the small hole in the bottom of the funnel ismeasured. A chart then provides a quick conversion from time to apparent viscosity.

The above are the most commonly used varieties in the oil industry, although it should beremembered that a wide variety of devices and methods are available.

4.5 Apparent Viscosity

The apparent viscosity of a fluid is the viscosity of the fluid at a specific shear rate. For a

Newtonian fluid, the apparent viscosity is the same as the actual viscosity. For all other fluids,the apparent viscosity is the slope of a line on a shear rate vs shear stress curve, from theorigin to the line, at a specific shear rate, as shown in Figure 4.5a:-

Figure 4.5a – Graph illustrating the change in apparent viscosity for a power law fluid at twodifferent shear rates.

As can been seen in Figure 4.5a, for a shear thinning power law fluid, the apparent viscosityof the fluid (the slope of the two lines) decreases as the shear rate increases. At shear rate

"a" the slope of line 1 (and hence the apparent viscosity) is greater than the slope of line 2 atthe greater shear rate "b". Hence the fluid is said to be shear thinning.

In practice, it is the apparent viscosity that is usually measured. The model 35 viscometer isset up so that at 300 rpm (with an R1 rotor, B1 bob and spring factor = 1), the apparatusreads apparent viscosity directly – no additional calculations are required.

The apparent viscosity can be calculated as follows, for a power law fluid:-

µ app =47879 K'

γ 1-n' ...................................................................... (4.9)

S h

e a r S t r e s s , τ ττ τ


0a b

1

2





4.6 Flow Regimes and Reynold’s Number

Figure 4.6a illustrates the three different flow regimes that a fluid can experience, with plugflow being at the lowest fluid velocity, and turbulent flow being at the highest.

Figure 4.6a – Diagram illustrating the three flow regimes

i) Plug Flow. At low flow rates, the fluid flows with an almost uniform velocity profile.The fluid moves with a uniform front across almost the entire flow area.

ii) Laminar Flow. As the flow rate increases, the velocity profile begins to change. Fluidclose to the walls of the pipe (or duct, or fracture) flows slowest, whilst fluid in thecenter of the pipe flows fastest. Fluid velocity is a function of distance from the pipewall. Also known as streamline flow.

iii) Turbulent Flow. As the flow rate continues to increase, the contrast in velocityacross the flow area becomes unsustainable, and the fluid breaks down into turbulentflow. This is characterised by a series of small scale eddies and whirls, all moving inthe same overall direction.

The friction pressure produced by the fluid flow is highly dependent upon the flow regime.Therefore, it is important to be able to determine the flow regime.

Reynold’s Number

The flow regime is found by using the Reynold’s number (N Re), as follows;

N Re < 100 Plug Flow100 < N Re < 2000 Laminar Flow

N Re > 2000 Turbulent Flow

It should be remembered that these are very generalised numbers. The actual numbers canvary significantly, depending upon the circumstances. The Reynold’s number itself can befound from the following formula:-

N Re = ρ d v

µ ........................................................................... (4.10)

Plug Laminar Turbulent





where ρ is the fluid density, d is the inside diameter of the pipe, v is the “bulk” fluid velocityalong the pipe and µ is the viscosity. Equation 4.10 is for SI units, whilst Equation 4.11 is forfield units;

N Re = 132,624 SG q

d µ ........................................................... (4.11)

where SG is the specific gravity, q is the flow rate in bpm, d is the inside diameter in inches

and µ is the viscosity in cp.

Obviously Equations 4.10 and 4.11 only apply to Newtonian fluids, i.e. fluids with a constantviscosity. As stated before, Frac Engineers only rarely deal with Newtonian fluids, so below isEquation 4.11 converted for power law fluids;

N Re = 15.49SG v

2-n'

K' (96/ d )n' ......................................................... (4.12)

where v is the velocity in ft/sec. To make things easier, v can be easily found from the flowrate, q :-

v = 17.157q

d 2 .................................................................. (4.13)

with q in bpm and d in inches.

Usually, when fracturing, it is best to keep abrasive fluids at flow rates below that needed forturbulent flow. This is to prevent the erosion of flow lines and the washing out of seals,caused by the action of the proppant. BJ Services' Standard Practices states that for abrasivefluids, the fluid velocity must be kept below 40 ft/sec.

4.7 Friction Pressure

One of the ultimate objectives of fluid mechanics - as far as the Frac Engineer is concerned,

anyway – is to be able to predict the friction pressure (∆P frict) of the fluids that are beingpumped. This is often very difficult, as fluid composition and temperature is constantlychanging as the treatment progresses. In addition, two-phase (liquid and proppant) and eventhree-phase (liquid, proppant and gas) flow is common.

Predicting fluid friction pressure is therefore an unreliable process and there really is nosubstitute for reliable bottom hole pressure data. Failing that, the next best option is to usefriction pressure tables, such as BJ’s Fracturing Fluids – Friction Pressure Data . These tablesare usually based on data generated by actually pumping the fluid around a flow loop, and soare based on a situation similar to the actual treatment process. Most modern fracture

simulators incorporate data from these tests in their fluid models, so friction pressurespredicted by these are also reasonably reliable (although not perfect, as the temperature ofthe wellbore is constantly changing) unless there is proppant in the fluid.

Finally, when the three methods outlined above are not possible, the friction pressure may becalculated from fluid data, using the one of several available methods. The method outlinedbelow, based on the use of Fanning friction factors, is fairly reliable (i.e. it is just as good asthe data used as inputs), but is not intended for use in narrow diameter pipes at higher thannormal flow rates (such as for coiled tubing treatments).

∆P frict = 0.325 SG L v

2 f

d ......................................................... (4.14)

where L is the length of pipe in feet and f is the friction factor (dimensionless).





The friction factor is determined by using the Reynold’s number. For plug and laminar flow:-

f =16N Re

............................................................................. (4.15)

whilst for turbulent flow:-

f =0.0303

N Re0.1612

.................................................................... (4.16)

So the first step in the process of finding ∆P frict is to determine the Reynold’s number. Oncethat has been found, the friction factor can be determined, which in turn leads to the frictionpressure.

References




Economides, M.J.: A Practical Companion to Reservoir Stimulation , Elsevier, 1992

FracRT Version 4.6 User’s Manual , BJ Services, 1995 onwards

Friction Pressure Manual , The Western Company, 1989 onwards

Fracturing Fluids – Friction Pressure Data , BJ Services, 1983 onwards

API Recommended Practice 39, Measuring the Properties of a Cross-Linked Water-Based Fracturing Fluid , 3

rd Edition, American Petroleum Institute, May 1998

Stimulation Engineering Support Manual , BJ Services, October 1996 onwards

Standard Practices , BJ Services, 2000 onwards



BJ Services’ Frac Manual5. Fluid Systems


5. Fluid Systems

The fracturing fluid is a vital part of the fracturing process. It is used to create the fracture, tocarry the proppant into the fracture, and to suspend the proppant until the fracture closes. On

a more basic level, the fluid system is the vehicle that allows us to transfer mechanical energy(in the frac pumps) into work performed on the formation.

In order to carry out these tasks efficiently, the ideal fluid must have a combination of thefollowing properties.

i) Low cost.ii) Ease of use.iii) Low tubing friction pressure.iv) High viscosity in the fracture, to suspend the proppant.v) Low viscosity after the treatment, to allow easy recovery.vi) Compatibility with the formation, the reservoir fluids and the proppant.vii) Safe to use.

viii) Environmentally friendly.

Some of these properties are not easy to combine in the same fluid. Usually, the process ofselecting a fracturing fluid is a trade off. It is up to the Engineers to decide which propertiesare most important and which properties can be sacrificed. In order to make this choiceeasier, there are a number of fluid systems available for fracturing.

5.1 Water-Based Linear Systems

The first fracturing fluid, used in Kansas in 1947, was gasoline gelled with war surplusnapalm. Obviously this was a highly dangerous fluid, and it wasn’t long before water basedsystems were available. The first of these systems used starch as the gelling agent, but by

the early 1960’s guar was introduced and soon became the most common polymer forfracturing. Today, polymers derived from the guar bean are used in most fracturing treatments- the other main source of polymers being cellulose and it's derivatives.

Before the dry polymer is added to the water, the individual molecules are tightly curled up onthemselves. As the polymer molecule hydrates in water, it straightens out – which is whythese fluids are referred to as linear gels – as illustrated in Figure 5.1a:-

Figure 5.1a – Hydration of polymer gels in water. 'A' shows a polymer molecule before hydrationin water, whilst 'B' shows a polymer molecule after hydration in water.

It is these long, linear molecules that produce the increase in viscosity. However, it should beremembered that this hydration only occurs at a specific pH range. Outside this range, the

A B





hydration rate can be very slow and sometimes almost non-existent. Different polymers havedifferent pH ranges, and buffers may have to be used to make the polymer hydrate. If apolymer that hydrates at a neutral pH is added to water, it may start to hydrate very rapidly.This leads to the formation of “clumps” of non-hydrated polymer, surrounded by partiallyhydrated polymer, surrounded in turn by hydrated polymer. These are known as fish-eyes andare a sign that the gel has been poorly mixed.

Several techniques can be employed to prevent the formation of fish-eyes.

i) Buffer the water so that the pH will prevent hydration. Once the polymer powder isthoroughly dispersed in the water, a different buffer is used to change the pH to apoint where the polymer will hydrate.

ii) Add the polymer through a high shear device (such as a jet mixer) to ensure that thepolymer does not form clumps.

iii) Circulate the hydrating gel through a high shear device, such as a choke, to break upany fish eyes.

iv) Slurry the polymer into a hydrocarbon-based fluid (such as diesel, kerosene or evenmethanol). The slurry is then added to the water, allowing the polymer to dispersebefore it hydrates.

A combination of these methods can also be used.

Common polymers used for linear gels include:-

StarchGuarHydroxypropyl Guar (HPG)Carboxymethyl Hydroxypropyl Guar (CMHPG)Carboxymethyl Guar (CMG)CelluloseHydroxyethyl Cellulose (HEC)Carboxymethyl Hydroxyethyl Cellulose (CMHEC)

XanthanXanthan derivatives (e.g. Bioxan

® , Xanvis

® , XC Polymer

® etc)

The most commonly used polymers for fracturing are Guar, HPG and CMHPG, mostly as thebasis for crosslinked systems (see below). HEC is probably the most widely used polymer forlinear gel fracturing, due to its popularity for fracturing low temperature, high permeabilityformations.

BJ’s range of water-based linear gel frac fluids includes the Aqua Frac system, which isbased on guar and its derivatives. Gelling agents are GW-3, GW-4 & GW-27 (guar), GW-32(HPG), GW-38 (CMHPG) and GW-45 (CMG). Also in BJ’s product range is the Terra Packsystem, which is primarily designed for gravel packing, but can also be used for fracturing.The gelling agent for Terra Pack II is GW-21 (HEC) and for Terra Pack III is GW-22

(Xanthan).

5.2 Water-Based Crosslinked Systems

The majority of hydraulic fracturing treatments are carried out using water based crosslinkedgels. These systems offer the best combination of low cost, ease of use, high viscosity andease of fluid recovery. Generally, water based crosslinked gels will be used unless there is aspecific reason not to use them – they are the default option.

The starting point for a crosslinked system is a linear gel, as described above in Section 5.1.When used for crosslinked systems, linear gels are often referred to as base gels. The most

commonly used linear gels are guar and its derivatives; HPG, CMG and CMHPG.





A crosslinked gel, as illustrated in Figure 5.2a, consists of a number of hydrated polymermolecules, which have been joined together by the crosslinking chemical. This series ofchemical bonds between the polymer molecules greatly increases the viscosity of the system,sometimes by as much as 100 times.

In order for an efficient crosslink to occur, two separate things need to happen. First, the base

gel needs to be buffered to a pH which will allow the crosslinking chemical to work. Usually,this is at a different pH to that required for polymer hydration, so a different pH buffer has tobe used. Secondly, the crosslinking radical needs to be present at sufficient concentration. Ifboth these conditions occur, the gel will experience a dramatic increase in viscosity.

Figure 5.2a – A crosslinked polymer. ‘A’ shows the hydrated polymer prior to addition of thecrosslinker. ‘B’ shows the crosslink chemical bonds between the polymer molecules.

Obviously, a fully crosslinked polymer is extremely viscous, and can result - under the wrongconditions - in a high level of fluid friction as it is pumped downhole. To counter this, it is quitecommon to use a delayed crosslinker. A delayed crosslinker can take anything up to 10

minutes before the gel is fully hydrated, depending upon the temperature, initial pH and shearthat the fluid experiences. The ideal crosslink delay system would delay the onset of crosslinkas long as possible, but would still have the fluid fully crosslinked by the time it reaches theperforations.

The most commonly used crosslinking systems are as follows:-

Borates“Exotic” BoratesZirconatesAluminatesTitanates

Figure 5.2b – pH ranges for crosslinkers (after SPE 37359)

A B

Zirconates

Aluminates

Organic Titanates

Borates

0 1 2 3 4 5 6 7 8 9 10 11 12





Of these, the borates and “exotic” borates are by far the most commonly used, followed bythe zirconates. Figure 5.2b illustrates the pH ranges of these crosslinkers, whilst Figure 5.2cshows their temperature ranges:-

Figure 5.2c – Temperature range for crosslinkers (after SPE 37359)

All crosslinked gels tend to be shear thinning, which means that the apparent viscosity of thefluid decreases with shear rate. This is because the shear acts to break the crosslink bondsbetween the hydrated polymer molecules. Borate crosslink bonds will reconnect and producea good quality gel after the shearing has taken place. However, zirconate bonds are muchmore shear sensitive and may not reconnect. Therefore, it is essential to consider the level ofshear that a fluid will experience when selecting a crosslinker.

Like most fracturing companies, BJ Services tends to classify its crosslinked fluids systems bythe type of crosslinker used:-

Viking™ is a guar-based system that uses conventional borates for the crosslink. It is acheap, easy to use fluid intended for low temperature applications. There is no crosslinkdelay. Crosslinkers used are XLW-4, XLW-32 or XLW-10.

Viking D is the delayed crosslink version of Viking, and uses the crosslinkers XLW-30 orXLW-30A.

Spectra Frac G ®

is probably the most commonly used of all BJ’s borate frac fluid systems. Itis guar based, and uses an organo-borate crosslinker for a much greater temperature rangethan the Viking systems. The system is a premium system at lower temperatures, typicallyproviding more viscosity. The crosslinker can be delayed, and the length of time for the delaycan be varied over a significant range. The crosslinker for the system is XLW-24.

Spectra Frac G ®

HT is the high temperature version of Spectra Frac G ®

. It is guar based,and uses an organo-borate crosslinker for a much greater temperature range than the Vikingsystems. The crosslinker also employs a self-breaking mechanism, which helps to reduce theviscosity over a period of time above +/- 230°F. The crosslinker can be delayed, and thelength of time for the delay can be varied over a significant range. The crosslinker for thesystem is XLW-56.

Lightning™ is a new fracturing fluid system that uses a newly developed low-residue guarpolymer, GW-3. The system uses the same borate crosslinkers as Viking™.

Medallion Frac ®

is a CMHPG based system that uses a zirconate crosslinker. Unlike theborate systems, which operate at a pH above +/- 9.0, Medallion Frac

® operates at a pH

below neutral, usually around 4.5 to 5.5. Because of its low pH, it is the fluid of choice for CO2

foam fracs, pads for acid fracs, and for formations which are sensitive to high pH’s.

100 150 200 250 300 350 400

Zirconates

Aluminates

Titanates

High Temperature Borates

Conventional Borates

Temperature, oF





Crosslinkers for the system are XLW-41, XLW-53 or XLW-60. XLW-60 is a delayed crosslink,whilst XLW-41 and XLW-53 are designed for a rapid crosslink. The crosslinkers can be usedtogether in varying proportions to adjust the crosslink time as desired.

Medallion Frac HT ®

is a high pH version of Medallion Frac ®

. It uses a different buffer toachieve the required pH (usually around 8.0 to 9.0), but otherwise is the same as Medallion

Frac ®

. The high pH zirconate system is more temperature stable than the low pH. Generally,the high pH system uses XLW-60 as the crosslinker.

Vistar™ is a low or high pH, zirconate crosslinked system, designed so that only very lowpolymer loading is needed, as compared to other fluid systems. The base gel is a guar-derivative (GW-45). Crosslinkers for the system are XLW-63 (lower temperatures) and XLW-14 (high temperatures).

Crosslinked systems are also characterized by the quantity of polymer used in the base gel.For instance, a “35 lb” system has the base gel mixed with 35 lbs of polymer in every 1000gals of water. If this base gel were to be used in Spectra Frac G

® , the fluid system would be

known as Spectra Frac G ®

HT 3500.

LFC, XLFC, VSP and GLFC

LFC (which stands for Liquid Frac Concentrate) and XLFC are slurried polymer systems,usually designed to carry 4 lbs of polymer in every gallon of slurry. Simply add the slurry towater and the base gel will form. Slurrying the polymer in an oil-based system helps dispersethe polymer in the water (preventing fish-eyes) and is much easier to meter when hydratinggel on-the-fly. The liquid base for the slurry is usually diesel or a low toxicity diesel-derivative.However, LFC and XLFC systems have been developed that use vegetable or fish oil as thebase liquid, although these hold reduced amounts of polymer per gallon. In addition to thebase oil and polymer, LFC and XLFC also contain suspending agents to prevent settlingduring storage, dispersants to help mix the slurry and wetting agents to help the polymerhydrate quickly once the LFC or XLFC is added to water. A pH buffer can also beincorporated to help the polymer hydrate more quickly, especially at low temperatures.

LFC-1, GLFC-1 and XLFC-1 contain guar (GW-27)LFC-2, GLFC-2 and XLFC-2 contain HPG (GW-32)LFC-3, GLFC-3 and XLFC-3 contain CMHPG (GW-38)XLFC-5 contains GW-3

XLFC is the updated version of LFC. VSP (or Vistar Slurried Polymer) is a version of XLFCdeveloped for the Vistar™ system and contains CMG (GW-45).

GLFC systems, which can be mixed with guar, HPG or CMHPG, use an organically-derivedbase oil in order to meet increasingly tight environmental regulations in many areas of theworld.

5.3 Oil-Based Systems

As stated previously, the very first hydraulic fracture treatment was carried out using gasolinegelled with war surplus napalm. The operation was performed on Pan American Petroleum’sKlepper No 1 well, Grant county, Kansas, (part of the Hugoton gas field) in 1947. Thetreatment was aimed at 4 gas bearing limestone formations, at about 2500 ft. The gasoline-based fluid was selected, as it was perceived to be more compatible with the formation. Thiscontinues to be the primary reason for selecting an oil-based fluid.

For the record, the treatment on Klepper No 1 failed to produce a significant productionincrease, and it was decided that the "Hydrafrac” process would never compete successfully

with acidising in this type of formation.





The first widely-used oil-based fluid system, was based on the reaction of an acidic material(tallow fatty acid) and basic material (caustic) to form a polymeric salt, in a process similar tothe manufacture of soap. These fluids provided viscosity, but where very unstable at elevatedtemperatures. As time progressed, this system was replaced by others based on the use ofaluminium phosphates, which were able to provide significantly increased viscosity and morestability at elevated temperatures.

In the early 70’s, the aluminium phosphate systems were replaced by the aluminium estersystems. The association of aluminium and phosphate esters is illustrated in Figure 5.3a.

These systems used a combination of two products to produce the required viscosity. Therelative ratio of these two products was extremely critical – so critical that it was difficult to mixthese systems on the fly. Consequently, a great deal of time and effort was spent in pre-gelling tanks full of hydrocarbons, resulting in considerable spillage and waste of chemicals.

Figure 5.3a – Aluminium phosphate association polymer

More recently, BJ Services has introduced a much more user-friendly system known asSuper RheoGel. The ratios of the various components of the system are not nearly ascritical, so that the gel can now be mixed on the fly. The following products are used in Super

RheoGel:-

GO-64 (gelling agent) and XLO-5 (activator) are the main components of the system. Theyare added in equal quantities, at different stages of the blending procedure, to produce therequired viscosity and stability.

NE-110W is a critical surfactant blend used in the continuous mix gelled oil system. Thismaterial aids in fluid recovery by acting as a hydrotropic material in the system. It helps toreduce emulsion tendencies of oils and also acts as a long-term breaker for the system. NE-110W also helps to counteract the oil-wetting surfactants contained in products such asdiesel.

GBO-5L, GBO-6 and GBO-9L are the breakers for the system.

Most gelled oil systems can be prepared with a wide variety of hydrocarbon based fluids,including diesel, kerosene, “frac oil”, condensate and many lease crudes. Because the fluidused to fracture the well is itself hydrocarbon based, the well can be put straight on toproduction after the treatment is over. This makes the fluid recovery phase of the operationsmuch easier.

The Super RheoGel system does not work like a conventional water-based crosslink system.There is no base gel viscosity when the GO-64 is added, as it does not react with the basehydrocarbon. Instead, the GO-64 disperses in the hydrocarbon. When the XLO-5 is added,the crosslinker joins up the GO-64 molecules, trapping the hydrocarbon molecules within theGO-64 / XLO-5 matrix and producing viscosity. Because the GO-64 does not react with thebase hydrocarbon, it is possible to gel any fluid system in which this product can be

dispersed, hence the ability of the system to be used in a wide variety of hydrocarbon-basedfluids.

OO

H H

OO

R R

OO

R R

OO

H R

OO

H R

O

Al

P P

O O O

AlAl

OOOO

P P





Methanol can also be used as the base for fracturing fluids, although the systems designedfor oil-based fluids (such as Super RheoGel) are not suitable. Instead, a polymer is used toproduce a base gel and a specialised crosslinker is used to provide the viscosity necessaryfor proppant transport.

Methanol-based fracturing fluids are used in water- and fluid-sensitive reservoirs where fluidrecovery after the treatment is critical. The methanol reduces interfacial tension between thefracturing fluid and the connate water and also helps remove and prevent capillary waterblocks. This allows for much easier recovery of the fracturing fluid from dry gas and water-sensitive reservoirs.

BJ Services' methanol-based fracturing fluid is called Methofrac XL. The system is designedfor continuous or batch-mixed applications. GM-55 is the guar-derivative polymer powder,whilst XLFCM-1 is the slurried polymer concentrate. The crosslinker is XLW-40, which is atitanium-based, is usually diluted before use. The diluted versions (XLW-40B, -41A and -41B)are mixed by adding 2.5 to 10% of XLW-40 by volume to methanol or iso-propyl alcohol, asappropriate (see BJ Services' Mixing Manual instructions). The breaker for the Methofrac XLsystem is GBW-5.

When mixing with lease crude or condensate, obtain fresh samples of the hydrocarbon andtest to make sure that the system performs as required. This practice should also be followedwhen mixing with fluids such as kerosene or diesel, as local variations in product quality canhave a significant effect on fluid performance. Additionally, be aware that BJ Services hasstrict safety and operations standards for the use of hydrocarbon based fluids, and for thehandling of low flash point liquids. These standards can be found in BJ’s Standard Practices Manual and BJ’s Corporate Safety Standards and Procedures Manual .

5.4 Emulsions

In general, emulsions are only rarely used in fracturing operations, but in some parts of theworld they have been found to have an ideal combination of fluid loss characteristics,formation compatibility and downhole viscosity. As a result, in these areas their use iscommon.

Most of these systems are oil-in-water emulsions and operate in a similar fashion. Water isgelled with a standard gelling agent and held in a tank(s). During the job, water and oil aremixed together at the ratio of 2 parts oil to one part gel. An emulsifier is either pre-blended inthe water phase (the gel) or added on the fly. The fluids very quickly form a brown emulsion,the viscosity of which is largely proportional to the initial viscosity of the water phase.

Some systems require an external breaker in order to destroy the emulsion and allow thefluids to be recovered. However, in most systems, the emulsion quickly falls apart after

exposure to the formation.

BJ Services emulsion-based fluid system is known as Polyemulsion for which theemulsifying agent is E-2.

5.5 Visco-Elastic Surfactant Fluids

Visco-elastic surfactant (VES) systems are water-based fluids that employ a completelydifferent method from all other water-based fluid systems for obtaining viscosity. They do notrely upon the hydration of a polymer. Instead, they use the unique properties of certainsurfactants when mixed at certain concentrations in brine-based fluids.

In aqueous fluids, surfactants will tend to expel their lipophilic (water-repelling) tails out fromthe surface of the fluid. As the concentration of the surfactant increases, close packing occurs





and no more surfactant molecules can expel their tails. At this point, the surfactant moleculeswill start to form spherical aggregates (or micelles) with the lipophilic tail facing inwards, andthe hydrophilic head facing outwards. The concentration at which these micelles start to formis called the critical micellar concentration (CMC), and is often around 0.5% by volume ofsurfactant. The CMC will decrease as the molecular weight of the surfactant increases.

As the surfactant concentration increases further, and in the presence of a suitable counterion (such as those produced by brines), these micelles can come together to form worm- orrod-shaped aggregates or micelles. It is these rod-shaped micelles that impart viscosity to thewater.

VES fluids have some rather unique properties, as follows:-

1. VES fluids are extremely shear thinning, with the property to quickly re-heal after theshear is removed. This means that the fluids have an extremely low friction pressure,whilst at the same time retaining excellent proppant transport characteristics.

2. VES fluids are very easy to mix. Simply start with the base brine and add thesurfactant on the fly.

3. VES fluids can be made to be very environmentally friendly, depending upon the

combination of surfactant and brine used.4. VES fluids often require no breaker system, as micelles can be disrupted by changes

in pH, high temperatures, dispersion in formation waters or by contact withhydrocarbons.

5. The VES system is as formation and proppant pack friendly as the base brine used tomix it. The systems contain no polymers, and therefore produce no polymer residue.Therefore, these fluids are capable of providing zero formation damage and 100%regained proppant pack permeability.

The two main disadvantages of VES fluids are that they are relatively expensive and that theyare limited by temperature. Proppant transport characteristics are rapidly lost abovetemperatures of +/- 230°F. Development work continues, however. Another problem with VESfluids is leakoff. Because they contain no polymers, they do not have any wall-building

characteristics, and so leakoff control is entirely dependent upon the fluid’s viscosity and/oradditives used in the system.

BJ Services’ has two VES fluid systems, called ElastraFrac and AquaClear.

ElastraFrac uses the surfactant MA-1. The system uses potassium, ammonium ormagnesium chloride as the base brine, although more exotic phosphate-based brines areused at temperatures above +/- 200°F. The surfactant used is anionic (unlike competitor’sproducts that use cationics and hence risk oil-wetting the formation).

AquaClear is also a surfactant-based fracturing fluid. The system uses either a combinationof FAC-1W and FAC-2, or the single surfactant FAC-3W as the VES. It is designed for mixingon-the-fly and is suitable for use up to +/- 250 °F. The system is easily used as an energised

fluid and does not need an additional foaming agent).

5.6 Energised Fracturing Fluids

Energised fluids consist of a liquid phase – usually a water-based linear or crosslinked gel – and a gaseous phase, which is typically N2, CO2 or a combination of these. Such treatmentsinvolve large amounts of equipment and personnel. Consequently, they are relativelyexpensive. These treatments are also referred to a foam fracs, as foam is generally what isarriving at the formation. Because of the safety implications of working with both cryogenicfluids and energised fluids, the procedures detailed in BJ’s Standard Practices Manual andBJ’s Corporate Safety Standards and Procedures Manual , should be closely followed at all

times.





Foamed fluids have several unique properties that make them advantageous under certaincircumstances:-

i) Viscosity and proppant transport. Stable foams have a comparatively high viscosityand make excellent fluids for carrying and suspending proppant.

ii) Foams have very good leakoff properties. This is due to the multi-phase flow effects

as the foam tries to move through the formation's porosity.iii) Because foams are typically only 30 to 40% liquid, they are more compatible with

water sensitive formations than frac systems which are 100% liquid.iv) The extra energy stored in the fluid, coupled with the low hydrostatic head of the

foam, makes fluid recovery relatively easy.

Foam Quality

The foam quality, often expressed as a percentage or just simply as a quality (i.e. “70 quality”or even “70Q”) is the percentage of foam or energized fluid that is gas, at the anticipatedbottom hole conditions. In order to design a foam treatment, an Engineer must have areasonable idea of the expected bottom hole treating pressure and temperature, as thevolume occupied by the gas phase will vary depending on both of these (although thetemperature is much less significant than the pressure). As illustrated by Figure 5.6a, foamviscosity (and hence it’s ability to transport proppant) is heavily influenced by the quality. If thebottom hole pressure is significantly less than anticipated, the foam quality will be too high,and the gas phase will expand to make a mist, rather than foam.

Figure 5.6a – Proppant transport as a function of foam quality. This graph is a combination of thework performed by several individuals and organisations. It is intended as a qualitative

illustration of the effect foam quality has on the ability of the fracturing foam to transport andsuspend proppant.

Gas assisted fluids use lower gas quality (typically 20 to 40%) than foamed fluids. The mainpurpose of the gas phase is to reduce hydrostatic head and hence aid fluid recovery. In suchtreatments, the proppant transport and fluid leakoff properties for a fully foamed fluid systemare not required.

Proppant Concentration

Because proppant is added to the liquid phase of the foamed frac fluid, there is a limit to the

overall proppant concentration that can be achieved downhole. Because it is not possible toblend and pump proppant at more than 18 or 19 ppg in the liquid phase, by the time the liquidphase has been mixed with the gaseous phase, the overall proppant concentration has been

0 20 40 60 80 100

STABLEFOAM

Foam Quality

P r o p p a n t T r a n s p o r t





reduced to 7 or 8 ppg. For this reason, it is not possible to place the very high proppantconcentrations required for fracturing high permeability formations. This means that foamfracturing is limited to medium and low permeability reservoirs, for skin bypass fracturing(although the extra cost can defeat the low cost objectives of this type of treatment) and forcoal bed methane fracturing.

Constant Internal Phase vs Constant External Phase

Foams can be thought of as being a multi-phase fluid, with a gas-internal phase, and a liquidexternal phase. The difficulty comes in deciding whether or not the proppant is part of internalphase or the external phase.

The traditional method of modeling foams and designing treatment schedules uses theconstant external phase method. This assumes that the proppant is part of the externalphase. It is easier to operate on location, as both the slurry rate and the gas rate remainconstant. However, under constant external phase, the actual fraction of the foam that isliquid can be severely reduced as higher proppant concentrations are reached. Obviously, theproppant has no properties that act to hold the foam together, so foams can become veryunstable as the proppant concentration increases.

The modern way of modeling foam is to use the constant internal phase method. This modelsthe proppant as being part of the gas phase. Therefore, in order to keep foam qualityconstant, the gas rate has to go down as the proppant concentration rises, and then increaserapidly as the treatment goes to flush. This method is harder operationally, but provides muchmore stable foam.

Foam Stability

The stability of foam is its ability to remain as foam, rather than separating out into two oreven three phases. Ideally, the fluid should remain as foam long enough for the fluid to berecovered as foam after the treatment. Obviously, temperature and fluid contamination will act

to reduce foam stability. There are three main methods for maximising foam stability:-

i) Mixing the liquid and gas phases at high shear, such as with a foam generator, or bypassing the mixed phases through a high shear device, such as a choke. The greaterthe shear that the foam experiences, the more stable it becomes. High shear acts toreduce the average size of the gas bubbles, which in turn makes it harder for then toseparate out.

ii) Crosslinking the fracturing fluid after the foam has been formed. By using a delayedcrosslinker, the onset of crosslink can be timed to take place after the foam has beengenerated, so that the gas bubbles are literally crosslinked into position.

iii) Foaming agents. These surfactants act to increase the surface tension of a material,so that the gas bubbles are much more stable.

Often a combination of these methods is used.

Foam ViscosityThe viscosity, proppant transport characteristics, fluid leakoff and stability of the foam are allinfluenced by the same foam characteristics - the liquid phase viscosity, the average gasbubble size, the foam quality and the surface tension properties of the liquid phase. All ofthese are affected by temperature and two of these are significantly affected by pressure.This means that calculating the viscosity – and hence the friction pressure and fluid leakoff – of the foam is very difficult.

Consequently, calculated bottom hole treating pressures for foam fracs are extremely

unreliable and should not be used for analysis unless there is absolutely no alternativewhatsoever. The results from such an analysis should be considered as educated guessworkonly.





N2 Foam Fracs

N2 foamed fracs are the most straightforward of all the types of energized fluid fracsperformed. Nitrogen is stored as a cryogenic liquid, in specialised, highly insulated tanks onlocation. Prior to the treatments, each tank uses a heat exchanger to vapourise a smallamount of the liquid into gas. This has the effect of pressuring up the tank, so that liquidnitrogen is forced from the tank to the N2 pumpers.

Before liquid N2 can be pumped, the pump itself has to be cooled down. This is done byflowing liquid N2 though the pump and out of a vent. Initially gas will bleed out if the vent.Eventually, as the unit cools down, liquid will be seen coming out of then vent, indicating tothe operator that the unit is now ready to pump. Therefore, when designing N2 foam fracs,sufficient liquid nitrogen should be on location for cooling the N 2 pumpers down at least 3times (once for the minifrac, once for the main treatment and one spare).

It is much easier to convert a liquid from low to high pressure, than it is to convert a gas fromlow to high pressure. Consequently, the N2 pumpers will be working on liquid N2 that is storedand pumped at around –320°F. This means that specialised equipment is required forpumping this cryogenic liquid. These pumpers also include a vapouriser, which will heat thehigh pressure liquid and convert it into a gas (for this reason, N 2 pumpers are often referred toas “converters”). These vapourisers can be diesel fired or run from the engine coolant.

As N2 is chemically inert, there are no limitations on the fluid systems it can be used with.

CO2 Foam Fracs

CO2 has a number of properties that make its use significantly different from N2. To start with,liquid CO2 is stored at –20°F. The much higher temperature means that the liquid can bepumped with a standard frac pumper (provided they have been specially prepared – see BJ’sStandard Practices Manual ). It also means that the liquid CO2 does not have to be converted

into a gas before it is mixed with the liquid phase – this will happen automatically as the CO 2

heats up.

The second major property difference of CO2 is its tendency to form a solid (“dry ice”) if storedor pumped under the wrong conditions. Obviously, this must be avoided. Dry ice will only formbelow +/- 80 psi. So at every stage, the liquid CO 2 is kept well above this pressure. Typically,CO2 is stored at between 150 to 300 psi. There are several different methods for pumping theliquid CO2 from the tanks to the pumpers. One method involves forcing it out with N 2 pressureapplied above the fluid level in the CO2 tank. Another method employs specialised boostpumps. Yet another method employs a combination of these two systems. Once again, BJ’s Standard Practices Manual should be consulted before designing any treatments.

The third major difference is that unlike N2, CO2 is not chemically inert. Specifically, on

contact with water based fluids, some of the CO2 will dissolve into the water to form an acid.This has the effect of lowering the pH of the system. This means that CO 2 is not compatiblewith high pH fracturing fluids, such as borate crosslinked gels.

Binary Fracs

Binary Fracs involve the use of a mixture of both CO 2 and N2 to provide the foam. They wereoriginally developed as a method of getting around one service company’s patent on CO 2

foam fracturing. Since then, the method has been extensively developed and is now thepreferred method of foam fracturing for many operating companies.

Binary fracs are the most complicated stimulation operations performed, requiring the use of

no less than three service supervisors (one for the CO2, one for the N2 and one for the liquidphase, who is in overall control). Consequently, these are relatively uncommon.





Poly CO2

Poly CO2 is a highly specialised fluid developed by Nowsco in Canada. In this fluid, aspecialised additive is mixed into the water-based liquid phase, which causes the water-based gel and the liquid CO2 to form an emulsion, rather than foam. The emulsion is notparticularly stable, and will break down after the fluid contacts the formation.

This fluid system has only ever been used in low temperature applications, and it is unclearas to whether the stimulation benefits come from the placing of proppant, or from the thermalshock experienced by the formation. However, in certain formations it has proved to be highlysuccessful.

5.7 Additives

There are an enormous number of additives used in the preparation of the various types offracturing fluids, and an exhaustive list is beyond the scope of this manual. However, below isa description of the general types of additive, together with the most commonly usedexamples from BJ’s product range.

Gelling Agents

Water-based gelling agents are designed to increase the viscosity of water. This water canbe fresh (rarely), 2% KCl, 3% NH4Cl, seawater or any of a myriad of different kinds of brines.Nearly all the gelling agents are some kind of polymer. A wide range is available, dependingupon hydration pH, temperature stability and polymer residue:-

Guar GW-4, GW-27High-yield guar GW-3Hydroxypropyl Guar (HPG) GW-32Carboxymethyl Hydroxypropyl Guar (CMHPG) GW-38Carboxymethyl Guar (CMG) GW-45Hydroxyethyl Cellulose (HEC) GW-21, GW-24L, AG-21RCarboxymethyl Hydroxyethyl Cellulose (CMHEC) GW-28Xanthan GW-22, GW-22L, GW-37Polysaccharide GW-23

Oil-based gelling agents are designed to increase the viscosity of oil-based fluids. Thesegelling agents work on a wide variety of hydrocarbons, but are primarily designed for dieseland kerosene. Any other hydrocarbon fluid should be tested prior to application.

GO-64 Gelling agent for Super Rheo GelGM-55 Gelling agent for Metho Frac XL

Crosslinkers and Complexers

Crosslinkers and complexers are designed to dramatically increase the viscosity of an alreadygelled fluid, so that high viscosity can be maintained for extended periods of time at hightemperatures. For many fluid systems, the crosslinker is the chemical that really defines itscharacteristics.

XLW-4, XLW-32, XLW-10 Crosslinkers for Viking and LightningXLW-30, XLW-30A Crosslinkers for Viking DXLW-14, XLW-63 Crosslinkers for VistarXLW-24 Crosslinker for SpectraFrac GXLW-56 Crosslinker for SpectraFrac G HTXLW-60 Crosslinker for Medallion Frac & Medallion Frac HT

XLW-40B, XLW-41A, -41B Crosslinker for Metho Frac™ XLXLO-5 Complexer for Super RheoGel





Breakers

Breakers are designed to reduce the viscosity of the fracturing fluid to a minimum, so that thefluid can be easily recovered after the treatment. They are also designed to minimise polymerresidues, so that damage to the proppant pack is minimised.

GBW-5, GBW-7, GBW-41L Oxidizing breakersGBW-23, GBW-24 Delayed oxidizersGBW-26C Enzyme breakers for cellulose + derivativesGBW-12CD Enzyme breaker for guar + derivativesGBW-14C Enzyme breaker for xanthan + derivativesHigh Perm CRB Encapsulated oxidizing breakerGBO-5L, GBO-6, GBO-9L Breakers for Super RheoGel

Buffers

Buffers are designed to either raise the pH or lower the pH, as required.

Low pH buffers BF-1, BF-10L, BF-10LEHigh pH buffers BF-7, BF-7L, BF-8L, BF-9L, caustic soda

Surfactants

The word Surfactant comes from the phrase SURFace ACTive AgeNT, and includes anychemical that affects the interface properties between materials. Because this covers such awide range of materials, it is necessary to discuss this group of products in more detail.Surfactants can also be grouped according to the type of charge they possess, so that somesurfactants are anionic (negative charge), some are cationic (positive charge), some areamphoteric (cationic at low pH and anionic at high pH), some are Zwitterionic (both cationic

and anionic simultaneously) and some are non-ionic. Generally speaking, it is best not to mixanionic and cationic products together, as they might form viscous deposits. Details of thiscan be found in BJ’s Mixing Manual .

Most of BJ’s surfactant products are designed to leave the formation water wet. This meansthat the relative permeability of the formation to water has been lowered, and the relativepermeability of the formation to oil has been raised. However, it is important to note thefollowing:-

Cationic surfactants will leave sandstones oil wet and carbonates water wetAnionic surfactants will leave sandstones water wet and carbonates oil wet.

Amphoteric surfactants can behave either way depending upon the pH. At acidic pH’s (less

than 7), amphoteric surfactants show cationic properties, whilst at alkaline pH’s (greater than7), they display anionic properties. At neutral pH, they behave like non-ionic surfactants.

Non-emulsifying surfactants are designed to prevent the formation of emulsions betweenthe crude oil in the formation and the treatment fluid. All water-based treatments should havea non-emulsifying surfactant added to them, unless they are being pumped into a waterinjection well or dry gas reservoir with no trace of condensate.

Inflo 100, Inflo 102 Blend of cationic and nonionicNE-13 Blend of cationic and nonionicNE-110W AnionicNE-118 NonionicNE-940 Nonionic

Note that some non-emulsifiers will also act to break existing emulsions.





Foaming agents work by increasing the surface tension of the fluid. This helps increase foamstability. Most foaming agents also acts as detergents and dispersants

FAW-4 AnionicFAW-18W AnionicFAW-20 Anionic

FAW-21 AmphotericFAO-25 Nonionic – foaming agent for oil-based fluids

Note that FAW-4, FAW-18W and FAW-20 will leave carbonate formations oil wet.

Low surface tension modifiers act to reduce the surface tension of the fluid. This helps thefluid penetrate into very small places, such as the pore spaces in low permeability reservoirs.These products also help the treatment fluid flow back out of the well after the treatment isfinished.

Flo-Back-20, Flo-Back-30 NonionicInflo-100 Blend of cationic and nonionicInflo-150 Nonionic

Mutual solvents will dissolve hydrocarbon based deposits and allow them to disperse waterbased fluids.

US-2, US-40 NonionicInflo-40 Nonionic

Emulsifiers are used to deliberately create emulsions. They only should be used as part ofan emulsion-based fluid system

AE-7 CationicE-2 Cationic

Biocides

Biocides, also known as Bactericides, are designed to kill bacteria. Any bacteria – especiallysulphate reducing bacteria – will eat the polymer used in frac fluids. A colony of bacteria canreduce a tank of good quality gel into foul-smelling slick water in less than an hour. Biocidesare used to prevent this. Initially, all tanks used for frac fluids should be as clean as possible.This will help reduce the risk of bacterial contamination. However, the water used to mix thegel can still contain these bacteria, especially if the climate is hot or seawater is being used.The biocide should be added either directly to the tank before the water is added, or it shouldbe thoroughly mixed into the water prior to the addition of any polymer. Once the biocide hasbeen added, it will quickly kill any bacteria that are present in the water.

It is recommended that a biocide is used on any treatment with involves pre-gelling the fluid.

It should be remembered that biocides are designed to prevent a colony of bacteria fromdeveloping in the first place, rather than for killing an existing colony - any gel that issuspected of being contaminated should be discarded, and its tank thoroughly cleaned. Inorder to break down the gel, bacteria secrete enzymes (similar enzymes to the breakersdescribed above). These enzymes will cause a tank of gel to degrade, so that even if all thebacteria in a tank have been killed, their enzymes are still present in the tank. This is whycontaminated tanks of gel need to be discarded, and not used again.

It should also be noted that in their concentrated form, biocides are very dangerous materials(after all, they are designed for killing living things) and should be handled with extreme care.

Magnacide 575XCide 102, 207





Gel Stabilisers

Gel stabilisers are used to prolong the viscosity of crosslinked gels at high temperatures.They work by one of two methods:- they can scavenge the oxygen in the fluid; or they canchelate cations which can contribute to the degradation of the gel.

GS-1, GS-1L, GS-9

Methanol

Clay Control Additives

Clay control additives are used to prevent the swelling, migration and disintegration of clayminerals such as illite, smectite, chlorite and montmorillonite. Fresh water by itself will causethese problems. The addition of chloride ions to fresh water will prevent these problems inmost formations, so that most treatments carried out with seawater do not need any additionalclay stabilisers. However, exceptionally water sensitive formations may need additionalprotection, which is where BJ’s range of synthetic clay control additives is applied.

KCl, NH4Cl, NaCl etc standard salts for brines

CaBr2, ZnBr2, etc specialised salts for high density completionbrines (some of these may be incompatiblewith BJ’s crosslinked fluids).

Clay Treat 3C KCl substitute, recommended for Vistar.ClatrolClaymaster 5C, FSP

Note that any salts containing calcium or magnesium should not be mixed with frac fluids, asthese are incompatible with some crosslinkers. Also note that some of the synthetic claycontrol additives are cationic in nature and should not be mixed with any anionic products.

Fluid Loss Control

Fluid loss control additives can be used for two main reasons; firstly, to lower a very highmatrix leak off rate; and secondly, to prevent fluid loss down natural fractures. The use of fluidloss additives is becoming less and less common, as the understanding of fluid leakoffincreases. Most Engineers also believe that pumping more fluid is preferable to usingadditives that can potentially produce permanent damage.

Silica flour, 100 mesh sand Used for blocking natural fractures5% dieselAdomite Regain

®

References

BJ Services’ Mixing Manual

BJ Services’ Stimulation Engineering Support Manual

BJ Services’ Products and Services Manual

BJ Services’ Product Bulletins

BJ Services’ Standard Practices Manual

BJ Services’ Corporate Safety Standards and Procedures Manual





Rae, P., and Di Lullo, G.: “Fracturing Fluids and Breaker Systems – A Review of State-of-the-Art”, paper SPE 37359, presented at the SPE Eastern Regional Meeting, Colombus OH, Oct1996.

Brannon, H.D., and Ault, M.C.: “New, Delayed Borate-Crosslinked Fluid Provides ImprovedConductivity in High Temperature Applications”, paper SPE 22838, presented at the SPE

Annual Technical Conference and Exhibition, Dallas TX, Oct 1991.

Cramer, D.D., Dawson, J., and Ouabdesselam, M.: “An Improved Gelled Oil System for HighTemperature Fracturing Applications”, paper SPE 21859, presented at the Rocky MountainRegional Meeting and Low-Permeability Reservoirs Symposium, Denver CO, Apr 1991.

Blauer, R.E., and Kohlhaas, C.A.: “Formation Fracturing with Foam”, paper SPE 5003,presented at the 49th Annual Fall Meeting of the SPE, Houston TX, Oct 1974.

Grundman, S.R., and Lord, D.L.: “Foam Stimulation”, paper SPE 9754, JPT pp 597 – 602,Mar 1983

Valkó, P., and Economides, M.J.: “Foam Proppant Transport”, paper SPE 27897, presented

at the SPE Western Regional Meeting, Long Beach CA, Mar 1994.

Tjon-Joe-Pin, R, DeVine, C.S., and Carr, M.: “Cost Effective Method for ImprovingPermeability in Damaged Wells”, paper SPE 39784, presented at the SPE Permian Basin Oiland Gas Recovery Conference, Mar 1998.

Di Lullo, G., Ahmad, A., and Rae, P.: “Towards Zero Damage: New Fluid Points the Way”,paper SPE 69453, presented at the SPE 2001 Latin American and Caribbean PetroleumEngineering Conference, Buenos Aires, Argentina, March 2001.



BJ Services’ Frac Manual6. Proppants


6. Proppants

The word proppant comes from the abbreviation of two words - “propping agent”. Proppantsare granular materials, which are placed inside the fracture in order to “prop” the fracture

open as the pressure falls below closure. The conductivity of the fracture is directly related tothe quantity of proppant within the fracture, the type of proppant, the producing conditions andthe size of the proppant grains.

The purpose of hydraulic fracturing is to place the right amount of the right kind of proppant inthe right place. When this is done correctly, the well is effectively stimulated.

6.1 Proppant Pack Permeability and Fracture Conductivity

As discussed in Section 2, one of the major factors affecting post-treatment well performanceis the fracture conductivity. This is the product of the proppant pack permeability and thewidth of the fracture. In other words, the fracture conductivity is a function of the type of

material holding the fracture open and the amount of this material within the fracture.

The permeability of the proppant pack is controlled by several factors:-

i) Proppant Substrate. The material that the proppant is made from obviously has abig effect on the permeability of the proppant pack. Some materials are stronger thanothers and are better able to withstand the enormous forces trying to crush theproppant as the fracture closes. The weaker the material, the more the proppant grainwill deform. Proppant deformation reduces the porosity of the pack and reduces theoverall fracture width. The more brittle the proppant is, the more likely it is that theproppant will produce fines as the grains are pushed together in a series of point topoint contacts. Any fines will significantly reduce the proppant pack permeability.

ii) Proppant Grain Size Distribution. A normal sedimentary formation has a widevariety of grain sizes, depending upon how well “sorted” the individual rock grains are.In general, any sandstone will be a mixture of small, medium and large grains. Themixture of grain sizes acts to reduce the formation's permeability and porosity, as thesmaller grains will occupy the pore spaces between the larger grains and will alsotend to plug up the pore throats. However, if a set of particles are of almost identicalsize, then there will be no fines to block up the pore spaces and pore throats, so thatthe porosity (and hence the permeability) are maximised.

This is why proppants are generally produced within a specific grain size distribution.This uniformity of grain size is one of the main reasons why proppant is usuallyseveral orders of magnitude more permeable than the formation, and also one of themain reasons why so much effort is spent in ensuring this uniformity of size. This is

illustrated in Figure 6.1a, below;

Figure 6.1a – The effect of uniform and natural grain size distribution on porosity

Uniform Natural





Proppants are supplied within a specific grain size range. This grain size refers to thesize of sieve used to sort the proppant. For instance, 20/40 size means that the vastmajority of the proppant will fit through a size 20 sieve (20 holes per square inch), butwill not fit through a size 40 sieve (40 holes per square inch). This is sometimesconfusing, as larger grain sizes correspond to smaller mesh numbers. Commonproppant sizes are 8/12, 12/20, 16/30, 20/40 and 40/60, although theoretically any

combination of sizes can be produced.

iii) Average Proppant Grain Size. Generally, the larger the average proppant grain sizeis, the higher the permeability of the proppant (provided the grain size distribution isreasonably uniform). This is because larger grains produce larger pore spaces andpore throats, allowing an increased flow rate for a similar porosity. However, thelarger grains are more susceptible to producing permeability reducing fines than arethe smaller grain sizes. This is because larger grains distribute the closure pressureacross fewer grain-to-grain points of contact and so the point contact loads tend to begreater. This is illustrated in Figure 6.1b;

Figure 6.1b – Diagram illustrating how larger grains have larger pore spaces and hence greaterpermeability.

iv) Sphericity and Roundness. These quantities define how spherical the proppant

grains are and how many sudden, sharp edges the grains have. Obviously, thesmoother and more spherical the proppant grain is, the higher the pack permeability.There are standard API procedures for checking these quantities, but unfortunatelythey rely on some subjective analysis. Consequently, it is often difficult to see a cleartrend between one proppant type and another. However, in general, artificialproppants will have better sphericity and roundness than naturally occurring types.This is illustrated in Figure 6.1c;

Figure 6.1c – Diagram illustrating the difference between a proppant with good sphericity androundness (left), and a proppant with poor sphericity and roundness (right).

Coarse, angular grains also tend to produce more fines, as corners and edges tend toget broken off as compressive stress is applied. Therefore, proppants with goodsphericity and roundness also tend to retain greater permeability at high stresses. Inaddition, because proppant with low sphericity and roundness will produce a more

convoluted flow path for the produced fluids, non-Darcy pressure losses tend to be





greater in these materials (see Section 10.9), leading to decreased effective proppantpack permeability.

iv) Frac Fluid Quality. The amount of residue left by the fracturing fluid can also have abig influence on the permeability of the proppant pack. In order to assess the effect ofthese fluids, a quantity called Regained Permeability is measured. Put simply, a

sample of the proppant is put into a load sell and is subjected to a closure pressure,at an elevated temperature. A standard, non-damaging fluid is then flowed throughthe test cell. By analysing the pressure drop and flow rate, the permeability of thepack can be calculated. Next, the frac fluid is flowed through the test cell, and allowedto remain there for a specific time, during which it is designed to break. Once the fluidhas broken, the permeability of the pack is measured again, by the same method asbefore. The two permeabilities are compared and the result (the regainedpermeability) is given as the percentage of the original permeability that remains afterthe test.

Figure 6.1d, below, illustrates the difference between fluids with a high and lowregained permeability;

Figure 6.1d – Three SEM micrographs showing the effects of frac fluid residue. The micrographon the left shows undamaged proppant before the addition of the frac fluid. The centermicrograph shows the residue left by a poorly designed crosslinked system. The finalmicrograph shows the same proppant pack after an enzyme breaker has been used.

Proppant packs can lose significant proportions of their permeability to fluid damage.Cheap, poorly designed fluids can cause regained permeabilities to be as low as only30% or even less, whereas the state-of-the-art fluids can produce values in excess of90%.

v) Closure Stress. As the proppant is crushed by the closure of the formation, it willstart to produce fines. As discussed above, these fines will reduce the permeability ofthe pack. The stronger the proppant, the fewer fines are produced - nevertheless, allproppant types experience a decrease in permeability as closure stress increases, toa greater or lesser extent. In addition, most proppants also have a “maximum” stress,above which whole-scale disintegration of the proppant substrate starts to occur,rather than simple fines production. At this point, pack permeability falls dramatically.

It should be noted that the reservoir pressure has an influence on the closure stressexperienced by the proppant. This phenomenon is discussed in greater detail later inthis manual (see Section 7.6). The relationship between reservoir pressure andclosure pressure is dependent upon a number of factors - there are circumstancesunder which a decrease in reservoir pressure can result in an increase in closurestress. Additionally, there can be localised areas of low reservoir pressure (such as

near the wellbore during drawdown) where once again the proppant experienceshigher closure pressure. This potential increase in stress with the life of the well mustbe allowed for when selecting a proppant.





vi) Non-Darcy Flow. This effect will be discussed on more detail in Section 10.9.However, as the flow rate through the proppant pack increases, the pressure drop willincrease at a rate faster than that predicted by Darcy’s law. This is due to the effectsof inertial energy loses, as the fluid rapidly changes direction as it moves through thepore spaces. As the fluid velocity increases, the pressure drop due to inertial flow

effects increases with the square of the velocity. So at low flow rates, (such as in areservoir rock), non-Darcy effects can safely be ignored, whilst at high rates (such asin a proppant pack), the effective proppant permeability has to be reduced to reflectthis effect. The phenomenon is particularly significant in high rate gas completions.

vii) Multi-Phase Flow. Multi-phase flow has a similar effect upon proppant packpermeability as it does on formation permeability. It reduces it, by an amount that isdependent upon the absolute permeability, and the relative saturation of each phase.As it is very rare for a reservoir to produce a single phase (with the exception of somegas reservoirs), it is also very rare for proppant to conduct only a single phase.Therefore, the actual effective permeability of the proppant pack may be significantlyless than the published data, which is generally produced for single-phase flow only(although this situation is improving).

6.2 Proppant Selection

As illustrated in Section 6.1, there are a substantial number of variables that must be takeninto account when selecting proppant. However, in many cases the selection process hasbeen simplified.

All proppant suppliers and manufactures publish data for pack permeability against closurestress, for all their proppant types and grain size distributions. Provided the closure stress isknown (taking into account any subsequent loss in reservoir pressure), the absolutepermeability of the proppant pack can be easily found. This eliminates the need for the FracEngineer to hold data on sphericity, roundness, crush resistance, grain size distribution,substrate material etc. Simply look up the proppant you are interested in, and see what thepermeability is for a given closure stress.

Most fracture simulators already have this data for most major proppant types. This allows thesimulator to predict the fracture conductivity for most given proppant/closure stresscombinations. Usually, there is also a “proppant damage factor”, which allows the user tosimulate the regained permeability effects of the fracturing fluids.

Some - but not all - fracture simulators will also model the effects of non-Darcy flow, showinga decrease in effective permeability as production rate rises.

However, no current fracture simulators allow for the effects of multi-phase flow. Data on this

has been published by a few sources, the most notable of these being the Stim-Lab Consortium’s PredictK software and Carboceramics' FracFlow proppant permeabilitysimulator.

Table 6.2a gives guidelines as the maximum closure stress each of the major proppant typescan withstand, before substrate failure begins to occur. Obviously, these limits are verygeneralised, and are highly dependent upon factors such as grain size and the quality of themanufacturing process and/or source of sand. More detailed information is available from themanufacturers or in the references;





Type MaximumClosure

Stress, psi

ProductExample

Frac Sand 5,000 Brady, Ottawa, Colorado Low Density Ceramics 9,000 CarboEconoprop, CarboLite,

ValueProp Intermediate Density Ceramics 12,000 CarboProp, InterProp Sintered Bauxite 14,000 Carbo HSP, Bauxite

Table 6.2a – Generalised maximum closure stresses for the main proppant types.

Important Note

The quality of the proppant, and the subsequent conductivity of the fracture, has a biggereffect on post treatment production than virtually anything else under the Frac Engineer’scontrol. In most cases, an economy made on proppant selection is a false economy. Forinstance, although low-density ceramics cost two to three times as much as frac sand, theyhave four to five times the pack permeability - even at low closure stresses - due to their highsphericity and roundness.

Resin-Coated Proppant

Many operating companies prefer to use resin-coated proppant or sand for some or all of theirfracture treatments. There are many different types of resin coat and the manufacturers arecontinually improving and updating their products. Therefore, the reader is advised to consultthe manufacturer’s specifications for details of any specific product. However, broadlyspeaking, resin-coated proppant can be divided into two main categories as follows:-

CurableCurable resin-coated sand or proppant is coated with a resin designed to harden when

exposed to temperature and/or closure stress. This allows the resin-coated grains to adhereto each other, and hence dramatically reduce the effects of proppant flowback (see Section10.7 for more details). At low temperatures, an activator is added to the fracturing fluid inorder to improve the adhesion.

Tempered or Pre-CuredTempered or Pre-cured resin coatings are harder than curable resin coats. They rely more onclosure pressure than temperature in order to make the sand or proppant grains adhere toeach other. These resin-coatings also have a secondary effect. Because the resin coat acts toreduce the localised contact stresses between proppant or sand grains and because anyfines produced by this process are kept within the resin coat, these materials tend to have ahigher closure pressure resistance than the same material without the resin coat. This meansthat they retain permeability under higher crush loadings and so can – for instance – extend

the range over which a cheaper material, such as frac sand, can be used.

Resin coated proppant or sand has a number of significant drawbacks, however:-

1. Cost. Coating the grains with resin can substantially increase the cost of theproppant, especially when coatings designed for high pressure and temperature areused.

2. Resin coats tend to affect the properties of the fracturing fluid. The exact variation inproperties depends upon the pH of the frac fluid and the type of resin coat. However,it is common for resin-coated proppant to make frac fluids much harder to break. It isrecommended that when resin-coated proppant or frac sand is being used, testing isperformed on the frac fluids with the proppant in the fluid.

3. Resin coat tail-in. Many operators like to save money on a treatment by only using

resin coated sand or proppant for the last 20 or 30% of the treatment. The theorybeing that only the part of the proppant close to the wellbore actually needs to





adhere together to prevent proppant flowback. However, due to the effects ofproppant convection and settling (see Section 10.6), there is no guarantee that theproppant pumped last in the treatment will be the proppant that ends up right by thewellbore. In fact, the only way to guarantee this is to pump 100% resin coatedmaterial.

6.3 BJ Services’ FlexSand and LiteProp

BJ Services’ has two proprietary products that have significant technological advantages overconventional proppant systems

FlexSandTM

FlexSand ™ is designed to prevent proppant flowback by dramatically increasing the internalfriction of the grains inside the proppant pack. Put simply, in order for proppant flowback tooccur, individual proppant grains have to be able to move relative to each other. FlexSand acts to prevent this by introducing deformable particles into the proppant pack.

The FlexSand grains are designed to be slightlydeformable relative to the proppant itself. The theory,as illustrated in Figure 6.3a, is that as the formationcloses on the proppant, the proppant causes theFlexSand to deform slightly, allowing the proppantgrains to “key into” the FlexSand and as a resultmaking it much harder for the grains to move relative toeach other. Typically, FlexSand is mixed into the sandor proppant at between 10 and 15% by weight. Thematerial can be either added on the fly – using aprocess controlled FlexSand “Bazooka” – or can be dryblended into the proppant or frac sand prior to the

treatment.

Because the FlexSand has to be only slightlydeformable relative to the proppant, there are threedifferent types supplied, for different sand or proppanttypes; FlexSand™ LS, FlexSand™ MSE and FlexSand™ HS. These are made of differentmaterials and – in the case of the FlexSand™ HS material – different shapes. BJ Services’patent for FlexSand ™ describes the method of preventing proppant flowback, and does notlimit BJ to any specific material, nor to any grain size or shape.

FlexSand also has a secondary effect. Because the FlexSand grains deform slightly, they actto “cushion” the sand or proppant grains, reducing the localised point contact stressesbetween grains. The reduces the quantity of fines produced, particularly by frac sand, and

helps to preserve proppant or sand permeability at higher closure stresses. Thus usingFlexSand can also lead to improved fracture conductivity in addition to preventing proppantflowback.

LitePropTM

LiteProp ™ is a proprietary low-density proppant system, designed to be neutrally buoyant inthe fracturing fluid. Currently, it comes in two versions, LiteProp™ 125 and LiteProp™ 175,with SG’s of 1.25 and 1.75 respectively. Table 6.3a illustrates how this compares to othertypes of proppant.

Because the LiteProp is designed to be neutrally buoyant, there is no need to use an

expensive crosslinked fracturing fluid. Instead, any brine with the same SG as the LiteProp can be used. This in turn significantly reduces the cost and complexity of fracturingoperations. However, there are a few points to be aware of when using LiteProp :-

Figure 6.3a – SEM micrograph of

FlexSand grain clearly showingthe indentations caused by the

closure of the surroundingproppant grains.





ProppantType

SpecificGravity

LiteProp 125 1.25LiteProp 175 1.75Frac Sand 2.65

Carbolite 2.71Carbprop 3.27

Carbo HSP 3.56

Table 6.3a – Specific gravity of selected proppant types

1. Although expensive fracturing fluids do not have to be used, heavy-weight brines willstill have to be mixed, if neutral density is required. For instance, 1.25 SG calciumchloride brine requires 2860 lbs of CaCl2 per 1000 gals of brine – mixing this quantityof material on location could present a logistical challenge in itself.

2. Although the proppant does not require fluid viscosity in order to stay in positionwithin the fracture, this is not the only reason for having viscosity in the fluid. If thefracture is experiencing significant tortuosity (see Section 10.1), viscosity will be

required to transport the proppant through the near wellbore region. A system withoutviscosity may experience premature screenouts.

3. Fracturing fluids are also designed to reduce leakoff. The polymer in a typicalcrosslinked gel will form a filter cake against the wall of the fracture, reducing the rateat which fluids leave the fracture. Brines will not have this polymer and so will leak offinto the formation much more quickly. Therefore, significantly higher fluid volumesmay be required.

4. At the time of preparation of this manual, LiteProp is limited to fairly shallowformations, as the maximum closure stress that can be sustained by the material isabout 5,000 psi (for LiteProp™ 125).

Nevertheless, in spite of these limitations LiteProp has the potential to revolutionise the wayfracturing treatments are performed.

References

Technical Data Interactive CD ROM, Carbo Ceramics Inc, 2000 onwards.

www.carboceramics.com, Carboceramics Inc. website, 2001 onwards

PredictK software, Stim-Lab Consortium, 1999 onwards

BJ Services’ Mixing Manual

BJ Services’ Stimulation Engineering Support Manual

Vincent, M.C., Pearson, C.M., and Kullman, J.: “Non-Darcy and Multiphase Flow in ProppedHydraulic Fractures: Case Studies Illustrate the Dramatic Effect on Well Productivity”, paperSPE 54630, presented at the SPE Annual Technical Conference and Exhibition, Houston, Oct1999.

API Recommended Practice 56 Testing Sand Used in Hydraulic Fracturing Operations, 2nd

Edition, American Petroleum Institute, December 1995.

API Recommended Practice 60 Recommended Practices for Testing High Strength Proppants Used in Hydraulic Fracturing Operations , 2

nd Edition, American Petroleum Institute,

December 1995.





Rickards, A., Lacy, L., Brannon, H., Stephenson, C. and Bilden, D.: “Need Stress Relief? ANew Approach to Reducing Stress Cycling Induced Proppant Pack Failure”, paper SPE49247 presented at the 1998 SPE Annual Technical Conference and Exhibition, NewOrleans, Louisiana, Oct 1998.

Wood, W.D., Brannon, H.D., Rickards, A.R. and Stephenson, C.: “Ultra-Lightweight Proppant

Development Yields Exciting New Opportunities in Hydraulic Fracturing Design”, paper SPE84309, presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver,Colorado, Oct 2003.



BJ Services’ Frac Manual7. Rock Mechanics


7. Rock Mechanics

Rock mechanics is the study of the mechanical properties of a rock, especially thoseproperties which are of significance to Engineers. It includes the determination and effects of

physical properties such as bending strength, crushing strength, shear strength, moduli ofelasticity, porosity and density, and their interrelationships.

7.1 Stress

Consider the situation illustrated in Figure 7.1a, in which a block of material is subjected to aforce F :-

Figure 7.1a – A block of material subjected to a force F .

The block of material has an area A, on the plane at right angles to the line of action of theforce. Therefore the stress, σ , is given by:-

σ =F A

.................................................................................. (7.1)

Note that this is very similar to the formula for calculating pressure. Stress and pressure havethe same units and are essentially the same thing – stored energy. The main differencebetween the two is that in liquids and gases, the material will flow away from an applied force,until the force and stress (or pressure) is the same in all directions (i.e. an equilibrium hasbeen reached). However, solids cannot deform in such a manner, so these materials willalways have a plane across which the stresses are at a maximum. They will also have aplane perpendicular to this, across which the stresses are at a minimum.

Properties such as mass and volume are said to be scalars – they require only a magnitudeto define them. Quantities such as force and velocity are vectors – they require not only amagnitude, but also a direction in which they are acting in order to be fully defined. Stresstakes this one step further, and is a tensor property – it can only be fully defined by amagnitude and an area across which it is acting.

7.2 Strain

Strain is measure of how much the material has been deformed when a stress is applied to it.Figure 7.2a illustrates how the block of material is compressed by the force F :-

F

Area = A





Figure 7.2a – Strain produced by the application of force F

As the force is applied, the height of the block of material changes from x 1 to x 2. The strain, ε ,is given by:-

ε =x 1 - x 2

x 1 ........................................................................... (7.2)

Note that the strain is defined in the same direction as the applied force F and perpendicularto the plane across which the stress acts.

Strain is important as this is the way we measure stress – by observing the deformation of aknown piece of material. Strain is dimensionless.

7.3 Young’s Modulus

Young’s modulus, E , (also known as modulus of elasticity or elastic modulus) is defined asfollows:-

E =σ

ε ................................................................................... (7.3)

E is the ratio of stress over strain. As strain is dimensionless, E has the same units as stress.Young’s modulus is a measure of how much a material will elastically deform when a load isapplied to it. This is another term for hardness.

On a more fundamental level, if stress and pressure are closely related (apply a pressure to asurface and it will induce a stress), then in fracturing, we can think of Young’s modulus as ameasure of how much a material (i.e. rock) will elastically deform when a pressure is appliedto it. As pressure is stored energy, E is also a measure of how much energy it takes to makethe rock deform.

Materials with a high Young’s modulus, such as glass, tungsten carbide, diamond andgranite, tend to be very hard and brittle (susceptible to brittle fracture). Conversely, materialswith a low E , such as rubber, Styrofoam and wax, tend to be soft and ductile (resistant tobrittle fracture).

Caution – Elastic vs Plastic. Elastic deformation is reversible – if the force (or pressure, or

stress) is removed, the material returns back to its original size and shape. If so much force isapplied to a material that it passes beyond its elastic limit then the material will start toplastically deform. This is permanent. A good illustration of this is the small spring from a ball

F

x 1

x 2





point pen. When the spring is lightly stretched, it will return to its original shape. However, ifthe spring is stretched too far, it will be permanently, or plastically, deformed. Young’sModulus only applies to elastic deformation. As a group of materials, rocks tend not toplastically deform very much. Instead they will elastically deform and then fracture if the stressgets too high. Notable exceptions to this are salt beds, soft carbonates (e.g. chalk) and youngcoals.

Static Young’s Modulus is the standard measure of E and is applicable to hydraulicfracturing. The material is being deformed slowly and in only one direction.

Dynamic Young’s Modulus is the rock property measured by special sonic logging tools.The material is no longer static – it is being continually stretched and then compressedrapidly. There is often a significant variation between static and dynamic values for E due to aprocess known as hysteresis . Hysteresis is a retardation of the effects of forces, when theforces acting upon a body are changed (as if from viscosity or internal friction). In thissituation, it represents the history dependence of the physical systems. In a perfectly elasticmaterial, elastic stress and strain is infinitely repeatable. In a system exhibiting hysteresis, thestrain produced by a force is dependent upon not only the magnitude of that force, but alsothe previous strain history (see Section 7.10)

Plane Strain Young’s Modulus. In hydraulic fracturing, the strain in the directionperpendicular to the fracture plane (i.e. the direction in which fracture width is produced) iseffectively zero. This is because in this situation the denominator in Equation 7.2 (the “ x 1”) isso large that the strain is effectively zero, even though there has been measurable materialdeformation. This is known as “plane strain”, which implies that strain only exists in adirections perpendicular to the direction in which strain is zero. To account for this anomaly,fracture simulators use the plane strain Young’s modulus, E’ , to calculate the fracture width:-

E’ = E

(1 - ν 2) ............................................................................. (7.4)

In fracturing, Young’s modulus will typically have values ranging from as low as 50,000 psi

(for a shallow, very soft chalk or weak sandstone) to as high as 6,000,000 psi for deep, tight,shaley sandstone. It should be noted that Young’s modulus may not be constant in weak orunconsolidated formations.

7.4 Poisson’s Ratio

Poisson’s ratio, ν , is a measure of how much a material will deform in a directionperpendicular to the direction of the applied force, parallel to the plane on which the stressinduced by the strain is acting. This is illustrated by Figure 7.4a:-

Figure 7.4a – Application of force F also produces a deformation in the y direction

F

x 1

x 2

y 1

y 2





The strain in the x direction, ε x, is given by Equation 7.2 (see Section 7.2). The strain in the ydirection is given by the following:-

ε y =y 1 - y 2

y 1 ........................................................................... (7.5)

Note that this value is negative – this is a result of the way the forces and the direction theforces act in are defined. Compressive strain is positive and tensile strain is negative.

Poisson’s ratio is defined by Equation 7.6:-

ν = -ε y

ε x ................................................................................. (7.6)

Poisson’s ratio is an important factor in determining the stress gradient of the formation, but isless important in defining fracture dimensions, although it does have some effect. Typical

values for ν for rocks are between 0.2 and 0.35 (ν is dimensionless).

7.5 Other Rock Mechanical Properties

Tensile Strength. The tensile strength of a material is the level of tensile stress that isrequired in order to make the material fail. Usually, as stress is applied the material willelastically deform (reversible), plastically deform and then fail. In most rocks this amount ofplastic deformation is negligible and the material will, for all practical purposes, elasticallydeform and then fail.

This property is important in hydraulic fracturing, as this stress level has to be overcome inorder to split the rock. Usually, the frac gradient (which is the pressure – a.k.a. the stress – needed to make the rock fracture) has two components – the stresses induced by the

overburden, and the tensile strength of the rock. See Section 7.6 below for a more detailedexplanation of in-situ stresses.

It should be noted that materials also have a Compressive Strength, which is the compressionload, beyond which a material will fail. Failure mechanisms are more complex, as the materialis often compressed in several directions at once. Generally, rocks are much stronger incompression than in tension, a fact which we take advantage of during fracturing.

Shear Modulus. The shear modulus is similar to the Young’s modulus, except that it refers tothe material being in shear, rather than in compression or tension. It defines how muchenergy is required to elastically deform a material in shear:-

Figure 7.5a – Force F applied to produce a shear stress

h

a b

F

x





With reference to Figure 7.5a, the shear stress, τ , is given by:-

τ =F A

.................................................................................. (7.7)

where A is the area of the block of material parallel to the line of action of the force F , (this is

the plane along which the shear stress acts) and is equal to a × b .

The shear strain, γ , is defined as follows:-

γ =x h ................................................................................... (7.8)

Therefore, the shear modulus, G , is equal to the shear stress divided by the shear strain:-

G =t g =

F h x A

....................................................................... (7.9)

Bulk Modulus. This is another elastic constant, which defines how much energy is requiredto deform a material by the application of external pressure. This is a special form ofcompressive stress, in which the applied compressive stress is equal in all directions.Suppose we have a block of material, which originally has a pressure P 1, applied to it, andhas a volume V 1. This pressure is increased to P 2 , which causes the volume to decrease toV 2 , as illustrated below in Figure 7.5b. The increase in bulk stress is the same as the increasein pressure, P 2 – P 1. The bulk strain is equal to the change in volume, V 2 – V 1 divided by theoriginal volume, V 1. Thus, the bulk modulus, K , is given by:-

K = -P 2 - P 1

(V 2 - V 1 )/V 1 = -

V 1(P 2 - P 1)V 2 - V 1

....................................... (7.10)

Figure 7.5b – Volume changes from V 1 to V 2 as pressure increases from P 1 to P 2.

K = - VdP dV

......................................................................... (7.11)

The minus sign is introduced into the equation due to the fact that the term V 2 – V 1 will alwaysbe of the opposite sign to the term P 2 – P 1.

The bulk modulus is therefore a measure of how much energy it takes to compress a materialusing externally applied pressure.

Relationships Between the Four Elastic Constants. The four main elastic constants – Young’s modulus, shear modulus, bulk modulus and Poisson’s ratio - are all related to each

other. If two of these material properties are known, the other two can be deduced:-





E = 3K (1 – 2ν ) ................................................................. (7.12)

K =E

3 - 6ν......................................................................... (7.13)

G =

E

2 + 2ν ........................................................................ (7.14)

ν =3K - E

6K ......................................................................... (7.15)

Therefore, if the Young’s modulus and the Poisson’s ratio are known, the shear modulus andthe bulk modulus can be deduced. Thus, fracture simulators only require the input of E and ν .

7.6 In-Situ Stresses

In situ stresses are the stresses within the formation which act as a load (usually

compressive) on the formation. They come mainly from the overburden, and these stressesare relatively easy to predict. However, factors such as tectonics, volcanism and plastic flowin underlying formations can significantly affect the in-situ stresses – these factors are muchharder to predict. In addition, the act of producing a localised anomaly – such as an oil well – can also significantly affect the stresses in a specific area.

The stresses due to the overburden are simply the sum of all the pressures induced by all thedifferent rock layers. Therefore, if there has been no external influences – such as tectonics – and the rocks are behaving elastically, the vertical stress, σv, at any given depth, H is givenby:-

σ v = 0

H

ρ ngh n ....................................................................... (7.16)

where ρ n is the density of rock layer n , g is the acceleration due to gravity and h n is thevertical height of zone n , such that h 1 + h 2 + ..... + h n = H .

This is usually modified (after Biot et al ) to allow for the effects of pore (or reservoir) pressure,such that:-

σ v = γ ob H - α P res ............................................................... (7.17)

where γ ob is the overburden pressure gradient (usually between 1.0 and 1.1 psi/ft) and α isBiot’s poroelastic constant, and is a measure of how effectively the fluid transmits the pore

pressure to the rock grains. α depends upon variables such as the uniformity and sphericity of

the rock grains. By definition α is always between 0 and 1, usually it is taken to be between0.7 and 1.0 for petroleum reservoirs.

Stresses under the ground do not just act on a single plane. There is a complex threedimensional stress regime. To simplify things, stresses are usually resolved into threemutually perpendicular stress components; the vertical stress, σ V , and two horizontalstresses, σ H, min and σ H, max.

Additionally, as the stresses are three dimensional, so are the strains. The elastic relationshipbetween these stresses and strains in three mutually perpendicular directions, x , y and z , isgoverned by Hooke’s law:-

ε x = 1E [ ]σ x - ν (σ y + σ z ) ........................................................ (7.18)





Now, for the case of elastic deformation with no outside influences (such as tectonics) insubterranean rock strata, there are two important things to note. First, σ H,min = σ H, max , as thestresses will be symmetrical on the horizontal plane. Secondly, as each individual unit of rockis pushing against another identical unit of rock with the same force, ε H, min = ε H, max = 0 (i.e. nodeformation on the horizontal plane).

Therefore:-

σ H =σ v ν

1 - ν ............................................................................ (7.19)

As a result of the work of Terzaghi, Biot and Handin et al., this Equation is generally modifiedto allow for the effects of the pore pressure:-

σ H =ν (σ v - 2α P )

1 - ν + α P ........................................................ (7.20)

From Equation 7.20 we can see that the Poisson’s ratio can have a considerable influence onthe horizontal in-situ stresses.

7.7 Stresses Around a Wellbore

A wellbore is essentially a pressure vessel with a very thick wall. Consequently, the sametheories that are applied to thick walled pressure vessels can also be applied to wellbores,providing that the in-situ stresses and reservoir pressure are accounted for. Figure 7.7aillustrates how the stresses at any given point near the wellbore can be resolved into threeprinciple stresses. Once again, these are perpendicular to each other.

Figure 7.7a – Three dimensional stresses around a wellbore

From Deily and Owens (1961) we can get expressions for the radial and tangential stressesinduced by a pressure in the wellbore, P wb , at a radius r , from the centre of the well. Thevertical stress is as given in Equation 7.17;

σ t = -[ ]P wb - α (P res + P wb - P r )

r w 2

r 2 +

1 + r w 2

r 2 σ v .............. (7.21)

σ σσ σ v

σ σσ σ v

σ σσ σ r σ σσ σ r

σ σσ σ t

σ σσ σ t





σ r = (P wb – P res )

r w 2

r 2 +

ν

1 - ν

1 -

r w 2

r 2 (P ob – P res ) ......... (7.22)

where P ob is the pressure due to the overburden (see reference for more details).

At the wellbore face, the stresses due to wellbore pressure will be at a maximum. Also, this isby definition the point at which the fracture initiates. Therefore, these are the stresses whichinterest us most. At the wellbore r → r w and P r → P wb so that:-

σ t =

2ν

1 - ν (γ ob H - α P res ) – (P wb – α P res ) .......................... (7.23)

σ r = P wb - P res ..................................................................... (7.24)

Furthermore, Barree et al (1996) went on to show that provided the rock does not have anysignificant tensile strength and no significant plastic deformation, failure of the rock (i.e.breakdown) occurred when the tangential stresses were reduced to zero;

P b =

2ν

1 - ν (γ ob H - α P res ) + α P res ...................................... (7.25)

7.8 Fracture Orientation

Fractures will always propagate along the line of least resistance. In a three dimensionalstress regime, a fracture will propagate so as to avoid the greatest stress. This means that afracture will propagate parallel to the greatest principal stress, and perpendicular to the planeof the greatest principle stress. This is a fundamental principle – therefore the key tounderstanding fracture orientation is to understand the stress regime itself.

Propagation parallel to the greatest principle stress usually means that the fracture willpropagate on a vertical plane. We can see from Equations 7.16 to 7.20 that the horizontalstresses in an undisturbed elastic formation will always be less than the vertical stress.However, there are some exceptions to this.

Figure 7.8a – Changes in stress regime due to erosion

Magnitude of In-Situ Stress

D e p t h

Magnitude of In-Situ Stress

D e p

t h

Formation lostdue to erosion

σσσσV

σσσσH

σσσσV

σσσσH

Original Stress Regime Stress Regime After Loss

of Height by Erosion





Equations 7.17 and 7.20 define the magnitude of horizontal and vertical stresses inundisturbed formations. The horizontal stresses are induced by the vertical stresses. There isevidence to suggest that these horizontal stresses somehow get “locked” into place(Economides, et al ), and remain relatively constant, regardless of what later happens to thevertical stress. Figure 7.8a illustrates what happens when the vertical stress is reduced.

If formation is lost due to erosion, then the overburden stresses are reduced. However,because the horizontal stresses are “locked-in”, they have not been reduced. Therefore, thereis a region, close to the new surface, where the horizontal stresses are greater than thevertical stresses. This means that the fracture will propagate horizontally – a “pancake frac”.Thus, in shallow formations in areas with a history of surface erosion, horizontal fracs are notonly possible, they are in fact likely. This does not apply to formations which are very weak orunconsolidated, as stresses cannot be “locked in” if the rock strata have no strength.

Another consequence of this phenomenon is that in formations where the σ V and the σ H areapproximately equal, it can be very hard to predict fracture orientation.

The action of outside forces, such as tectonics and volcanism, can also significantly affectfracture orientation. The extra stresses imposed by the movement of the Earth’s crust, which

does not usually alter the overburden stress, but can significantly alter the horizontal stresses.In addition, formations can sometimes be bent and buckled. In Barbados, there is a formationthat has experienced so much tectonic stress that it now runs vertically. Its stresses havebeen locked into place, so now the original vertical stress is horizontal, and vice versa . So thefractures propagate horizontally.

Influence of Wellbore Orientation. Drilling a well can significantly alter the stress regime inan area around the well. The distance away from the wellbore that is affected by this changeis dependent upon the Young’s modulus of the formation. Hard formations (high E) tend totransmit stress more easily than soft formations (which will deform to reduce the stress).Therefore hard formations are affected more than soft formations.

In the area around the wellbore – the area affected by the new stress regime – fractures may

propagate parallel to the wellbore, even if the wellbore is highly deviated or even horizontal.As the fracture propagates away from the wellbore, it will eventually reach a point at which thenormal stress regime of the formation becomes more significant than the near wellbore stressregime. At this point, the fracture will change orientation. Sometimes this re-orientation can bequite sudden, resulting in sharp corners in the fracture, which can cause premature screenouts.

7.9 Breakdown Pressure and Frac Gradient

The breakdown pressure is the pressure it takes to initiate a fracture from the wellbore. Dueto the effects of the stresses induced by the presence of the wellbore, the breakdown

pressure is usually significantly greater than the fracture - or frac – gradient, which is ameasure of how much pressure it takes propagate the fracture through the formation, awayfrom the influence of wellbore effects. Both are usually expressed as pressure gradients (i.e.in psi/ft or kPa/m) so that similar formations in different wells at different depths can be moreeasily compared. The frac gradient is a very important quantity in fracturing, as it is the mostsignificant contributor to the bottom hole treating pressure, which in turn helps to define thesurface treating pressure, the loading on the completion and the proppant selection.

In order to produce a fracture in the formation, two forces have to be overcome. The first forceis the in-situ stress, which is defined in Equations 7.19 and 7.20 when there are no externalinfluences such as tectonics etc. The second force that has to be overcome is the tensilestrength of the rock, which is usually in the region of 100 to 500 psi. Roegiers, in his chapteron Rock Mechanics in Economides and Nolte’s excellent Reservoir Stimulation , defined the

breakdown pressure in the following Equations:-

P b, upper = 3 σ H,min - σ H,max – P + T ............................................... (7.26)





P b, lower =3σ Hmin - σ Hmax - 2η P + T

2(1 - η ) ............................................. (7.27)

where η is a parameter defined by the Poisson’s ratio and Biot’s constant, as follows:-

η =α (1 - 2ν )2(1 - ν )

..................................................................... (7.28)

P b, upper is the breakdown pressure assuming no fluid invasion into the formation (and hence

the maximum possible theoretical breakdown pressure), P b, lower is the lower boundary forbreakdown pressure, assuming significant alteration of the near wellbore pore pressure dueto fluid invasion, σ H,min is the minimum horizontal stress, σ H,max is the maximum horizontalstress, P is the reservoir pressure and T is the tensile strength of the rock. From this we cansee that the higher the reservoir pressure, the easier it is to fracture the rock, so that depletedreservoirs tend to have higher breakdown pressures than undepleted reservoirs. In addition,we can see that when we have fluid invasion, the breakdown pressure can be significantlyreduced, which implies that lower viscosity fluids provide lower breakdown pressures. In thecase where there are no significant external influences on the stress regime, the twohorizontal stresses are equal and the Equations can be simplified to:-

P b, upper = 2 σ H – P + T ................................................................ (7.29)and

P b, lower =2σ H - 2η P + T

2(1 - η ) ............................................................ (7.30)

The breakdown gradient is simply the breakdown pressure, P b , divided by the TVD.

The frac gradient is the pressure required to make the fracture propagate, outside of theinfluences of the wellbore (the region referred to as “far-field”). As stated above, this is oftensignificantly lower than the breakdown pressure, depending upon the viscosity of the frac

fluid, the reservoir pressure and the contrast between maximum and minimum horizontalstresses.

In general, the far field fracturing pressure is equal to the minimum horizontal stress, modifiedto allow for the effects of pore pressure. In general, any external effects such as tectonics orfaulting, will only act to increase the stresses. Therefore Equation 7.18 defines the fracgradient, g f , as follows:-

g f =

1

TVD

ν (σ v - 2α P )

1 - ν + α P ....................................... (7.31)

Important Note. The best way to get the frac gradient for a formation is to pump some fluidsinto it and measure the response. There are many influences on the formation that Equations

7.26 and 7.27 do not account for, such as tectonics (there are very few areas of the world thatare completely free of tectonics), and the only way to account for these is to actually measurethem. The second best way to get the frac gradient is to look at data from offset wells. Makesure that you are looking at data from the same formation. Compare values for Poisson’s ratioand reservoir pressure. If these values are similar (provided they come from the sameformation), then the frac gradient will probably be similar as well. Once these two methodshave been rejected, the remaining way to get the frac gradient is to use the Equations above.This method should only be used if attempts at carrying out the other two methods havefailed.





7.10 Rock Mechanical Properties from Wireline Logs

Certain types of open hole wireline logs can be used to provide useful information about themechanic properties of the formations involved in the fracturing process. The dipole sonic orsonic array is the main tool used to do this. This is a special tool, and is different from thesonic logging tool used to generate the sonic transit time seen on most logs.

In order to be able to quantify the rock mechanical properties, the logging tool must be able togenerate and measure two completely different types of sonic waveform, the shear or s-waveand the compression or p-wave, as illustrated in Figure 7.10a, below:-

Figure 7.10a – The left hand side shows the shear or s-wave, whilst the right hand side showsthe compression or p-wave. In both diagrams, the blue arrows illustrate the overall movement of

the sonic waveform, whilst the red arrows indicate the movement of individual particles.

For the shear wave, the material is continually sheared in one direction and then the oppositedirection, back and forth. The plane across which the material is being sheared isperpendicular to the direction the shear wave is travelling. For the compression wave, the

material is subject to alternating compression and tension, on a plane that is againperpendicular to the direction of wave travel.

The dipole sonic tools measures the transit time of both the shear wave, t s and compression

wave, t p. These values are usually expressed in units of µsec/ft, so that the transit time is thereciprocal of the wave velocity. The transit time of the sonic waves through the formation canbe used to derive dynamic rock mechanical properties as follows:-

ν d =0.5(t s / t p)

2 - 1

(t s / t p)2 - 1 ............................................................... (7.32)

E d = 2

ρ bt s2 (1 + ν d) ............................................................ (7.33)

= 26,950

ρ b

t s2 (1 + ν d) (in field units)............................. (7.34)

Where ν d is the dynamic Poisson’s ratio, E d is the dynamic Young’s modulus (see below for

an explanation of dynamic and static properties) and ρ b is the bulk density, usually taken fromthe corrected bulk density log. For Equation 7.34 in field units, ρ b is in g/cc and t s is in µsec/ft – the units most commonly used on logs - whilst E d is in psi x 10

6.

Other rock mechanical properties can also be found (in “log” field units):-





G d =E d

2(1 + ν d) ..................................................................... (7.35)

K d = 26,950 ρ b

1

t p2 -

13t s

2 ..................................................... (7.36)

c b = 1K d

............................................................................... (7.37)

c r =1

26950 ρ b

1

t ma 2 -

43t sma

2

............................................... (7.38)

α = 1 -c rc b

.......................................................................... (7.39)

Where G d is the dynamic shear modulus, K d is the dynamic bulk modulus, c b is the bulkcompressibility of the formation, c r is the rock, or zero porosity, compressibility t ma is the rockmatrix compression wave transit time (see below), t

sma is the rock matrix shear wave transit

time (see below) and α is Biot’s poroelastic constant. Table 7.10a lists commonly used valuesfor t ma and t sma:-

Commonly used values for sonic waverock matrix transit times, µµµµsec/ft

RockMatrix

Compression Wavet ma

Shear Wavet sma

Quartz 55.5 or 51.0 83.3

Calcite 49.7 90.0

Dolomite 43.5 78.7

Anhydrite 50.0 87.7

Granite 50.8 89.3

Salt 66.7 125.0

Table 7.10a – Commonly used values for compression and shear wave rock matrix sonic transittimes (after Schlumberger, 1989)

Figure 7.10b shows an example dipole sonic log with interpreted values for Poisson’s ratio,Young’s modulus and horizontal stress.

Stress can be derived by using the dynamic Poisson’s ratio and the density log (to give thevertical stress) using Equation 7.19. However, it should be remembered that these “stresslogs” are based on dynamic properties (see below) and do not take poroelastic effects intoaccount. Nevertheless, whilst the absolute values for these logs cannot be trusted, they canbe useful for determining stress contrasts.





Dynamic and Static Rock Mechanical Properties

In most applications, including hydraulic fracturing, we are using values for rock mechanicalproperties that are based on static material properties. However, because of the conditionsthat sonic-based rock mechanical properties are measured under, they are said to bedynamic, and there is often a significant difference between the static properties that the FracEngineer needs and the dynamic properties that are measured by open hole logs.

Figure 7.10b – Example interpreted dipole sonic log. The left track shows gamma ray (GR) andcaliper (HCAL) logs. The center track shows compression (DTCO) and shear (DTSM) wave transit

times. The right track shows interpreted values for Poisson’s ratio (PR), Young’s modulus(YOUNGS) and horizontal stress (HSTRESS).

To put things simply, when a stress related event happens to a material, the changes thatoccur to the stresses in the material to not occur instantly. Instead, any change to the stresswill spread through the material at the speed of sound in that material. Usually, the time taken

for this to happen is so small compared for the time taken for the applied stresses to change(as in fracturing) that it does not affect the process. However, when the stresses applied to amaterial alter at a speed that is a significant fraction of the speed of sound of that material,then the time taken for the change in stress to propagate can significantly affect the stressesthemselves. For instance, when a compression wave is passing through a material, any givenportion of that material is constantly being subjected to alternating tensile and compressionloads. The speed at which the load changes is directly proportional to the frequency of thesound wave, whilst the speed that the compression wave moves through the material is thespeed of sound for that material. At low frequencies, the length of time taken for a piece of thematerial to undergo one full stress cycle is much less than the length of time it takes onesound wave to travel past that piece of material. However, as the frequency increases, thelength of time between stress cycles decreases, whilst the wave transit time stays constant,and it becomes increasingly difficult for the material to return to it’s original state before the

next wave passes through. This causes a deviation away from linear elastic behaviour, asillustrated by Figure 7.10c.

GR0 200

HCAL4 14

PR0 1

YOUNGS1 3.5

HSTRESS5000 7500

DTCO50 250

DTSM50 250

9,050

9,100

9,150

9,200





Figure 7.10c – Static (left) and dynamic (right) cyclic stress loading.

The left side of Figure 7.10c shows cyclic loading under static conditions. As the load isalternated between tension and compression, the relationship between stress and strain islinear (proportional to the Young’s modulus) and follows the same path on the stress strainplot every time, provided the elastic limit is not exceeded and the material is not plasticallydeformed. This relationship between stress and strain is referred to as linear elastic.

The right side of Figure 7.10c shows the dynamic case. The behaviour of the material underloading is now dependent upon the stress history of the material. The relationship betweenstress and strain is different depending upon whether the loading is being applied or removedand whether it is tensile or compression. This deviation away from linear behaviour becomesmore pronounced as the frequency of the sound waves (i.e. the frequency of the stress

cycling) increases. When an alternating stress is applied to a material the induced alternatingstrain moves through this material at the speed of sound, for that material. However, as thefrequency of the changes gets closer to the speed of sound in that material, the material hasinsufficient time to return to its original state, before the next deformation occurs. Thus thesubsequent deformation is influenced by the previous deformation.

This deviation from linear elastic behaviour under high frequency stress cycling is oftenreferred to as hysteresis . Hysteresis is a general term used throughout science andengineering to denote when the behaviour of a material under certain conditions is dependentupon the historical application of these conditions. The behaviour of a material that does notexhibit hysteresis (such as that shown on the left hand side of Figure 7.10c), is the sameevery time, regardless of what has happened previously.

In order to convert from dynamic to static properties, several correlations are available.Usually these are based on empirical data derived from tests on core samples and thenextrapolated back to BH conditions. As such, there is a degree of inaccuracy associated withthem. Lacy’s method (1997) is recommended for Young’s modulus:-

E = 0.018 E d2 + 0.422 E d................................................... (7.40)

However, there is no such correlation for Poisson’s ratio.

Stress

Strain

TENSION

COMPRESSION

Stress

Strain

TENSION

COMPRESSION





Frac Gradient

The horizontal stresses (assumed to be equal) can be calculated using the log data andEquation 7.20. To use this Equation, three important pieces of information must be acquired:-

• Vertical stress. Usually found by taking the bulk density back to the surface and usingEquation 7.16.

• Pore pressure.• Biot’s poroelastic constant, usually found using Equation 7.37 – 7.39 and table 7.10a.

Otherwise use 0.8 for a poorly consolidated formation and 1.0 for a consolidatedformation

References



Biot, M.A.: “General Theory of Three-Dimensional Consolidation,” Journal of Applied Physics ,1941, 12, p155-164.

Biot, M.A.: “General Solutions of the Equations of Elasticity and Consolidation for a PorousMaterial,” Journal of Applied Mechanics , 1956, 23, p91-96.

Deily, F.H., and Owens, T.C.: “Stress Around a Wellbore”, paper SPE 2557, presented at theAnnual Fall Meeting of the SPE, October 1969.

Barree, R.D., Rogers, B.A., and Chu, W.C.: “Use of Frac-Pack Pressure Data to DetermineBreakdown Conditions and Reservoir Properties”, paper SPE 36423, presented at the SPEAnnual Technical Conference and Exhibition, Denver, October 1996.

Handin J., Hager, R. V. Jr, Friedman, M., and Feather, J. N.: “Experimental Deformation ofSedimentary Rocks Under Confining Pressure: Pore Pressure Tests,” Bulletin AAPG, 1963,47, p717-755.

Terzaghi, K. van: “Die Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf derHydrodynamischen Spannungserscheinungrn,” Sber. Akad. Wiss , Vienna, 1923, 123, p105(in German)

Bradley, H.B. (Editor), Petroleum Engineering Handbook , Society of Petroleum Engineers,Richardson, Texas, 1987, 51.

Log Interpretation Principles/Practices , Schlumberger Educational Services, Houston, Texas,1989, 5.

Lacy, L.L.: “Dynamic Rock Mechanics Testing for Optimized Fracture Design”, paper SPE38716, presented at the 1997 SPE Annual Technical Conference and Exhibition, SanAntonio, Texas, Oct 1997



BJ Services’ Frac Manual8. 2-D Fracture Models


8. 2-D Fracture Models

2-D fracture models were the industry’s first attempt at mathematically modelling the processof fracture propagation. By today’s standards, they are crude approximations. However, there

are two important points to note. First, in order to understand how the modern 3-D modelswork, it is first necessary to understand the 2-D models. Second, there are somecircumstances in which certain 2-D models can be valid. These include coal bed methanefracturing (KZD) and fracturing in massive, uniform formations (radial).

8.1 Radial or Penny-Shaped

Figure 8.1a – Propagation of a radial or penny-shaped fracture

Figure 8.1a shows the propagation of a radial or penny-shaped fracture. In this model, theheight, H , is a function of the radius or half-length of the fracture, R , such that H = 2R . Thisproduces a fracture, which is circular in shape. The width of the fracture is given by:-

W max =8 ( 1 - ν

2 ) ∆P R

π E ............................................................ (8.1)

Where ∆P is the net pressure, ν is the Poisson’s ratio and E is the Young’s modulus.

In this model, the width at any part of the fracture is a function of the distance between thecenter and the edge of the frac such that:-

w (r ) = W max 1 -

r

R .......................................................... (8.2)

w̄ =815 W max ........................................................................ (8.3)

Note the following points, which are applicable to all the 2-D fracture models:-

i) W max is inversely proportional to the Young’s modulus. This means that as the

formation gets harder (i.e. the Young’s modulus increases), the net pressure requiredto produce a given width increases. So it takes more energy to produce width in ahard formation than it does in a soft formation.

R H

W max





ii) W max is directly proportional to the half-length of the fracture – if the half-length isdoubled, the width is doubled. Note that this is the created width, not the finalpropped width, which is what the post treatment production increase will be partiallydependent upon. The propped width will always be equal to or less than the createdwidth, and is a function of the volume of proppant placed per unit area of the fracture.

iii) W max is relatively insensitive to changes in Poisson’s ratio. An increase in ν from 0.2

to 0.25 (an increase of 25%) will change the term (1 - ν 2) from 0.96 to 0.9375, a

decrease of only 2.34%. Therefore, it is pointless to spend too much time trying to get

accurate values for ν . However, as seen in Chapter 6, ν can have a significant effecton the magnitude of the horizontal stresses – if the frac gradient is unknown, then

finding accurate values for ν can be important.

The radial model has no limits to height growth. As long as the fracture is growing outwards(i.e. R is increasing), then it will also be growing up and down the wellbore (i.e. an increase inH ). This type of propagation can be found in a massive uniform formation with no verticalvariations in rock properties and hence no “barriers” to height growth. It can also be found forsmall fractures that have not contacted any “barriers”, such as in skin bypass fracturing.

The volume of the fracture is obtained from the volume of fluid pumped into the fracture, lessthe volume of fluid leaked off. The volume of fluid leaked off is a function of the leakoff area ofthe fracture (which is equal to 2πR

2), so that if the fluid efficiency (η ), injected volume of fluid,

E , ν and ∆P are known, R can be easily obtained:-

R =3

3 η Q t E

16 ( 1 - ν 2 ) ∆P

....................................................... (8.4)

where Q is the average pump rate and t is the pump time.

8.2 Kristianovich and Zheltov - Daneshy (KZD)

This model was originally developed by two Russians, Kristianovich and Zheltov, and waslater modified by Daneshy, Geertsma and de Klerk , and also by Le Tirant and Dupuy. Often,this model is referred to as GDK, after Geertsma and de Klerk. In this model, the height isfixed, and remains constant throughout. It is usually set as the gross height of the formation:-

Figure 8.2a – Schematic showing the general shape of the KZD fracture

W max

H L





As we can see from Figure 8.2a, the KZD model produces a fracture with a constant height.This means that there must be slippage between the formation being fractured and theformations above and below. This is unlikely (but not unknown) in most situations, but canhappen when fracturing coal beds. The maximum width is related to the half length L by thefollowing Equation:-

W max = 4 ( 1 - ν 2

) ∆P LE

............................................................ (8.5)

Note that for a given net pressure and half length, the maximum width of a KZD fracture is

greater than the maximum width of a radial fracture by a factor of π / 2.

The average width is given by:-

w̄ =π 4

W max.......................................................................... (8.6)

Therefore, for two “wings”, the length of the fracture is given by

L =2

η Q t E

2 π ( 1 - ν 2 ) ∆P H

.................................................. (8.7)

where η is the fluid efficiency, Q is the average pump rate and t is the pump time.

8.3 Perkins and Kern - Nordgren (PKN)

This fracture model was originally conceived by Sneddon and later developed by Perkins andKern, with further work by Nordgren, Nolte and Advanti et al . In this model, the maximumwidth is related to the height of the fracture, such that:-

W max = 2 ( 1 - ν

2 ) ∆P H

E ............................................................... (8.8)

whilst the average width, w̄ , is given by:-

w̄ = π

5 W max ............................................................................. (8.9)

Figure 8.3a – The Perkins and Kern - Nordgren fracture

H

W max

L





Thus, both fracture height and width are constant down the length of the fracture. Figure 8.3aillustrates the shape of this fracture.

The length of the fracture can be determined by a method similar to those used for the radialand KZD fractures:-

L = 5 η Q t E

4 π ( 1 - ν 2 ) ∆P H

2 ........................................................ (8.10)

The PKN fracture geometry was used for many years by the industry as the standard, untilthe advent of pseudo-3D fracture simulators and an improved understanding of fracturepropagation and fracture mechanics (see Sections 9 and 11).

References

Abé, H., Mura, T., and Keer, L.M.: “Growth Rate of a Penny-Shaped Crack in Hydraulic

Fracturing of Rocks”, J. Geophys. Res. (1976) 81, 5335.

Zheltov, Y.P., and Kristianovitch, S.A.: “On the Mechanism of Hydraulic Fracturing of an Oil-Bearing Stratum”, Izvest. Akad. Nauk SSR, OTN (1955) 5, 3-41 (in Russian)

Daneshy, A.A.: ”On the Design of Vertical Hydraulic Fractures”, JPT , Jan 1973, 83-93.

Geerstma, J., and de Klerk, F.A.: “Rapid Method of Predicting Width and Extent ofHydaulically Induced Fractures”, JPT , Dec 1969, 1571-81

Le Tirant, P., and Dupuy, M.: “Fracture Dimensions Obtained During Hydraulic FracturingTreatments of Oil Reservoirs”, Rev. Inst. Français du Pétrole (1967) 44-98 (in French).

Sneddon, I.N.: “The Distribution of Stress in the Neighbourhood of a Crack in an ElasticSolid”, Proc. Royal Society of London, (1946) 187, 229.

Perkins, T.K., and Kern, L.R.: “Widths of Hydraulic Fractures”, JPT , Sept 1961, 937-949.

Nordgren, R.P.: “Propagation of a Vertical Hydraulic Fracture”, SPEJ , Aug 1972, 306-314.

Nolte, K.G.: “Determination of Proppant and Fluid Schedules From Fracturing PressureDecline”, SPEPE , July 1986, 255-265.

Advanti, S.H., Khattib, H., and Lee, J.K.: “Hydraulic Fracture Geometry Modeling, Predictionand Comparisons”, paper SPE 13863, presented at the SPE/DOE Low-Permeability GasReservoirs Symposium, Denver, May 1985.






BJ Services’ Frac Manual9. Fracture Mechanics


9. Fracture Mechanics

Fracture mechanics is the study of how fractures propagate through a material. The aim offracture mechanics is to predict how fast a crack will grow, and at what point the fracture

becomes “critical” – i.e. the fracture will suddenly spread across the entire material causingcatastrophic failure. In hydraulic fracturing we use fracture mechanics to predict how far ourfracture will grow – both horizontally and vertically.

When reading this section, it should be remembered that stress and pressure are essentiallythe same thing. This means that a pressure in a fracture puts a stress of equal magnitude inthe formation at the fracture face, in a direction perpendicular to the fracture face. Therefore,when the fracture is propagating, the critical stress (the stress needed to make the fracturegrow) has to be equal to the net pressure.

9.1 Linear Elastic Fracture Mechanics and Fracture Toughness

Linear Elastic Fracture Mechanics (LEFM) is all about the prediction of how much stress (i.e.energy) it takes to make a fracture propagate. LEFM assumes linear elastic deformation(constant Young’s modulus) followed by brittle fracture – it is assumed that no significantenergy is absorbed by non-linear or non-elastic effects. That is to say, energy stored as stressin the material is transferred directly to fracturing the material, and no energy is lost to plasticdeformation. LEFM was used almost exclusively in the earlier fracture models (see Section8), and is still used – to a greater or lesser extent - in a number of fracture models currentlyavailable in the industry (e.g. MFrac , StimPlan – see Section 11).

The Griffith Crack

The first person to adopt a meaningful analytical approach to studying the mechanics of

fracture propagation was Griffith, in the 1920’s. Figure 9.1a illustrates the concept of theGriffith crack, which can be expressed with the following Equation;

δU

δa =

2πσ 2a

E ..............................................................................9.1

Figure 9.1a – The Griffith crack

2a

σσσσ

σσσσ





where U is the elastic energy (i.e. the energy used to produce elastic stress on the material),

a is the characteristic fracture length, σ is the far field stress (i.e. the “bulk” stress away fromthe influence of the fracture) and E is the Young’s modulus. Therefore, Equation 1 describesthe amount of additional energy (δU ) required to make the fracture grow from length a tolength a + δa .

Usually, δU / δa is replaced by 2G . G is referred to as the “elastic energy release rate” and alsothe “crack driving force”, such that;

G =πσ

2a

E ............................................................................. (9.2)

In order to reach this relationship, Griffith makes a significant assumption – that there is noenergy lost at the fracture tip and not used to propagate the fracture. Energy is used either toelastically deform the material or to rupture the material. Therefore, there can be no plasticdeformation at the tip, and the Griffith model is only applicable to materials liable to elasticdeformation followed by brittle fracture.

Griffith Failure Criterion

Given that for a uniform material with constant geometry δU / δa is a constant, there is a critical

value of stress, σ c, at which the material will experience catastrophic failure, i.e. the fracturepropagates at high velocity across the material causing failure. This critical stress is definedas follows;

σ c =2

EG Icπa

....................................................................... (9.3)

The critical energy release rate, G lc, is determined experimentally and is a material property,although it will vary with both temperature and the overall geometry of the test specimen.

Equation 9.3 also defines - for a given stress - a critical fracture length. If the fracture is lessthan this critical length, the material will not fail. However, if the fracture grows above thiscritical length, the material will fail.

The subscript "I" refers to the failure mode, as illustrated in Figure 9.1b. Failure mode I is the"opening mode", mode II is the "sliding mode" and mode III is the "tearing mode". In hydraulicfracturing, we are usually only concerned with failure mode I.

Figure 9.1b – Failure modes in Linear Elastic Fracture Mechanics

Mode IOpening

Mode IISliding

Mode IIITearing





Stress Intensity Factor

With reference to Figure 9.1c, the stresses in the principal directions, at some point awayfrom the fracture tip, can be expressed as follows;

σ xx =K

2 πr

cos θ 2

1 - sin

θ 2 sin

3θ 2 ...................................... (9.4)

and

σ yy =K

2 πr cos

θ 2

1 + sin

θ 2 sin

3θ 2 ...................................... (9.5)

where K is the stress intensity factor.

Figure 9.1c – Coordinate system for stress intensity factor

Considering the plane strain situation (i.e. ε zz = 0, an object with a thickness large enough tomake strain on the z-axis negligible), and the case that a >> r , then the stress in the y-

direction – “across” the line of the fracture (i.e. θ = 0) – can be expressed as follows;

σ yy =K

2πr........................................................................... (9.6)

Obviously in Equation 9.6, as r tends to 0, σ yy tends to . This represents a fundamental flawin this approach to modelling fractures – it fails close to the fracture tip.

Using this approach, K is the only factor that affects the magnitude of the stress at a givendistance from the fracture tip. Whilst K is a material property, it is also a variable, dependingupon the gross geometry of the fracture and its surroundings, as well as temperature.

Assuming a constant temperature in any given instance, relationships linking K , a and σ for

most situations have been solved, either analytically or numerically. At material failure, σ c canbe described in terms of a critical stress intensity factor, K Ic, which is more commonly referredto as the fracture toughness ;

σ c =K Ic

β πa ........................................................................... (9.7)

This is the fundamental Equation of Linear Elastic Fracture Mechanics, where β is ageometrical factor and is equal to 0.4 for a radial fracture. K Ic is related to G Ic as follows;

σσσσ

σσσσ

a

Fracture

y

x

r θ θθ θ





GIc = (1 - ν 2)

K Ic2

E ................................................................... (9.8)

For a given geometry, the fracture toughness is a material property. Equation 9.8 shows thatit represents the amount of mechanical energy a material can absorb before it fails by brittle

fracture. Put simply, a material with a low K Ic is brittle and a material with a high K Ic is tough.The term E /(1 - ν

2) is often referred to as the plane strain Young's modulus or E ', so that G lc is

equal to K lc divided by E '.

9.2 Non-Linear and Non-Elastic Effects

From the extensive work done in this field, it is clear that LEFM alone does not adequatelyaccount for the pressure needed to make the fracture grow. There is a tip over pressureeffect, which means that more pressure (energy) is required than is predicted by LEFM. Twopossible – and not necessarily mutually exclusive – theories for this are described below.

Crack Tip Dilatency

The theory of crack tip dilatency was first put forward by Cleary et al , and has been usedextensively by them in the FracPro model. This approach has almost entirely done away withthe concept of fracture toughness, which means that users of simulators based on this modelfind that changes to input fracture toughness values have little or no effect on fracturegeometry. Instead the theory states that deep underground, the effect of the confining stressis much more significant than the effect of the fracture toughness. Thus K Ic can be ignored ifthe following condition is satisfied;

σ π R >> K Ic ..................................................................................... (9.9)

where R is the radius of the fracture and is analogous to the LEFM characteristic fracturelength. Equation 9.9 shows us that fracture toughness is more significant for small fractures inshallow formations, such as during skin bypass fracturing.

The fracturing fluid does not penetrate to the very end of the fracture. This means that there is

a very rapid change in net pressure at a distance ω from the tip of the fracture, as illustrated inFigure 9.2a.

Figure 9.2a – The Cleary et al approach.

If the condition described in Equation 9.9 is satisfied, then ω can be found as follows;

ω ωω ω P net

Dilation Contribution

r





ω ≈ R 2

P net

P net + P c

2 ...................................................... (9.10)

Because the fluid does not penetrate into the tip of the fracture, energy is lost as the tip of thefracture deforms. It is postulated that this deformation occurs in a non-linear or dilatentfashion. This crack tip dilatency reduces the energy left for the fracturing fluid to propagate

the fracture, and hence reduces the size of the fracture, for a given P net.

Crack Tip Plasticity

The crack tip plasticity theory allows for a significant region of plastic deformation at thefracture tip. All materials exhibit some level of plastic deformation prior to failure – it isassumed in LEFM, and most of the other approaches to modeling hydraulic fracturing, thatthis is not significant. This may be true in some formations. However, there may be a widerange of circumstances under which significant plastic deformation is not only possible, butprobable.

Even so-called brittle materials can experience plastic deformation when exposed to extreme

tri-axial stresses.

As the load on a material containing a fracture increases, the stresses around the fracture tipalso increase. Because of the geometry of the area of the fracture tip, these stresses areusually far in excess of the overall stress on the material - as illustrated in Equation 9.6. Asthe overall stress increases, the stress around the fracture increases to a point where itexceeds the yield point of the material (σ y). The material then starts to plastically deform, andto move in a direction that will relieve the stress – away from the crack tip. This produces acrack tip of finite radius, as opposed to the infinitely small fracture tip modeled in LEFM. Thediameter of the fracture tip, d , is given by the following Equation:

d =K I

2(1 - ν

2 )

E σ y .................................................................... (9.11)

For a long, narrow fracture, having a tip of finite radius can significantly reduce the overalllength of the fracture. This is illustrated in Figure 9.2b:-

Figure 9.2b – Crack tip diameter and the plastic zone. Note that r p is the radius of the plasticzone.

Figure 9.2b shows the plastic zone as a circle around the fracture tip. However, this is notnecessarily the case. By using the principle stresses given by Equations 9.4 and 9.5, and

assuming plane strain (ε zz = 0), the von Mises yield criterion gives the following result:

Fracture

σ σσ σ yy

r

σ σσ σ y

r p

d

The plastic zone





σ y2π r p

K I2 =

14

3

2 sin2θ + (1 - 2ν )

2(1 + cosθ ) ............................ (9.12)

By plotting, in polar coordinates, σ y2πr p / K I2 (dimensionless plastic radius) against θ , we can

see the shape of the plastic zone at the fracture tip, as illustrated in Figure 9.2c. Thisproduces two plastic “ellipses” either side of the fracture plane.

Figure 9.2c – The shape of the plastic zone, for a Poisson’s ratio of 0.25 (after Martin , 2000)

In hard rocks, the actual size of the plastic zone is quite small, compared to the volume of thefracture. However, as Young’s modulus and yield stress decrease, the relative size of the

plastic zone increases until it reaches a relatively large volume. At this point, the energyabsorbed by the plastic deformation of this volume becomes a significant fraction of theenergy contained in the fracturing fluid.

This means that in a formation liable to significant plastic deformation, it requires significantlymore energy to propagate the fracture than is predicted by LEFM. As discussed below, if thefracture tip takes more energy, the fracture will be smaller and will have less width.

9.3 The Energy Balance

The process of propagating a fracture through a formation is all about the transfer of energyfrom the frac pumps to the formation. Energy transfer occurs as shown in Figure 9.3a.

Reducing all the processes occurring in the creation of a fracture to energy, allows them to berelated to each other in the most fundamental fashion. To start with, we must remember thatpressure and stress are essentially energy per unit volume.

Therefore, the total energy per unit time (a.k.a. power) in the fluid available for creating afracture is:-

U̇ = BHTP.Q ...................................................................... (9.13)

Not forgetting that:-

BHTP = STP + HH – P frict ....................................................... (9.14)

Therefore, the total energy available to the fracturing fluid is given by:-

-0.5

0.5

-0.5 0.5

σσσσy2ππππr p

K I2

ν νν ν = 0.25

θ θθ θ



P a g e

7 8

V er si on

1 . 0 J un e2 0 0 5

U n c on t r ol l e d C o p

y–D O N OT D I S T R I B U T E

F i g ur e 9 . 3 a– S o ur c e s of E n er g y G a

i n s an d L o s s e sf or t h ef r a c t ur i n gf l ui d .

E n er g y G ai n s +

E n er g yL o s s e s= 0 .

The Frac Fluid

At the WellheadSTP

Energy Gains Ene

By the PerforationsBHTP

In the Near WellboreRegion, Pnet

At the Fracture TipPnet- Fluid Friction

in Fracture

Chemical Energy from the DieselFuel is Changed into MechanicalEnergy by the Engine, which is

Changed into Pressure andKinetic Energy by the Frac Pump

Energy fromHydrostatic Head

Friction Lin

Perforati

OverStres

Compto P

Flu

Moving Down theFracture, Pnet





Where t p is the total pumping time. Equation 9.15 looks intimidating, but it is simply the areaunder the graph of (bottom hole) horsepower against time.

A substantial portion of the energy is used up, simply by overcoming the in-situ stresses ofthe formation. Another portion of the energy is used up in overcoming friction in the near

wellbore area. Therefore, the final amount of energy available for fracturing the formation isgiven by:-

U fluid = 0

t p P netQ dt ................................................................ (9.16)

Given that in most cases the rate is relatively constant, a plot showing P net versus time canshow a great deal about how much energy is being used to create the fracture. This is thebasis of Nolte analysis (see Section 10.2).

Most fracture simulators spend a great deal of time quantifying these energy loses and gains,so that the amount of energy left in the fracturing fluid for propagation and the production ofwidth can be a found. If the Young’s modulus is known, the fracture width – for a given P net – can be easily determined. This then leaves the amount of energy available for the

propagation of the fracture, which in turn defines how big the fracture gets. This is the ultimategoal of the fracture simulator.

References

Griffith, A.A.: “The phenomena of rupture and flow in solids”, Phil. Trans. Roy. Soc. ofLondon, A 221 (1921), pp. 163 – 167

Broek, D.: Elementary Engineering Fracture Mechanics , Kluwer Academic Publishers, 4th Ed.(rev), 1986.


Cleary, M.P., Wright, C.A., and Wright, T.B.: “Experimental and Modeling Evidence for MajorChanges in Hydraulic Fracturing Design and Field Procedures”, paper SPE 21494, presentedat the SPE Gas Technology Symposium, Houston TX, Jan 1991.

de Pater, C.J., Weijers, L., Savi, M., Wolf, K.H.A.A., van den Hoek, P.J., and Barr, D.T.:“Experimental Study of Nonlinear Effects in Hydraulic Fracture Propagation”, paper SPE25893, SPEPF , Nov. 1994, pp. 239 – 246.

Dugdale, D.S.: “Yielding of steel sheets containing slits”, J. Mech. Phys. Sol., 8, 1960, pp. 100

– 108.

Martin, A.N.: “Crack Tip Plasticity: A Different Approach to Modeling Fracture Propagation inSoft Formations”, paper SPE 63171 (revised), presented at the SPE Annual TechnicalConference and Exhibition, Dallas TX, Oct 2000.



BJ Services’ Frac Manual10. Advanced Concepts


10. Advanced Concepts

In this section we shall deal with some of the more advanced concepts used in the process ofdesigning hydraulic fracture treatments, as well as in diagnosing what may (or may not) have

happened during a frac or minifrac treatment.

10.1 Tortuosity

Hydraulic fractures are created by pressure, not rate. Often we use rate to help generate therequired pressure, but we shouldn’t loose sight of the fact that it’s pressure that splits therock. Over a long perforated interval, fractures can form anywhere that the fluid pressureexceeds the local frac gradient. Generally, the rock will have one point that is weaker than therest and the initial fracture will form here. However, if the pressure continues to rise, additionalfractures may be formed. Potentially, every single perforation is a source of fracture initiation.Many of these fractures will be very small – but some may be large enough to take asignificant proportion of the treatment fluid.

Away from the artificial stress environment around the wellbore, treatments tend to produce arelatively small number of larger fractures. Normally, fractures do not tend to join together – the stress regime around the fracture tip tends to keep fractures apart. However, under theinfluence of the complex stresses around the wellbore and perforations, fractures can jointogether, sometimes giving several narrow paths towards a single, large fracture. So thetreating fluid has to travel from a region containing a large number of small fractures to aregion containing a small number of large fractures. In doing so, the fluid has to move througha series of convoluted, narrow fractures – or put another way, through a tortuous path. Thistortuosity can produce a significant loss in pressure, resulting in a smaller than expectedfracture and possible early screenouts. Screenouts can also be caused by tortuosity foranother reason – the width of these channels through the rock is often not large enough tocarry the proppant concentration passing through it. This causes the proppant to bridge off,

preventing any further flow of proppant.

Tortuosity manifests itself as a pressure drop through the near wellbore region. There arealso other phenomenon that can result in a near wellbore pressure loss (such as poor qualityperforations). However, the important point is that there is a loss of pressure, which can be asubstantial proportion of the observed net pressure (i.e. the total energy available topropagate the fracture). Because the pressures inside the fracture drive the pressures at thesurface, the pressure loss due to the tortuosity actually produces a higher BHTP and hencehigher STP. This gives the surface observer the impression that the net pressure is higherthan it really is. For instance, for a well with 200 psi net pressure and 300 psi pressure lossdue to tortuosity, it appears, to an Engineer who is unaware of the tortuosity, that the netpressure is 500 psi. This means that Engineer thinks that the frac fluid has much more energyfor creating fracture volume than it has in reality, potentially resulting in a treatment design

that contains more proppant than can physically fit into the fracture. It is therefore important tounderstand the magnitude of the near wellbore pressure loss, so that this can be allowed forwhen designing the treatment.

Hard Rocks (that is, rocks with a high Young’s modulus and low fracture toughness) tend tobe more susceptible to tortuosity than soft rocks. In this type of brittle formation, there isalready a fracture formed at each perforation by the explosive action of the perforatingcharges – all we are doing when we pump fluid is making these fractures extend, through amedium that allows easy fracture extension. Because of the high Young’s modulus, the stressconcentrations at the fracture tip are more intense and so these smaller fractures are lesslikely to link up. This means that hard rocks are more likely to produce a large number ofsmall fractures than soft rocks.

Deviated Wellbores tend to be more susceptible to tortuosity than vertical wells. As fracturespropagate, they compress the rock either side of them. This makes it harder for other





fractures to propagate in this region. As discussed in section 7, fractures tend to propagate ona vertical plane. This means that the more deviated the wellbore, the less each fractureinterferes with its neighbour, and so they propagate more easily. Additionally, as each fractureis further apart, there is less joining together of fractures. Finally, there is some evidence tosuggest that on some deviated wells, the fracture can initiate along the wellbore. At somepoint not too far from the wellbore, the fracture grows out far enough so that the influence of

the wellbore is less significant than the influence of the in-situ stresses. At this point thefracture has to change its orientation, rapidly if the rock is very hard. This produces a “corner”around which the fluid and proppant has to flow, which causes further loss of pressure.

Thus, highly deviated wells in hard rocks are more likely to experience tortuosity problemsthan vertical wells in soft formations. This does not mean that significant tortuosity will not beencountered in soft formations or in vertical wells – it simply means that it is less likely.

Perforation Strategy. Often Service Companies are asked to treat wells which are alreadyperforated. In such wells, it is very difficult to control fracture initiation. However, sometimesthe well to be treated is new and we can perhaps influence the perforation strategy. This canhave a significant effect on the tortuosity, and is explained in detail in Section 14.

Horizontal Stress Contrast. As illustrated in Figure 10.1a, the contrast between themaximum and minimum horizontal stresses can also influence the tortuosity. For the left hand

side of Figure 10.1a, there is a large contrast between σ h,max and σ h,min. This produces anarrow fracture close to the wellbore and a very tight radius turn for the fracture. For the righthand side of Figure 10.1a, there is little difference between the two horizontal stresses, so thefracture starts with a wider width and gradually changes direction. Therefore, depending uponthe initial fracture orientation (which is turn is affected by the perforation strategy and wellboredeviation), the contrast between horizontal stresses can have a significant effect on tortuosity.

Figure 10.1a. Diagram illustrating the effects of horizontal stress contrast on tortuosity (after

GRI-AST 1996).

Curing Tortuosity. If tortuosity is detected before the main treatment (see Sections 15 and16), it can sometimes be cured. This is done by pumping proppant slugs. The first company tosuccessfully accomplish this on a regular basis was Mærsk Olie og Gas , a Danish companyoperating in the North Sea. Several SPE papers have been produced by Mærsk and theircontractors to document this. Mærsk had the advantage that they were operating off a largefrac boat, mixing gel with seawater on the fly. This meant that they had an effectively limitlesssupply of both gel and proppant at their disposal – most of the time this is not the case.

To start with, Mærsk would pump a proppant slug in the minifrac, ideally at the maximumanticipated proppant concentration for the main treatment. If this slug passed into theformation without a significant rise in pressure, they could be reasonably sure that the

tortuosity would not significantly affect the treatment. Sometimes they would pump a series ofslugs, mixed at increasing proppant concentrations. If these slugs encountered a significant

σ σσ σ h,min

σ σσ σ h,max

σ σσ σ h,max > σ σσ σ h,min σ σσ σ h,max = σ σσ σ h,min~>





rise in pressure, or worse still screened the well out, they knew they had a problem. The curewas to deliberately screen the tortuosity out.

This is done by pumping proppant slugs and then shutting down with the slug in theperforations and near wellbore region. The effect of this is to block up the narrow channelsand force open the wide channels.

After a few years, Mærsk became so proficient at this – and so familiar with their formations – that they developed a standard method used on every treatment. This involved pumping arelatively long stage of 100 mesh sand at 1 or 2 ppa during the minifrac, followed by arelatively short stage with 20/40 proppant at 4 or 5 ppa. The minifrac was shut down with the20/40 proppant in the perforations. The 100 mesh sand blocked the narrow channels, whilstthe 20/40 proppant held open the wide channels, so that they would accept fluid when themain treatment started. Using this method, Mærsk achieved a near perfect record for placingtreatments, in an area notorious for tortuosity problems.

10.2 Nolte Analysis

Nolte analysis is a branch of frac theory originally developed by Ken Nolte of Amoco in theearly 1980’s. It uses a plot of log P net against log time to determine the shape of the fracture,as illustrated in Figure 10.2a:-

Figure 10.2a – The Nolte plot

Basically, pressure is stored energy – or in the case of the fracturing fluid, stored energy perunit volume. As work (a.k.a. horsepower) is the rate of using energy, on a graph of pressureagainst time the gradient is the amount of work being performed. In this case, it is the amount

of work being performed by the fracturing fluid on the formation.

Nolte used a mathematical analysis to show that at certain gradients on the log P net againstlog job time plot, certain fracture geometries will apply (with reference to Figure 10.2a):-

Mode I - Good height containment, fracture propagates preferentially in the horizontaldirection.

Mode II - Even fracture growth, fracture is propagating elliptically with vertical as wellas horizontal growth.

Mode IIIa - Screenout, fracture is filling with proppant and is having to balloon in order tocope with the volume of fluid entering the fracture.

Mode IIIb - Screenout, near wellbore event. It is no longer possible to pump proppant intothe fracture.

Mode IV - Uncontrolled height growth. Also radial fracture geometry.

I

II III

IV

b

a

l o g P n e t

log (job time)





Nolte’s work was carried out with respect to the three main 2-D models that were widely usedat the time. However, it is still a useful tool for the Frac Engineer to assess fracture geometrywithout using a fracture simulator, or as a back up to a simulator.

Nolte analysis became popular at the same time that Service Companies began to usecomputer monitoring and data storage systems on location. It became possible to have a

Nolte plot running real time – providing the industry with its first real-time fracture simulationand diagnosis tool.

10.3 Dimensionless Fracture Conductivity

Dimensionless Fracture Conductivity (F CD or – as recently redefined by the API - C fD) orRelative Fracture Conductivity is a measure of how conductive the fracture is compared to theformation. In order to produce a production increase, the propped fracture has to be moreconductive than the formation (setting aside the effects of bypassing the skin damage). InSection 2 we defined the fracture conductivity (F C) as being the product of the fracture widthand the permeability of the proppant. Dimensionless fracture conductivity is defined asfollows:-

C fD =F c

x f k =

k p w̄x f k

......................................................... (10.1)

where x f is the fracture half length, k p is the permeability of the proppant, w ¯ is the averagefracture width and k is the permeability of the formation. In order for the fracture to be moreconductive than the formation, the dimensionless fracture conductivity has to be greater thanone.

Equation 10.1 compares the ability of the formation to deliver fluids to the fracture, with theability of the fracture to delivery fluids to the wellbore. If the C fD is less than one, then posttreatment production increase is limited by the relatively low conductivity of the fracture, and

the fluids will flow more easily through the formation. If the C fD is significantly greater than 1,then the limiting factor is the formation’s ability to deliver hydrocarbons to the fracture.

Of the four components on the right hand side of Equation 10.1, the permeability of theformation is fixed, whilst the permeability of the proppant is defined by the proppant type, theclosure stress and the producing conditions. In order to maximise C fD, it is necessary tocontrol the fracture half-length, whilst at the same time getting the width and the proppantpermeability as large as possible. Under most circumstances – for any given fracture situation – there is a fixed relationship between width and length. For so much length created, therewill be so much width created. However, created width is not the same as propped width,unless the well has screened out from tip to wellbore. The more proppant that is placed perunit area of the fracture, the wider the propped fracture will be. Therefore, two ways toincrease C fD are; one – pump more proppant; or two – pump better quality proppant.

In higher permeability formations, this is not enough. Even with the fracture completely full ofgood quality proppant, the C fD can still be less than one. Therefore, a technique called the TipScreen Out must be used (see section 10.4, below).

10.4 The Tip Screen Out (TSO)

The Tip Screen Out is a technique used to artificially increase the width of the fracture,without increasing the length. As previously discussed, for any given fracture, there is a fixedrelationship between width and length. If we can artificially overcome this, then we candramatically increase the C fD. Figure 10.4a illustrates this:-





Figure 10.4a – The Tip Screen Out

The TSO is a technique that is generally used in high permeability formations. The highformation permeability means that it is very difficult to get a C fD greater than one. In order togenerate the TSO, proppant is pumped into the fracture earlier than would normally be thecase. As the formation has high permeability, the fracturing fluid is leaking off relativelyquickly. This acts to dehydrate the proppant-laden slurry. If the treatment is correctlydesigned, this dehydration will cause the proppant to collect at the fracture tip. In order for thefracture to continue to propagate, a positive P net must be maintained at the fracture tip. As the

proppant builds up in the fracture tip, fluid has to flow through it to reach the tip and maintainthe P net. Whilst flowing through the proppant build-up, the fluid loses pressure due to frictionas it passes between the proppant grains. When the proppant build-up gets large enough, the∆P of the fluid equals and then exceeds P net and the fracture ceases to propagate.

At this point, fluid is still being pumped into the fracture and has to go somewhere. Some ofthis fluid is leaking off, but not all of it – so the fracture volume still has to grow. This meansthat the fracture starts to get wider. It also means a rise in net pressure as the formation getsincreasingly compacted – this is how the onset of a TSO is spotted during a treatment.

The TSO technique relies on two things; high permeability (and hence high fluid leakoff), andlow Young’s modulus. High leakoff is necessary so that the slurry will dehydrate sufficiently toallow proppant build-up at the tip. Low Young’s modulus is necessary to allow the width to

increase. If the formation is too hard (i.e. Young’s modulus too high), the pressure will risevery rapidly and quickly exceed the maximum treating pressure at surface.

10.5 Multiple Fractures and Limited Entry

As previously discussed, any perforation is potentially a source of fracture initiation. All ittakes is for the fluid pressure to exceed the fracture extension pressure at any given point anda fracture is formed. How large that fracture is depends upon the volume of fluid the fracturereceives. Usually, most of the small fractures get “squeezed out” as larger fractures close bydevelop. However, if the fractures are far enough apart (which is easy enough on deviatedwellbores), more than one fracture will develop into a significant size. This is oftendetrimental, as multiple fractures that cover the same vertical plane are largely wasted, unlessthey are widely spaced out. In addition, as the rate (and hence frac fluid volume) is splitbetween two or more fractures, the treatment ends up producing a range of smaller, narrower(i.e. less conductive) fractures, rather than a single large fracture. Finally, although eachfracture receives only a fraction of the total rate, the proppant concentration remainsunchanged. As the fracture width is less, and the slurry velocity down each individual fractureis decreased, there is a much greater chance of proppant bridging and a prematurescreenout.

In short, multiple fractures can lead to less effective stimulation and an increased chance of job failure.

The majority of wells worldwide are completed with more than one set of perforations. Unless

something is done to isolate these perforations and control the point of fracture initiation,multiple fractures are likely. However, there is one situation where this is deliberately used toproduce stimulation of an entire interval at one go. This is called Limited Entry fracturing.

∆∆∆∆P

Fracture TipProppant





Limited Entry Fracturing. Even whilst fracturing, fluids follow the path (or paths) of leastresistance. The resistance to the flow of the fluids comes from three sources:- perforationfriction; tortuosity; and the formation’s fracture extension pressure. All of these can vary withfluid rate. However, the fracture extension pressure and tortuosity are not controllable,whereas the perforation friction is. Therefore, if the fracture extension pressure of each

formation is known, as well as the tortuosity (usually assumed to be zero), the number andsize of the perforations can be varied to balance the fluid flow, so that each set of perforationsreceives the same proportion of fluids. This technique is called Limited Entry, as we are tryingto limit and control the amount of fluids entering each zone.

This technique can be taken one step further. By further varying the number of perforations,the proportion of each fluid going into each zone can be adjusted to produce the optimumtreatment for that zone – more fluid enters zones needing most stimulation, for example.

Obviously, the calculations for working out the size and number of perforations can get prettycomplex – once there are more than two zones you need a computer model to keep thingsstraight. In addition, the results are only as good as the data input – if you are guessing at thefrac gradient, then you are also guessing at the number of perforations needed. Finally, this

analysis also assumes perfect perforations – something that cannot be guaranteed.Therefore, limited entry fracturing is unreliable unless exact data is available.

In addition to being unreliable, limited entry fracture treatments tend to be very big. Thetreatment is trying to place effective fractures in several zones simultaneously. This meanslots of rate and large fluid volumes, as well as lots of proppant, as this treatment is trying to dothe work of several smaller treatments in one go.

10.6 Proppant Convection and Settling

Proppant Convection. Proppant Convection is caused by variation in slurry density, and canlead to the majority of the proppant being placed in the bottom of the fracture. Put basically, a10 ppa slurry is much denser than a – for instance – 5 ppa slurry. This means that if a 10 ppaslurry follows a 5 ppa slurry into the formation, it will tend to slide beneath the lighter slurry,leading to the placement of the higher proppant concentration at the bottom of the fracture,where it may not necessarily connect with the perforations. This is illustrated in Figure 10.6a.

Obviously, proppant convection is not really an issue on TSO designs, as the plan is tocompletely fill the fracture from tip to wellbore. However, when fracturing lower permeabilityformations, proppant convection can cause significant problems. The way to prevent this is touse long proppant stages mixed at the same concentration. Once in the formation, slurries willdehydrate with time due to leakoff - increasing the ppa of the slurry - so it may be necessaryto gradually increase the proppant concentration at the blender as the treatment progresses.

Figure 10.6a – Proppant convection. As the heavier slurry enters the fracture it sinks anddisplaces the lighter slurry upwards





Proppant Settling. Proppant settling occurs when the frac fluid has insufficient viscosity tosuspend the proppant inside the fracture. Proppant moves downward, leading in the worstcases to a fracture that only has proppant right at the bottom. This may be completelyunconnected to the wellbore. Once again, this phenomenon is not an issue when a TSOtreatment is being performed. However, on lower permeability formations, especially thosewith very long closure times, settling can be a significant issue.

The key to preventing proppant settling is to design the frac fluid correctly. In order to preventsettling, the frac fluid must exhibit good proppant transport qualities at BHST for at least theanticipated job time, plus the anticipated closure time, plus a safety factor. This can be testedby the use of the model 50 high temperature rheometer. A widely accepted criterion forproppant transport is to have at least 200 cp apparent viscosity at a shear rate of 40 sec

-1.

Note that this criterion is not an API standard and is somewhat subjective – differentstandards are used in different places.

Equation 10.2 gives an Equation for calculating the terminal velocity (i.e. the maximumpossible velocity) for a spherical particle falling through a power law fluid (note that thisassumes the fluid is almost at rest):-

v t =

1

36 n' 0.04212 d p

n'+1 (SG p - SG f)

K ' ............................ (10.2)

where v t is the terminal velocity (ft/sec), d p is the proppant grain diameter (inches), SG p is theproppant absolute specific gravity, SG f is the fluid specific gravity, n ’ is the flow behaviourindex (dimensionless) and K ’ is the consistency index (lbs.sec

n’ ft

–2).

10.7 Proppant Flowback

Proppant flowback is when the proppant that been placed in the fracture flows back into thewell during production. It has been the subject of intense industry debate and investigation

over the last 10 years. Some of the causes of proppant flowback are listed below:-

i) Stress Cycling. Every time the well is drawn down, the closure stress on theproppant increases, as the reservoir pressure in the fracture is effectively reduced.When the well is shut in, the pressure builds up again and the closure pressure isreduced. This is stress cycling, which was first identified in 1994 by Shell and Stim- Lab as a major cause of proppant flowback. As the well is opened and closed, theproppant pack expands and contracts slightly, weakening its integrity. If the stress iscycled enough times – or too suddenly – the pack will literally break apart, allowingproppant to flow back into the wellbore. Wells that have been fractured should behandled with care – don’t shut them in unless there is no alternative, and if it has tobe done, then it should be done slowly.

ii) Weak Formations. Obviously, if the formation holding the proppant in place fallsapart, then the proppant will flow back. Formations that are susceptible to this need tobe frac and packed, rather than just fractured.

iii) Insufficient Fracture Conductivity. If the propped fracture has insufficientconductivity, especially in the near wellbore area, then the higher velocity of theproduced fluids, coupled with the increased pressure gradient along the plane of thefracture, will result in an increased net force acting to push individual proppant grainsout if the fracture.

iv) Poor Quality Frac Fluid. If the frac fluid does not have sufficient viscosity to keep theproppant suspended until the fracture closes, then the proppant will settle into thebottom part of the fracture. In extreme cases, this can result in the bottom half of thefracture having all the proppant, whilst the top half closes up on nothing. This createsa void space at the top of the proppant pack, as illustrated in Figure 10.7a.





Figure 10.7a – Illustration of the “Pipelining” effect.

As the well is produced, fluid flows rapidly across the top of the proppant pack,through the void space, as this is the path of least resistance. As it does so, it picksup proppant grains and can carry these out of the fracture and even up to the surface.This effect is known as “pipelining” and can result in almost all of the proppant beingproduced back out of the fracture.

Preventing Proppant Flowback

Once proppant flowback has started, it is usually very difficult to stop. Therefore, the bestoption is to prevent proppant flowback from happening in the first place. Obviously, a welldesigned treatment using a good quality frac fluid, together with good well management, can

go a long way to mitigating proppant flowback. However, it is also true that for someformations, this is not sufficient. To combat this, there are several different methods whichcan be employed:-

i) Resin Coated Proppant. By far the most common method for controlling proppantflowback, resin coated proppant (RCP) is simply proppant which has been coatedwith a layer designed to make the proppant grains stick together. Usually, it requirestemperature and a closure stress for this to happen. RCP tends to come in two mainvarieties, curable and pre-cured (or tempered). Curable RCP has a softer coating,which is designed to chemically cure when exposed to temperature. Pre-cured RCPhas a harder resin coat, which relies more on the closure pressure to make theproppant grains stick together. RCP has an additional effect, in that it makes theproppant more tolerant to closure pressure, as the resin coat will capture

permeability-reducing fines produced as the fracture closes.

RCP is generally used as an alternative to ordinary proppant, either for the wholetreatment, or for the last few proppant stages. This latter method, whilst beingcheaper, is less reliable as there is no guarantee that the stage which is pumped lastwill be the stage that is positioned by the wellbore (see earlier section on ProppantConvection).

RCP can be highly effective, but has three main disadvantages. First, it is expensive,often being more than twice as expensive as the non-coated proppant. Second, it canhave a significant effect on the fracturing fluid, especially at high pH’s, as some of theresin is stripped off and dissolves in the fluid. Finally, the standard bulk pneumaticsystems generally used for handling large volumes of proppant cannot be used for

RCP, as it the resin coat can be chipped off.

No Proppant

Proppant

Void Space





ii) Micro-Fibers. Another method for preventing proppant flow back is to pump verysmall fibers with the proppant. These fibers, if used in sufficient quantity, will form athree dimensional mesh within the proppant pack, acting to prevent individual grainsslipping past one another. The use of these fibers can result in a slight decrease inproppant pack permeability, but this can be allowed for in the frac design. The fibersare usually made from a polymer.

The main problems with this system (other than its cost) are operational. Because thefibers are very small, they have a very high surface area to mass ratio. This in turnmeans that it can very difficult to actually mix the fibers into a fluid, especially on thefly during a treatment. Because of the large difference in specific gravity between theproppant and the fibers, it is also very difficult to mix the proppant and fibers togetherbefore adding them to the gel.

The fibers also have a limited maximum temperature above which, they willdisintegrate. This significantly reduces the number of wells that are suitable for thistype of treatment. Finally, if used in the wrong proportions with the proppant (dueeither to poor design or ineffective mixing), the fiber itself can be produced out of theformation, sometimes resulting in a “hair ball” somewhere in the production facilities.

iii) Micro-Sheets. In order to get around the patent held by one service company for themicro-fibers, a competitor introduced a product that uses small sheets or platelets ofpolymer, which act to wrap around the proppant grains. This has several effects. First,and unfortunately foremost, is a significant reduction in permeability of the proppantpack. Secondly, the sheets will form a three dimensional mesh, acting in a similarfashion to the micro-fibers. The sheets also act a little like a resin coat, in that theycan cushion the proppant grains and tie up fines.

Unfortunately, the micro-sheets also suffer from many of the same operational andtemperature limitation problems experienced by the micro-fibers.

iv) Deformable Particles, such as BJ’s FlexSand , is another approach. These particles,

mixed at 10 to 15% by weight with the proppant, will deform – to a limited extent – around the proppant as the fracture closes. This acts to lock the proppant grainstogether and reduce the tendency for them to slide past each other. The deformableparticles also have the effect of cushioning the proppant grains and increasing thegrain to grain area of contact. This acts to increase the proppant pack permeability,by reducing the production of fines.

The main disadvantage of the deformable particles is the extra equipment needed tohandle it and mix it at the correct proportions. However, this is no worse than for themicro-fibers and the micro-sheets.

10.8 Forced Closure

Forced closure is a technique used to produce a very tight proppant pack in the near wellborearea. As soon as the treatment is finished, the well is opened up and flowed back at 0.5 to 1.0bpm. This is before the fracture has closed and before the fluid has broken. Although theexact mechanism by which this prevents proppant flowback is not clear, there is sufficientempirical evidence to make this a valid technique, in a suitable formation. However, there areno methods for deciding which formations are suitable, apart from actually trying thetechnique.

Modern treatment monitoring software and fracture simulators are set up to allow for forcedclosure. Many of them even allow input from a flowmeter placed on the flowback line whilstmonitoring the post-treatment pressure decline.





10.9 Non-Darcy Flow

Darcy defined fluid flow through a porous media, in terms of the flow dimensions, the fluidviscosity, the pressure differential and the permeability of the media, in an Equation that isfundamental to the oil industry:-

q =kh ∆P

µ (r e /r w ) ....................................................................... (10.3)

However, this doesn’t tell the whole story. Whilst this Equation can be very reliable for fluidflow through relatively low permeability media (such as rocks), it does not take into accountinertial flow effects. On the microscopic scale, the fluid is constantly changing direction as itmoves through the pore throats and pore spaces. This represents a loss of kinetic energy,and so also an increased loss in pressure per unit distance. This effect is quantified in theForcheimer Equation:-

- dP L

= µ v k p

+ β ρ v 2............................................................. (10.4)

(1) (2) (3)

The term –dP / L is the pressure drop per unit length along the propped fracture, µ is theviscosity, v is the overall “bulk” velocity of the fluid, k p is the permeability of the proppant pack,

β is a constant (the “beta” factor, non-Darcy flow factor or turbulence factor), and ρ is thedensity of the fluid.

In Equation 10.4, parts (1) and (2) are essentially the Darcy Equation. Part (3) is the non-Darcy term, and is basically kinetic energy per unit volume. Obviously, the effect of the non-Darcy term varies with the square of the velocity, so at lower flow rates (such as for oil flowingthrough a permeable rock) this effect is negligible. However, at high flow rates (such as forgas flowing through a highly permeable fracture) this term becomes highly significant and can

produce a pressure gradient many times greater than that caused by Darcy flow.

Obviously, the magnitude of the non-Darcy effect is also highly dependent upon the betafactor. The magnitude of beta is determined by a number of factors, but experimentaldetermination of beta factors, has revealed two relationships:-

β ∝ D ................................................................................. (10.5)

where D is the average grain diameter, and:-

β ∝ 1

k p ........................................................................... (10.6)

It is also true that artificial proppants tend to have lower beta factors than naturally occurringsands, due to their greater sphericity and roundness. In practice, beta factors have beendetermined for a wide range of proppants and closure stresses, and can be easily obtainedfrom the proppant manufacturers, such as in Table 10.1:-

Closure β , atm sec2 /gramStress, psi 12/18 16/20 20/40

2000 0.0001 0.0001 0.00024000 0.0002 0.0002 0.00036000 0.0007 0.0003 0.00048000 0.0018 0.0007 0.0007

10000 0.0023 0.0015

Table 10.1 – Beta factor data for CarboLite artificial ceramic proppant (Carbo Ceramics Inc )





As the expected production rate from the treatment increases, so does the pressure loss dueto non-Darcy effects, and this should always be taken into account when selecting proppantand predicting production increase.

References

Wright, C.A., Weijers, L., and Minner, W.A.: Advanced Stimulation Technology Deployment Program , report GRI-09/0075, Gas Research Institute, March 1996

Cleary, M.P, et al .: ”Field Implementation of Proppant Slugs to Avoid Premature Screen-Outof Hydraulic Fractures with Adequate Proppant Concentration”, paper SPE 25892, presentedat the SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium, Denver CO,April 1993.

Kogsball, H.H., Pits, M.J., and Owens, K.A.: “Effects of Tortuosity in Fracture Stimulation ofHorizontal Wells – A Case Study of the Dan Field”, paper SPE 26796, presented at theOffshore Europe Conference, Aberdeen, UK, Sept 1993.

Nolte, K.G.: “The Application of Fracture Design Based on Fracturing Pressure Analysis”,paper SPE 13393, SPEPE (Feb 1988) p31-42.

Nolte, K.G., and Smith, M.B.: “Interpretation of Fracturing Pressures”, paper SPE 8297, JPT (Sept 1981) p1767-75.


Vreeburg, R-J., Davies, D.R., and Penny, G.S.: “Proppant Backproduction During HydraulicFracturing – A New Failure Mechanism for Resin Coated Proppants”, paper SPE 27382, JPT ,1994.

Ely, J.W.: “Experience proves forced closure works”, World Oil , Jan 1996, p 37 – 41.

Rickards, A., et al .: “Need Stress Relief? A New Approach to Reducing Stress CyclingInduced Proppant Pack Failure”, paper SPE 49247, presented at the SPE Annual TechnicalConference and Exhibition, New Orleans, Sept 1998.

Forcheimer, P.: Wasserdewegung durch Boden. ZVDI (1901), Vol. 45, p. 1781. (in German)

Martins, J.P., Milton-Taylor, D, and Leung, H.K.: “Effect of non-Darcy Flow in ProppedHydraulic Fractures”, paper SPE 20709

Vincent, M.C., Pearson, C.M., and Kullman, J.: “Non-Darcy and Multiphase Flow in ProppedHydraulic Fractures: Case Studies Illustrate the Dramatic Effect on Well Productivity”, paperSPE 54630, presented at the SPE Annual Technical Conference and Exhibition, Houston, Oct1999.



BJ Services’ Frac Manual11. 3-D Fracture Simulators


11. 3-D Fracture Simulators

The three main fracture simulation models used in the industry today are FracPro , FracproPT and MFrac . Between them, they are used on well over 90% of all treatments currently

performed. Other simulator’s, such as StimPlan , GOHFER and the proprietary simulatorsproduced by Schlumberger , Halliburton , Shell and others, are available, but their use islimited mainly to Engineers who work for the actual company that produced the simulator.

Most of the 3-D and lumped-parameter 3-D simulators described below are produced bycompanies whose main tasks are producing software or providing a fracturing service. Assuch, there is a considerable amount of detail concerning these simulators that is proprietaryand not available in the public domain. Therefore, detailed descriptions of the actualalgorithms behind the model are not possible and in any case beyond the scope of thismanual. The reader is referred to the references for more information. The term pseudo orlumped-parameter 3-D is applied to most of the simulators, as they relate everything back to asingle characteristic dimension (usually fracture half-length), which is found by a variety ofmethods. Fully 3-D models have every dimension as independent variables.

As stated, most simulations are performed by one of three simulators (and it should be notedthat FracPro and FracproPT are essentially the same model). In the industry, there is aperception that the FracPro -FracproPT model is more applicable to low permeability “hard”formations, whilst the MFrac model is more applicable to high permeability “soft” formations.The reliability of this perception is a matter of some debate, but it may be due to therespective origins of the two models. In any case, it should be remembered that the producersof these simulators are all competitors. Most of the discussions about the relative merits ofeach model are subjective and partisan.

For a discussion on the limitations of the 3-D fracture simulators, refer to the discussion onpressure matching in Section 19.1.

11.1 RES’ FracPro and Pinnacle Technologies’ FracproPT

FracPro and FracproPT originally started out as onesimulator, FracPro . The model was originally developedusing funding from the Gas Research Institute , a joint USGovernment and gas industry funded organisation.Eventually, a company called Resources Engineering Systems (RES) produced a commercial simulator based onthe work carried out by the GRI. However, a couple ofyears ago, a group of people dissatisfied with thecompany’s approach, split away from RES and moved overto Pinnacle Technologies. For a variety of reasons, they

were able to take the FracPro technology with them and FracproPT was the result. At thispoint in time, there is very little difference between how the two models work. The majordifferences between the two models concentrate on the way they interface with the user, andwith the on-screen graphics.

The FracPro approach has almost entirely done away withthe traditional concept of fracture toughness, which meansthat users of simulators based on this model find thatchanges to input fracture toughness values have little or noeffect on fracture geometry. Instead the theory states thatdeep underground, the effect of the confining stress ismuch more significant than the effect of the fracturetoughness. Thus K lc can be ignored if the followingcondition is satisfied;





σ p R >> K Ic ................................................................................ (11.1)

where R is the radius of the fracture and is analogous to the characteristic fracture lengthused in classical linear elastic fracture mechanics. The above Equation shows us that fracturetoughness is more significant for small fractures in shallow formations, such as during skinbypass fracturing.

The fracturing fluid does not penetrate to the very end of the fracture. This means that there is

a very rapid change in net pressure at a distance ω from the tip of the fracture. If the conditiondescribed in the above Equation is satisfied, then ω can be found as follows;

ω ≈ R2

P net

P net + P c

2 ....................................................... (11.2)

Because the fluid does not penetrate into the tip of the fracture, energy is lost as the tip of thefracture deforms. It is postulated that this deformation occurs in a non-linear or dilatentfashion (see Section 9.2). This crack tip dilatency reduces the energy left for the fracturingfluid to propagate the fracture, and hence reduces the size of the fracture, for a given P net.Once the energy absorbed by the fracture tip has been found, the model then goes on tosolve the fracture geometry using a series of Equations which relate mass conservation,energy conservation, fluid dynamics and heat transfer. The model is 3-dimensional, allowingseparate rock mechanical and reservoir properties to be input for each different rock strata.

This model was the first to incorporate various aspects that are now taken as standard, suchas near wellbore friction, proppant convection and multiple fractures. This model alsoincorporates a data conversion and editing facility, an acid fracture simulator and a simpleproduction simulator.

Although all of the three main simulators can model the fractures real time, only FracPro andFracproPT have the ability to predict forward to the end of a job, whilst in the middle of atreatment. This is a very powerful tool, which allows the fracture characteristics can be

predicted in the middle of a treatment. The model takes the treatment data received up to thatpoint, and then uses the remaining input treatment schedule to predict the fracture at the endof the treatment. Thus the Frac Engineer can “see how things are going” based on actualtreatment data, and alter the treatment schedule as the job is being pumped. So far no othercommercially available simulator has mastered this.

11.2 Meyers & Associates’ MFrac

MFrac is produced and developed by Meyer and Associates. This methodology sticks muchmore closely to the conventional Linear ElasticFracture Mechanics (LEFM) approach to fracturepropagation, than the FracPro/FracproPT

approach. The model uses the basic LEFMcriterion, which states that in order for the fractureto propagate, the stress intensity factor (K ) must

be greater than K Ic (the critical stress intensity factor, or fracture toughness). It uses a

characteristic length (referred to as H ξ) and a geometry factor, γ , in the classic LEFMEquation:-

σ c = K Ic

γ H ξ

........................................................................... (11.3)

The actual value for g depends upon the fracture model being used (PKN, KZD, Ellipsoidal or3-D), as does the dimension actually being used for the characteristic length. For the 3-D

model, the characteristic length is found from a set of partial differential Equations, whichrelate mass conservation, mass continuity, momentum conservation, and vertical and lateralpropagation rates.





The authors of this fracture propagation model acknowledge that there is a “tip over-pressure”effect that cannot be accounted for. This is handled by using an “over-pressure factor” - thathas to be obtained empirically - or by using huge values for fracture toughness.

11.3 Other Simulators

StimPlan

StimPlan is a pseudo 3-D numerical simulator produced by NSI Fracturing Technologies . Thesimulator works by performing implicit finite difference solutions to basic Equations of massbalance, elasticity, height growth, and fluid flow. The simulator is based on LEFM. It isprobably the most widely used of the non-FracPro / FracproPT / MFrac simulators.

Recently, NSI have started introducing E-StimPlan , a fully 3-D fracture simulator. Thissimulator divides the formation into a series of grids of variable size, allowing fully 3-D fracturegrowth and irregularly-shaped fractures (as opposed to the elliptical fractures almost alwayspredicted by the lumped–parameter 3-D models). This model also allows 2 dimensional

proppant transport. At the time of writing this manual, this simulator is still too slow forpractical use, but shows great promise

GOHFER

GOHFER (Grid Orientated Hydraulic Fracture Extension Replicator) has taken a completelydifferent approach to modelling fracture growth. Of the four main models described, onlyGOHFER and E-StimPlan said to be fully 3-D and only GOHFER has a significant history ofuse. The model takes a finite element approach to fracture propagation, modelling thereservoir and the formations above and below it as a series of elements, rather than as acontinuum. The fracture propagates along a plane between elements, so in order to producefracture width, elements either side of the fracture have to be compressed. At the fracture tip,

there is a single element just ahead of the fracture, so that the tip is positioned at some pointon the side of the element. Fracture propagation occurs when the tensile stress in theelement exceeds the failure criterion for the material, and the element splits into two pieces,along the plane of the fracture. The fracture has then propagated by a distance equal to thewidth of the element.

The advantages of this approach are that it is very simple to give each element its own set ofrock mechanical and reservoir properties, making simulation of multiple formations very easy.The main disadvantage is the use of a tensile failure criterion, which tends to make hard rocksharder to fracture than soft rocks, which tends to be the opposite way around to conventionaltheories. Additionally, because each element in the model can be assigned individual rockmechanical and leakoff properties, it is very easy to "dial-a-frac", that is, produce a fracturegeometry that has more in common with uses wishes than with reality.

References

Crockett, A.R., Okusu, N.M., and Cleary, M.P.: “A Complete Integrated Model for Design andReal-Time Analysis of Hydraulic Fracturing Options”, paper SPE 15069, presented at the 56

th

California Regional Meeting of the SPE, Oakland CA, April 1986.

Cleary, M.P., Wright, C.A., and Wright, T.B.: “Experimental and Modeling Evidence for MajorChanges in Hydraulic Fracturing Design and Field Procedures”, paper SPE 21494, presentedat the SPE Gas Technology Symposium, Houston TX, Jan 1991.

Johnson, E., and Cleary, M.P.: “Implications of Recent Laboratory Experimental Results for

Hydraulic Fracturing”, paper SPE 21846, presented at the SPE Rocky Mountain RegionalMeeting and Low Permeability Reservoirs Symposium, Denver CO, April 1991.





Wright, T.B., Aud, W.W., Cipolla, C., Perry, K.F., and Cleary, M.P.: “Identification andComparison of True Net Fracturing Pressures Generated by Pumping Fluids with DifferentRheology into the Same Formations”, paper SPE 26153, presented at the SPE GasTechnology Symposium, Calgary, Alberta, Canada, June 1993.

FracPro Version 8.0 onwards On-Line Help, RES/Gas Research Institute, March 1998onwards.

FracproPT Version 9.0 onwards On-Line Help, Pinnacle Technologies/Gas ResearchInstitute, July 1999 onwards.

Meyer, B.R.: “Design Formulae for 2-D and 3-D Vertical Hydraulic Fractures: ModelComparison and Parametric Studies”, paper SPE 15240, presented at the SPEUnconventional Gas Technology Symposium, Louisville KY, May 1986.

Meyer, B.R.: “Three Dimensional Hydraulic Fracturing Simulation on Personal Computers:Theory and Comparison Studies”, SPE 19329, presented at the SPE Eastern RegionalMeeting, Morgantown WV, Oct 1989.

Meyer, B.R., Cooper, G.D., and Nelson, S.G.: “Real-Time 3-D Hydraulic FracturingSimulation: Theory and Field Case Histories”, paper SPE 20658, presented at the 65

th SPE

Annual Technical Conference and Exhibition, New Orleans LA, Sept 1990.

Hagel, M.W., and Meyer, B.R.: “Utilizing Mini-Frac Data to Improve Design and Production”,Journal of Canadian Petroleum Technology , March 1994, pp. 26 – 35.

MFrac III Version 3.5 (onwards) On-Line Help, Meyer and Associates Inc, December 1999onwards.

NSI Fracturing Technologies Web Site, www.nsitech.com

Barree, R.D.: “A Practical Numerical Simulator for Three-Dimensional Fracture Propagation inHeterogeneous Media”, paper SPE 12273, presented at the SPE Reservoir SimulationSymposium, San Francisco CA, Nov 1983.

StimLab division of CoreLab, Web Site, www.corelab.com/StimLab/Depts/GOHFER_ prodinfo.asp, 2002 onwards.



BJ Services’ Frac Manual12. Predicting Production Increase


12. Predicting Production Increase

Being able to accurately predict a production increase from a formation is an important part ofthe process of designing a frac treatment. All treatments have to be economically justifiable,

before approval by the operating company. In order to be able to produce an economic justification, the Engineer must have a reasonable idea of what the post fracture productionincrease will be. Moreover, this prediction must be reliable, as the Engineer will have a hardtime justifying subsequent treatments, if previous justifications have proved to be inaccurate.

In order to be able to produce an accurate prediction of the increase in production, theEngineer needs accurate pre-treatment production data. Items like permeability, skin factor,BHP and downhole producing rate are all critical. If accurate values for items such as thesecannot be obtained, then the subsequent predicted production increase will also beinaccurate.

Nevertheless, because of the uncertainties associated with most of the data used in theanalyses below, any estimate of post fracture production remains just that – an estimate. The

Frac Engineer must make this clear to any customer. As a result, it is often more reliable tobase post-treatment production estimate on the results of offset wells, if any are available.

12.1 Steady State Production Increase

Steady state production is when all reservoir parameters remain unchanged during theproduction process. Items such as radial extent and reservoir pressure are fixed. Most of thetime this does not exist, and the reservoir is at least in a pseudo-steady state (see below).Consequently, production increases based on steady state are an approximation only.

However, they are often useful as a “first look”, “back-of-the-envelope” calculation, to quicklysee if a fracture is viable or not.

Darcy’s Equation (which is for steady state flow only) can be expressed as follows for a skindamaged reservoir:-

q = 0.00708 k h ∆P

µ ln[r e / (r w e-S

)] ............................................................ (12.1)

where q is the downhole producing rate in bpd, k is the effective reservoir permeability in md,h is the net height of the formation in ft, ∆P is the pressure differential between the edge ofthe reservoir and the wellbore (the drawdown ) in psi, µ is the downhole viscosity of thereservoir fluid in cp, r e is the radial extent of the reservoir, r w is the wellbore radius and S isthe skin factor (dimensionless). Note that r e and r w should always have the same units,

usually either feet or inches.

To provide a fair comparison between production at different times, which may be at varyingdrawdown, the productivity index, J , is usually used instead of the production rate. The unitsof productivity index (or PI) are usually bbls/day/psi, or bpd/psi.

J =0.00708 k h

µ ln[r e / (r w e-S

)] ................................................................ (12.2)

To avoid confusion, the symbol J will be used to signify the PI from a real, damaged reservoir.J o is used to represent the PI from an undamaged reservoir and J f for the fractured reservoir.

In Darcy’s Equation, the term kh is often referred to as the permeability-thickness, or

conductivity. This equates to the fracture conductivity, F c, of the propped fracture. By





replacing the term kh with F c we can obtain an expression for the PI of the fracturedreservoir:-

J f =0.00708 F c µ ln(r e /r w)

.................................................................... (12.3)

Equation 12.3 should be used with some caution. As explained earlier, this is a steady stateapproximation to a situation that in reality is far from steady state. The Equation no longeruses the skin factor term, as it is assumed that the fracture has completely bypassed the skin,rendering it irrelevant. This Equation also assumes that all production into the wellbore comesvia the fracture. This is a valid assumption for fractures with a very high C fD, but becomes lessand less accurate as the contrast between the fracture and reservoir conductivity becomeslower. Indeed, if the fracture conductivity is too low, this method may actually predict aproduction decrease – something that is theoretically impossible, unless the fluid or proppantsomehow damages the formation. This Equation also assumes that the formation has nodifficulty delivering reservoir fluids to the fracture – the Equation is independent of fracturelength.

Nevertheless, Equation 12.3, still provides a “first guess” to see how viable a fracture

treatment is. However, it is less accurate for low permeability reservoirs and for fractureswhich relatively low fracture conductivity.

The “folds of Increase” (J f / J ) can be calculated, by dividing Equation 12.3 by Equation 12.2,which gives the following:-

J f

J =

F c

kh

ln[r e /(r we

-s )]

ln(r e / r w) ......................................................... (12.4)

Another way of getting a “quick look” at potential post-treatment production is simply to use askin factor of -5 in Equation 12.1.

12.2 Pseudo-Steady State Production Increase

Pseudo-steady state flow is when the reservoir has been producing for a sufficient period oftime, so that the effects of reservoir boundary can be felt. In practical terms, this means thatthe reservoir has an outer boundary.

Figure 12.2a – Transient production. The red lines illustrate the variation of pressure withdistance from the wellbore, as time increases. The radius of the disturbed formation iscontinually increasing

r w r eDistance from Well

P r e s s u r e

0

P wb

P r

Increasing

Time

Radius of DisturbedFormation





As the well is produced, the radius from the wellbore at which the reservoir has beendisturbed by production increases at a rate proportional to the square root of the producingtime. During this period, flow into the wellbore can be described as transient, as the effectiveradial extent of the reservoir is continually increasing. However, at some point the area offormation disturbed by the production from the well will hit an outer boundary. At this point,the radial extent of the reservoir ceases to expand, and the reservoir pressure starts to fall. At

this point, the reservoir switches from transient to pseudo-steady state. The differencebetween transient and pseudo-steady state is illustrated in Figures 12.2a and b.

Figure 12.2b – Pseudo-steady state production. The radius of the disturbed formation hasreached the reservoir boundary, r e, and now the reservoir pressure is decreasing

Most reservoirs will spend the majority of their producing lives in pseudo-steady stateproduction.

McGuire and Sikora

The best known method for predicting production increase during pseudo-steady stateproduction was developed in 1960 by McGuire and Sikora. This work was based on earlierwork carried out on electrical circuits by Dyes, Kemp and Caudle. Basically, they used aseries of resistors and capacitors to represent the reservoir – resistors to representpermeability (the lower the resistance the higher the permeability), capacitors to represent theporosity or storage capacity of the reservoir, voltage to represent pressure and current torepresent flow rate.

These experimentally-derived curves, shown in Figure 12.2c, define for a given dimensionless

fracture length (L/r e) and a given fracture relative conductivity (see below – note that thisdefinition is different from that used throughout the rest of this manual), the dimensionlessproduction increase that can be expected. McGuire and Sikora used L for fracture half length,instead of the usual x f.

Note that the following use a different system of nomenclature than the rest of this manual:-

Relative conductivity =Wk f k

40 A

................................................... (12.5)

where W is the average propped fracture width in inches, k f is the permeability of the proppantin md, k is the formation permeability in md, and A is the well spacing in acres.

r w r eDistance from Well

P r e s s u r e

0

P wb

P r

IncreasingTime





Figure 12.2c – The McGuire-Sikora Curves

Dimensionless fracture half length =Lr e

........................................... (12.6)

Where L is the fracture half-length (x f normally) in feet and r e is the reservoir drainage radiusor radial extent, also in feet.

Dimensionless production increase =

J

J o

7.13

ln 0.472 (r e / r w) .......... (12.7)

Where J is the pre-frac productivity index, J o is the post-frac productivity index (J f normally)and r w is the wellbore radius.

McGuire and Sikora is an approximation based on the limits of the experimentation theyconducted. The main assumption is that the fracture is significantly more conductive than the

formation, so that the main rate limiting variable is the fracture half length. Vertical fluid flow isassumed to be negligible, fluids are assumed to be incompressible and in single-phase flowand skin factor is assumed to be zero. However, it is often relatively easy to find theproduction increase if the skin was reduced to zero. The McGuire-Sikora production increasecan simply be added to this.

Skin Bypass Fracs

Rae et al presented a simple method for predicting the production increase from a skinbypass frac. It combines elements of the McGuire-Sikora and Prats methods and allows forthe existence of a skin factor:-

J f

J =

ln[r e /(r w . e-S )]ln[4/(F cd . x fD)] ................................................................ (12.8)

0

2

4

6

8

10

12

14

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

k = AVERAGE FORMATION PERMEABILITY, md.(BASED ON GROSS THICKNESS)

L = FRACTURE LENGTH FROM WELL BORE, Ft.

re= DRAINAGE RADIUS, FEETA = WELL SPACING, ACRESWkf = CRACK CONDUCTIVITY, md-in.W = PROPPED WIDTH OF FRACTURE, in.kf = PERMEABILITY OF PROPPING

MATERIAL, md.rw = WELL BORE RADIUS, FEETJ = PRODUCTIVITY INDEX AFTER

FRACTURINGJo= PRODUCTIVITY INDEX

BEFORE FRACTURING

Wkf

k40A

Wkf

k40A

7 . 1 3

l n 0 . 4 7 2

r e r w

7 . 1 3

l n 0 . 4 7 2

r e r w

L/re = 1.0

.9

.8

.7

.6

.5

.4

.3

.2

.1

RELATIVE CONDUCTIVITY,

J / J o





This method is valid for fracture with a C fD greater than 1 – i.e. more conductive than theformation.

12.3 Nodal Analysis

The most modern method for predicting production increase is the Nodal Analysisprogramme. These simulators work by analysing the flow from the reservoir at a node, whichcan be down hole at the “sand face”, at the wellhead or at some distance from the wellhead ina separator. By defining the flowing conditions at this node, the software can then calculateback to the flow rate from the reservoir.

Nodal analysis can be used to produce inflow performance relationship (IPR) curves, whichrelate the ability of the reservoir to deliver fluids, with the ability of the completion to carryfluids out of the reservoir. These curves are particularly useful for oil wells with a GOR (i.e.real wells and not “black oil” approximations), gas wells and wells producing at significantwater cuts, where the ability of the completion to carry the fluids is not always easy orstraightforward to calculate. Figure 12.3a shows an example for a gas well with a fracture ofvarying average propped fracture width.

Figure 12.3a – Nodal analysis IPR curves for a gas well with a fracture of varying propped

fracture width.

With reference to the example in Figure 12.3a, note the following points:-

• The blue curves represent five different production scenarios. In this case, each curverepresents varying propped fracture width. However, they could just as easily be varyingskin factor, permeability or water cut. This ability to test the sensitivity of the system tovarying producing scenarios makes nodal analysis very powerful.

• The blue curves are the inflow curves. For these, the node is fixed at bottom hole (or the“sand face”). Each of these curves represents the inflow into the well from the formationfor hydrocarbons at various FBHP’s (flowing bottom hole pressures). The drawdown isthe difference between the reservoir pressure and the FBHP, so the smaller the FHBP,the greater the drawdown.

• The red curve is the outflow or tubing curve. This represents the ability of the completionto carry the hydrocarbons out from the well. In this case, the node is fixed at the wellhead.A set of wellhead conditions are specified, and then the software calculates (for a fixed

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000 6000 7000

Gas Rate, mscfpd

F

B H P , p s i

Average ProppedFracture Width, inches

0.1 0.2 0.3 0.50.4

Tubing





FWHP – flowing wellhead pressure – and surface temperature) what the bottom holepressure must be for a variety of different flow rates.

• The point at which the red curve and the blue curve cross represents the point at whichthe two sets of conditions coincide. Therefore, this is the rate and FBHP at which the wellwill produce. For instance, in Figure 12.3a, for a frac width of 0.2 inches, the well will flowat 4250 mscfpd at a FBHP of +/- 1450 psi.

Most nodal analysis programmes allow the user to produce the well through a proppedhydraulic fracture of varying geometry. This is very useful to the Frac Engineer, who may wellend up spending more time with the nodal analysis than with the fracture simulator.

When using nodal analysis to predict production increase, the following steps should befollowed:-

1. Get production data from the well. If the well is new, get production data from an offset. Ifno offsets are available, use the well test data.

2. History match the production data with the nodal analysis (and without a fracture beingpresent). Vary items such as skin factor, permeability and reservoir pressure to make thenodal analysis production match the historical production data. The nodal analysis

production simulator is now tuned to the real data.3. Introduce a fracture. Vary characteristics such as fracture length and fracture conductivity

(or average propped width) to produce the biggest possible increase in production.4. Be aware of what is achievable and what is efficient. For instance, the nodal analysis may

indicate that doubling the fracture length gives an extra 50% production. What it does nottell you is that doubling the fracture length means at least 4 times as much proppant, 8times as much fluid and a corresponding increase in equipment. Such an increase in jobsize may not be practical and could well be uneconomic.

5. Once the optimum fracture geometry has been obtained, go to the fracture simulator anddesign a treatment to make a fracture of these dimensions. Often, it is at this point thatthe Engineer finds out what is realistically achievable and so the final design may be theproduct of several alternating runs on both the nodal analysis and the fracture simulator.

References

Prats, M.: “Effect of Vertical Fractures on Reservoir Behaviour – Incompressible Fluid Case”Trans AIME (1961), 222 105-118

Dyes, A.B., Kemp, C.E. and Caudle, B.H.: “Effect of Fractures on Sweep-Out Pattern”, Trans AIME (1958), 213, 245

McGuire, W.J. and Sikora, V.J.: “The Effect of Vertical Fractures on Well Productivity”, Trans AIME (1960), 219, 401-403



Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,paper SPE 54673, presented at the 1999 SPE Annual Technical Conference and Exhibition,Houston, Texas, Oct 3–6 1999.

Archer, J.S. and Wall, C.G.: Petroleum Engineering Principals and Practices , Graham &Trotman, London, 1986.

Perform (Well PERFORMance Analysis TM

) Nodal Analysis Software, version 3.00 and higher,PSG/IHS Energy Group, Richardson, Texas, USA, 1999 onwards.



BJ Services’ Frac Manual13. Candidate Selection


13. Candidate Selection

Virtually any zone in any well is a potential candidate for hydraulic fracturing. Given a freehand, it is possible to produce an increase in productivity index in almost any formation using

hydraulic fracturing. However, often the Frac Engineer is limited by considerations such aswater-oil contacts, gas-oil contacts, poor cement bonding, completion restrictions andplacement of perforations. Moreover, the formation must also have the reserves andproduction potential to economically justify the large expense often associated with fracturing.

This section of the manual is designed as a guide to the science and art of frac candidateselection. Guidelines will be given, as to when an interval is a good candidate for fracturingand when it is not. However, there are often considerable “grey areas” between goodcandidates and poor candidates. In these cases, there is no substitute for experience.

It should never be forgotten that the best wells are also the best candidates for fracturing.Fracturing cannot add reserves (although economically recoverable reserves and drainageefficiency can be improved) nor can it increase reservoir pressure – if there is nothing there to

start with, there will be nothing there afterwards. A 50% increase in production from a goodwell is often more valuable than a 500% increase from a poor well.

13.1 Economic Justification for Fracturing

Fracturing – as with any other operation performed on an oil or gas well – has to beeconomically justified. That is to say, the increased revenue generated by the treatment mustsatisfy economic criteria set by the operating company. This is vitally important – it is notenough for the Frac Engineer to simply produce a production increase. Instead, the FracEngineer must usually either produce at least a minimum production increase or increaseeconomically recoverable reserves, in order to meet the economic criteria.

Part of the skill in designing a fracture treatment is deciding whether or not these economic justifications can be met. An inability to meet these criteria is adequate grounds for rejecting awell as a candidate for fracturing. However, given that a treatment such as a skin bypassfracture can cost less than $20,000 to carry out, usually any reasonable criteria can besatisfied, unless the well has very low productivity indeed.

Economic criteria can often be simple. For instance, many companies insist that the cost ofthe treatment be paid back within a period of three months. In such a case, the Frac Engineerhas to estimate the increase in production and from that the total extra production over thefirst three months. Once the extra production has been calculated, the total extra revenue caneasily be calculated by multiplying by the oil or gas price, as appropriate. If the total extrarevenue is greater than the cost of the treatment, then the treatment is economically justified.

All parties involved in the fracturing operation must be willing to accept a certain element ofrisk. Fracturing is not an exact science. Although many of the theories associated withfracturing are very rigorous and thoroughly proven, the fact remains that they are only asgood as the available data. Often this data is of poor quality or is absent entirely. Even whenconsiderable time, effort and expenditure have been taken to obtain data, it is usually onlyvalid for a few inches around the wellbore. In order to complete a frac design, the Engineerhas to assume this data is valid for sometimes hundreds of feet from the wellbore,encompassing a huge volume of rock. In addition to this lack of adequate data, the FracEngineer also has to cope with the fact that no one really understands how the fracturepropagates through the formation. This is illustrated by the fact that there are several differentfracture simulators on the market, all using different methods to model the fracture.

This uncertainty regarding how the fracture will propagate is in addition to the standard risksassociated with any operation on an oil or gas well.





Internal Rate of Return

Many operating companies use a criterion known as the Internal Rate of Return. This is apercentage value, and any potential project requiring an AFE (Authorisation For Expenditure),must make a return on investment greater than this value. The theory is that the companywould be better off spending the money elsewhere if a project cannot meet this criterion. Forinstance, if a Company Man wishes to spend $1,000,000 on a project, and his company hasan internal rate of return criterion of 18% over one year, then the expenditure of $1,000,000must generate additional production worth at least $1,180,000 in the first year after thetreatment.

The internal rate of return is also referred to as the discount factor, or DCF.

Net Present Value

Net Present Value (or NPV) is a useful tool that can be used in two ways. First, the operatingcompany can set an NPV criterion that has to be met. Secondly, it can be used to comparedifferent fracture designs, and decide which one is the most cost effective. For instance, aFrac Engineer may be confronted with the following question – is it worth pumping twice the

quantity of proppant for only a 10% gain in production ? This question can be answered byusing NPV analysis.

NPV is calculated using the following method:-

Net Revenue = Production Increase x Price ...................................... (13.1)

where the Production Increase is the total extra production due to the fracture treatment.

Discounted Revenue =

Net Revenue for year X

(1 + i )X .................................. (13.2)

where n is the payback period, usually measured in years, and i is the internal rate of return,

expressed as a fraction.

NPV = Discounted Revenue – Total Treatment Costs ............. (13.3)

Remember that the Total Treatment Costs are the total cost that the customer has to pay,which includes the cost of the frac job (i.e. BJ’s ticket), plus items such as rig time, workovercosts, wireline work, well testing, coil tubing etc.

Example – NPV Calculation

Calculate the NPV, given the following data:-

Oil price $20 per bbl

Payback period 3 yearsInternal rate of return 15%Total treatment costs $1,250,000Production gain, yr 1 400,000 bblsProduction gain, yr 2 200,000 bblsProduction gain, yr 3 100,000 bbls

Therefore

Net Revenue, yr 1 = 400,000 bbls x $20 per bbl= $8,000,000

Net Revenue, yr 2 = 200,000 bbls x $20 per bbl

= $4,000,000

n

X = 1





Net Revenue, yr 3 = 100,000 bbls x $20 per bbl= $2,000,000

And so

Discounted Revenue, yr 1 =

$8000000

(1 + 0.15)1

= $6,956,522


$4000000

(1 + 0.15)2

= $3,024,575


$2000000

(1 + 0.15)3

= $1,315,032

Therefore

Total Discounted Revenue = $6,956,522 + $3,024,575 + $1,315,032= $11,296,129

And finally

NPV = $11,296,129 - $1,250,000= $10,046,129

Now, let’s return to the Engineer’s original question - is it worth pumping twice the quantity of proppant for only a 10% gain in production?

Let’s say that the cost of the actual fracturing was $500,000, and of that, the cost of theproppant was $200,000 and the cost of the fluid was $50,000. If we double the amount ofproppant, we will probably need to at least double the amount of fluid. So the cost of the frac

job goes up by $250,000. The final cost of the frac is now $750,000 and the overall cost of thetreatment is now $1,500,000.

A 10% increase in production gives us the following:-

Production gain, year 1 = 440,000 bblsProduction gain, year 2 = 220,000 bblsProduction gain, year 3 = 110,000 bbls

So thatDiscounted Revenue, yr 1 = $7,652,174Discounted Revenue, yr 2 = $3,327,033Discounted Revenue, yr 3 = $1,446,535

andTotal Discounted Revenue = $12,425,742

which givesNPV = $12,425,742 - $1,500,000

= $10,925,742

So the answer to the Engineer’s question is yes – in this case, using a payback period of 3years and an internal rate of return of 15%, it is worth doubling the volume of proppant.

So the answer to the Engineer’s question is yes – in this case, using a payback period of 3years and an internal rate of return of 15%, it is worth doubling the volume of proppant.

Of course, two other things that the Frac Engineer must consider are;





1. Can the customer afford the increase in the initial treatment cost? Small operators cannotalways generate enough cash flow to do this.

2. Is it physically possible to place twice as much proppant in the fracture? Is this to beaccomplished by increasing the fracture length, width or by some combination of the two?

In more remote locations the Frac Engineer must also make sure that the equipment neededto store and blend the extra fluids and proppant is available.

13.2 Completion Limitations

Tubing Cooldown

As relatively cold fracturing fluid is pumped down a completion, the tubing will start to cooldown. As it cools down, it will shrink and decrease in length. On some wells, this can result inshrinkage of several feet

Usually, wells are completed using packers with polished seal bores, and tubing with sealassemblies. When the completion is run, the packer is set at the required depth. Then thetubing is run, complete with a seal assembly on the bottom.

The seal assembly is a length of pipe with a number of rubber seals on the outside. The ideais that these seals slide into the polished bore of the production packer, providing the requiredisolation. The seal assembly is usually several feet in length, so that it can slide up and downinside the polished bore, allowing the tubing to expand or contract whilst still retainingcompletion integrity.

However, if the tubing is cooled down too much, the seal assembly can sting right out of thepolished bore, and the completion will loose its integrity. This is highly undesirable.Additionally, as the tubing re-heats after the treatment, it probably will not sting back into the

polished bore, and thus will produce additional stress on the packer, wellhead and othercompletion components.

In order to prevent this from happening, special software programmes are used to simulatethe effects of tubing shrinkage, to predict if the tubing will shrink too much. BJ’s programmefor predicting this is DTools .

There are two obvious answers to a tubing cool down problem:-

1. Reduce the size of the treatment, so that the tubing does not get cooled down asmuch, or pump the treatment at a lower rate, so that the fluid heats up more as ittravels down the well.

2. Heat up the treating fluid before it goes down the well. This can be done in two ways.The first way is to pump the fluid through a heat exchanger, which contains a hotfluid, such as steam or burning oil. Such heat exchangers are often called “hot oilers”.The advantage of this system is that it can be used on the fly. The second way is tocirculate the fluid through a choke, using the high-pressure frac pumps. A frac tank offluid circulated through a choke can be quickly heated up – if the choke is set smallenough so that the pumps can develop significant horsepower. 4000 HHP producesthe approximately the same amount of energy as a 3MW power plant. Thedisadvantages of this method is that heating multiple frac tanks can be very timeconsuming, and individual tanks will cool down as other are heated up. Therefore, hotoilers tend to be used for large treatments, whilst pumping through a choke is usedfor smaller treatments.





Tubing Expansion

Another effect of fracturing on tubing is to cause its expansion, due to an elevated internal –orburst – pressure. This increase in diameter is usually not too much of a problem. However, asthe tubing expands radially and circumferentially, it also contracts axially, reducing the lengthof the tubing string.

Obviously, the effect of tubing expansion and the effect of tubing cool down will combine toproduce an even worse effect. Once again, software must be used to model these effects.

There are two ways to help mitigate the effects of tubing expansion:-

1. Put pressure on the outside of the tubing, as it is an increase in the differentialpressure across the tubing wall that causes the expansion. However, this is notalways possible – especially on a completion with multiple packers. If it is possible,the maximum allowable pressure may be insufficient.

2. Reduce the pumping rate. Obviously, the BHTP is pretty much fixed. However, byreducing the rate, and hence the friction pressure, the internal pressure that most ofthe tubing experiences can be reduced.

Maximum Wellhead Pressure

Often, a treatment will be constrained by a low maximum wellhead pressure. It is very rarethat a treatment is completely prevented by this, but a low wellhead rating can sometimesseverely limit what can be achieved by the treatment.

One solution to this problem is to use wellhead isolation tool or WIT (commonly referred to asa “Tree Saver”). This tool, which is described in detail in Section 20, actually bypasses the

wellhead, by allowing the frac fluid to be pumped directly into the tubing, rather than throughthe wellhead and into the tubing.

Another potential solution to this problem is to reduce the friction pressure. This can be doneby either reducing the pumping rate or by altering the friction properties of the fluid (which canbe done by either reducing the polymer loading or by delaying the crosslink). Both of theseparameters are usually flexible to a certain extent. However, some wells have a frac gradientso high that even with zero friction pressure, the maximum wellhead pressure is exceeded.

A third method for reducing the wellhead pressure is to pump a high density frac fluid. Thishas the effect of increasing the hydrostatic head, which in turn lowers the wellhead pressure.These fluids are usually mixed using high density brine. Potassium chloride brines can beused up to about 9.6 ppg, sodium chloride to about 10 ppg and calcium chloride to 11.0 ppg.

Above that, things start to get expensive and considerably less environmentally friendly.Examples of materials used to weight brine above 11.0 ppg include caesium formate and zincbromide. It should also be remembered that heavy-weight brines are harder to recover fromthe well after the treatment

Completion Jewelry

Completion jewelry is a general term, used describe all the various special tools that wereadded to the completion as it was run. Examples include:-

• Sub surface safety valves (SSSV)• Sliding side doors (SSD)

• Gas lift mandrels• Blanks, used to close off gas lift mandrels





• Gauges and gauge carriers• Non-return valves

All of these items will have a pressure rating. Ideally, this should be in excess of the overallpressure rating for the completion. However, this is not always the case, and such itemsshould be checked.

SSSV’s will form a restriction in the completion and may be abraded by the proppant. Thesealways need to be locked open during a treatment, as the potential damage caused by anaccidental closing is not worth the risk. Sometimes this can be performed from the surface,using the hydraulic control lines. In other instances, this has to be performed by installing anisolation sleeve by wireline.

SSD’s can be both beneficial and detrimental to a fracture treatment. They can be beneficial,as they often allow the fracture treatment to be precisely injected into a specific zone. Theycan be detrimental, as they can get stuck both open and closed, and even when fullyfunctional, usually require wireline intervention in order to manipulate them.

Non-return valves should be avoided. Obviously, treatments cannot be pumped through a

non-return valve. Treatments can be placed above a non-return valve, provided the non-return valve is isolated from the treatment by a bridge plug or similar tool.

Justifying a Workover

Often, the only feasible way to fracture a formation is to carry out a workover. This allows thetreatment to be pumped through a dedicated workstring, usually with some kind of packer.Consequently, the Frac Engineer has maximum control over the process – the treatment isplaced in the right interval and the treatment can be pumped at relatively high rates andpressures.

There are two ways to justify a workover; economically and technically. Generally, the first

kind carries all the influence – there are very few companies that will approve a workoverpurely on technical grounds alone, unless there is some kind of research project going on.

Workover operations can vary from the very cheap (such as a shallow land well) to the veryexpensive (offshore, deep water). Consequently, the grounds for justifying such a workovercan also vary. In general, the best way to justify the cost of the workover is to first obtain anestimate for cost of the workover. Then, work out two different production increases. The firstproduction increase assumes that a workover is performed and the Frac Engineer can placethe optimum treatment. The second production increase uses the best stimulation methodavailable, assuming no workover (this may not even be a frac – it could be an acid treatment).Then calculate rate of return and net present value for both of these methods. If the frac +workover generates a better return on investment, then it is economically justified.

Another way to get a workover performed is to frac a well that is already in need of aworkover. Then the costs of the workover can be split between the frac and the existingcompletion programme. Alternatively, a well can be selected for treatment that is in need of aworkover which cannot be economically justified. The combined effects of the frac and theexisting need may be enough to justify the additional expense.

13.3 Things to Look For

Listed below are a number of items that may make an interval a good, or bad, candidate forhydraulic fracturing.

1. Skin Factor. All wells have skin damage, to a greater or lesser extent, unless they

have been stimulated in some fashion. This means that all unstimulated wells areproducing significantly below their full potential. As a general principle, the higher the





permeability, the higher the skin factor – so that the most productive wells are alsothe ones which produce least efficiently. All this means that in practice, all wells arepotential candidates for fracturing.

Figure 13.3a shows the effect skin factor, S , has on the production of a well. Thehorizontal axis shows the well’s original Skin Factor. The vertical axis shows the

effect this has on productivity, relative to the undamaged production (S = 0), so thatproduction from the undamaged well equals 100%. Note that this graph does notinclude the stimulation effects of the frac – it merely illustrates how much productionis lost due to skin factors. A hydraulic fracture will punch a highly conductive paththrough the skin damage, producing a production increase by two methods; throughbypassing the skin damage and through stimulation of the undamaged reservoir.

Therefore, an interval with a high skin factor is a good candidate for fracturing.

Figure 13.3a – The effect of skin factor upon production rate. Note that this Figure is basedpurely on skin factor effects. No fracture stimulation is included.

2. Low Permeability Wells. So-called “tight” formations are where fracturing firstbecame widely accepted by the industry. These formations cannot produce enoughhydrocarbons purely because the rock matrix itself is not conductive enough. Anyproduction loss due to the (usually) low skin factor is generally not significant.Therefore, in order to unlock the potential of the reservoir, a fairly large hydraulicfracture treatment is required.

3. Weak or Unconsolidated Formations. Hydraulic fracturing is a very effectivemethod for completing a weak or unconsolidated formation. Fracturing can helpreduce or eliminate sand production by a number of methods:-

• By reducing the drawdown on the formation• By re-stressing the formation• By acting as a filter, provided the proppant is sized correctly.

A hydraulic fracture can also be used as part of a gravel pack completion, providing aso-called frac and pack treatment. This is probably the most effective way ofdeveloping an unconsolidated formation.

0

20

40

60

80

100

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Skin Factor, S

P r o d u c t i o n R e l a t i v e t o S = 0 , %

r e = 2000 ftr w = 4.25 inches





4. Water and/or Gas Contacts. In general, these are to be avoided. The presence of awater or gas contact close to the perforations can often prevent fracturing. If apropped fracture were to propagate into a water or gas zone, then the well will quicklystop producing oil, and start producing water or gas. Once a propped fracture hasconnected with a water or gas zone, it is very difficult to halt the water or gas

production.

5. Poor Cement Bond. If the bond between the casing and cement, or cement andformation, is poor or non-existent, then fracturing should be avoided. In thesesituations, it is possible to make the poor bond even worse and to connect withseparate formations above and below the zone of interest. However, in the case of a“micro-annulus”, the pressures induced by the fracturing, coupled with the filter-cakebuilding properties of the fluid, will usually permit successful fracturing operations.

6. Corroded Casing or Tubulars. Badly corroded casing or tubulars will probably notstand up to the differential pressures produced by fracturing. Therefore these wellsshould be avoided.

7. Perforation Strategy. The position of the perforations can often prove to be thedifference between a successful and an unsuccessful frac. Section 14 discusses thisin more detail.

8. Logistics. This is a measure of how easy it is to get materials and equipment tolocation. For instance, there is a big difference between a land location a few milesdown the road from the base, and an offshore location on a satellite platform with a 5tonne crane limitation. These two locations may have wells and formation that requiresimilar treatments. However, it is very unlikely that the offshore would be treated inthe same manner to the land well, unless a stimulation vessel was available. Moreoften than not, it is the logistics of the operations – rather than any formationparameters – that has the biggest influence on the treatment.

References







BJ Services’ Frac Manual14. Perforating for Fracturing


14. Perforating for Fracturing

Of all the things under our control, the position, number, size and phasing of the perforationshas the single biggest influence on the effectiveness of the hydraulic fracture treatment. Many

times this is outside of the control of the Frac Engineer, as a high proportion of treatments arecarried out on existing wells that have already been perforated. However, if a well or aninterval is new, the Frac Engineer can often greatly increase the effectiveness of a treatmentby perforating for fracturing, rather than in a more conventional manner.

When perforating for fracturing, it is often desirable to only perforate a very limited section ofwellbore, usually located towards the centre of the gross interval. This controls the point offracture initiation and helps to reduce tortuosity. However, there are quite legitimate reasonsfor wanting to perforate all of the net pay (which can often result in several sets ofperforations). One of these reasons is well testing, which is used by reservoir engineers tohelp determine the recoverable reserves in the formation - obviously a very important task.Results from well test analysis can be misleading if the entire interval is not perforated,especially if the formation contains several discrete intervals. Therefore, the need to reduce

the number of perforations and to reduce the length of the perforated interval, must bebalanced with the operating company's other interests. A compromise must be reached.

14.1 Controlling Fracture Initiation

Perforations can be used to control the point of fracture initiation, as illustrated in Figure14.1a, below. On the left-hand side, there is an interval that has been perforated across itsentire section. When the treatment commences, fracture initiation takes place. At this point, itshould be remembered that fractures are initiated by pressure, not by rate. As FracEngineers, we often use rate to create pressure (as a consequence of Darcy’s law), but it’sthe pressure that makes the fracture. As the pressure increases, a fracture will initiate whenthe pressure rises above the breakdown pressure of the weakest point along the perforated

interval. This can be in at the top of the zone (frac A, below), in the middle of the zone (B), atthe bottom of the zone (C) or somewhere else. There can also be more than one fracture – wherever the fluid pressure exceeds the breakdown pressure, a fracture will be initiated.Multiple fractures (see Section 10.5) can result in poor fracture conductivity and earlyscreenouts.

Figure 14.1a – The Effect of perforations on fracture initiation

A

B

C

D





If the interval is perforated as shown in the left-hand side of Figure 14.1a, the point at whichthe fracture or fractures initiate is beyond the control of the Frac Engineer. Fracs A and Chave substantial sections propagated outside the interval. This results in poor coverage of theinterval and a considerable amount of wasted proppant. There is also a risk that Frac A couldpenetrate into a gas cap or that Frac C could penetrate into a water zone.

Alternatively, the interval could be perforated as shown in the right-hand side of Figure 14.1a.In this example, the zone has been perforated over a very short interval (5 to 10 ft). Thiscontrols the point at which the fracture initiates, and dramatically reduces the chances ofmultiple fractures forming. If this short perforated interval is in the center of the zone, thenthere is a good chance that the fracture will propagate both up and down, covering the entiresection and using the proppant efficiently. Alternatively, if there is a water zone close by, theinterval can be perforated towards the top. This causes the fracture to initiate near the top,reducing the chances of the fracture penetrating down into the water.

Of course, once the interval has been fractured, there is nothing - other than cost – to stop asecond perforation run being made to cover the rest of the interval. However, if the treatmenthas been effective, the fracture will be many times more conductive than the formation.

Consequently, any perforation that is not directly connected to the fracture will beunproductiv:-

We have recognized point-source perforating improves your ability to successfully stimulate an interval........to improve our completions and ultimate recoveries. We have learned from perforating for stimulation that it does not take 100 ft of perforations to produce a 100 ft zone. We have proven that 5ft placed in the proper place will outperform all 100 ft.

Robert Lestz, Production Engineer, ChevronHart’s E&P , February 2000

Another example of perforating to control fracture initiation is the case when multiple zones

are treated simultaneously in a single treatment. The conventional method is to try a limitedentry treatment (see Section 10.10), but these are unreliable and difficult to control.

Figure 14.1b – Perforating for zonal coverage





Figure 14.1b illustrates this concept. Conventionally, each productive section of the formationis perforated individually. When this well is fractured, a portion of the fluid (dependent upon anumber of variables) will enter each of the intervals, as in the left-hand side of Figure 14.1b.Limited entry fracturing is all about controlling how much fluid goes into each interval and canbe very unreliable. However, if the well has not already been perforated, another method is toperforate a small section in the center of the formation, and allow the fracture to connect up

all of the individual intervals (right-hand side of Figure 14.1b). Under any circumstances, atreatment that produces a single fracture is much easier to predict and control than atreatment that produces multiple fractures.

Once again, a small section (5 to 10 ft) of perforations is shot. These need to be placedroughly in the center of the interval to be covered, or slightly towards the bottom, dependingupon the stress regime. Consequently, this may even mean deliberately perforating a non-productive formation, such as a shale. It can often be quite hard to convince an oil or gascompany to deliberately do this.

Important Note:- Sometimes, if there is a significant contrast in Young’s modulus betweenthe various formations, sections were the fracture is significantly narrower than the averagecan form. These narrow bands can act to prevent proppant transport, leaving formations

above and below un-propped. The reader should not use the above method unless reliableinformation on Young’s modulus contrasts – such as from a sonic array log – is available.

Perforating to control fracture initiation also makes fracture simulation and post-treatmentpressure matching more reliable. By controlling the point of fracture initiation, the FracEngineer defines a significant simulation variable and reduces the complexity of any possiblesolution by an order of magnitude.

14.2 Controlling Tortuosity

In order to minimise tortuosity, it must be as easy as possible for the fracture to propagatefrom the perforations. Every single perforation is a potential source of fracture initiation, soone of the steps taken is to reduce the number of perforations to an absolute minimum,consistent with the anticipated production rate. This in turn means big holes.

Figure 14.2a – Perforation strategy for vertical wells

Another important factor is the phasing of the perforations. Ideally, this should be 180°, withthe guns oriented so that they shoot perpendicular to the maximum horizontal stress. Thisway the holes are lined up with the direction of fracture propagation, minimising any changesof direction between the hole in the casing and the main fracture. Most of the time it is notpossible to orientate the guns in this fashion – the best strategy will then depend upon factors

such as the contrast between the maximum and minimum horizontal stresses and theformation’s Young’s modulus. The situation is complex, but in general it is best to minimisethe number of holes shot, to use big holes to minimise perforation friction, and to perforate to





that the holes line up along the wellbore (see Figure 14.2a), rather than produce a spiral ofholes around the circumference. The best strategy for perforating for fracturing was presentedby Behrman in 1998. However, it is the author’s experience that 90º phasing usually producesthe least near wellbore friction in vertical or near-vertical wellbores, without getting involved invery complex strategies.

Deviated Wellbores

Hydraulic fractures tend to propagate on a vertical or near vertical plane (see Section 7). On avertical well, this means that the fracture will propagate along or close to the wellbore. Thisminimises the formation of multiple fractures, as the compression of the rock on either side ofthe fracture will make it harder for parallel fractures to grow. However, on a deviated orhorizontal wellbore, the horizontal distance between potential points of fracture initiation ismuch greater, making it much easier to produce tortuosity and/or multiple fractures.

Consequently, it is common practice for highly deviated or horizontal wells, to perforate a veryshort section of the formation (+/- 2 ft or less), with as many big holes as possible. This isshown in Figure 14.2b (for a horizontal well):-

Figure 14.2b – Perforation strategy for horizontal wells

14.3 Perforating for Skin Bypass Fracturing

Figure 14.3a – The Effect of fracture initiation point on skin bypass fracs

Skin Bypass Fracturing (SBF - see Section 3.4) is a special type of small-scale fracturingoperation designed to penetrate through skin damage, and to provide effective stimulation

1

2

3





without the cost and logistics of larger-scale treatments. Whilst it is true that SBF’s may notnecessarily offer such a large production increase as conventional fracturing, the stimulationis still effective, and is usually more than adequate to justify the cost of the treatment. As withany type of fracturing, the position of the perforations can have a significant effect on theresults of the treatment.

Figure 14.3b – Multiple skin bypass fracs over a long interval

With reference to Figure 14.3a, it is easy to see how the point of fracture initiation can effect afracture not designed to cover the entire height of the formation, such as in skin bypassfracturing. Obviously, fracture B will produce more stimulation than fractures A or C. If theentire section of the formation is perforated, it is usually not possible to control the point offracture initiation (although a sand fill can be used to ensure that the fracture doesn’t initiatetowards the bottom). Therefore, when planning a perforation strategy, it would be better toshoot holes over a small, central section, than over the entire interval.

Figure 14.3b shows a different approach to perforating for SBF’s. Over a large section, one ofthe most cost effective methods of stimulation is to carry out several small consecutivetreatments, as listed below (with reference to Figure 14.3b):

Zone Step ActionLower 1 Perforate bottom zone

2 Frac lower zone3 Recover fluids

4 Isolate lower zone by placing bridge plugMiddle 1 Perforate middle zone2 Frac Middle zone3 Recover fluids4 Isolate middle zone by placing bridge plug

Upper 1 Perforate upper zone2 Frac upper zone3 Recover fluids

All 1 Remove bridge plugs2 Place on production

This method ensures maximum coverage of the interval for minimum of effort, although itdoes involve three separate perforating runs and the use of coiled tubing to remove the bridge

plugs or sand fill.

C

B

A





References

Behrmann, L.A.: “Perforating Requirements for Fracture Stimulations”, paper SPE 39453,presented at the SPE International Symposium on Formation Damage Control, Lafayette LA,Feb 1998.

Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,paper SPE 56473, presented at the SPE Annual Technical Conference and Exhibition, SanAntonio TX, Oct 1999.

Behrmann, L.A., and Nolte, K.G.: “Perforating Requirements for Fracture Stimulations”, paperSPE 59480, SPE Drilling and Completions , December 1999, pp 228 – 234.

Venkitaraman, A., Behrmann, L.A., and Chow, C.V.: “Perforating Requirements for SandControl”, paper SPE 65187, presented at the SPE European Petroleum Conference, Paris,Oct 2000.



BJ Services’ Frac Manual15. The Step Rate Test


15. The Step Rate Test

Step rate tests are usually performed before a hydraulic fracture treatment, as part of thefracture design process. Together with the minifrac (see next section), they are often referred

to as calibration tests, as they are used to adjust the fracture model to the actual pressureresponse of the formation.

There are two types of step rate test, the step up test and the step down test. One is used fordetermining fracture extension pressure, whilst the other is used for determining nearwellbore friction. Both tests can be extremely useful when designing the treatment. Wheneverpossible, bottom hole pressure data should be used, as this is more accurate and reliablethan calculated BHTP.

15.1 The Step Up Test

The step up test is used to determine the fracture extension pressure, P ext. This is usually 100

to 300 psi higher than the fracture closure pressure, P closure, which is a very important factor infracture design. Usually the results of the step up test will be used to determine an upperboundary for P closure and to give the expected BHTP.

To carry out the step rate test, it is common practice to use either KCl water or linear gel.However, if this test is to be combined with the minifrac (see Section 16), then the actual fracfluid should be used.

The test itself consists of pumping fluid into the formation at various rates. These rates startoff slowly and gradually increase. For example, these could be the pump rates for a typicaltest; 0.25 bpm, 0.5, 0.75, 1.0, 1.5, 2.0, 3.0, 5.0 and 10 bpm. The first step is usually thelowest rate that the pumps can manage. It is important to get as many stages at low rate aspossible. At each stage, first achieve the rate, then wait for the pressure to stabilize and finally

record the exact pressure and rate. Then move on to the next stage.

Figure 15.1a – The step up test

What is important with this test is to get stabilized pressure. It is not that important to get theexact rates. Often, pump operators will fiddle with the rate for 30 seconds or so in order to get

Rate

P r e s s u

r e

P ext





exactly 0.75 bpm. This is not necessary. Get approximately the correct rate and then leave italone, so that the pressure can stabilise and be recorded. Once the test has been carried out,a plot of pressure against rate can be made, as illustrated in Figure 15.1a.

The change in gradient of the slope shown in Figure 15.1a marks the change from Darcyradial flow (lower rates) to Darcy linear flow at higher rates. This is the point at which our

fracture is created and hence this is our extension pressure.

When carrying out a step up test it is important that no artificially induced fracture exists priorto the test. Thus, if any pumping above the frac gradient has already been carried out,sufficient time should be taken for the fracture to heal up before commencing the step ratetest. On very tight rocks, this could be several days.

The step rate test can also provide an indication of fracture toughness, at least in theformation close to the wellbore. In theory, the difference between the extension pressure andthe closure pressure (usually obtained from the minifrac) is directly related to the fracturetoughness. However, it is also heavily influenced by wellbore orientation, perforation strategyand the orientation and magnitude of the horizontal stresses.

15.2 The Step Down Test

This test is used to determine the nature of any near wellbore friction that may exist, i.e. tosee if it is perforation or tortuosity dominated. As the name suggests, the step down test is theopposite of the step up test. Instead of starting at low rates and increasing, the rates arestarted high and decreased.

Figure 15.2a – The step down test

When performing the step down test, it is important that the fracture is open the whole time,otherwise the test is invalid. Therefore, this test is often carried out after a step up test. It isnot uncommon to step up then step down right after. Another factor to remember whenconducting a step down test is keeping the stages short as the rate is stepped down. Unlikethe step up test, which starts with no fracture and ends with an open fracture, the step downtest must be performed with the fracture open all the way through. Consequently, if the stepsdown take too long, the fracture will close before the end of the test, making the low rate datapoints invalid. 4 or 5 steps down, taking 10 to 15 seconds each, is all that is required. Also,make sure that before starting the step down, that the fracture has been open for at least 5

minutes - the longer the better, as smaller fractures will close more quickly than largerfractures.

Rate

P r e s s u r e

Tortuosity Dominated

Perforation

Dominated





Figure 15.2a shows the relationships between pressure and rate for the step down test. Thedifferent shapes of the curves indicate how the near wellbore friction is dominated by theperforations, by the tortuosity or by a combination of the two.

For perforation friction:-

P nwb ∝ Q2.................................................................................. (15.1)

In theory, perforation friction follows the same theory as flow through orifices, involvingBernoulli’s Equation and stagnation pressure. Allowances have to be made for the diameterof the perforation (assumed to be constant) and for the discharge coefficient (a measure ofhow “smooth” the flow is as it goes through the orifice). The discharge coefficient is alsoassumed to be constant. As a result, the pressure loss is proportional to the rate perperforation, as illustrated in Equation 2.3. Generally, at this stage no significant volumes ofproppant have been pumped and so the assumption that perforation diameter is constant isvalid.

For tortuosity:-

P nwb ∝ Q .................................................................................. (15.2)

In theory, for tortuosity dominated near wellbore friction, as the pumping rate increases, sodoes the width of the near wellbore flow channels, as the width of these is dependent uponpressure – the higher the rate, the higher the pressure and hence the greater the width. Thisis why, for tortuosity, P nwb does not increase as fast as rate.

In reality, the relationship between rate and near wellbore friction may be a lot more complexthan that suggested by Equation 15.2. Recent work by the GRI suggests that P nwb may beproportional to Q

0.25 rather than the square root of rate. On top of this, it is likely that the

relationship between P nwb and Q is also controlled by the nature of the tortuosity, so thatdifferent relationships exist for tortuosity generated by perforations, for tortuosity generated by

horizontal stress contrasts, or for tortuosity generated by wellbore deviation (to name butthree potential causes). To further complicate the situation, it is entirely possible that a wellcould experience tortuosity that is a combination of two or more causes. However, in spite ofthis complex relationship between pressure loss and rate, the geometry of the tortuosity willalways be pressure-dependent and hence under most circumstances the pressure-ratecrossplot will have the characteristic convex shape for tortuosity-dominated near wellborefriction.

Of course, usually the near wellbore friction is a combination of perforation friction andtortuosity. Although Meyer ’s MinFrac minifrac analysis programme is not recommended bythe author, as it is based on a rather simplistic 2-D analysis, the step rate test analysis sectionwithin MinFrac is excellent, especially for the step down test. It incorporates a feature thatallows the theoretical perforation friction to be backed out, allowing the user to view the total

tortuosity-based friction, regardless of the exact relationship between pressure loss and rate.In addition, both MFrac and Fracpro (both versions) allow data from a step down test to beinput directly into the simulator, so that the model can allow for the effects of tortuosity relatedpressure losses when calculating net pressure. However, given that most step rate tests areperformed using a different fluid to the actual treatment (slick water rather than crosslinkedgel), it must be remembered that the actual pressure loss will probably be greater than datagenerated by the step rate test indicates.

15.3 Step Rate Test Example – Step Up/Step Down Test

The following data was taken from a step rate test in which the rate was stepped up and then

immediately stepped down again, using slick water. The data generated by the step rate testis given in table 15.3a.





Figure 15.3a shows the step up pressure-rate crossplot. Figure 15.3b shows the step downcrossplot, whilst Figure 15.3c shows the same step down crossplot using surface pressure.This illustrates why bottom hole pressure must always be used for step rate test analysis,even if it has to be calculated from surface data.

Rate STP BHTPbpm psi psi

0.5 2030 59580.9 2310 62111.0 2445 63371.2 2600 64741.6 2730 65592.0 2850 66232.3 2910 66363.2 3120 66714.2 3450 67535.2 3780 6783

6.3 4224 68388.4 5290 699610.2 6280 704111.8 7281 70768.4 5180 68866.3 4160 67744.2 3271 65742.0 2580 6353

Table 15.3a – Example step rate test data.

Figure 15.3a – Step up pressure-rate crossplot using the example data. This plot shows thefracture extension pressure to be at +/- 6570 psi.

5800

6000

6200

6400

6600

6800

7000

7200

0 2 4 6 8 10 12

Slurry Rate, bpm

B H T P , p s i

Fracture Extension = +/- 6570 psi





Figure 15.3b – Step down pressure-rate crossplot for the example data. The convex shape of thecurve indicates near wellbore friction dominated by tortuosity.

Figure 15.3c – Step down pressure-rate crossplot for the example data, using surface treatingpressure (STP). This graph illustrates the danger of using STP for step rate test analysis, as in

this case, the near wellbore friction would have been incorrectly diagnosed as being perforationdominated.

6200

6400

6600

6800

7000

7200

0 2 4 6 8 10 12

Slurry Rate, bpm

B H T P , p s i

Tortuosity Dominated

2000

3000

4000

5000

6000

7000

8000

0 2 4 6 8 10 12

Slurry Rate, bpm

S T P , p s i

Perforation Dominated?





References

Lacy, L.L. and Hudson, H.G.: ”Step Rate Test Analysis for Fracture Evaluation”, SPE 29591,presented at the SPE Rocky Mountain Region/Low Permeability Reservoirs Symposium,Denver, Colorado, March 1995.



Cleary, M.P.:, Johnson, D.E., Kogsbøll, H-H., Owens, K.A.: Perry, K.F., de Pater, C.J.,Stachel, A., Schmidt, H., and Tambini, M.:” Field Implementation of Proppant Slugs to AvoidPremature Screen-Out of Hydraulic Fractures with Adequate Proppant Concentration”, paperSPE 25892, presented at the SPE Ricky Mountain Regional/Low Permeability ReservoirsSymposium, Denver CO., April 1993.

Cleary, M.P., Doyle, R.S., Meehan, D.N., Massaras, L.V. and Wright, T.B.: “Major NewDevelopments in Hydraulic Fracturing with Documented Reductions in Job Costs andIncreases in Normalized Production”, SPE 28565, presented at the SPE 69

th Annual

Technical Conference and Exhibition, New Orleans, Louisiana, September 1994.

Wright, C.A., Weijers, L., and Minner, W.A.: Advanced Stimulation Technology Deployment Program , report GRI-09/0075, Gas Research Institute, March 1996.



BJ Services’ Frac Manual16. The Minifrac


16. The Minifrac

The purpose of the minifrac is to provide the best possible information on the formation, priorto pumping the actual treatment. Any time that the quality of information available for a frac

candidate is poor, a minifrac should be planned. This includes most wells, as it is not usual tohave detailed rock mechanical and leakoff data for a formation (and for the non-productiveformations surrounding the zone of interest). The only time a minifrac should not be pumpedis when there is reliable data available from offset wells that have been fractured (as is oftenthe case in the US).

The minifrac is designed to be as close as possible to the actual treatment, without pumpingany significant volumes of proppant. The minifrac should be pumped using the anticipatedtreatment fluid, at the anticipated rate. It should also be of sufficient volume to contact all theformations that the estimated main treatment design is anticipated to contact. A well plannedand executed minifrac can provide data on fracture geometry, rock mechanical properties andfluid leakoff – information that is vital to the success of the main treatment.

16.1 Planning and Execution

Bottom Hole Data

Do whatever it takes to get bottom hole pressure data for the minifrac (and also for the steprate test), as this is far more accurate than data calculated from the surface pressure. Bottomhole data can be obtained using three acquisition methods:-

1. Real Time Gauges. These can be run on wireline or can be part of the well’scompletion. These gauges allow both pressure and temperature to be recorded realtime at the surface. Usually, it is possible to run a data cable so that the pressure data

can be incorporated real time with the standard frac data already being recorded.This is the best possible situation for the Frac Engineer.2. Memory Gauges. These are gauges that are run in on wireline or slick line, and hung

in either a specially designed gauge carrier, or some other suitable position (such asan empty gas lift mandrel). Alternatively, they can just be held on slick line at aspecific depth. After the mini-frac and the step rate test are completed, the gaugesare retrieved and the data is downloaded at the surface. This data is then mergedwith the surface data that has already been collected. This is the most commonmethod of using gauges, even though there is a delay caused by the retrieval of thegauges.

3. Dead String/Live Annulus. Both of these methods work on the same principle. Withthe live annulus, the well is completed with tubing but no packer (or the packer hasnot been set, or the packer is fitted with a circulating valve that is left open during the

treatment). Basically, the annulus is exposed to the BHTP during the treatment, andshows a corresponding surface pressure. As the fluid is not moving in the annulus,BHTP can be easily calculated, provided the density of the fluid in the annulus isknown. Most fracture monitoring programmes have the capability to perform this realtime. A dead string relies on the same principle, but instead employs a small diametertubing string, inside the actual treatment tubing. A common example of this is coiledtubing placed inside a large diameter frac string.

Remember that it is more important to get downhole pressure data during the minifrac and thestep rate test, than it is during the actual treatment. Companies that supply gauges are oftenreluctant to have proppant pumped past them (this also applies to wireline cables).Consequently, it is common to have the gauges in the well for the minifrac and the step ratetest, and then retrieve them prior to pumping any proppant.





Most bottom hole pressure gauges also record temperature. This data, whilst not as importantas pressure data, can also be useful:-

1. The data can provide a good check of the bottom hole static temperature, to ensurethat the correct temperature has been used for designing the fluid system.

2. The data can provide a good value for the bottom hole treating temperature. This is

especially important when performing treatments with nitrogen and/or carbon dioxideand also for treatments where tubing shrinkage due to cooldown is critical.

3. If the gauges have been run on wireline or slick line, then it is possible to run thegauges past the perforations after the minifrac and the step rate test, to perform atemperature log. This is a plot of temperature against depth. By looking at how fareach the perforations have cooled down – and how this cooling down varies acrossthe perforated interval – it is possible to get a qualitative indication of where the fluidsare going and hence were the fracture(s) is(are) initiating.

Because the rheology of the fracturing fluid is constantly changing as the minifrac is beingpumped, and because the well is continually cooling down, calculated friction pressures canoften be unreliable. This in turn means that a BHTP calculated from a STP can also beunreliable. This is why it is important to obtain reliable downhole data, from which to base the

frac design.

Fluid Volumes and Rates

Deciding what volume to pump for the minifrac can be difficult. Ideally, we wish to pump theminimum volume necessary to gather accurate formation and fracture data. However,remember that we are not just interested in getting data on the producing formation – we arealso after data on any formation above and below that may be contacted by the fracture. Thismeans that as a minimum, we must pump at least the two-thirds of the anticipated padvolume. On low permeability wells we may have to pump significantly more than the padvolume.

The best method to decide the minifrac volume, is to run a few simulations for the minifrac,based on the data used to design the main treatment. Adjust the minifrac volume such that itwill contact all the formations that main treatment will contact.

As we are trying to create a treatment that is a close as possible to the actual treatment(minus the proppant), the minifrac should be pumped at the same rate as the anticipatedtreatment.

The minifrac should be displaced with slick water. The displacement volume should beenough to displace the minifrac to just short of the perforations, to ensure that the nearwellbore fracture(s) close on frac fluid, rather than slick water. To do this, it is common tounder-displace by +/- 5 bbls.

Fluid Type

As stated above, we are trying to create a test that is as close as possible to the actualtreatment, minus the proppant. This means that the minifrac should use the same fluid as theanticipated treatment. In fact, every step should be taken to ensure that the fluids used in theminifrac and the main treatment are as identical as possible, so that fluid related datagathered in the minifrac is as valid as possible for the main treatment.

Often, an operating company will suggest using slick water for the minifrac, as a way ofsaving time and money. This is a false economy, as the subsequent minifrac will have only apassing resemblance to the fracture that will be created by the main treatment. In particular,

the fluid leakoff will be (usually) significantly greater with slick water. This results in faster thannormal fracture closure, and smaller than normal fracture geometry.





Recently, some Engineers have argued that because of the wall building effects of the fluidused in the minifrac, the leakoff for the main treatment can be lower than that for the minifrac.To compensate for this, increased breaker loadings are used in the minifrac.

Wellbore Fluid

Usually, there is some kind of fluid in the wellbore prior to the minifrac. Often, this fluid will beslick water from the step rate test, or produced fluids. Unless this fluid can be circulated out ofthe well ahead of the minifrac fluid, it will be injected into the formation as part of the minifrac.Obviously, having two different fluid types in the fracture makes the job of analysing theminifrac data that much more difficult, so every effort should be taken to minimise the volumeof fluid ahead of the minifrac fluid. On some wells, this can be achieved by circulating theminifrac fluid into position. However, on most wells this cannot be done, and the FracEngineer has to live with the situation.

Pressure Decline

The data collected during the pressure decline (i.e. after the minifrac has been displaced andthe pumps are shut down) is just as vital as the data collected whilst pumping. It is thereforeimportant to monitor the pressure decline, sometimes for up to 2 hours after the minifrac iscompleted. During this period, it is important that nothing is done to compromise the quality ofthis data. Any opening or closing of valves, hammering on equipment or circulating of fluidsshould be avoided at all costs. In particular (and this may sound obvious, but it does happen)the wellhead should not be closed during this period. There should also be no pumping intothe annulus, as this will affect the tubing pressure. Once the Frac Engineer is sure that thefracture has closed, the well can be shut in and normal activities resumed.

Proppant Slugs

Many Engineers prefer to pump a proppant slug in the minifrac. This is a proppant stage inthe middle of the minifrac, often containing as little as 500 lbs of proppant. This slug will testthe near wellbore region for tortuosity. Ideally, the proppant slug should pass into theformation with no detectable pressure rise. If the pressure rises when the proppant flows intothe formation (and worse still, if it rises and does not come down again), then there isrestricted flow in the near wellbore region – tortuosity. A series of proppant slugs of increasingconcentration can be use to effectively diagnose the severity of a tortuosity problem. SeeSection 10.1 for more details on tortuosity.

Multiple Minifracs

Some companies, especially those operating in high permeability formations, prefer to usemore than one minifrac. The first minifrac is designed to be small, to penetrate only into thezone of interest and provide good leakoff and closure data on this formation. The secondminifrac is larger, designed to penetrate further and give a better idea of the overall fracturegeometry. Obviously, the use of two minifracs provides more data than just a singletreatment. However, in most cases this is probably not necessary. A well-designed andexecuted treatment should be able to provide the Frac Engineer with all the necessary data.However, there are cases when it is very difficult to interpret the minifrac data, through nofault of the treatment. Some formations are just too complex to easily analyse. In such cases,when the data from the first minifrac defies scrutiny, often the only way to proceed is to pumpa second minifrac, in the hope that this data will be better.





16.2 Anatomy of a Minifrac

Figure 16.2a shows a typical job plot from a minifrac:-

Figure 16.2a – Typical minifrac job plot, showing BHTP, STP and rate

Three important parameters are used – to a greater or lesser extent – in obtaining therequired data from the minifrac. The BHTP (ideally actual pressure data, rather thancalculated) is the main variable, as this tells us the way the fracture is behaving and theamount of work being performed on the formation by the fluid (or visa versa). The rate isimportant for determining the fracture geometry, as the volume of fluid pumped into theformation, less the volume of fluid which has leaked off, is equal to the volume of the fracture.In addition to these two parameters, the proppant concentration can also be important, ifproppant slugs have been pumped.

Figure 16.2b – Expanded plot showing BHTP

Figure 16.2b shows an expanded portion of Figure 16.2a, giving the BHTP more detail.Generally, a large number of minifracs will have this same basic shape, although by nomeans all. The area between the start of pumping and the shut down is often shaped like this,with the pressure declining initially and then increasing towards the end. In terms of Nolteanalysis (see Section 10.2), this means that the fracture is initially growing in a shape which isradial or preferentially vertical (rather than horizontal), but after a period of time the heightgrowth becomes more controlled, and the preferential growth direction is horizontal.

P r e s s u r e , R a t e

Time

BHTP

STP

Rate

B H P

Time

Start

Pumping

Shut

Down

Pressure

Decline





16.3 Decline Curve Analysis

As soon as the pumps shut down, the pressure will start to decline. Initially, the net pressurewill still be positive, and the fracture may still propagate. However, as soon as the fluid inputinto the fracture stops, the fracture will start to decrease in volume, as fluid is still leaking intothe formation. As the fluid volume in the fracture (and hence the volume of the fracture itself)decreases, the fracture width also decreases until the fluid volume in the fracture is zero – thefracture has closed.

The time taken for the fracture to close defines the rate at which the leakoff is occurring,whilst the pressure at which the fracture closes (and the difference between the treatingpressure and the closure pressure) tells us how hard it will be to produce the requiredfracture. Both of these parameters have been more rigorously defined in previous sections ofthis manual, but suffice to say that they are both extremely important parameters for definingthe size and shape of the fracture.

A typical pressure decline curve is shown in Figure 16.3a.

Figure 16.3a – Typical minifrac pressure decline curve

It is possible to see several distinct features on this curve, although it must be emphasizedthat Figure 16.3a is idealised and that actual minifrac pressure decline curves are rarely thisclear. Features which the Frac Engineer needs to identify include:-

1. BHTP – the actual bottom hole treating pressure. This is the pressure inside the well,at the middle of the perforated section that is being treated. Ideally, this should bemeasured via a gauge or a dead string.

2. ISIP – the instantaneous shut-in pressure, also referred to as the instantaneous shutdown pressure, or ISDP. This is the bottom hole treating pressure just after thepumps shut down, and before the pressure the pressure starts declining. Often, thispoint is hidden by noise generated by “pipe ring” as the pressure suddenly drops. Inthat case, the decline curve has to be extrapolated backwards in order to find theISIP.

The difference between the ISIP and the BHTP is due purely to friction pressure loses in thenear wellbore area. Therefore, this difference can often be used as a quantitative assessmentof tortuosity.

3. Closure Pressure, P closure, is the pressure at which the fracture closes, and is oftendenoted by a change in gradient on the pressure decline curve. The differencebetween the ISIP and the closure pressure is referred to at the net pressure, or P

net(see Sections 2.2 and 10.2). As discussed previously, the net pressure is a measureof how much energy is being used to create the fracture and so is a very important

B H P

Time

ISIP

BHTP

Closure Pressure

LinearFlow

Radial Flow





parameter. However, it should be remembered that the net pressure will usually varythroughout the treatment, and that this method only captures the net pressure right atthe end of the treatment. The closure pressure is also a measure of the in-situstresses in the formation (see Section 6, Rock Mechanics).

4. Closure Time. The closure time is the time taken for the fracture to close, after thepumps have shut down. If the geometry of the fracture is known (or, more likely, can

be estimated from a model), then the volume of fluid in the fracture is also known.Therefore, if the length of time taken for the fracture to close is also known, the rate atwhich the fluid is leaking off can be easily calculated.

The are various different methods for helping the Frac Engineer pick closure pressure, asoften it is very difficult to spot the change in gradient on the pressure decline curve.Additionally, there may be more than one closure pressure, if multiple fractures are closing.Finally, the effects of tortuosity may mask the closure pressure, as there is evidence tosuggest that the tortuosity can, in some cases, close before the main part of the fracture.

Various Methods for Displaying Time

In order to help find the closure pressure(s) on the pressure decline curve, various methodshave been developed for plotting the data. Some of these will be described in more detailbelow. As part of these methods, and for general information, there are various methods ofplotting time along the horizontal axis, listed in Table 16.3a, below:-

Description Symbol Equal toTime, general t Usually time since start of pumpingData Time t data Time since data collection startedPump Time t p Length of time spent pumpingShut in Time t s Time since ISIPDelta Time ∆t t - t pSquare Root Time t

0.5

Horner Time log10 t p + t s

t s

Nolte Time or DimensionlessTime

t D

t

t p

Delta Nolte Time ∆t D

t - t p

t p =

t

t p - 1

Nolte G Time or G Function G

or G (∆t D)Dimensionless function of ∆t D (seebelow)

Table 16.3a – Table illustrating the various ways of calculating and using time during pressuredecline analysis.

Square Root Time Plots

According to Equation 2.9, the volume of fluid leaked off into the formation (and hence thefracture volume) is proportional to the square root of time that the fracture has been open.However, once the fracture is closed, the fluid is no longer leaking off from the fracture faces,and is now leaking off according to Darcy’s radial flow law:-

q = k h ∆P

µ ln (r e / r w) ...................................................................... (16.1)





where q is the leakoff rate, k is the permeability of the formation, h is the net height of the

formation, µ is the fluid viscosity, r e is the radial extent of the formation, r w is the wellboreradius and ∆P is the pressure differential between the formation and the wellbore. Therefore,if a plot is made, showing BHP as the y-axis and square root time as the x-axis, the periodbefore fracture closes should have the pressure decline as a straight line. The point at whichthe fracture closes is defined as the point at which the straight line starts to curve, as

illustrated in Figure 16.3b:-

Figure 16.3b – Use of a square root time plot to determine closure pressure.

Square root time plots are both the easiest to use, and the easiest to understand, of all thepressure decline curve plots. However, their usefulness is limited by the ease with whichmultiple fractures and tortuosity can mask and obstruct the point at which the flow regimechanges. The method is also dependent upon the reliability of Equation 2.9, which itself is anapproximation, assuming that leakoff is independent of pressure. However, because of its

ease of use, the square root time plot is usually the first stop in an often rather involvedprocess.

Horner Plots

Horner plots are taken directly from well test theory, and can very useful in helping todetermine closure pressure. However, these plots must always be used in conjunction withother methods, as the Horner plot will only determine the lowest possible pressure at whichclosure could have existed. In other words, it will give a lower boundary, above which theclosure must be found. Remember that the step rate test (step up variety – see Section 15.1)will give an upper boundary, so that using these two methods in conjunction will provide a

region within which the closure pressure lies.

Horner plots work by plotting BHP on the y-axis and the Horner time on the x-axis. Hornertime is defined as follows:-

t Horner = log10

t p + t s

t s ................................................................. (16.2)

According to Horner’s theory, on a plot of pressure against Horner time, pseudo-radial flow(which, for our purposes, means flow when the fracture is closed) produces a straight line onthe plot, and non-pseudo-radial flow (i.e. the fracture is open) produces a curve. A typicalminifrac pressure decline Horner plot is shown in Figure 16.3c:-

B H P

Square Root Time

ISIP

BHTP

Closure Pressure

LinearFlow

Radial Flow





Figure 16.3c – Typical minifrac pressure decline Horner plot

As the minifrac pressure decline progresses, the BHP will eventually reach the reservoirpressure, P res. So, for Equation 16.2, as t s tends to infinity, the right hand side of the Equationtends to zero. This means that if the pressure decline is extrapolated back to the point wheret Horner equals zero, the average reservoir pressure can be determined (also referred to as P *).

Nolte G Time Analysis

Below is a summary of Nolte’s work on G Time and minifrac analysis. A full derivation of themethod is beyond the scope of this manual, and the reader is referred to the references.

Nolte derived the following relationships for the decline curve:-

g (∆t D)=

4/3(1 + ∆t D)3/2

- ∆t D3/2

(1 +∆t D)sin-1

(1 + ∆t D)-1/2

+ ∆t D1/2 ................................. (16.3)

where the upper part of the RHS represents the upper boundary and the lower part of theRHS is the lower boundary. In practice, to find the actual value of g(∆t D), both values arecalculated, and an extrapolation is made based on the power law exponent of the fracturingfluid (n ’) and the fracture geometry (radial, PKN or KZD). Remember that when calculatingfrom the lower boundary, the trigonometrical function works in radians, not degrees.

The extrapolation is performed between two values of the variable α . At the lower boundary α

= 0.5 and at the upper boundary α = 1. The actual value for α is given as follows:-

α = (2n ’ + 2)/(2n ’ + 3) - PKN ......................................... (16.4)α = (n ’ + 1)/(n ’ + 2) - GDK......................................... (16.5)α = (4n ’ + 4)/(3n ’ + 6) - radial ........................................ (16.6)

The actual value of α used for the extrapolation is dependent upon the fluid efficiency and n ’.Values tend to be almost always in the region of 0.5 to 0.7, and in practice 0.6 is often used.Also, given the fact that n ’ is often variable, a quicker method is just to take the average of the

upper and lower expressions for g(∆t D). As shown in Figure 16.3d, as ∆t D increases, thedifference between the upper and lower boundaries becomes smaller and eventuallybecomes negligible compared to the accuracy of the rest of the system:-

B H P

Horner Time

Closure Pressure

P res

0





Figure 16.3d – Graph showing the variation of g (∆∆∆∆t D) with ∆∆∆∆t D.

Nolte G time is then a function of t D such that:-

G (∆t D) = g (∆t D) – g (∆t D = 0) .......................................................... (16.7)

Note that for α = 1 and α = 0.5, g (∆t D = 0) is equal to 4/3 and π /2 respectively.

A typical plot of a pressure decline against Nolte G time is shown below in Figure 16.4e.

Figure 16.3e – Typical Nolte G time pressure decline plot. The match pressure is the gradient ofthe straight line section in the middle of the decline, before closure.

Figure 16.3e illustrates three important points. First, the ISIP recorded using field data may beartificially high, due to the effects of fracture storage and fluid friction. Second, that there is aperiod of constant gradient before the fracture closes, which is often referred to as the match

B

H P

G (∆∆∆∆t D)

Closure Pressure

0

Additional Fracture Extension

“Ideal” ISIP

0

1

2

3

4

5

0.01 0.1 1 10

Dimensionless Time, ∆∆∆∆t D

g ( ∆ ∆∆ ∆ t D )

Upper (α = 1, g (∆t D) = 4/3[(1 + ∆t D)3/2

- ∆t D3/2

])

Lower (α = 0.5, g (∆t D) = (1 + ∆t D)sin-1

(1 + ∆t D)-1/2

+ ∆t D1/2

)

g (∆t D = 0) = 4/3

g (∆t D = 0) = π /2





pressure (P m) and has pressure units (as G time is dimensionless). This is an importantparameter in Nolte’s minifrac pressure decline analysis. Finally, closure occurs when thedecline pressure deviates from this constant gradient. At this point G(∆t D) = G c.

It should be noted that if the closure time equals the pump time, then G c = 1.

From the g(∆t D) time at closure [ = g(∆t cD)], the fluid efficiency can be determined as follows:-

η =

g (∆t cD) - g (∆t D = 0)

g (∆t cD)

1 - v prop

1 - v prop / η ................................ (16.8)

where v prop is the fraction of the total fracture volume occupied by proppant. For a minifrac,v prop will be equal to zero. Therefore:-

η =

g (∆t cD) - g (∆t D = 0)

g (∆t cD) ..................................................... (16.9)

This can be simplified to:-

η ≈G

c2 + G c .......................................................................... (16.10)

which is a quick and easy method for determining fluid efficiency. Most modern real time datamonitoring systems can plot G-Function real time, so if the closure pressure can bedetermined, the fluid efficiency can be easily calculated from Equation (16.10).

The fluid loss coefficient can be calculated as follows:-

C eff =P m β s

r p t p E ' X ..................................................................... (16.11)

where P m is the match pressure (see Figure 16.3e), β s a geometry-dependent factor (see

below), r p is the ratio of fracture area in permeable formation over total fracture area (i.e. netto gross area ratio for the fracture), E ’ is the plane strain Young’s modulus (see below) and X is a factor dependent upon which geometry model is being used, such that for KZD, X = 2x f,

for PKN, X = h f and for radial, X = (32R / 3π 2).

(2n ’+2)/(2n ’+3+a ) PKN

β s ≈ 0.9 KZD ........................................ (16.12)(3π

2 /32) Radial

where n ’ is the power law exponent for the fluid and a is a variable describing how constantthe viscosity of the frac fluid is in the fracture, such that for a constant viscosity, a = 1 and fora falling viscosity a < 1. Usually, a is assumed to be 1. Finally, the plane strain Young’smodulus can be easily calculated:-

E’ =E

1 - ν2 ........................................................................... (16.13)

Thus, not only is Nolte G time a useful tool for finding the “ideal” ISIP and the closurepressure, it can also be used to find fluid efficiency and fluid leakoff (provided a 2-dimensionalfracture geometry is assumed).

Finally, Nolte G time can be used to find the fracture dimensions:-

Af =(1 - η)V i

2 g (∆t D = 0)C effr p t p ................................................... (16.14)

Where Af is the area of one fracture wing and V i is the total volume of fluid injected.





Given that for the 2-D models:-

2x fh f PKNAf = 2x fh f KZD ............................................ (16.15)

πR 2 Radial

then the fracture length or fracture radius can be easily found. Average fracture width canalso be obtained:-

w̄ =2 g (∆t D = 0)C effr p t pη

(1 - η) .................................................. (16.16)

Derivative Plots

When carrying out pressure decline analysis, a lot of time is spent trying to find variouschanges in gradient on the curve, or points were the pressure decline changes from a straight

line to a curve (or visa versa). Therefore, it is often easier to spot these changes in gradientby actually plotting the gradient - or derivative – itself.

On a derivative plot, a horizontal line (i.e. constant gradient) indicates a straight line on theparent plot (not necessarily horizontal, however). Changes in gradient on the parent plot,produce rapid changes in value on the derivative plot. An example is shown below in Figure16.3f.

All of the main types of plots - and their derivatives - can be plotted by most modern fracturesimulators with the minimum of effort. Often, these plots can be displayed real-time by thedata acquisition systems. Consequently, there is always a temptation to stop recording datatoo early – the Frac Engineer notices a change in gradient and assumes the fracture isclosed. This is not necessarily the case, and so it is important to keep recording data for as

long as feasible. It takes relatively little effort to record the data for an extra 10 minutes and alot of embarrassment can be avoided.

Figure 16.3f – Example derivative plot based on a Horner Plot

16.4 Pressure Matching

Another method for analysing minifrac data, is to carry out a process known as a pressurematch (also referred to as a history match). In this process, the fracture simulator is “tuned”

B H P

t Horner

Closure Pressure

0

d ( B H P )

d t H o r n e r

Derivative





until the simulator’s predicted net pressure matches the actual net pressure. This “tuning”process is carried out by adjusting variables such as Young’s modulus, Poisson’s ratio,fracture toughness, stress gradient, near wellbore friction, leakoff rate, and spurt loss.

Pressure matching, which is discussed in more detail in Section 19, is a very powerful tool,providing the user is aware of the limitations. The user is actually adjusting the computer

model to produce the same pressure response as the formation. Once the model has beenadjusted (the pressures have been “matched”), any potential treatment schedule can be runon the simulator, and its effects assessed. This means that once the match has been made,the Frac Engineer can very quickly adjust the treatment schedule to produce a fracture of therequired geometry.

Limitations of Pressure Matching

1. Complexity. Because so many variables are adjusted, in so many different rockstrata, a Frac Engineer may often have to keep track of 20 or more variables. Each ofthese variables can affect the overall outcome of the simulation. Therefore, a FracEngineer must remain aware of what variable changes and values are realistic andwhat are not.

2. Non-Unique Solution. Because there are so many variables to adjust, it is quitepossible for 2 Frac Engineers to produce good pressure matches, using differentvalues. Often, these solutions will only produce similar net pressure responses for theparticular data set being analysed, so that when a different treatment schedule issimulated (such as the actual treatment schedule to be pumped), two significantlydifferent fractures are generated. Which one is closest to the truth?

3. Data Quality and Model Inaccuracies. As with any type of computer analysis, theresults are only as good as the raw data (garbage in = garbage out ). In particular,errors generated by the use of surface pressure data to calculate BHTP cansometimes render pressure matching almost ineffective. For instance, it is quitepossible to interpret a gradual rise in STP as good fracture containment, whereas inreality it may have been caused by variations in fluid properties. Even if the quality ofdata is good, the final result is only as good as the model itself. Just because a modelpredicts a fracture that is 150 ft long and 100 ft high, doesn’t mean that this is whathappens in the ground. In fact, two different fracture simulators will almost alwaysproduce different fractures, when fed the same input data. Again, which one is closestto the truth?

The study of the theory of how the fracture models work will only get a Frac Engineer so far intrying to solve these conundrums, especially as the companies responsible for the mostwidely used fracture models do not publish significant parts of their theory. Unfortunately, inthis case there is no substitute for experience.

16.5 Near Wellbore Effects and Multiple Fractures

Most of the time, minifrac analysis is not simple. Often, it is not possible to find closurepressure, or obtain a pressure match. More often that not, this is due to the effects oftortuosity and/or multiple fractures.

Both of these concepts were explained in Section 10. However, it is worth discussing theparticular effects that these phenomena can have on minifrac analysis.

Tortuosity

As previously discussed in Section 10, tortuosity consists of a number a small, restricted, flowchannels in the near wellbore area, connecting the perforations to the fracture(s). Generally,this phenomenon is detected by the pressure drop it produces whilst the frac fluid is being





pumped. Obviously, it is much easier to detect and quantify tortuosity from bottom holepressure data, as pipe friction effects can easily mask its effect if surface pressure data isused.

Tortuosity can confuse the results of a minifrac analysis in two ways:-

1. The pressure drop produced by tortuosity represents a loss of energy from thefracturing fluid. This means that the frac fluid does not have as much energy as thepressure data indicates. The pressure inside the fracture remains the same,irrespective of whether or not tortuosity exists, as the fluid flow rate out of the nearwellbore area is the same as the flow rate into it. As the inlet rate and fluid propertiesgoing into the fracture are unchanged, so the fracture dimensions remain unchangedand hence the net pressure remains unchanged. Tortuosity does not produce a lowerthan normal pressure in the fracture – it produces a higher than normal pressure inthe wellbore. However, the effect of this is to lead the Frac Engineer into believingthat the pressure in the fracture is higher than it actually is. Consequently, the FracEngineer is led to believe that the fracture is significantly bigger than it really is, andcan be tempted to plan a treatment with larger volumes of proppant than can actuallybe pumped into the fracture.

2. Tortuosity can also cloud the interpretation of the minifrac pressure decline. Thechannels which form the tortuosity are always significantly narrower than the mainfracture (otherwise they wouldn’t produce a pressure drop), and so can often closeentirely before the main fracture(s) itself closes. This means that the main fracture isno longer hydraulically connected to the wellbore and so the actual closure pressurecan be very difficult to spot. In addition, the pressure at which the tortuosity closescan itself cause a change in gradient on the pressure decline plot, causing a falsevalue to be selected for closure pressure, at a higher pressure.

The only way to allow for these effects is to be fully aware of the existence of tortuosity, andto have some idea of its magnitude. The main ways of obtaining this information is to usebottom hole pressure data, and to pump a step down test (see Section 15).

Multiple Fractures

The existence and causes of multiple fractures have already been discussed in some detail inSection 10. Sufficient to say that under the right circumstances multiple fractures are not onlypossible, they are likely.

Of course, the classic way to identify multiple fractures is to see two or more closurepressures on a minifrac pressure decline curve. However, in reality this very rarely happens.In order for multiple closures to be apparent on a decline curve, there must be significantdifferences in the actual closure pressures of each individual fracture, otherwise they will

merge into one closure on the plot. Usually, the multiple fractures all exist in the sameformation(s) and so will close at approximately the same pressure.

The main problems for minifrac analysis associated with multiple fractures are as follows:-

1. Although the multiple fractures will close at approximately the same pressure, theywill almost never close at exactly the same pressure. Variations in depth and bisectedformations will cause a variation that could be as much as 20 psi or more. This meansthat when the fractures close, instead of a nice, easy-to-spot, change in gradient onthe pressure decline curve, there is a significant region where the gradient graduallychanges between the open fracture environment and the Darcy flow wellbore leakoffenvironment. This “smudging” of the closure pressure can make it very hard toidentify.

2. As discussed above, multiple fractures will usually close at around the samepressure, allowing for the effects of variations in depth. However, they probably will





not have similar fracture geometries, and so some fractures will be much larger thanothers. As stated previously, the leakoff rate is proportional to the fracture area, whilstthe time taken for the fracture to close depends upon the fracture volume. For mostfractures, the area of the fracture faces is proportional to the square of the length,whilst the volume of the fracture is proportional to the cube of its length. So a fracturewhich is twice the length of another fracture will leakoff at four times the rate, but will

have eight times as much volume to lose before closure, so that the fracture takestwice as long to close.

Therefore the bigger fractures tend to take longer to close than smaller fractures.However, all of our fractures are connected hydraulically via the wellbore. We knowthat our fractures will tend to close at the same time, because they will all have similarclosure pressures. Therefore, in order to prevent the smaller fractures closingsignificantly before the larger fractures, there must be fluid flow from the largerfractures to the smaller fractures, at a rate equal to the difference in leakoff rates. Thismeans that the smaller fractures have an artificially long closure time and the largefractures have an artificially short closure time. In a situation where there are severalfractures, the flow dynamics can get very complex indeed.

This flow of fluids from one fracture to another, as well as the pulling in of extra fluidfrom the wellbore, can produce complex shapes on the pressure decline curve. Thiscan make analysis very difficult.

16.6 Minifrac Example 1 - 2D Minifrac Analysis

The following minifrac treatment was pumped into an oil-bearing formation, located in SouthKalimantan, in the Indonesian part of island of Borneo. Bottom hole memory gauge data wasavailable. This example will demonstrate the use of the Nolte G Function analysis techniqueto obtain the leakoff coefficient, closure pressure, and fracture geometry.

Well and Formation Data

Reservoir Type: OilReservoir Temperature: 145 FReservoir Pressure: unknownPerforations: 986 m (3235 ft) to 1032 m (3386 ft)Deviation at Perforations: VerticalLiner: 7”, 23#Treating String: 3.5”, 9.3# tbgPacker set at: 940 m (3084 ft)End of Tubing: 950 m (3117 ft)Top of Formation: 986 m (3235 ft)Bottom of Formation: 1032 m (3386 ft)

Permeability: 6 mDPorosity: 18%Young’s modulus: 500,000 psi (assumed)Poisson’s ratio: 0.25 (assumed)

Treatment Data

Wellbore Fluid: Slick water(from step rate test)

Treatment Fluid: Crosslinked gel(SpectraFrac G 4500, n ’ at BH = 0.65)

Treatment Volume: 50 m3 (314 bbls)

Displacement Fluid: Slick water

Displacement Volume: 5.3 m

3

(33.3 bbls)Treatment Rate: 3 m3 /min (18.8 bpm)





Figure 16.6a – Minifrac example 1 job plot.

We can see from Figure 16.6a that the treatment was well executed, with the rate stayingconstant. The pressure was monitored for a significant length of time, probably longer thannecessary. However, it is better to record too much data than too little. Figure 16.6a actuallyshows merged bottom hole gauge and surface data. This plot would not have been availablewhilst the treatment was being performed.

Figure 16.6b shows the gauge BHTP pressure decline in more detail, whilst Figure 16.6cshows the pressure against the square root of elapsed time.

Figure 16.6b – BH gauge pressure decline against elapsed time. Possible closure pressure at +/-2770 psi (where the two red lines cross, marking a change in gradient). Note the sudden drop of

about 50 psi as the pumps shut down at t = +/- 13 mins.

0

1,000

2,000

3,000

4,000

0 10 20 30 40 50 60

Elapsed Time, mins

P r e s s u r e , p s i

0

10

20

30

40

S l u r r y R a t e , b p m

Slurry Rate

Gauge BHTP

STP

2,300

2,500

2,700

2,900

3,100

3,300

10 20 30 40 50 60

Elapsed Time

G a u g

e B H T P , p s i





Figure 16.6c – BH gauge pressure decline against the square root of elapsed time. Possibleclosure pressure at +/- 2790 psi (where the two red lines cross, marking a change from straight

line to curve).

These two plots are basically in agreement – closure pressure at about 2780 psi. On bothplots we see a sudden drop of about 50 psi, as soon as the pumps shut down. This is almostcertainly due to near wellbore friction. This drop in pressure makes the true ISIP (the treatingpressure inside the fracture) difficult to spot exactly. However, 50 psi is quite low and isunlikely to cause any problems as far as pumping the treatment is concerned (see laterexample number 3 for a case where near wellbore friction did effect the treatment).

Figure 16.6d shows the G Function plot, which should enable a “true” ISIP to be determined,by extrapolating the straight line back to the y-axis:-

Figure 16.6d – G function plot. The “true” ISIP is at +/- 3150 psi, whilst the closure pressureappears to be at +/- 2780 psi (where the two red lines cross). This gives a G c of 1.30.

2,300

2,500

2,700

2,900

3,100

3,300

3.0 4.0 5.0 6.0 7.0 8.0

Square Root Time, mins1/2

G a u g e B H T P , p s i

2,600

2,700

2,800

2,900

3,000

3,100

3,200

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

G Function

G a u g e B

H T P , p s i





Figure 16.6e – Horner plot. The results from this plot are ambiguous and do not help in theanalysis.

Figure 16.6e shows the Horner plot for the minifrac pressure decline. As can be seen, there isno clear change in gradient from linear flow to pseudo-radial – several different points couldbe picked. Therefore this plot is not much help in the analysis. This is a commonphenomenon in minifrac analysis – one plot being ambiguous, whilst others show clearerresults. This is one reason why the Frac Engineer must be familiar with the various types ofplots that exist. Most fracture monitoring and analysis software packages allow the user to

easily display several different types of decline curve.

Results of Graphical Analysis

There is a high degree of agreement between the pressure decline plot, the square root timeplot, and the G function plot. In fact, any experienced Frac Engineer reading this examplemay find this data suspicious – minifracs are rarely this easy to interpret. However, this is realdata – later on we shall see an example from a similar formation that is much less easy toanalyse.

To summarise the results of the graphical analysis:-

ISIP 3150 psiClosure pressure 2780 psiClosure time 31 mins (elapsed time)

17.5 mins (shut in time)Pump Time 13.5 minsG function at closure, G c 1.30

Nolte G Function Analysis

Assumptions Radial geometry, initial fracture radius estimate 50 ft, initial r p estimate 1.0 (i.e. the fracture iscompletely contained in the production formation).

1. From Equation 16.10, we can find the fracture efficiency at pump shut down:-

2,000

2,300

2,600

2,900

3,200

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Horner Time

G a u g e B H T P





η = 39.9%

2. From Equation 16.11, we can find the leakoff coefficient:-

C eff = 0.00686 ft/min1/2

3. From Equation 16.14, we can find the area of the fracture:-

Af = 20,147.56 ft2

4. From Equation 16.16 we can get the average width of the fracture:-

w ¯ = 0.604 inches

5. From Equation 16.15 we can obtain a revised value for the fracture radius:-

R = 80.1 ft

Obviously, this final result is significantly different from the initial fracture radius estimate of 50ft. They both cannot be right, and are in fact both wrong. In order to find the final answer, aniterative process must be performed, bringing the initial and final values of the fracture radiuscloser and closer together until the difference is negligible.

To start the first iterative step (in this example) steps 1 to 5 are re-worked using the averageof the initial and final values for R , 65 ft. Remember that our formation height is 118 ft – andour fracture height is now 130 ft (2R ). In this case of radial geometry, once the fracture heightexceeds the formation height, the ratio of net to gross area (r p) must be less than 1. With afracture radius of 6 5ft, r p can be calculated (using relatively simple geometry) as 0.967.

6. Using a new initial R of 65ft and a r p of 0.967, we get the following result:-

η = 39.4 % (unchanged, as this depends upon G c only)C eff = 0.00922 ft/min

1/2

Af = 15,498.13 ft2

w ¯ = 0.785 inchesR = 70.2 ft

The iterative process continues until the difference between the initial and final values for R are negligible. This gives the final minifrac analysis result:

η = 39.4 %C eff = 0.00988 ft/min

1/2

Af = 14,728 ft2

w ¯ = 0.826 inches

R = 68.4 ft

These values can now be plugged into the 2-D fracture simulator as the basis for a simulatedtreatment with proppant.

Note that in order to obtain this result, both Young’s modulus and Poisson’s ratio have to beassumed. In addition, it was also assumed that the formations above and below the zone ofinterest had the same rock mechanical properties as the main zone. Finally, it was assumedthat each fluid that entered the formation had the same leakoff properties. These are thelimitations of using a 2-D model.





16.7 Minifrac Example 2 – 3D Pressure Matching with FracProPT

The next example was pumped in an offshore well in Vietnamese waters. The well itself wasan exploration well that was extensively tested before and after the treatment – and thenabandoned. The operating company wished to determine if hydraulic fracturing was a viablefield development technique.


Reservoir Type: Gas CondensateReservoir Temperature: 249 FReservoir Pressure: unknownPerforations: 3122 m (10,243 ft) to 3137 m (10,293 ft)Deviation at Perforations: VerticalCasing: 9-5/8”, 47#Treating String: 3-1/2”, DST stringPacker set at: 3094 m (10,151 ft)Ported XOver Sub: 3098 m (10,164 ft)Top of Formation: 3116 m (10,222 ft)Bottom of Formation: 3143 m (10,312 ft)Permeability: naPorosity: na

Treatment Data – Step Rate Test

Wellbore Fluid: SeawaterTreatment Fluid: Slick Water (20 ppt GW-27)Treatment Volume: 2.4 m

3 (15 bbls)

Treatment Rate: 0.08 to 2.4 m3 /min (0.5 to 15 bpm)

Treatment Data - Minifrac

Wellbore Fluid: Slick water(from step rate test)

Treatment Fluid: Crosslinked gel(SpectraFrac G 4500)

Treatment Volume: 18.9 m3 (119 bbls)

Displacement Fluid: Slick waterDisplacement Volume: 5.3 m

3 (33.3 bbls)

Treatment Rate: 2.4 m3 /min (15 bpm)

Step Rate Test

Figure 16.7a shows the job plot for the step rate test. We can see from this Figure that thiswas not a particularly well executed step rate test – the rate, and hence the pressure, neverreally stabilises for each of the steps. Nevertheless, Figure 16.7b does show quite a markedchange in gradient, indicating that the fracture extension pressure is around 8700 psi, whichgives a frac gradient of 0.85 psi/ft – quite high, but not unheard of.

Unfortunately, there is no step down portion for this step rate test. This is recommended inany situation where tortuosity is suspected. As this was a formation that had never been

fractured before, it would have been prudent to perform the step down test.





Figure 16.7a – Minifrac example 2 step rate test job plot.

However it appears that in this case there are no indications of tortuosity, as the step rate testpressure decline shows no immediate drop in bottom hole pressure as the pumps are shutdown.

Also note that the bottom hole pressure is taken from memory gauges mounted in the DST

string. Therefore, the frac engineer on site did not have access to this data.

Figure 16.7b – Step rate test crossplot for minifrac example 2, step rate test, showing fracture

extension at +/- 8700 psi.

0

2,000

4,000

6,000

8,000

10,000

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Elapsed Time, mins


0

4

8

12

16

20

R a t e , b p m

Slurry Rate

Surface Pressure

Gauge BHTP

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Slurry Rate, bpm

G a u g

e B H T P , p s i





Minifrac

Figure 16.7c shows the job plot for the minifrac. Execution for this treatment was not perfect,with significant variations in rate throughout the treatment.

Figure 16.7c – Minifrac example 2 job plot.

Figure 16.7d – Comparison between gauge and calculated BHTP for minifrac example 2. Notethat whilst the calculated BHTP follows the same general trend as the gauge BHTP, the actual

value is quite different. Short term variations in the trend of the calculated BHTP are caused by

the variations in rate. The general offset of the data is probably caused by incorrect input data inthe fracture monitoring package (in this case FracRT ).

0

2,000

4,000

6,000

8,000

10,000

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Elapsed Time, mins


0.0

4.0

8.0

12.0

16.0

20.0

R a t e , b p m

Gauge BHTP

Surface Pressure

Slurry Rate

5,000

6,000

7,000

8,000

9,000

10,000

11,000

0 5 10 15 20 25 30 35 40

Elapsed Time, mins

P r e s s u r e , p s i Gauge BHTP

Calc BHTP





Figure 16.7d compares the gauge BHTP with the calculated BHTP. In this plot, we can see asignificant variation between the actual BHTP and the calculated value. This plot is includedto make an important point – be aware that any data you receive can contain errors. In thiscase, it looks as though the fracture monitoring software had the wrong data entered. If thecalculated BHTP data had been used by itself, it would have indicated a large amount of

tortuosity (note the large drop in pressure at ISIP ). Remember that there is no step down testto corroborate this. In fact, as we can see from the gauge BHTP, there is very little nearwellbore friction.

Figure 16.7e – Minifrac example 2 pressure decline with derivative.

Figure 16.7f – Minifrac example 2 pressure decline square root time plot, with derivative.

8,500

8,600

8,700

8,800

8,900

9,000

14.0 15.0 16.0 17.0 18.0 19.0 20.0 21.0

Elapsed Time, mins

G a u g e B

H T P , p s i

-500

-400

-300

-200

-100

0

D e r i v a t i v e

d B H T P / d T

8,500

8,600

8,700

8,800

8,900

9,000

3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5

Square Root Time, mins1/2


-5000

-4000

-3000

-2000

-1000

0

D e r i v a t i v e d P / d T 0 . 5





Figure 16.7e shows the pressure decline for minifrac example two, together with it’sderivative. There are two clear features to be noted on this plot. First, there appears to be animmediate pressure loss at ISIP of +/- 60 psi, which is probably due to tortuosity. Second, thederivative plot shows a clear change in gradient at about t = 16.1 minutes, giving a closurepressure of +/- 8725 psi (which corresponds closely with the fracture extension pressure from

the SRT). Note that this closure pressure would have been very difficult to spot without thederivative plot.

Figure 16.7f shows the same pressure decline, but this time against the square root of time.Once again, the derivative is included. This plot seems to indicate similar results to theprevious plot (Figure 16.7e), with the fracture closure happening perhaps a little more quicklyand at a slightly higher pressure.

Pressure Match

The pressure match was performed using Pinnacle Technologies ’ FracProPT fracturesimulation software package. The first step in the process was to merge the surface data(collected in this case by FracRT ) with the bottom hole data. This was performed using thedata merging, conversion and editing functions of the software.

Once this had been accomplished, the model was run with the “run from database data”option selected.

Table 16.7a shows the initial formation data used to produce the initial fracture design and toprovide a basis for the design of the minifrac. As we can see, the reservoir is very layered,with lots of thins beds of different strata. In reality it is often not necessary – or practical – touse this much definition when designing a fracture. However, it is included in this example toillustrate the detail that can be used if necessary.

Depth Lithology Stress Leakoff Young’s Poisson’s Fractureft psi Coefficient Modulus Ratio Toughness

ft/min-05

psi x 106

psi.in0.5

0 Shaley Sand 7120 0.0024 3.75 0.225 150010220 Shaley Sand 7154 0.0024 3.75 0.225 150010278 Sandstone 6372 0.0024 3.5 0.2 100010284 Shale 7712 0 6.0 0.25 2000

10312 Sandstone 6393 0.0024 3.5 0.2 100010320 Shale 7740 0 6.0 0.25 200010342 Sandstone 6412 0.0024 3.5 0.2 1000

10368 Shale 7776 0 6.0 0.25 200010386 Sandstone 6439 0.0024 3.5 0.2 100010420 Shaley Sand 7294 0.0024 3.75 0.225 150010430 Sandstone 6467 0.0024 3.5 0.2 100010456 Shale 7842 0 6.0 0.25 200010477 Sandstone 6496 0.0024 3.5 0.2 1000

Table 16.7a – Initial simulator data before pressure match.

Figure 16.7g shows the initial pressure match, using the original input data. As we can see,there is a large difference between the actual data and the simulated data, especially withregard to the stress data.





Offshore VietnamInitial Pressure Match

Time (mins)

Simulated Net Pressure (psi) Observed Net (psi)Slurry Flow Rate (bpm)

0.00 4.00 8.00 12.00 16.00 20.00 0

1000

2000

3000

4000

5000

0

1000

2000

3000

4000

5000

0.00

4.00

8.00

12.00

16.00

20.00

Figure 16.7g – Initial pressure match for minifrac example 2.

The first step is to increase the stresses in the formation to produce an approximate match atISIP . Once this has been done, the match looks better, but is still not complete (see Figure16.7h).

Offshore VietnamInterim Pressure Match

Time (mins)


0.00 4.00 8.00 12.00 16.00 20.00 0

200

400

600

800

1000

0

200

400

600

800

1000

0.00

4.00

8.00

12.00

16.00

20.00

Figure 16.7h – Interim pressure match after the stresses have had a first approximate

adjustment. In this case, the stress gradient for the sandstone was increased from 0.62 to 0.68psi/ft, and then 1300 psi was added to each stress. Note that the pressures are on a largervertical scale than in Figure 16.7g.





From this, there are some important points to be noted:-

• From the decline curve analysis, we know that the fracture closes at t = +/- 16 minutes ata bottom hole pressure of +/- 8725 psi. In Figure 16.7h, the simulated net pressure showsfracture closure at +/-16.5 minutes. This is close to reality. However, we must remember

that this will change as we alter other variables.• The shape of the simulated curve is close to the actual data to start with, but then

deviates from the gauge data. Variables such as Young’s modulus, fracture toughnessand stress will be changed for all formations in order to match this.

• Remember that changes in leakoff coefficient will affect the shape of the curve as well.• From the decline analysis, we observed +/- 60 psi tortuosity/near wellbore friction. This

should be remembered when matching the pressures. It should also be remembered thatthis may not be constant throughout the treatment.

• When pressure matching, it is essential to be able to differentiate between short termvariations, and long term trends. In this example, it will be hard to adjust the model so thatthe pressure will rise after +/- 7 minutes, as the actual data does. This point correspondsto the time when the wellbore fluid has been completely displaced with crosslinked fluid,and this fluid now starts to enter the formation. This could be a function of tortuosity –

which is very sensitive to fluid viscosity – or it could be a sign that the fracture has nowstarted to extend at a relatively higher rate.

• Given that we have a decrease in pressure after +/- t = 10 minutes, it is possible that therise and then fall in pressure is due to near wellbore effects. However, the Frac Engineershould closely examine the fluid samples and question both the blender tender and thelab technician, as this variation could be due to a change in crosslinked fluid properties(i.e. loss or reduction of crosslinker and/or buffer).

Figure 16.7i shows the final pressure match, after all the adjustments have been made to thesimulator model.

Offshore Vietnam

Final Pressure Match

Minifrac Example 2

Time (mins)


0.00 4.00 8.00 12.00 16.00 20.00 0

200

400

600

800

1000

0

200

400

600

800

1000

0.00

4.00

8.00

12.00

16.00

20.00

Figure 16.7i – Minifrac example 2 final pressure match

Note that in Figure 16.7i, it proved very difficult to model the observed net pressure after thecrosslinked fluid entered the formation. As discussed previously, this is almost certainly due tonear wellbore and/or tortuosity effects. Note also that the pressure decline after shut down





does not have the same curve as the observed net pressure. However, it does have the sameclosure pressure and closure time, implying that the fluid must be leaking off at the same rate.

Depth Lithology Stress Leakoff Young’s Poisson’s Fracture

ft psi Coefficient Modulus Ratio Toughness ft/min

-05psi x 10

6 psi.in

0.5

0 Shaley Sand 8530 0.0015 6.0 0.225 150010220 Shaley Sand 8720 0.0015 6.0 0.225 150010278 Sandstone 8550 0.0033 1.5 0.2 50010284 Shale 8780 0 1.0 0.25 2000

10312 Sandstone 8480 0.0033 1.5 0.2 50010320 Shale 8690 0 1.0 0.25 200010342 Sandstone 8480 0.0033 1.5 0.2 50010368 Shale 8730 0 1.0 0.25 200010386 Sandstone 8510 0.0033 1.5 0.2 500

10420 Shaley Sand 8740 0.0015 6.0 0.225 150010430 Sandstone 8540 0.0033 1.5 0.2 50010456 Shale 8790 0 1.0 0.25 200010477 Sandstone 8590 0.0033 1.5 0.2 500

Table 16.7b – Final simulator data after pressure match.

In the actual pressure matching process, it became apparent that fracture only penetrated thetop five formations, as described in Table 16.7b, above. Therefore, the only changes thatmade any difference to the simulation where those made to formations 1 through 5. In fact, asfar as the simulation was concerned, the bottom 8 formations didn’t need to be in thesimulator at all. Figure 16.7j shows the estimated fracture profile, as produced by the now-

calibrated fracture simulator. As we can see, the fracture grows preferentially upwards.

Figure 16.7j – FracProPT estimated fracture dimensions for minifrac example 2.

8000 8500 9000 9500 1000010400

10380

10360

10340

10320

10300

10280

10260

10240

10220

10200

Stress Profile

Closure Stress (psi)

Permeability

Low High

Fracture Profile

100 75 50 25 0 25 50 75 100

Propped Length (ft) Hydraulic Length (ft)

D e p t h ( f t )





In order to get the pressure match, 60 psi of tortuosity was used. This was kept constant,throughout the simulation. However, it is possible that some of the changes in observed netpressure are due to changes in near wellbore friction (NWF), rather than the response of theformations themselves. Using a modern fracture simulator like FracProPT means that theNWF, and especially the tortuosity, can be adjusted on a continuous basis. As a result, thesimulated net pressure can be made to fit any pressure match, just be adjusting NWF. This is

one of the disadvantages of using these advanced models. Because they have so manyfactors that can be adjusted, it is possible to make the simulator match any pressure profiledesired. However, it is up to the user to be able to understand which changes to the modelare realistic, and which are not. A certain level of expertise, in both frac theory and in the waythe model itself works, is required before the simulator can be use reliably. These aredefinitely not “expert” systems.

After the treatment was redesigned, the job was pumped successfully and 100,000 lbs of20/40 CarboProp was paced in the fracture. Post-treatment DST testing showed an increasein PI of between 4 and 7 times – the uncertainty being due to a leak in the DST string.

16.8 Minifrac Example 3 - Problems with Tortuosity

This well, which is located in the same field as Minifrac Example 1 (although in a different,slightly deeper formation), had a completely different response to the minifrac. Severeproblems were encountered with the formation’s response to the minifrac. Although effortswere made to mitigate this, resources and expertise on location were limited, and the jobeventually screened out about two thirds of the way through the treatment.


Reservoir Type: OilReservoir Temperature: 145 FReservoir Pressure: unknown

Perforations: 1121 m (3678 ft) to 1130 m (3707 ft)Deviation at Perforations: VerticalLiner: 7”, 23#Treating String: 3.5”, 9.3# tbgPacker set at: 1105 m (3625 ft)End of Tubing: 1115 m (3658 ft)Top of Formation: 1121 m (3678 ft)Bottom of Formation: 1157 m (3796 ft)Permeability: 30 mDPorosity: 20%

Treatment Data

Wellbore Fluid: Produced FluidsTreatment Fluid: Crosslinked gel

(SpectraFrac G 4500)Treatment Volume: 45 m

3 (314 bbls)

Displacement Fluid: Slick waterDisplacement Volume: 5.3 m

3 (33.3 bbls)

Treatment Rate: 3 m3 /min (18.8 bpm)

Figure 16.8a shows the treatment plot for this minifrac. This is a well executed minifrac. Thereis a slight spike in the rate, as it is being increased initially, but this is not significant. Themajor point of interest, however, is the large pressure drop in the gauge BHTP just as thepumps are shut down. This is shown in Figure 16.8b, which displays more detail of the BHTPat shut down.





Figure 16.8a – Minifrac example 3 treatment plot.

Figure 16.8b – Minifrac example 3, detail of post-treatment pressure decline.

Figure 16.8b shows 5 main points of interest, labeled A to E as follows

A Initial pump shut down.B Note how the pressure drops immediately by 400 to 500 psi as soon as the pumps

shut down. This is due entirely to near wellbore friction. A step down test would berequired to tell for sure if this was due to perforation friction or tortuosity, but this wasnot performed. However, as the zone had been re-perforated just prior to the minifrac,

0

1,000

2,000

3,000

4,000

5,000

0 10 20 30 40 50 60

Time, mins


0

5

10

15

20

25

R a t e , b p m

Slurry Rate

Gauge BHTP

Surf. Press.

2,000

2,300

2,600

2,900

3,200

3,500

10 15 20 25 30 35 40

Time, mins


A

B

C

D

E





it is likely that this pressure drop is due to tortuosity. This pressure drop is very largeand is an immediate cause for concern.

C This point shows a clear change in gradient at +/- 2350 psi and is almost certainlyfracture closure.

D This area of the plot is unusual. It is rare (but not unknown) to see a post treatmentpressure decline of this shape – especially as the decline actually increases for a

short period of time. This area of the plot is probably caused by poor communicationbetween the fracture and the wellbore, and is potentially another sign of tortuosity.

E Point E, obtained by extrapolating the straight line pressure decline back until it getsto the point at which the pumps were shut down, is probably a good approximation forthe true ISIP. A G function plot will be used to confirm this.

A post treatment pressure decline like Figure 16.8b should set alarm bells ringing in the headof any experienced Frac Engineer. It is obvious that there is a severely restricted flow path inthe near wellbore area. This means that the net pressure, which initially appears to be +/- 900psi, is in fact probably less than half of this. This in turn means that the fracture issubstantially smaller than it initially appears to be. In addition, the restricted flow pathsbetween the fracture(s) and the wellbore, will make it very difficult to place even moderateconcentrations of proppant.

Figure 16.8c shows the square root of time pressure decline plot. This plot shows a highdegree of similarity with the pressure decline plot in Figure 16.8b. On this plot, with a slightlyexpanded vertical scale, the closure can be seen to be around 2320 psi.

Figure 16.8c – Minifrac example 3, square root time pressure decline plot.

Figure 16.8d shows the Horner plot for the pressure decline. This plot is a little ambiguous,with potentially two or three different gradients and y-axis intercepts. Consequently, this plotwill only be used if the other plots prove to be unreliable.

In order to help verify both the closure pressure and the true ISIP , a G function plot is used,as shown in Figure 16.8e. Obviously, to do this we must assume a 2-D geometry. In thiscase, radial geometry was assumed. However, the fact that the plot is based on 2-D geometrydoes not detract from its ability to pick the true ISIP , and the closure pressure will also bereasonably reliable.

2,000

2,200

2,400

2,600

2,800

3,000

3,200

4 4.5 5 5.5 6 6.5 7

Square Root Time, mins

1/2

G a u g e B H T P , p

s i





Figure 16.8d – Horner plot for minifrac example 3. Note that several lines may be fitted to thefinal slope on the LHS of this plot. In fact, the reservoir pressure is substantially lower than thatindicated on the plot (as the well is produced by ESP’s), so all of these lines may be unreliable.

Figure 16.8e – G Function plot for minifrac example 3. Note the true ISIP of +/- 2730 psi, and theclosure pressure of +/- 2320. These values are in agreement with the value obtained from other

plots, such as the pressure decline and the square root time plots.

1,800

2,000

2,200

2,400

2,600

2,800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Horner Time


2,000

2,200

2,400

2,600

2,800

3,000

0 0.5 1 1.5 2 2.5

G Function

G a u g e B H P , p s i





Pressure Match with MFrac 3-D Fracture Simulator.

After the data was imported into the MFrac 3-D fracture simulator, via the data collectionprogramme MView , an initial run was performed to see how close the initial, pre-minifracfracture model was. The results are shown in Figure 16.8f, above.

Bottomhole Treating Pressure

0 10 20 30 40 50 60

Time (min)

2000

2500

3000

3500

4000

4500

B H T P ( p s i )

0

4

8

12

16

20

R a t e ( b p m )

BHTPMeasured BHTPMeasured Surface Rate

Figure 16.8f – MFrac output showing the initial pressure match before any adjustments weremade. There is very little agreement between the predicted and actual BHTP’s.

As can be seen in Figure 16.8f, to begin with there is very little agreement between the initialfracture model and the actual response of the formation. Remember also that the BHTP isfrom a gauge. We can see that the slope of the pressure decline is significantly different,indicating (in this example), that the actual fluid loss rate was somewhat faster than predicted.In addition, the pressures predicted whilst pumping are completely different both in magnitudeand in the trend that they follow. Clearly, this model needed significant adjustment. This iswhy we perform minifracs.

The effects of tortuosity also manifest themselves on this plot. We can see that, because ofthe huge pressure drop as the pumps shut down, the model predicts lower pressures whilstpumping and higher pressures during the decline.

Obviously, some allowance needs to be made in the model for the tortuosity. It is at this pointthat experience and intuition start to take over. The fact is, tortuosity is not necessarilyconstant throughout the treatment. The fall in measured BHTP that we see whilst pumpingcould be due entirely to a continuous decrease in near wellbore tortuosity. Or it could be dueto a reduction in perforation friction as more perforations are opened up. Worse still, it couldbe due to a combination of tortuosity, perforation friction and fracture geometry effects.

However, three other factors help the Frac Engineer. Firstly, we need to remember that wehave pumped no proppant and we have kept the rate constant. Changes in tortuosity areusually (but not always) associated with either a change in rate, or the action of the proppant.Secondly, changes in tortuosity (other than those associated with rate) tend to produce rapidchanges in the BHTP (“spikes” and “dips”), rather than slow, smooth changes. Lastly, thezone had just been re-perforated prior to the treatment, and probably had very low perforation

friction (although this cannot be guaranteed – perforating does go wrong occasionally).Therefore, it is probably a reasonable assumption that – in this case - the pressure loss due





to tortuosity is relatively constant. However, the Frac Engineer must be aware that this is notnecessarily the case.

Bottomhole Treating Pressure

0 10 20 30 40

Time (min)

2000

2500

3000

3500

4000

B H T P ( p s i )

0

5

10

15

20

R a t e ( b p m )

BHTPMeasured BHTPMeasured Surface Rate

Figure 16.8g – Final MFrac output, after the model has been adjusted.

In Figure 16.8g, we can see the results of the pressure match. The match is not perfect, but ispretty close. At the beginning of the treatment, the initial pressure spike has not beenmatched. Later on, at the start of the pressure decline, matching the shape of the curveproved to be very difficult. In this area, the general trend has been matched, whilst the curvehas not. The effects of the poor communication between the fracture(s) and the wellbore arevery difficult to model mathematically. The changes made to the model are listed in Table16.8a.

Formation

PropertyUpper Shale Sandstone Lower Shale

Before After Before After Before After

Stress Gradient, psi/ft 0.75 0.62 0.70 0.62 0.75 0.62

Young’s modulus, psi x 106

0.6 0.3 0.4 0.3 0.6 0.3

Poisson’s ratio 0.25 0.25 0.25 0.25 0.25 0.25

Fracture Toughness, psi in1/2

1000 1000 1000 7500 1000 1000

Leakoff Coefficient, ft min-1/2

0.0004 0.0004 0.007 0.015 0.0001 0.0001

Tortuosity ∆P , psi na na 0 550 na na

Table 16.8a – Changes made during the pressure matching process.





Treatment Results

The fact that we now have a reasonable pressure match does not alter the fact that it will bevery difficult to place the treatment. The pressure drop due to tortuosity is very large. Thismeans that it will be very difficult to place proppant inside the fracture – it will almost certainlybridge off in the near wellbore area. Therefore, the tortuosity needs to be removed. Theprocesses for doing this were described in Section 10.1, and were originally detailed byCleary et al in SPE 25892 and Køgsball et al in SPE 26796.

In fact, the normal process to cure tortuosity – such as pumping a series of proppant slugs – were not an option in this instance. The well was drilled in a remote location and the expertisenecessary for such an operation was not available on location. In addition, the operatingcompany was not willing to go through the potentially lengthy processes needed – theeconomics of the situation demanded low cost treatments, in order for them to be justifiable.

In the end, it was decided to place a +/- 6 ppa proppant slug in the middle of the pad, andobserve what happened as it went into the formation. If a significant pressure rise wasobserved, the plan was to shut down and re-assess the situation.

In fact, the well screened out as soon as the proppant slug hit the perforations.

However, once the pressure had fallen and more fluids had been mixed, it was possible tobreak down the formation again and re-start the treatment. This time, the well treated at asignificantly lower pressure – indicating that the proppant slug may have helped to removesome of the tortuosity.

As it turns out, not all of the tortuosity was removed. The treatment screened out at 8 ppa,with 35,000 lbs of the planned 50,000 lbs placed in the formation. The rapid pressure riseassociated with the screenout indicated a near wellbore event. However, the operatorconsidered this a success – given the circumstances – and the production increase more than justified the expense of the treatment.

16.9 Minifrac Example 4 – Perforation Problems

This minifrac was carried out on a well in New Zealand, using an oil-based fracturing fluid. Oil-based fracturing fluids are harder to pressure match, as there is less data available on itemssuch as the wall-building coefficient and tubing friction. The properties of these fluids arehighly dependent upon the hydrocarbon used as the base for the fluid. Even fluids mixed withdiesel show a marked variation in properties, when using with different sources of diesel. Pre- job testing is essential.

Luckily, on this treatment, bottom hole pressure gauges were used, allowing uncertainties due

to tubing friction to be eliminated.

New Zealand, as far as the fracturing industry is concerned, is a remote location and thesuccess or failure of these treatments depended as much upon the logistics and organisationof the operations, as it did upon the formation or the skill of the crew.


Reservoir Type: GasReservoir Temperature: 185 FReservoir Pressure: 5200 psiPerforations: 3397 m (11,145 ft) to 3407 m (11,178 ft)

Deviation at Perforations: VerticalCasing: 7”, 23#





Treating String: 3.5”, 9.3# tbg to 3342.6 m (10,966 ft)2”, 6.5# tbg to 3379 m (11,086 ft)

Packer set at: 3343 m (10,968 ft)End of Tubing: 3379 m (10,966 ft)Top of Formation: 3397 m (11,145 ft)Bottom of Formation: 3407 m (11,178 ft)

Permeability: 12 mDPorosity: n/a

Treatment Data

Original Wellbore Fluid: Formation water and gasTreatment Fluid: Crosslinked gelled diesel

(Super Rheogel 500)Treatment Volume: 237 m3 (1488 bbls)Displacement Fluid: Diesel + surfactantDisplacement Volume: 15.3 m

3 (96.1 bbls)

Treatment Rate: 2.4 m3 /min (15 bpm)

First Step Rate Test

The first step rate test was pumped using diesel with surfactant. Initially, a wellbore volumewas pumped ahead, to ensure that no gas remained in the well. Then the pumps were shutdown for 15 minutes, to ensure that the effects of this injection did not cloud the results of thestep rate test.

It should be remembered that on location, the first step rate test was followed immediately bythe minifrac, and neither where analysed until later on, after the BH gauge data had beenretrieved. Therefore, the results of the step rate test were not available before the minifracwas pumped. The significance of this will become apparent as we progress.

Figure 16.9a shows the job plot for the first step rate test, Figure 16.9b shows the step upcrossplot and Figure 16.9c shows the step down crossplot.

Figure 16.9a – Job plot for Minifrac Example 4, Step Rate Test 1

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70 80 90

Elapsed Time, mins


0

2

4

6

8

10

12

S l u r r y R a t e , b p m

Gauge BHTP

Slurry Rate

Surface Pressure





Figure 16.9b – Step up crossplot for Step Rate Test 1. Fracture extension seems to be atapproximately 9100 psi.

The step rate test was executed reasonably well, except for one mishap when bringing anadditional pump in line, when going for 10 bpm. The results from the analysis of the step upcrossplot, indicate a fracture extension of 9100 psi. This gives an extension gradient of 0.82psi/ft – high, but not exceptionally so.

However, the real problems show themselves in Figure 16.9c – the step down crossplot. This

plot clearly shows the characteristic shape of perforation friction.

Figure 16.9c – Step down crossplot. Note the concave shape of the best fit curve, indicating thatthe near wellbore friction is dominated by the perforations.

6000

7000

8000

9000

10000

11000

0 1 2 3 4 5 6 7 8 9 10

Slurry Rate, bpm


Fracture Extension at +/- 9100 psi

9000

9300

9600

9900

10200

10500

0 1 2 3 4 5 6 7 8 9 10

Slurry Rate, bpm

G a u g

e B H T P , p s i





Minifrac

Figure 16.9d – Minifrac Example 4 job plot.

The minifrac was pumped directly after the step rate test, before any analysis was carried outon the step rate test data. Initially, the minifrac was programmed at 8 bpm and without aproppant slug. However, previous experience had shown that these formations were subjectto tortuosity, and so it was decided to include the proppant slug, to assess how conductive the

near wellbore region was. Figure 16.9e shows what happened when the proppant slug arrivedat the formation. Note that this plot shows bottom hole proppant concentration.

Figure 16.9e – Detail of job plot showing bottom hole proppant concentration, gauge BHTP and

slurry rate, as the proppant slug enters the formation. Note the +/- 400 psi rise in pressure.

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70 80 90

Elapsed Time, mins


0

3

6

9

12

15

18

R a t e , b p m &

P r o p p a n t C o n c , p p a

Gauge BHTP

Surface Pressure

Slurry Rate

Proppant Conc

8000

8400

8800

9200

9600

10000

30 31 32 33 34 35 36 37 38 39 40

Elapsed Time, mins


0

4

8

12

16

20

R a t e , b p m &

P r o p p a n t C o n c , p p a

Gauge BHTP

Slurry Rate

Bottom Hole

Proppant Conc

+/- 400 psi Pressure Rise

as Proppant Reaches Perfs





From Figure 16.9e, we can see a +/- 400 psi pressure rise as the proppant enters theformation. This is not good, and indicates that we will not be able to get even moderateproppant concentration slurries into the formation.

Figure 16.9f – Minifrac pressure decline, showing +/- 650 psi near wellbore friction and a closurepressure of +/- 8350 psi.

Figure 16.9g – Square root of time plot for the minifrac pressure decline. This gives a slightlylower closure pressure than Figure 16.9f, at +/- 8230 psi.

Figure 16.9f show the ISIP and pressure decline after the minifrac. As we can see, this alsodoes not look good. Immediately, we can see a +/- 650 psi pressure drop as the pumps areshut down. This can only be due to near wellbore friction, as we are using gauge bottom holetreating pressure. This result, together with the result from the step down test, indicates that

8000

8300

8600

8900

9200

9500

48 50 52 54 56 58 60 62 64 66 68

Elapsed Time, mins

G a u g e B H T P , p s i +/- 650 psi Near Wellbore Friction

Fracture Closure at +/- 8350 psi (0.75 psi/ft)

7800

8000

8200

8400

8600

8800

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Square Root Time, mins0.5


Fracture Closure at +/- 8230 psi (0.74 psi/ft)





this well has severely restricted perforations. As a result of this analysis, the decision wasmade to re-perforate and run another step rate test. We can also see a closure pressure of +/-8350 psi, which is slightly different from the closure seen in Figure 16.9g, the square root oftime pressure decline plot. This gives a lower closure pressure of +/- 8230 psi. These closurepressures translate to gradients of 0.748 and 0.739 psi/ft (16.9 to 16.7kPa/m) respectively.

Second Step Rate Test

Figure 16.9h – Job plot for second step rate test.

Figure 16.9i – Step down crossplot for the second step rate test.

0

2000

4000

6000

8000

10000

0 5 10 15 20 25 30 35 40 45 50

Elapsed Time, mins

P r e s

s u r e , p s i

0

4

8

12

16

20

R a

t e , b p m

Surface Pressure

Gauge BHTP

Slurry Rate

8600

8800

9000

9200

9400

0 2 4 6 8 10 12

Slurry Rate, bpm

G a u g

e B H T P , p s i





The second step rate test was performed after the well was re-perforated. Originally, theintent had been to re-perforate the entire 10 meter section of (original) perforations. However,on entering the well, the wireline operators indicated that there was some kind of fill in thewell, sufficient to block access for the perforating guns to the lower 7 meters of perforatedinterval. The decision was made on location to shot holes in the upper 3 meter section only.

After perforating the upper 3 meters of the zone, the BH pressure gauges were re-run into thewell, and the second step rate test was performed. Figure 16.9h shows the job plot for this,whilst Figure 16.9i shows the step down crossplot.

By comparing Figures 16.9c and 16.9i, we can see that the near wellbore situation haschanged dramatically:-

1. The slope of the best fit curve as changed from concave (perforation dominated) toconvex (tortuosity dominated).

2. The overall bottom hole pressure has dropped significantly. At 8 bpm, the first step ratetest shows a BHTP of +/- 9950 psi, whereas at 8 bpm in the second step rate test, theBHTP is +/- 9270 psi.

So, as a result of the re-perforation, the restricted perforations have been removed (actually,by-passed) and the overall level of near wellbore friction appreciably reduced.

Minifrac Pressure Match

The minifrac was performed before the well was re-perforated, and so still includes the effectsof the restricted perforations. MFrac was used for this pressure match. Figure 16.9j shows thepredicted and actual bottom hole treating pressures before the pressure match wasperformed, whilst the post pressure match pressures are shown in Figure 16.9k.

This treatment was difficult to pressure match, largely due to the dynamic nature of therestricted flow path in the near wellbore. As we can see from Figure 16.9k, the early part ofthe treatment, at the lower rate, was not matched. In fact, the only part of the treatment thatcould be matched was after the proppant slug had entered the formation.

Consequently, because of the unreliable nature of the data and the analysis, the final designhad to be pretty cautious.

Figure 16.9j – Minifrac Example 4 BHTP plot before pressure matching.





Figure 16.9k – Minifrac Example 4 pressure match using MFrac .

The minifrac was performed before the well was re-perforated, and so still includes the effectsof the restricted perforations. MFrac was used for this pressure match. Figure 16.9j shows thepredicted and actual bottom hole treating pressures before the pressure match wasperformed, whilst the post pressure match pressures are shown in Figure 16.9k.

This treatment was difficult to pressure match, largely due to the dynamic nature of therestricted flow path in the near wellbore. As we can see from Figure 16.9k, the early part ofthe treatment, at the lower rate, was not matched. In fact, the only part of the treatment thatcould be matched was after the proppant slug had entered the formation.

Consequently, because of the unreliable nature of the data and the analysis, the final designhad to be pretty cautious.

Stresses All the formations’ stresses had to be significantly increased.Young’s Modulus All the formations’ moduli had to be significantly decreased.Leakoff The only way the leakoff could be matched to allow significant fluid

loss through the shale formations above and below the zone ofinterest.

Perforations The initial model had 170 x 0.3” perforations. Obviously, with 7m ofthe 10 m covered by fill, this number had to be reduced. However, inorder to get a pressure match, the perforations had to be modeled as1 x 0.07”! This was the only way that the BHTP during the change inrate at t = 46 minutes could be matched.

Total NWB Friction In addition to the restricted perforations, an extra 600 psi in nearwellbore friction had to be added, in order to match the pressure dropas the pumps were shut down.

It is unlikely that the perforations had been reduced to the equivalent of one 0.07” diameterperforation. For one thing, the average grain diameter of 20/40 Carbolite (the proppant usedin the proppant slug) is 730 microns or 0.029” (from manufacturer’s data). Thus, theperforation opening is less than 2.5 times the median grain diameter. It is probable that a 4ppg proppant slug would have blocked this off.

The simulator results also show that the overall near wellbore friction Figure is probably aresult of a combination of poor perforations and tortuosity.





This illustrates the two sides of using simulator. On one hand it is clear that we have veryrestricted perforations and that something should to be done about this. (However, weprobably could have worked this out without the simulator, based on the step down test andthe pressure drop at the end of the minifrac.) On the other hand, the extent to which theperforations are blocked is probably exaggerated by the simulator. Good engineering judgement, based on experience and knowledge of the underlying theories, needs to be

applied in order to decide what is realistic and what is not.

As a consequence of the restricted near wellbore situation, and the fact that the well was re-perforated, much of the data used to produce the pressure match is not relevant to the maintreatment design. Only the fluid leakoff data and – to a lesser extent – the stresses andmoduli – can be used. For modeling the final treatment, the perforation data was re-set to fifty0.3” diameter holes, and the total near wellbore friction reduced to 200 psi (based on thesecond step rate test). In an ideal world, where the Frac Engineer has a free hand with regardto technical issues, the minifrac should have been repeated. In reality, it was not repeated, fora variety of reasons.

Main Treatment

Although the re-perforating had dramatically improved the near wellbore situation, it was clearthat there were potentially still some problems with tortuosity. Without a minifrac, completewith proppant slug, it was difficult to assess just how bad this problem was. Consequently, themain treatment was designed with three proppant slugs in the pad.

1. 100 mesh sand at 1 ppa.2. 20/40 Carbolite at 4 ppa.3. 20/40 Carbolite at 6 ppa.

These stages were spaced out so that the effect of each one could be assessed before thenext one arrived at the perforations. Based on the response of the formation to these stages,the treatment would be redesigned on the fly.

Figure 16.9l shows the main treatment job plot and Figure 16.9m shows a detail of the bottomhole sand concentration as the 3 proppant slugs arrive at the formation hole sandconcentration as the 3 proppant slugs arrive at the formation.

Figure 16.9l – Job plot for the main treatment for Minifrac Example 4. Note the proppantconcentration is measured at the surface.

0

2000

4000

6000

8000

10000

0 20 40 60 80 100 120 140

Elapsed Time, mins


0

5

10

15

20

25

R a t e , b p m &

P r o p p a n t C

o n c , p p a

Slurry Rate

Surface Pressure

Calculated BHTP

Proppant

Concentration





As we can see, there was very little response from the formation as these three stages wentthrough the perforations. On the basis of this, it was decided to continue with the treatment asplanned. As the job progressed, it became apparent that the proppant was entering theformation very easily. Originally, the treatment had been planned for 107,000 lbs of proppant,pumped at 1 to 6 ppa. After assessing the well’s response to the proppant slugs, and

watching the early proppant stages, it was decided to extend the treatment. 130,000 lbs ofproppant was placed, by extending the 4 and 5 ppa stages.

Figure 16.9m – Detail of the main treatment for Minifrac Example 4, showing the formation’sresponse to the proppant slugs. Proppant concentration is bottom hole.

References





Nolte, K.G.: “Determination of Fracture Parameters from Fracturing Pressure Decline”, paperSPE 8341, 1979.

Dempsey, Brett.: “Competing with G Function Analysis”, BJ Services’ Engineering News , Vol.12, No 1, Winter 2001

Nolte, K.G.: “A General Analysis of Fracture Pressure Decline With Application to Three

Models”, paper SPE 12941, SPEFE , p. 571-583, 1986

6000

6400

6800

7200

7600

8000

25 30 35 40 45 50

Elapsed Time, mins

P r e s s u r

e , p s i

0

5

10

15

20

25

R a t e , b p m &

P r o p

p a n t C o n c , p p a

Slurry Rate

Surface Pressure

BH Proppant

Concentration





FracRT Version 4.6 User’s Manual , BJ Services, 1995

Cleary, M.P, et al .: ”Field Implementation of Proppant Slugs to Avoid Premature Screen-Outof Hydraulic Fractures with Adequate Proppant Concentration”, paper SPE 25892, presentedat the SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium, Denver CO,April 1993.

Køgsball, H.H., Pits, M.J., and Owens, K.A.: “Effects of Tortuosity in Fracture Stimulation ofHorizontal Wells – A Case Study of the Dan Field”, paper SPE 26796, presented at theOffshore Europe Conference, Aberdeen, UK, Sept 1993.

FracproPT Version 9.0 onwards on-line Help, Pinnacle Technologies/Gas Research Institute,July 1999 onwards.

MFrac III Version 3.5 onwards on-line Help, Meyer and Associates Inc, December 1999onwards.



BJ Services’ Frac Manual17. Designing the Treatment


17. Designing the Treatment

As previously discussed, different types of formation require different types of fracture. Forinstance, a high permeability formation requires more fracture conductivity than a low

permeability formation. This section of the manual contains important tips on which fracturecharacteristics the Engineer should be designing for, and how to go about achieving them.

As a quick rule-of-thumb, the following guidelines may be used:-

i) Skin bypass fracturing is for when eliminating the effect of the skin or extremely lowcost are the primary goals.

ii) High permeability fracturing is when maximising fracture conductivity is the primarygoal.

iii) Low permeability fracturing is when maximising fracture inflow area is the primarygoal.

iv) Frac and pack fracturing is when fracture conductivity and sand control are the dualprimary goals.

17.1 General

At its most basic level, every fracture is designed to do the same thing – increase theproductivity (or injectivity) of the fractured interval. At the limit, all a fracture has to be is moreconductive than the skin damage around the wellbore in order to do this. This is a relativelyeasy thing to accomplish, which is why skin bypass fracture treatments are very low cost andare also easy to perform.

However, often simply bypassing the skin is not enough – bigger production gains are neededto economically justify the treatment or to efficiently develop the reservoir. In such cases, thefracture has to be significantly more conductive than the formation. When this happens, it is

easier for the formation fluids to flow down the fracture, than it is to flow through the formationand into the perforations, and the productive interval will have a negative skin. Truestimulation has occurred, rather than just simple damage removal or elimination. The bestway to assess if the fracture is more conductive is to calculate the relative or dimensionlessconductivity, C fD as previously discussed in Section 10.3:-

C fD =k p w̄x f k

.............................................................................. (10.1)

where k p is the permeability of the proppant, w ¯ is the average fracture width, x f is the fracturehalf length and k is the permeability of the formation. Generally, if the C fD is greater than 1,then the fracture is more conductive than the formation.

This seems easy enough to calculate, but there are two important points which can oftenmake estimates of C fD unreliable:-

1 The proppant permeability is often not easy to find, nor indeed is it a constant. Thepermeability of the proppant will vary with closure pressure. As the reservoir pressuredrops (or the drawdown is increased), the closure pressure on the proppant willchange, possibly producing more fines and a permanent drop in permeability. If theproppant or sand is at the upper limit of its closure stress range, a drop in reservoirpressure can produce a significant drop in fracture conductivity. In addition, high ratewells (especially gas wells) can experience non-Darcy flow through the proppantpack, which can dramatically decrease the effective permeability. Lastly, multi-phaseand/or non-Darcy flow can also significantly reduce the proppant pack’s permeability.Therefore, the value used for k

p needs to be an effective permeability, under a given

set of production conditions. The Frac Engineer should also be aware of how theseproduction conditions can vary over the life of the well and design for this. Recent





information published by proppant vendors and the StimLab consortium, providesdetailed information for the effective permeability of different proppant types undermany different condition.

2. The effective width has to be estimated from a fracture model or simulator. The widthgenerated by these models (which will vary from model to model, even when the

same formation and treatment parameters are used), is highly dependent upon theYoung’s modulus and closure pressure of the formation. These two parameters areoften unknown and may even (as in the case of Young’s modulus in certainformations) be variable.

Therefore it is important to realise that a fracture must be designed with a safety margin builtinto the fracture conductivity, to allow for all these uncertainties. It is therefore recommendedthat the Frac Engineer design for a minimum C fD of 20 to 40% greater than theoreticallyrequired (see Section 17.9)

Finally, the Frac Engineer should be aware of the upper limits for fracture conductivity. As theconductivity increases, the contrast in conductivity between the formation and the fracture willincrease as well. Eventually, a point will be reached at which the formation is delivering

reservoir fluids to the fracture as fast as it can. Further increases in fracture conductivity (orthe conductivity contrast) will therefore produce no subsequent further increase in production.This is the so-called infinite conductivity situation, where the fracture behaves as if it has aninfinite conductivity compared to the formation. Making a fracture this conductive is simply awaste of proppant, as the same production increase can be achieved for a reduced proppedwidth. Generally, therefore, it is often not cost effective to design a treatment to produce a C fDof greater than 10, unless the formation permeability is very low.

17.2 Designing for Skin Bypass

Skin bypass fractures are the easiest fractures to design. Operationally, they are simple toexecute and have a relatively low probability of screening out early. This is because they arerelatively insensitive to inaccuracies in formation data.

Often, the two biggest factors influencing the design of the skin bypass frac, are notformation- or perforation-related. In fact, the biggest influences are the volume of fluid alreadyin the wellbore (which acts as additional pad fluid) and the volume of fluid and proppant thatcan be pre-pared and pumped on often very limited or remote locations. (Remember that skinbypass fracs are very low cost treatments, and that performing workovers or similaroperations - allowing the wellbore volume to be reduced or eliminated - are often unfeasible.)

The volume of fluid in the wellbore is often significantly greater than the desired pad volume.This means that the size of the actual fracture created is usually out of the control of the FracEngineer, and the only factor that can be controlled is the volume of proppant pumped into

the fracture. This in turn is often limited by the available equipment or deck space. However, itshould be noted that highly effective skin bypass fracs can be placed with very small volumesof proppant, provided the effective pad volume can be minimised (so that the proppantdoesn’t get too dispersed in the fracture).

This inability to control either minimum pad volume or maximum proppant volume, actuallymakes designing skin bypass fracs very simple, as the number of variables available for theFrac Engineer to alter are greatly reduced.

Skin bypass fracs should really be thought of as an alternative to acidising. Consequently,they should be designed to be cost-effective, as compared to a matrix acid treatment.Relative to other types of fracturing, this means that low cost and ease of operation are thebiggest single considerations. These treatments should be cheap, relatively low-tech and

easy to pump.





The following Equation describes the production increase that can be expected from a skinbypass treatment, as described in Section 12 (after SPE 56473):-

J J o

= ln[r e /(r w.e-s )]ln[4/(C fD .x fD)]

................................................................. (17.1)

This Equation provides a more realistic measure of the effectiveness of the fracture thanmethods based solely on assessing the C fD, as it takes the skin factor into account.

Given that the dimensionless fracture half length, x fD, is defined as follows:-

x fD = x f r e

................................................................................. (17.2)

Then the lower part of the RHS of Equation 17.1 can be reduced as follows:-

C fD . x fD =k p w̄ x f k

x f r e

........................................................................ (17.3)

= k p w̄ r e k

............................................................................... (17.4)

For skin bypass fracturing, it seems that the production increase is largely independent ofpropped fracture length per se . However, it must not be forgotten that as average width is afunction of fracture length, (and vice versa ). In this case, w ¯ is the average propped fracturewidth, not the average created fracture width. This is a significant difference that helps toreinforce the concept that skin bypass fracture effectiveness is much more dependent uponaverage propped fracture width than it is upon fracture length. This is why skin bypass fracscan be so cost effective and easy to perform – almost any kind of pad will suffice, as long asthe proppant is kept near the wellbore at a sufficient concentration.

17.3 Designing for Tip Screenout

The tip screenout (or TSO), as previously described in Section 10.4, is a technique used toartificially induce increased fracture width, whilst at the same time limiting fracture half-lengthand height. In order to obtain the tip screenout, proppant has to be forced into the tip of thefracture. Once sufficient proppant has been forced into the tip, the fracture fluid is no longerable to maintain a positive net pressure at the tip, and the fracture stops propagating.

At this point, the fracturing fluid is still being pumped into the fracture at a rate substantiallygreater than the leakoff rate. This means that the fracture volume has to increase somehow.As the treatment has artificially stopped the fracture from increasing length or height, thewidth has to increase. In order for the width to increase, extra net pressure (i.e. energy) is

required to further compress the formation either side of the fracture. This is why a TSO ischaracterised by a steady increase in net (and hence surface) pressure from the point atwhich the TSO initiates until the end of the treatment.

Obviously, the TSO must not happen too early. If this happens, the fracture may not achievethe required vertical coverage of the formation. In addition, it must be remembered that thelonger the fracture is, the easier it is to produce width. Therefore, if the TSO occurs early, thetreatment may not be able to produce sufficient width before the maximum surface treatingpressure is exceeded – a screenout.

In order to generate a TSO at the correct point in the treatment, it is necessary to pump apad, sized such that it will have leaked off completely at the point at which the TSO mustoccur. In order for the proppant following the pad stage to produce the TSO, all of the pad

fluid has to leak away, otherwise the proppant will not get into the fracture tip.





Therefore, in order to achieve a TSO, a formation must have a relatively high fluid leakoffrate. It is generally not possible to produce a TSO on very low permeability formations. This isgenerally not a problem however, as TSO’s are usually only required on high permeabilityformations.

In order to be able to predict (and hence control) the point at which the TSO occurs, it is

therefore essential to know the rate at which the pad fluid is leaking off. This can only usuallybe achieved if a minifrac has been pumped prior to the treatment (unless there is aconsiderable history of fracturing a particular formation, and the characteristics of thisformation have been shown to be reliable). In addition, it is essential to retain uniform fracfluid characteristics throughout the minifrac and main treatment. If the fluid characteristicschange, the leakoff rate will almost certainly change.

The minifrac is also essential for determining the Young’s modulus of the formation. This hasa big influence on a TSO treatment, as it determines how much net pressure is required toproduce a given fracture width. It is the Young’s modulus that determines whether or not therequired width can be achieved without exceeding the maximum surface treating pressure.

Therefore, the two key points to designing a successful TSO treatment are the fluid leakoff

and the Young’s modulus. Every effort should be made to determine accurate values forthese variables.

17.4 Designing for Frac and Pack

Frac and Pack treatments contain all the elements described in Section 17.3 (above) for aTSO design, plus some extra elements specific to the completion being installed.

Figure 17.4a – The diagram on the LHS illustrates the position of the slurry and the ‘pack’ atscreenout – with the top of the ‘packed’ proppant at the top of perforations, and the annular

space between the completion and the wellbore full of slurry, up until the crossover ports. TheRHS shows the position of the pack after all the proppant has been allowed to settle.

Figure 17.4a illustrates a schematic of the frac and pack completion, complete with the settingtool (assumed to be in the squeeze position). Towards the end of the treatment – as with anyTSO design – the formation will screenout, preventing the pumping of any further slurry into

‘Packed’ Gravelor Proppant

Blank Pipe

Frac PackSlurry





the formation. However, the frac and pack treatment is designed with an extra volume ofslurry on the end of the final stage. This stage is added so that the annular space between thecompletion and the casing can be filled with proppant.

When the completion is made up, sections of “blank pipe” (usually regular P-110 tubing) areadded above the screens. This produces extra distance between the crossover ports (the

point at which the slurry enters the annulus) and the screens. This extra distance provides anextra volume of slurry in the annulus after the screenout, so that once all the proppant hassettled down onto the pack, the height of the pack is significantly above the top of thescreens.

So - basically - the frac and pack treatment is a TSO treatment, designed with some extraslurry on the final stage, so that the annular space is completely packed to above the heightof the screens. This is verified after the treatment by pumping a circulation test (also referredto as re-stressing). By comparing the results of these with a similar pre-frac test, the height ofproppant in the annulus can be calculated, as follows:-

H =(P final - P initial ) k p A

2

(1279 µ q A) + (4.63 ρ q 2 k p

0.45) .................................... (17.5)

In Equation 17.5, P initial is the surface pressure for the pre-frac circulation test (psi), P final is thesurface pressure for the post-frac circulation test (psi), k p is the proppant permeability

(darcies), A is the annular capacity between the casing and the blank pipe (ft3/ft), µ is theviscosity of the fluid being circulated (cp), q is the flow rate (bpm) and ρ is the density of thefluid (ppg). H is the height of proppant above the screens in feet. Use the same fluid, pumpedat the same rate, for both the pre- and the post-frac tests. The above relationship is based onthe Forcheimer Equation (Equation 10.4) and so allows for inertial flow effects.

17.5 Designing for Tight Formations

In general, tight formations have low permeability, hard rock and require some form ofstimulation in order to be economic. Normally, these formations require a completely differentapproach to the treatments described in the previous sections. These previous treatmentshave relied upon the bypassing of skin damage and on the conductivity of the fracture toproduce the production increase. This is not true of tight formations, in which the skin factor isusually relatively low, and it is easy to obtain a fracture that is many times more conductivethan the formation.

In fact, for the purposes of fracture stimulation, it is possible to define a tight formation as onein which the most important fracture characteristic is not propped width, but propped length.

When defining a tight formation, it is also useful to think in terms of mobility, rather thansimple permeability. Mobility, m , is defined as follows:-

m = k

µ .................................................................................. (17.6)

where k is the permeability of the formation to the produced fluid and µ is the viscosity of thatfluid at reservoir conditions. This allows us to see that a tight oil formation has considerablygreater permeability than a tight gas formation.

In the case of a tight formation – especially a tight gas formation – it is relatively easy toproduce a fracture of essentially infinite conductivity (i.e. a fracture so conductive that anyfurther increase in fracture conductivity produces no subsequent increase in production). Insuch a situation, the factor limiting the potential production increase is the ability of theformation to deliver hydrocarbons to the fracture. This is controlled by the permeability of the

formation and by the inflow area of the fracture. Obviously, increasing the permeability of the





entire formation is beyond the abilities of stimulation engineering. However, maximising inflowarea – by increasing the size of the fracture faces – is relatively easy.

Therefore, fractures in tight formations are designed to produce maximum size, with aminimum necessary proppant concentration.

Of course, there are diminishing returns on increasing fracture size – doubling the fracturelength will increase the fracture area by approximately 4 times (as the height will increase atthe same relative rate as the length). This means that the proppant volume (which is spreadover the entire area of the fracture) is also increased by a factor of 4. As the fracture heightincreases, an increasingly greater proportion of the fracture will be outside the zone of interest(unless a “massive” formation is being fractured). Therefore, an increasing proportion of theproppant will be placed out of zone (i.e. it is wasted). In addition, the fluid volume required willincrease by between 4 to 8 times. Thus, doubling the length – which at best can only doublethe production – will can increase the cost of the treatment by 4 to 6 times.

Whilst fracture conductivity is not the most important consideration for tight formationfracturing, it is important to remember that some fracture conductivity is required. Rememberthat the proppant pack will lose permeability due to factors like residual polymers, non-Darcy

flow and multi-phase flow, and also that the pack may lose permeability as the reservoirpressure depletes (i.e. as the closure pressure increases). Therefore, when designing a tightformation fracture treatment, it is important to carefully define the minimum fractureconductivity, and to ensure that the produced fracture always remains above this.

Tight formations – especially tight gas formations – tend to have the following characteristics:-

i) Low permeabil ity and hence low fluid leakoffii) High Young’s modulus and hence;iii) Low fracture toughness

Because of the often extremely low fluid leakoff, it is possible to treat these formations withvery low pad volumes. Often, it is not necessary to crosslink the pad and a linear gel is used

(a "hybrid" frac). In some formations, it is even possible to frac without any pad whatsoever – the formation can be fractured with the first slurry stage.

Because of the very low fluid leakoff, these fractures can take a long time to close after thetreatment is finished (work by Cleary et al suggests that some fractures may take 24 hours toclose). Therefore, it is important to design the fracturing fluid with very good proppanttransport characteristics, so that it is capable of supporting the proppant for as long as it takesthe fracture to close.

Another major issue for tight formations, especially tight gas formations, is fluid recovery. Inmany cases, extra care and attention must be paid to the design of the fracturing fluid toensure that it does not form fluid blocks in the formation. This is usually done by addingsurfactants to reduce the surface tension of the fluid system. It is also important to break the

fluid to as low a viscosity as possible. Dry gas reservoirs may be sensitive to fluids or anytype – water or hydrocarbon. These can cause extensive damage due to changes in relativepermeability. In such formations, it is common practice to perform treatments using N2 or CO2

foams (or with binary foams), to reduce the liquid content to a minimum. Alternatively, it isalso common practice to treat dry gas wells with methanol-based fluids, as these are veryeasily recovered after the treatment.

Tight gas fracturing is probably the single most common form of hydraulic fracturing. In manyareas of the world, tight gas reservoirs can only be produced economically because ofhydraulic fracturing. In these places, fracturing has become the accepted method ofcompleting wells and whole reservoirs are developed using this technique.





17.6 Designing for Injection Wells

Injection wells are basically fractured in the same way as production wells, although there area number of minor points which must be observed:-

i) Take careful note of the closure pressure after the treatment. When the well is placedback on injection, on no account must this pressure be exceeded, as this will open upthe fracture and (potentially) allow the proppant to fall downwards.

ii) Remember that the build-up of pressure in the near wellbore area (caused by theinjection) may act to reduce the local closure pressure.

iii) Clean up the well after the fracture as much as possible before placing the well oninjection. Any polymer residue or proppant fines left in the proppant pack will act toblock the formation permeability and will not be produced back from the formation.

iv) When fracturing existing injection wells, fluid leakoff will often be much higher than inoffset producing wells, due to the higher than normal water saturation of theformation.

v) Do not use surfactants that leave the formation water-wet. These will act to reducethe injectivity of the water.

v) When fracturing a new well, remember that water injection – and the control of wherethe water goes – is an important part of reservoir management. Select the zone to befractured carefully and always in consultation with the Reservoir Engineer. Be awareof the consequences of fracturing into high permeability and/or low pressureformations.

vi) Consider using polymer-free fracturing fluids (e.g. visco-elastic fluids or brine withLiteProp ). Such fluids have very low permeability once broken and no polymerresidues. Consequently, they do not have to be flowed back - simply place the wellback onto water injection once the fluid has broken

17.7 Designing CBM Treatments

The vast majority of the coal bed methane fracturing that takes place in the US in 9 or 10major basins in the US, Australia and in China. In addition, CBM fracturing also takes place ina number of locations, including the UK, the Middle East and Russia. In all of these places,each particular coal field or basin tends to be dominated by a single operating company.

Each of these basins has its own particular characteristics, in terms of the age and maturity ofthe coal, the reservoir pressure, the fines mobility, the water production and the mechanicalcharacteristics of the coal seams and their surrounding rock layers. As a result of this, eachoperating company has developed its own particular method for producing the gas, and whenthis involves fracturing, they have developed their own method for this as well.

CBM fracturing remains to this day very difficult to simulate on a computer. Conventional

models cannot be applied to the coal, due to the extensive cleat systems that exist in theseams, the extremely plastic nature of the coal and the shear decoupling that exists betweenthe coal and the over- and under-lying rock strata. Without the aid of reliable fracture models,Engineers have developed a number of “rules of thumb” for CBM fracturing, most of which arespecific to a particular basin.

In short, operating companies that are successfully producing coal bed methane, are thosewhich have been prepared to experiment, to try out a few different methods and to except afew failures along the way.

Completions

i) There are many different completions being used, from open hole to multipleperforated monobores. There is very little agreement over which is ideal, although acemented and perforated completion is best when fracturing is being considered.





ii) Formations tend to be several thin seams, rather than a single large seam. As such,most completions contain several sets of perforations.

iii) In such cases, it is essential that each set of perforations is broken down before thefracturing operation. This usually involves using a straddle packer (or packer andbridge plug) positioned over each set of perforations in turn. The breakdown isachieved by pumping small quantities of acid (usually formic) into the zone. Some

companies prefer to do this with water.iv) The breakdown can also be achieved using ball sealers, but this is less reliable.v) Without the breakdown of each individual zone, it is likely that most of the perforated

intervals will receive no stimulation during a treatment, whilst the other zones willreceive everything.

Fluid Systems

i) All sorts of different fluid systems are still being used, including foams, fresh water,slick water and crosslinked gels.

ii) Slick water and fresh water have the advantages that they are very cheap andpotentially non-damaging to the coal seam. Their major disadvantage is that their lowviscosity makes it difficult to carry proppant deep into the cleat system. This can alsolead to pre-mature screenouts. However, neutral density proppants could potentiallyrevolutionise this type of treatment, although the cost of the proppant may beuneconomic.

iii) Foams have good proppant transport characteristics, and are very good for placingthe proppant in the wider cleats and not in the narrower channels. Foam is also verygood for unloading the well after the treatment. However, foam is very expensive touse, requiring a lot of additional specialised equipment on location for the treatment.

iv) The best fluid system to start out with seems to be a cheap, reasonably low polymerloading crosslinked borate guar or guar derivative. This is a standard water-basedfracturing fluid, reduced to the minimum necessary to carry proppant into the cleatsystem. Polymer loading would be 25 to 30 lbs/mgal. It is essential that an enzymebreaker be used, as it has been shown that oxidizing breakers can seriously damagethe cleat faces.

Proppant Selection

i) Generally, it is best to pump as large a proppant grain size as possible. This is for twomain reasons: First, the larger the proppant grain, the higher the proppantpermeability and the less susceptible the proppant is to embedment in the cleatfaces; Second, the larger proppant grains allow the coal fines to past through, ratherthan collect and gradually plug up the conductivity.

ii) The recommended proppant size is 12/20 Sand, although sometimes this can behard to obtain.

iii) Some operators like to pump a fine grain sand (such as 100 mesh) in the early stages

of the treatment (in the pad). The purpose of this is to block up the narrow cleats, andforce the fracture and the larger main proppant grains into the wider cleats.

iv) Proppant volume ranges from 3,000 to 10,000 lbs per vertical ft of net height. Someoperators claim to be able to place 15,000 lbs/ft, but this is not confirmed. A goodstarting point is to aim to place 5,000 lbs per vertical ft of coal. If this is placed withoutany problems, the proppant volume can be gradually increased on subsequenttreatments.

Fracture Geometry

i) Although it is very difficult to predict the geometry of the fracture(s), it is still possible

to divide the fractures into two main regimes.ii) The first regime occurs when the fracture penetrates up and down into the over- andunder-lying rock strata. Fractures tend to have an overall radial or elliptical geometry,





although the actual shape of the fracture(s) within the coal seam will be very complex.This regime is characterised by a moderate to low frac gradient (0.5 to 0.7 psi/ft), asthe fracture is pushing against the minimum horizontal stress.

iii) The second regime occurs when the coal seam shears relative to the over- andunder-lying rock strata, so that the fracture does not penetrate out of the coal seam.This results in the famous T and I –shaped fractures, where the fracture grows

horizontally between the coal seam and the confining rock strata. This regimeproduces better stimulation, as all of the proppant is placed in the coal seam.However, pressures tend to be much higher, with the frac gradient being 1.0 psi/ft orgreater, as the fracture has to lift the overburden in order to propagate. Also, it isimportant not to confuse the high pressures of this type of frac, with the highpressures produced by near wellbore friction (see below).

Notes on Job Design

i) In addition to breaking down each set of perforations individually, it is also worthwhileperforming a full-scale minifrac. This involves pumping into the formation at theanticipated treatment rate, using the actual treating fluid but no proppant. This allowsthe frac engineer to assess the overall fracture geometry (from the frac gradient) andthe level of near wellbore friction (from the difference between the BHTP and theISIP ).

ii) Surface facilities should be designed to cope with fines production. All treatments,regardless of the fluid used and the additives mixed into the fluid, will cause theproduction of coal fines. These fines should be produced back to the surface andhandled there. If they are not produced back to surface, they will block up theproppant pack and cause a loss in production that will increase with time.

iii) Treatment pump rate should be 1.0 to 1.5 bpm per vertical ft of coal. Treatmentsusing fresh or slick water are usually pumped at higher rates. This is because the fluidhas no proppant transport characteristics, and so it is essential to keep the proppantmoving within the cleat system.

iv) Pad volume should be 20 to 25% of the overall treatment volume, although this is anarea that varies considerably – some treatments use only 5% or even less.

v) Proppant concentration should be 6 to 8 ppg (lbs per gal) for the crosslinked fluid andfoam. Slick and fresh water systems are only capable of carrying proppant up toabout 2 ppg.

vi) If significant near wellbore friction is present, then it is likely that 6 to 8 ppg will causea premature screenout. If this friction is detected, the maximum proppantconcentration should be reduced to 4 ppg. If this happens, more fluid will be requiredto place the same volume of proppant.

17.8 Designing for Coiled Tubing Fracturing

Coiled tubing fracturing is really a method for placing the fracture treatment, rather than aspecific method of treating a type of formation. Any of the types of treatment previouslydescribed can be placed with coiled tubing.

The advantages of using coiled tubing have already been explained in Section 3.6. Tosummarize, they are as follows:-

i) Isolation of completion.ii) Isolation of individual zones.iii) Rapid turn around between multiple treatments.iv) Use of the coil to gas lift the well back to production.

The main problem with fracturing through CT is the narrow diameter of the tubing itself. This

means that the most important factors in designing CT fracs are the friction pressure of thefracturing fluid and the maximum allowable pressure that can be imposed on the CT.





BJ’s Circa Coiled Tubing Simulator can be used to predict the maximum allowable injectionpressure, for any given CT string. However, it must be remembered that the CT string will bestatic when the treatments are pumped. The maximum injection pressure usually generatedby CT simulators assumes that the CT is either moving in or moving out of the hole. Thismeans that the CT is being continuously plastically deformed, as the internal pressure is

applied. However, if the CT is static – and hence it is not being plastically deformed – the CTwill be able to withstand much greater internal pressures. For instance, normal maximuminjection pressures for CT are in the region of 5,000 to 6,000 psi. However, during staticfracturing operations, treatments have been pumped at pressures up to 13,000 psi.

However, in spite of this, the friction pressure of the frac fluid (and the subsequent surfacetreating pressure it produces) will still dominate the design of the treatment. It is oftennecessary to use very low friction pressure fluids (i.e. low polymer loading gels or visco-elastic surfactant-based fluids) in order to be able to maintain the desired rate. These fluidsare often significantly more expensive than their conventional alternatives.

Notwithstanding the increased allowable internal pressure and a possibly reduced frictionpressure, even with large diameter CT strings (2” or greater), the Frac Engineer will still be

rate limited to between 5 and 12 bpm. This can often significantly limit the size of treatmentthat can be placed in the formation. Obviously, the shorter the string, and the larger the ID,the greater the maximum rate. However, it should also be noted that generally with CT, thelarger the ID, the smaller the maximum allowable pressure (unless so-called heavy-walled CTis used).

Therefore, the Frac Engineer has to balance the need for rate against the desire for a cheapfluid and the maximum allowable injection pressure. Usually, the requirements of thetreatment take precedence over the cost of the fluid, allowing the Frac Engineer morefreedom to design a suitable pumping schedule.

CT fracturing has found niche applications in a number of areas, most notably southernAlberta. However, it remains economically viable only in areas where there are relatively

shallow multi-zone formations, and where the cost of a workover is expensive.

17.9 Unified Fracture Design and Proppant Number

In 2002, Economides, Oligney and Valkó, published their principles of Unified FractureDesign, and introduced the concept of a dimensionless proppant number, or N p . This wasdefined as follows:-

N p =2x f

r e π C fD (radial flow system) ....................................... (17.7)

N p = 2x f x e

C fD (square reservoir, area = x e 2) ............................ (17.8)

Rearranging and substituting in Equation 10.1 gives the following result, for a radial flowsystem:-

N p =2k p w̄

r e k π ........................................................................... (17.9)

According to the theory, for each value of N p there is a corresponding optimum value of C fD,which produces the maximum production increase. Therefore, this theory allows the FracEngineer, for any given reservoir and proppant combination, the optimum balance betweenaverage proppant width (w ¯ ) and proppant fracture half length (x f), as illustrated in Figure17.9a.





Figure 17.9a also shows us that for N p values less than 0.1 the optimum value of C fD is 1.6.This gives the Frac Engineer a very powerful tool – for medium to high permeability fracturing(i.e. N p < 0.1) the fracture should always be designed for C fD = 1.6. For low permeabilityfracturing, the relationship is not so simplistic and specific values for Np have to be calculatedfor each proppant-reservoir-fracture combination.

As can be seen from Equation 17.9, proppant number varies inversely with formationpermeability. It can therefore be thought of as a measure of the effectiveness of the proppant,as a transport medium, relative to the formation. Whilst very low values of N p are easy toobtain, in practice it is hard to get values higher than 10 (as r e is limited).

Under most circumstances, the changeover from N p < 0.1 to N p > 0.1 occurs in the range of0.5 to 5 mD formation permeability. Obviously, the exact value is highly dependent upon theeffective proppant permeability (allowing for the effects of multi-phase and non-Darcy flow).

0.1

1

10

100

0.0001 0.001 0.01 0.1 1 10 100

Proppant Number, N p

D i m e n s i o n l e s s F r a c t u r e C o n d u c t i v i t y , C f D

C fD = 1.6 for N p < 0.1

Medium to High Permeability Low Permeability

Figure 17.9a – Optimum dimensionless fracture conductivity against dimensionless proppantnumber (after Economides et al , 2002).

17.10 Net Present Value Analysis

Net Present Value (NPV) analysis is a method for comparing one treatment to another, on acost basis, to determine which treatment is the most cost effective. It allows one treatment tobe compared to another on economic grounds. NPV takes into account the cost of thetreatment, the revenue generated and the customer’s requirements. When comparingtreatments, the option that produces the greatest NPV should be selected. Within theconstraints of equipment, materials, completion and cost, the Frac Engineer should design formaximum NPV.

A more detailed explanation of NPV analysis, together with an example, is contained inSection 13.1.





References


Gidley, J.L., et al : Recent Advances in Hydraulic Fracturing , Monograph Series Vol 12, SPE,

Richardson, Texas (1989).


Jiang, T., Shan W.W., Ding, Y.H., Wang, Y.H. and Wang, Y.L.: “Systematic FracturingTechnology and its Application in Development of Low Permeability Reservoir”, SPE 50910,presented at the SPE international Conference and Exhibition in China, Beijing, China,November 1998.

Phillips, A.M. and Anderson, R.W.: “Use of Proppant Selection Models To Optimize FracturingTreatment Designs In Low-Permeability Reservoirs”, SPE/DOE 13855, presented at theSPE/DOE 1985 Low Permeability Gas Reservoirs, Denver, Colorado, May 1985.

Voneiff, V.W., and Holditch, S.A.: “A Economic Assessment of Applying Recent Advances inFracturing Technology to Six Tight Gas Formations”, SPE 24888, presented at the 67

th

Annual Technical Conference and Exhibition, Washington, DC, October 1992.

Yong Fan, and Economides, M.J.: “Fracture Dimensions in Frac&pack Stimulation”, SPE30469, presented at the SPE Annual technical Conference and Exhibition, Dallas, Texas,October 1995.

Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,SPE 56473, presented at the SPE Annual Technical Conference and Exhibition, Houston,October 1999.

O’Driscoll, K.: Middle-East Region Coal Bed Methane Fracturing Manual , BJ Services, 1995.

Gavin, W.G.: “Fracturing Through Coiled Tubing – Recent Developments and CaseHistories”, SPE 60690, presented at the 2000 SPE/ICoTA Coiled Tubing Roundtable,Houston, April 2000.

Cramer, D.D.: “The Unique Aspects of Fracturing Western US Coal-beds”, SPE 21592,presented at the Petroleum Society of CIM/Society of Petroleum Engineers InternationalTechnical Meeting, June 10-13, 1992, Calgary, Alberta, Canada.

Nimerick, K.H., et al : “Design and Evaluation of Stimulation and Workover Treatments in CoalSeam Reservoirs”, SPE 23455, presented at the Petroleum Society of CIM/Society ofPetroleum Engineers International Technical Meeting, June 10-13, 1990, Calgary, Alberta,

Canada.


Wong, G.K., Fors, R.R., Casassa, J.S., Hite, R.H., and Shlyapobersky, J.: “Design, Executionand Evaluation of Frac and Pack (F and P) Treatments in Unconsolidated Sand Formations inthe Gulf of Mexico”, SPE 26563, presented at the SPE Annual Technical Conference andExhibition, Houston TX, Oct 1993.

Tiner, R.L., Ely, J.W. and Schraufnagel, R.: “Frac Packs – State of the Art”, SPE 36456,presented at the SPE Annual Technical Conference and Exhibition, Denver CO, Oct 1996.

Economides, M.J., Oligney, R.E. & Valkó, P.P.: Unified Fracture Design , Orsa Press, Alvin,TX, 2002.



BJ Services’ Frac Manual18. Real-Time Monitoring & On-Site Redesign


18 Real-Time Monitoring and On-Site Redesign

Thanks to the advent of electronic data gathering systems, personal computers and efficient,reliable fracture simulators, it is now possible to actually model the fracture as the treatment

progresses. This process, known as Real-Time Monitoring , allows the Frac Engineer toactually re-design the treatment on-the-fly.

The more traditional form of on-site redesign is when data from a step rate test and/orminifrac is used to redesign the main treatment. This is usually carried out on-site, with thewhole of the frac spread and frac crew waiting for the Frac Engineer to produce the new fracdesign.

18.1 Real-Time Data Gathering

Figure 18.1a – Process loop for real-time fracture modeling and redesign

With a modern frac spread, it is now possible to measure, record and monitor every singletreatment parameter, including items such as liquid additive rates, sand screw rpm’s andannulus pressure. However, for the Frac Engineer, there are three main variables which arerequired:- bottom hole pressure, proppant concentration and slurry rate. It is useful and oftennecessary for a whole range of data to be recorded during the treatment, but it is only thesethree variables which will be needed for the redesign. Often it is useful for the Frac Engineerto use surface treating pressure, in order to calculate BHTP or pipe friction data. Also, is itsometimes quite helpful for the Frac Engineer to record stage number, in order to keep trackof which stage is at the perforations (especially if there are tortuosity problems).

Data is recorded using three basic types of measuring devices; pressure transducers, nuclear

densometers and flow meters (as illustrated in Figure 18.1a).

3600 orIsoplex JobMaster

Frac Model

RedesignedTreatmentSchedule

PressureTransducers

Flowmeters

NuclearDensometers

FracEngineer

Voltage

Frequency

Frequency

ASCII Data

SelectedASCII Data

Bottom HolePressure Data





Flow Meters

Flow Meters come in three main types:- turbine, magnetic and inertial or mass flow meters.

Turbine flow meters are the most commonly used, as they are easy to employ, require noexternal power supply and are cheap. They can also be used in high pressure flow lines. Fluidflow is measured by a single turbine, which is positioned in the centre of the flow stream. Thisturbine rotates when fluid passes through the flowmeter. The faster the fluid flow, the fasterthe turbine spins. A magnetic pick up measures how fast the turbine is rotating, sending anoutput in the form of a frequency to the control centre.

The turbine flowmeter has several disadvantages. It is easily obstructed or damaged bydebris in the frac fluid. This means that the flowmeter needs to be checked and potentially re-dressed after every treatment. The turbine flowmeter requires a separate calibration factor foreach different fluid type (i.e. linear gels, gelled acids, gelled oils etc). The turbine flowmeteralso has a relatively high flow rate threshold, below which the turbine will not rotate. Thismeans that for 2 or 3 different turbine flow meters are usually required for measuring over awide range of flow rates. Turbine flow meters can only be used for liquids.

Magnetic flow meters (often referred to as mag flowmeters ) rely of the physics of generatingelectrical current. This states that it you have motion and a magnetic field, then you will getcurrent flow, provided there is a conductive path. The magnetic flow meter provides themagnetic field, the fluid provides the motion and a current is generated. The magnitude of thecurrent is proportional to the flow rate. These flow meters are easy to use (once they havebeen set up) and very reliable, requiring little maintenance (they have no moving parts orrestrictions). The main disadvantages of these flow meters are that they require an externalpower source, they are expensive and they can only be used for measuring conductive fluids(so they cannot be used for measuring gelled hydrocarbons or gases).

Inertial or mass flow meters (such as the MicroMotion flowmeter) work by using two flowloops. As the fluid enters the flow meters, it is split into two loops of equal diameter. One loopmeasures the density of the fluid, whilst the other loop measures the mass flow rate.Volumetric flow rate is obtained by dividing the mass flow rate by the density.

Density is measured by forcing the flow around a loop that is vibrating. This vibration isproduced by a calibrated agitation system, which always provides the same force, at thesame frequency. A measuring system compares the known “input” agitation with the vibrationof the flow loop. Generally, as the mass of the flow loop + fluid increases, the frequency withwhich the loop vibrates will slow down. As the mass and volume of the flow loop is known, thedensity of the fluid can be quickly calculated.

Mass flow rate is measured by the second flow loop. This loop is offset slightly from the main

direction of flow, so that the inertia of the fluid as it flows causes the loop to twist slightly. Theamount of twist is measured by a number of strain gauges placed along the flow loop. Theforce causing the flow loop to twist (and hence the reading on the strain gauges) is directlyproportional to the mass flow rate.

This type of flow meter has several advantages. Most types of fluids can be measured by thismethod, including gases, hydrocarbons and cryogenic fluids. The flow meter can also be usedto output density, eliminating the need for a separate densometer. If the pressure differentialacross the flow meter is carefully measured, the apparent viscosity of the fluid can also beobtained. Unfortunately, this flowmeter also has several disadvantages. Because the fluidflow is forced around two flow loops, it cannot be used for abrasive fluids (the flow loops arequickly abraded until they fail). These flow meters are quite large and heavy. They areexpensive. Finally, because of the sensitive measuring apparatus inside the flow meter, these

devices are also quite fragile.





The above listed three methods are all direct methods of measurement. However, it shouldalso be noted that flow rate is often measured indirectly, by reading the rpm's of an input shaftpowering a pump (often referred to as a "stroke counter"). Basically, the computer reading therpm's has a calibration factor which converts rpm's to flow rate, a quickly and easilycalculation. Whilst these flowmeters are very easy to use and also very mechanically reliable,they suffer from 2 main drawbacks. First, no pump is 100% efficient, and so the stroke

counter has to be calibrated to allow for this. Second, if the pump loses prime (or doesn't haveprime to start with), then the stroke counter will give a false reading. It is therefore advisableto use a direct flow rate measurement as the primary source of flow rate measurement, usingstroke counters only as a back up.

Nuclear Densometers

Nuclear densometers (or densimeters, or densiometers) all work on the same basic principal.A radioactive source is held on one side of the flow stream, whilst a detector on the oppositeside of the flow stream measures the radioactivity that passes through the flow stream, incounts per second. Basically, the higher the density of the fluid, the lower the number ofcounts per second.

Nuclear densometers vary in the type of output they provide. The basic densometer has nodata processing capabilities, and outputs a frequency signal (the same frequency as thenumber of counts per second being received by the detector). A separate data processingfacility (such as a PC) is required to turn the basic data into a density or a proppantconcentration. It is this type of densometer that is most commonly used in the fracturingindustry. More sophisticated densometers come complete with data processing, and canoutput density, SG, proppant concentration or acid %.

The radioactive source used in the densometer is usually Caesium 137 (or137

Ce). This metalis a medium energy beta and gamma radiation emitter, with a half-life of 30 years. Thismeans that the radioactive source gradually gets weaker with time – after 30 years it is onlyhalf as radioactive as it initially was. Consequently, all radioactive densometers have to beregularly calibrated, to allow for the fact that the source is gradually producing less and lessradiation. Therefore, the data processing facility (usually a PC, an Isoplex or a 3600 , butsometimes also a box on the side of the densometer) has to have this calibration installed, inorder that density can be output.

Proppant concentration is easily calculated from the overall bulk density of the fluid, using thefollowing formula:-

PC = ( ρ sl - ρ gel)

( )1 - [ ρ sl / ρ p] ................................................................... (18.1)

where PC is the proppant concentration in ppa (see below), ρ sl is the slurry density in lbs per

gallon (ppg), ρ gel is the base fluid (usually gel) density in ppg and ρ p is the proppant density,

also in ppg. Proppant density is often also quoted as an absolute volume in gals/lb. This issimply the reciprocal of the density in ppg.

Proppant concentration is measured in ppa or Pounds of Proppant Added. This is the numberof pounds of proppant that have been added to 1 gallon of clean base fluid (which is how theblender adds the proppant – it measures the clean flow rate in gallons per minute, andcalculates how many lbs per minute of proppant need to be added). Sometimes, proppantconcentrations are also quoted in ppg – meaning pounds of proppant per gallon of clean fluid.The use of these units should be avoided for proppant concentrations, as they can get easilyconfused with fluid or slurry densities.

Pressure Transducers

Pressure transducers are the simplest of the measuring devices used in fracturing. Thetransducer is consists of a strain gauge, that is mounted so that as pressure is applied, the





strain gauge is compressed. As the strain gauge is compressed, its electrical resistance willincrease slightly. The higher the applied pressure, the greater the increase in resistance.

The pressure transducer is connected, via a transducer cable, to a special measuring circuitknown as a Wheatstone’s Bridge. This is an electrical circuit consisting of three knownelectrical resistances and an unknown electrical resistance (the transducer + cable). Because

of the nature of the circuit, if the potential difference (or voltage drop) across the bridge circuitis known, the values of the three known resistances can be used to calculate the value of theunknown resistance, to a high degree of precision. Therefore, if the resistance of the cable isknown, the resistance of the pressure transducer can be obtained. So in order to measure thepressure applied to a transducer, the voltage drop must be measured.

Pressure transducers are regularly calibrated by applying a known pressure to them, usuallyvia a dead weight tester. This calibration produces a relationship between resistance andpressure, so that if the resistance is known, the pressure can be quickly obtained.

Because a large increase in pressure produces only a relatively small change in electricalresistance, it is important to have good quality cables that are well looked after (as the circuitmeasures the resistance of the cable at the same time). This also means that the cables must

be of a fixed length, producing a limit to how far the control cabin can be away from thepressure transducer. Transducer cables cannot be spliced, repaired or re-used if they aredamaged.

Processing the Data

Raw data from the transducers, flow meters and densometers is not usable by the monitoringcomputers. It has to be converted to a digital form by an analogue to digital converter. Oncethe data has passed through this, it can be processed to give the actual treatmentparameters.

For instance, the turbine flowmeter is actually measuring the number of times a turbine bladepasses the magnetic pick up, rather than a volumetric flow rate. Every time a blade passesthe pick up, electrical current is generated, reaching a peak as the blade is directly oppositethe pick up. As the blade moves away from pick-up, the current drops off. This means thatthe output from a turbine flow meter is cyclic – the higher the frequency of these cycles, thefaster the turbine blades are rotating and the faster the fluid is flowing. The cyclic analogueinput is the converted to a digital output, by the analogue to digital converter. A digital outputsimply means that the converter is sending the computer a number – in this case the numberof cycles per second, or frequency.

As stated, the output from the analogue to digital converter is passed on to a computer forprocessing. This computer can be a PC, an Isoplex or a 3600 . Whatever form it comes in, theprocessing computer converts (in the case of the turbine flow meter) a number of cycles persecond, into a flow rate, by applying a calibration. This calibration is user input, and will vary

according to the type and size of flowmeter, and the fluid being used.

For pressure transducers, the analogue to digital converter measures the voltage across thebridge circuit, and outputs this as a number. For the nuclear densometer, a similar process iscarried out as for the turbine flow meter, in which a frequency is converted into a number. Theprocessing computer will contain a calibration algorithm for each of these devices, convertingthe numerical output from the analogue to digital converter, into psi or ppa as appropriate.

Displaying and Analysing the Data

Usually the Frac Operator or an electronics technician will run the JobMaster computer. Thiscomputer will display all the parameters being monitored by the system, and is the primarysource of information for the person actually running the treatment. The Frac Operator usually

has the option to run several different displays, so that unprocessed data can be displayed(such as real-time pressure, rate and proppant concentration), along with parameters that





have been processed on the fly, such as calculated BHTP , cumulative volumes and of coursethe Nolte plot.

The Frac Engineer usually operates the second computer. This machine receives selecteddata from the first computer, almost always in ASCII format. The Frac Engineer will use aspecialised treatment monitoring programme or fracture simulator to display and analyse this

data.

The Frac Engineer’s computer is usually capable of receiving ASCII data from more than onesource. The primary source of data will almost always be the JobMaster computer. This datausually comes in via the COM 1 serial port. However, if a second COM port is fitted to theEngineer’s computer, it is possible to receive data from a second source (such as a bottomhole pressure gauge) and merge it with the primary data, real time, so that it can be displayedand analysed. Computers fitted with USB ports can use adapters to allow several COM portsto be used simultaneously.

During the treatment, most of the people in the control centre will be watching the displayscontrolled by the JobMaster computer.

Figure 18.1b – Inside of a typical frac control van, showing the numerical display and some ofthe displays being run by JobMaster .

Remote Data Transmission

Remote data transmission is a specialised service which allows the customer and the FracEngineer to remain in the office, whilst the treatment is carried out. Provided there is someoneon location to look after the fluids, run JobMaster and handle the data transmission process(this will usually be a junior Engineer), then the only reason that the senior Engineers arerequired on location is for data analysis.

If the data can be transmitted to a separate location, then the customer and service companyEngineers do not have to be on location. They can remain back at the office. This hasparticular advantages when the treatment is being carried out in remote locations (such asoffshore). Instead of the Engineers being tied up for (sometimes) several days, remote data

transmission means that they are only directly involved in the treatment for a few hours – thetime taken for the step rate test and minifrac to be pumped, for the redesign to be carried outin the office and for the main treatment to be performed.

JobMaster DisplaysNumerical

Display





Figure 18.1c – Remote data transmission schematic

Data transmission is carried out real time, using software packages like JobMaster , whichhave been specifically designed to carry out this process as part of its capabilities. Both thetransmitting and receiving computers run JobMaster , coordinated so that receiving computeris expecting the same channels that the transmitting computer is sending. The voice link is anessential part of the process, so that the data link can be properly coordinated and also sothat the on-site Engineer and keep the office-based Engineer’s fully informed of developmentsand as they happen.

Thanks to modern communications, it is a relatively easy task to transmit the data real time.Data transmission is usually pretty reliable, but interruptions can sometimes happen. In thiscase, the software package should be set up so that transmission can be easily resumed, and

that data that is not transmitted during the break in communications is stored for transmissionas soon as communication is re-established.

The latest versions of the remote data transmission systems actually use internet-basedcommunications. Each control cabin or frac van has it's own web address, and broadcasts thetreatment onto the internet. Anyone with the job-specific password can log onto to monitor atreatment, from any computer that has internet access.

It is also useful to have a separate file transfer programme or internet access for e-mailinstalled on both computers, allowing quick and easy transmission of data files betweencomputers.

18.2 On Site Redesign

On site redesign is the science and art of redesigning a fracture treatment after the step ratetest and minifrac. Usually it is done on location (or - via remote data transition – back in theoffice) whilst the frac crew and equipment are waiting. Consequently, there is usually areasonable amount of pressure on the Frac Engineer during this process, which may takeseveral hours. For example, in the offshore environment, were the rig may be costing over$300,000 per day, every hour spent redesigning (which is usually down time for the rig), coststhe customer over $12,000.

However, this down time is usually money well spent. The Frac Engineer should take asmuch time as is necessary and must not produce a hasty, poorly designed treatment. The

object of the fracturing exercise is to maximise production increase, after all. Minimising rigtime is obviously highly desirable, but it should not take precedence over the main objective.

DataModem

DataModem

Satellite orCellular

Phone Line

On Location Office

Satellite or

CellularPhone Line

DataLink

Voice

Link





Figure 18.2a – On-site redesign process flowchart

Raw Data

Revised

Treatment

Schedule

Required

Fracture

Properties

Materials &

Equipment

on Location

Yes

No

Yes

No

Fracture

Model

Closure

ISIP

Formation

Properties

Pressure

Match

Fracture

Simulator

Minifrac

Analyser

Fracture

Simulator

Fracture

Meets

Requirements?

Customer

Approval?

P R E S S U R E M A T C H I N G

C

O N V E N T I O N A L A N A L Y S I S

Final

Treatment

Schedule





One way to minimise down time is to restrict the number of Engineer’s involved in theredesign process. It is not exaggeration to state that the time taken for the redesign isproportional to the square of the number of Engineer’s involved.

On site redesign is something that improves with practice and experience.

Figure 18.2a shows a process flow chart for the redesign process. The process starts with thecollection of the raw data. This includes not only the minifrac and step rate data (collectedeither real-time or from separate files), but also other items such as wireline logs, completiondiagrams, tracer surveys, temperature logs, BHTP gauge data, data from previous fracs onoffset wells and so on. Once all this has been collected, the Frac Engineer can start toanalyse the data from the step rate test(s) (see Section 15) and the minifrac (see Section 16).As discussed previously, this process can often take some time and can sometimes becarried out under quite stressful conditions. Nevertheless, once this process has beencompleted, the Frac Engineer should have been able to tune the fracture model, so that whatis in the computer is a reasonable representation of what is in the formation.

Once this has been achieved, the hardest part of the redesign process has been completed.However, the Frac Engineer still has to produce the final treatment design. In order to do this,

the Engineer has to design a treatment schedule based on two important parameters:-

1. The objectives of the treatment. Usually, the objective of the treatment is to place afrac in the formation, with a certain geometry, and relative conductivity. Theseobjectives are usually set up before arriving on location. Usually, these objectives willremain unchanged after the calibration tests (step rate test and minifrac). However,the results of these tests may change the specifics of how this is achieved. Forinstance, if the minifrac shows the permeability of the formation to be significantlydifferent from that anticipated, the optimum fracture geometry will have to be alteredin order to meet the C fD requirements.

2. The available equipment and materials. Usually, the Frac Engineer has to work withinthe limitations for the equipment available for the treatment, in terms of tank volumes,

maximum pumping rates etc., so that the Engineer is producing the optimumtreatment design the frac spread is capable of pumping. In remote locations (wherematerials cannot be “hot-shotted” out to location), the Engineer can also be restrictedby the quantity of materials available on location (volume of gel that can be mixedand the volume of proppant).

Working within these restrictions (and also remembering the maximum allowable pumpingpressure), the Frac Engineer must produce the optimum possible frac design. This is not justa question of producing a production increase – for a lot formations, this is relatively easy todo. The Frac Engineer must also maximise the production increase, to meet or exceed theeconomic criteria for the treatment, as there is usually a significant cost associated withfracturing, and a small production increase may not be sufficient.

18.3 Real-Time Fracture Modeling

Some fracture simulators, such as MFrac , FracPro and FracproPT , have a facility thatenables the fracture to be modeled real-time. This is a very powerful tool that - under the rightconditions - can enable the Frac Engineer to redesign the main treatment on-the-fly, as it isbeing pumped.

The modeling computer is set up to receive data from either the data processing computer orthe Frac Engineer’s computer, usually in ASCII format. The user then runs the fracture model,selecting the “real-time data input” option. The user enters the relevant formation data andtreatment schedule, which can be loaded from a previously created data file. The treatment

starts, and the computer starts to collect the data. As the treatment progresses, the simulatormodels the created fracture. The model will take fluid, proppant, formation and wellborecharacteristics from the input model, and will take the pump rate, pressure and proppant





concentration from the real time data. Using this data, the simulator will model the fracturethat has already been created, constantly updating as more data is collected. This enablesthe user to perform two separate operations:-

1. The Frac Engineer can perform a pressure match with the data that has already beencollected by the simulator, until the net pressure predicted by the computer matches

up with the actual net pressure.2. The Frac Engineer can instruct the simulator to run the job until completion, predicting

the characteristics of the fracture, based on the ongoing pressure match. For thetreatment schedule, the simulator will use the actual treatment data as far aspossible, and then project forward until the end of the job using the remaining inputtreatment schedule. This allows the Engineer to predict the fracture characteristics,based on the most accurate data possible. This process can be taken one stepfurther, as the Engineer can alter the remaining treatment schedule, and predict thefracture characteristics based on this revised schedule. Thus the Engineer canredesign the treatment schedule on-the-fly. This capability is limited to FracPro andFracproPT .

Limitations of Real-Time Modeling

This ability to redesign on the fly – whilst usually not very popular with the frac crew – is avery powerful tool, provided the Frac Engineer is aware of the following:-

1. Do not over-react to short term trends. All fracture simulators treat formations ashomogenous materials with uniform rock mechanical properties throughout. In realitythis is usually not the case. The fracture is constantly propagating through rock withvarying properties, producing unpredictable variations in the net pressure plot. In fact,what the Frac Engineer should be doing is trying to find an “average” value for eachof these properties, such that the simulator’s predicted net pressure curve follows thetrend (and “average” value) of the job plot, but does not necessarily follow everyminute rise and fall in pressure.

2. However, the Frac Engineer must be able to react quickly when a short term trendhas become a long term trend. When this happens, it’s time to start adjusting some ofthe formation properties.

3. Real-time modeling is only effective on long treatments, where the Engineer has timeto spot the long term trends, adjust the model, and still be able to make changes tothe treatment schedule in time for them to have some effect. If the job is too short, thecrew can be pumping the displacement before the Frac Engineer has finished thepressure match.

4. The problem outlined in Point 3 (above) is exacerbated if the wellbore volumerepresents a significant part of the treatment. If this is the case, the treatment can beclose to displacement before the proppant has even passed into the fracture. In suchcases, there is little point in modeling the fracture real-time.

References

Standard Practices Manual, BJ Services, January 2001 onwards

Equipment and Technology Catalogue, BJ Services, 1990 onwards


Johnson, D.E., Wright, C.A., Stachel, A., Schmidt, H., and Cleary, M.P.: “On-Site Real-TimeAnalysis Allows Optimal Propped Fracture Stimulation of a Complex Gas Reservoir”, paperSPE 25414, presented at the SPE Production Operations Symposium, Oklahoma City, March

1993.





Crockett, A.R., Okusu, N.M., and Cleary, M.P.: “A Complete Integrated Model for Design andReal-Time Analysis of Hydraulic Fracturing Options”, paper SPE 15069, presented at the 56th


Meyer, B.R., Cooper, G.D., and Nelson, S.G.: “Real-Time 3-D Hydraulic FracturingSimulation: Theory and Field Case Histories”, paper SPE 20658, presented at the 65

th SPE

Annual Technical Conference and Exhibition, New Orleans LA, Sept 1990.

FracPro Version 8.0+ On-Line Help, RES/Gas Research Institute, March 1998 onwards.

FracproPT Version 9.0+ On-Line Help, Pinnacle Technologies/Gas Research Institute, July1999 onwards.



BJ Services’ Frac Manual19. Post-Treatment Evaluation


19. Post-Treatment Evaluation

The Frac Engineer’s job is not over once the treatment has been pumped. Aside frommonitoring fluid samples and preparing a post job report, the Engineer also needs to evaluate

exactly what has happened in the formation. This is essential if the operating company plansto do more than one frac in a formation.

The simplest method for assessing the effectiveness of the treatment is to compare beforeand after production. However, this does not really tell us much. In order to increase theeffectiveness of future treatments, we need some idea of the size and shape of the fracturethat was actually produced.

Some of the methods described below – such as pressure matching - are relatively easy forthe Frac Engineer to perform. However, other methods, such as tiltmeters and microseismic,require considerable expenditure and planning by the operating company. This means thatplans for post-treatment evaluation must be made when planning for the treatment itself.

19.1 Pressure Matching

Pressure matching is part science and part art. In order to perform a quick and efficientpressure match, it is essential to have a good knowledge of the fracturing process, anunderstanding of the various rock mechanical properties, an understanding of fracturemechanics and, ideally, a reasonable idea of how the fracture simulator works. In spite of thisneed for an understanding of the physics behind the fracturing process and the fracturesimulation, there is still an art to pressure matching. Some Frac Engineers have a feeling forthis process, and some do not.

Pressure matching is a very powerful tool that allows the Frac Engineer to “tune” the fracturesimulator to the formation. The idea being that once the simulator has been tuned, further

fracture simulations can be performed with a high degree of accuracy.

The Process of Pressure Matching

Pressure matching is all about making the simulator predict the same pressure response asthe reaction actually produced by the formation. This is illustrated in Figure 19.1a, as shownbelow:-

Figure 19.1a – Pressure matching. The variables in the simulator are adjusted to make thecalculated net pressure match the actual net pressure.

With reference to Figure 19.1a, before the pressure match (LHS), the net pressure predictedby the fracture simulator does not match the actual net pressure in any way. After the

Actual Net Pressure

Calculated Net Pressure

N e t P r e s s u r e

Job Time

Actual Net Pressure

Calculated Net Pressure

N e t P r e s s u r e

Job Time

Before After





pressure match has been performed (RHS), the computer predicts a very similar pressureresponse to that of the actual treatment data. Now - according to the theory - the simulatorhas been “tuned” to the formation. This allows the Frac Engineer to input any desiredtreatment schedule, and the simulator will be able to predict the fracture geometry with areasonable degree of precision.

There is no doubt that the advent of pressure matching has greatly improved the success rateand effectiveness of hydraulic fracturing. Modern fracture simulators equipped with this facilityhave gradually made the process increasingly user-friendly, helping to reduce the “black art”associated with frac engineering, as more and more Engineers feel capable of designing afracture treatment.

However, there are some definite limitations to this process:-

1. Garbage In = Garbage Out. The computer model of the formation generated by thisprocess is only as good as the data used to create it. Poor data on items such aspermeability, net height, fluid properties (both formation and fracturing fluids) andperforations can make an otherwise perfect pressure match almost irrelevant.Another major source of errors is the use of surface pressure data to calculate BHTP .

In order to calculate BHTP , the model first needs to calculate the fluid frictionpressure, something that is notoriously difficult to do for a crosslinking fluid. Variationsin fracturing fluid properties (such as those caused by problems with liquid additivesystems, or varying gel properties) can also be very difficult to account for. Therefore,the Frac Engineer should do everything possible to get reliable bottom hole pressuredata, such as that from a gauge or dead string.

2. No Unique Solution. The process of pressure matching involves adjusting four majorvariables (Young’s modulus, stress, fracture toughness and leakoff) and many otherminor variables, for each rock strata affected by the fracture, until the pressureresponse predicted by the model matches the actual pressure response of theformation. This means that the Frac Engineer may have 30 or 40 variables availablefor adjustment. It is therefore quite possible for two Frac Engineers to get good

pressure matches, but with significantly different sets of variables.

3. The Fracture Model. At the end of the day, the results of the pressure match are onlyas good as the fracture model itself. Without a doubt, modern fracture simulators aretremendously advanced – the product of more than 20 years of innovation,experimentation and inspiration. However, the fact remains that different fracturesimulators will predict different fracture geometries for the same input data. Whichone is right? Probably they are all wrong – so the correct question to ask is which oneis closest to the Truth? This is difficult to say, and the subject of considerable debatein the fracturing industry. The popular conception is that one fracture simulator isgood for a certain type of formation, whilst another is good for a different type. Thedebate continues.

It should also be remembered that in general (GOHFER excepted) the widely used fracmodels all predict a single eliptically-shaped fracture, either side of the wellbore, symmetricalaround the wellbore. In reality, the fracture is probably much more complex than this. It ishighly unlikely that the fracture - or more likely fractures - behaves in such a regular andpredictable manner. What the fracture simulators do is predict a simplified fracture thatbehaves, on average, in a similar fashion to a much more complex reality

The Four Main Variables

There are four main variables that the Frac Engineer should be adjusting in order to achievethe pressure match – that is to say, four main variables in each formation affected by thefracture. These variables are Young’s modulus, stress, fracture toughness and fluid leakoff.So even for the most basic formation lithology, the Frac Engineer will have to be able to keep

track of a minimum of 12 variables (the zone of interest, plus the formations above andbelow)..





Of course, each fracture simulator comes complete with a whole plethora of variables that theuser can adjust. In fact there are so many, that it could be possible to vary several hundredparameters for a complex reservoir with several rock strata. This is for fracture simulator androck mechanical experts only. Unless there is a really good reason, the Frac Engineer isadvised to stick to the four variables listed below.

Whilst pressure matching, the Frac Engineer should be aware of the fact that the processworks the opposite way around to designing a treatment. In pressure matching, the bottomhole treating pressure is fixed, whereas it is a variable in fracture design. For example, anincrease in in-situ stress will have the effect of decreasing the net pressure in the pressurematching process, whilst in the fracture design process, this net pressure will remain constantand the bottom hole treating pressure will increase. In pressure matching, the Frac Engineeradjusts unknown formation properties to match a known pressure. In treatment design, theseformation parameters are (hopefully) already known, and the process instead involves seeingthe effect they produce for a given treatment schedule.

Fracture Toughness, K 1c

Strictly speaking, K 1cis the critical stress intensity factor for failure mode 1 (see Section 9,

Fracture Mechanics). However, it is commonly referred to as the Fracture Toughness and is ameasure of how much energy it takes to propagate a fracture through a given material. Inhydraulic fracturing, where the energy needed to propagate the fracture comes in the form offluid pressure, fracture toughness tells us what proportion of the available energy is used tophysically split the rock apart at the fracture tip. As pressure is essentially energy per unitvolume, K 1c tells the Frac Engineer how much net pressure is required to propagate thefracture.

Generally speaking, soft plastic formations will have high fracture toughness, whilst hardbrittle formations will have low fracture toughness. There is also an approximate inverserelationship between Young’s modulus and fracture toughness – hard formations tend to havea high E and a low K 1c, and soft formations tend to be the other way around. For the FracEngineer, increasing the value of fracture toughness will tend to make it harder for a fracture

to propagate through the rock. Therefore, an increase in fracture toughness will generallymake the fracture shorter and wider. However, an increase in fracture toughness for just oneformation will tend to divert the fracture into an adjacent formation. For example, if the K 1c isincreased in the perforated interval, the fracture will grow into the adjacent formations, aboveand below. This has the effect of limiting the fracture length and increasing the fracture height.In soft formations, do not be afraid to use quite large values for this property, even severaltimes the default values included in the simulator

Fracture toughness is a material property and cannot be altered by anything under the controlof the Frac Engineer. It is also a property that is very difficult to measure. There are severallaboratory methods for determining K 1c, but these are limited in their reliability, as fracturetoughness is highly dependent upon down hole conditions and the overall geometry of thefracture. However, if core samples are available, fracture toughness can be estimated from

laboratory measurements of yield stress and Young’s modulus, provided this is determinedunder tri-axial loading, at bottom hole temperature and pressure.

Remember that some fracture models (e.g. FracPro and FracproPT ) have moved away fromthe concept of Fracture Toughness and instead model non-linear elastic effects at the fracturetip as being more significant. In such models, variations in Young’s modulus and in-situstresses are far more significant.

Young’s Modulus, E In order for the fracture to propagate it must obtain width, to a greater or lesser extent. Inorder to do this, the rock on either side of the fracture has to be compressed. As discussed inSection 7 (Rock Mechanics), Young’s modulus defines how much energy is required toperform this compression. Rocks with a high Young’s modulus will require a lot of energy

(a.k.a. net pressure) to compress. In these formations, fractures tend to be relatively thin, andthe rock is referred to as “hard”. Similarly, rocks with a low Young’s modulus require relatively





little energy to produce width. In these formations, fractures tend to be relatively wide, and therock is referred to as “soft”.

Young’s modulus is a fundamental material property and, like the fracture toughness, cannotbe altered by anything under the Frac Engineer’s control. It can be measured from coresamples, provided these tests are carried out under tri-axial load conditions, at bottom hole

temperature and pressure. In some formations (especially weak or unconsolidated rocks),Young’s modulus may not be constant.

Fracture mechanics, rock mechanics and fracture simulation require the use of the staticYoung's modulus. This is the Young’s modulus measured under static - or relatively static – conditions, such as those that occur whilst fracturing. Another form of Young’s modulus, thedynamic Young’s modulus (the Young’s modulus measured under dynamic conditions), canbe measured by so-called “stress logs”. These logs, generated by a dipole sonic wireline tool(also called a sonic array), measure dynamic Young’s modulus and Poisson’s ratio bymeasuring the transit time of both shear and compression sonic waves. However, there canoften be a significant difference between dynamic and static values, which renders the actualvalues reported on stress logs to be unreliable. This is covered in more detail in Section 7.10.However, stress logs can accurately report contrasts in Young’s modulus, which are almost

as important as the absolute values themselves.

An increase in Young’s modulus makes it harder for the fracturing fluid to produce width.Therefore, increasing this variable will make the fracture thinner, higher and longer, and vice versa . Increasing E only in the perforated interval will have the effect of forcing the fractureout of the zone of interest – i.e. increasing fracture height. A decrease in E has the oppositeeffect.

In-Situ Stress, σ σσ σ

In-situ stress (often referred to as confining stress or horizontal stress) is the stress induced inthe formation by the overburden and any tectonic activity. Put simply, it is pre-loading on theformation, the stress that has to be overcome (or pressure that has to be applied) in order to

actually start pushing the formation apart. The actual bottom hole fracturing pressure is thepressure required to overcome these in-situ stresses, plus the pressure required forpropagating the fracture (as a consequence of fracture toughness) and the pressure requiredto produce width.

As previously discussed in Section 7, fractures will tend to propagate perpendicular to theminimum horizontal stress (i.e. along the line of least resistance). So the in-situ stress of aformation is the minimum horizontal stress of the formation, plus any tensile strength the rockmay posses, and less any effects due to reservoir pressure.

As the horizontal stress only exists because of the overburden (ignoring tectonic effects), it ishighly dependent upon the Poisson’s ratio of the formation, as illustrated in Equation 7.18. Atthe limit, a Poisson’s ratio of zero means that the horizontal stresses are equal to zero, plus

the effects of pore pressure. This is a theoretical minimum – in practice no material will everhave a Poisson’s ratio of zero. At the other limit, the maximum theoretical value for Poisson’sRatio is 0.5 – at this value, the horizontal stresses will be equal to the overburden, plus theeffects of pore pressure.

So-called “stress logs” actually measure the dynamic Young’s modulus and Poisson’s ratio ofthe formation. Therefore, if the overburden is known (derived from a density logs and the TVDof each formation), the approximate in-situ stress can be calculated. However, the stressesgenerated from this procedure are derived from the dynamic (rather than static) Poisson’sratio. Therefore, any stresses generated by this method are unreliable. The absolute value ofthese stresses cannot be trusted – however, stress contrasts between formations can beused as an indication of potential fracture height containment.

In the pressure matching process, an increase in s means a reduction in net pressure (for afixed BHTP ). This means that the fracturing fluid has less energy available to fracture the





formation, and so the width, the height and the length of the fracture are all decreased. This inturn means that the volume of the fracture has decreased. However, the same volume of fluidhas been pumped into the formation, so an increase in s also has the effect of increasingleakoff rate and decreasing fracture efficiency. The opposite effect applies for a decrease inin-situ stresses.

Fluid Leakoff Rate, Q L

The fluid leakoff rate can be controlled by altering a number of variables, depending upon thefracture simulator being used, and the fluid leakoff model being employed:-

Pressure differential (fracturing fluid pressure minus pore pressure)Formation permeabilityFormation porosityFormation compressibilityFormation fluid viscosityFracturing fluid filtrate viscosityFracturing fluid wall-building coefficientSpurt loss.

A lot of these variables are difficult to measure or determine. However, the Frac Engineershould remember the ultimate objective of determining fluid leakoff – to calculate the volumeof the fracture. To this end, the simulator has to be able to accurately calculate the volume offluid lost through each unit area of the fracture face. Whether or not this is achieved byvarying the permeability or the wall building coefficient is almost irrelevant. On top of this, fluidleakoff can be dramatically complicated by fracture fluid flow into fissures or natural fractures,the geometry of which can vary with the net pressure.

In most cases, the Frac Engineer will have reasonable data for some of these values – andwill have to guess at others. Therefore, a good strategy is to fix those values that havereasonable data, and vary the others, until the desired leakoff is obtained.

Fluid leakoff is a loss of energy from the fracturing fluid, as the total energy available forpropagating the fracture is equal to the net pressure multiplied by the fracture volume. Highleakoff means low fracture volume, and vice versa . Therefore, and increase in fluid leakoff willtend to decrease width, height and length. The opposite applies for a decrease in leakoff.

Summary of the Effects of the 4 Main Variables

The basic effect of each of these variables – when applied to a fracture in a single formation – can be summarised in Table 19.1a, below:-

Variable

Effect of an Increase in Selected Variable

Height Length WidthNet

Pressure

Fracture Toughness, K 1c Decrease Decrease Increase Increase

Young’s Modulus, E Increase Increase Decrease Increase

In-Situ Stress, σ Decrease Decrease Decrease Decrease

Fluid Leakoff Rate, Q L Decrease Decrease Decrease Decrease

Table 19.1a – The effects of an increase in each of the four, main pressure matching variables.Note that these are the overall effects when the change is taken in isolation (i.e. no other

changes take place). It also assumes that the fracture is unaffected by boundary layers aboveand below.





This table should be used with caution, as it applies only when the fracture is confined withina single formation. If the fracture propagates into separate formations above and below theproductive interval, then an increase in (for instance) fracture toughness will make it harderfor the fracture to propagate through the main formation, forcing the fracture up and down.So, in this instance, an isolated increase in a property in just one formation, can actually

increase the fracture height.

The Effect of Poisson’s Ratio

Poisson’s ratio is at the same time both important and largely irrelevant to pressure matching.It is important, because it has a major effect of defining the horizontal stresses in a formation.However, in most cases, the Frac Engineer will be determining these stresses form pressuredata, not from Poisson’s ratio data. In most fracture simulators, Poisson’s ratio is used in theform (1 - ν

2 ) to modify Young’s modulus (i.e. E /(1 - ν

2 ) – the plane strain Young’s modulus).

This means that a large change in Poisson’s ratio, say from 0.25 to 0.35, only produces a

change in (1 - ν 2 ) from 0.9375 to 0.8775 (so that a 40% increase in n produces only a 6.4%

decrease in(1 - ν 2 ).

Therefore, the Frac Engineer should not spend too much time varying Poisson’s ratio duringthe pressure match. Input what seem to be reasonable values, and then ignore it.

Tips for Pressure Matching

1. “The Fundamental Interconnectedness of Everything” *

The Frac Engineer must be aware that the fracture is a continuous, dynamic entity. It is notcomposed of a number of discrete pieces, functioning independently of each other. Thismeans that any change to any single variable will affect the whole of the fracture, to a greater

or lesser extent. This can sometimes be very discouraging for the Frac Engineer, as a changeto match one part of the pressure curve can alter a match already achieved in another part ofthe curve. However, remember that in reality, a pressure match that only matches a limitedpart of the plot is not really a pressure match at all.

This means that the Frac Engineer should try to change only one variable for each simulatorrun. This can be time consuming, but is essential if the Engineer intends to keep track of howindividual changes affect the overall simulation.

* - Acknowledgement to Douglas Adams, Dirk Gently’s Holistic Detective Agency

2. Ignore Short-Term Trends

Fracture simulators model a formation as a homogenous material, whose properties areuniform throughout the material. In reality, this is not the case. Real rock formations will tendto have variations – large and small – throughout their structure. These will produce anynumber of short-term pressure spikes and drops during the treatment. Do not even attempt tomodel them.

In practice during the pressure match, try to use average values for formation properties thatwill produce a good “overall” value. Thus, the ideal pressure match will produce a relativelysmooth curve that closely follows the trend of the real data, but does not match every singlevariation (see Figure 19.1a).

In particular, most treatments see a “break down” pressure, right at the beginning of thetreatment. This generally means a large pressure spike, followed by a lower, more stable

pressure. This pressure spike is caused by near wellbore effects and should not be matched.





3. Watch Out for Tortuosity

Tortuosity can seriously affect the bottom hole treating pressure. Remember that even if theFrac Engineer has access to bottom hole gauge pressure data, this data will be from insidethe wellbore, not inside the fracture. Tortuosity can often vary significantly during a treatment.

In particular, an increase in proppant concentration can often produce a pressure rise iftortuosity is present.

The various methods for identifying and quantifying tortuosity have been discussed in earliersections of this manual. If these methods are used it is possible – to a certain extent – toallow for these effects.

Another thing to be careful of is an overuse of the tortuosity tables in the fracture simulator.The latest versions of the main models allow different pressure drops to be entered fordifferent periods during the pumping. By putting enough detail and enough stages into thesetables, it is possible to get the simulator to predict virtually any net pressure profileimaginable. The Frac Engineer must have a grasp of what is realistic and what is not. Thismainly comes with experience.

4. Start with the Pressure Decline

The best place to start the pressure match is with the post-treatment pressure decline. This isbecause the fluids are stationary and effects such as pipe friction, perforation friction andtortuosity are eliminated. It is also often possible to identify the closure pressure on thedecline curve. This value is equal to the in-situ stress for the formation next to theperforations. Once this value has been obtained, the end of treatment net pressure is defined(the difference between the ISIP and the closure pressure). The four main variables should beadjusted to produce this net pressure and to match the shape and length of the pressuredecline between ISIP and closure.

This gives the Frac Engineer a good starting point. Obviously, as the pressure match

continues and the Engineer alters variables to match the rest of the treatment, the pressurematch for the pressure decline will be altered. So further changes have to be made to bringthis back into match. Which in turn will affect the rest of the pressure match, and so on. Thisis a part of pressure matching – the process of gradually making smaller and smaller changesto the variables until all the seemingly contradictory requirements are met.

5. Early Time vs Late Time

At the start of the treatment the fracture is relatively small, and will be confined to theformations at, or near to, the perforations. Therefore, during this “Early Time” period, there islittle point in altering the properties of formations that are away from this area. However, asthe treatment progresses into “Late Time”, the fracture will become increasingly influenced bythe properties of formations vertically further away from the perforations.

Therefore, if the first stage in the pressure match process is to match the pressure decline,the next stage is to match the Early Time fracture. At this point, there will be fewer variablesto alter. Once an Early Time match has been obtained, match the Late Time section. Thenkeep repeating until the match has been achieved.

6. Remember Nolte Analysis

In spite of the fact that Nolte analysis is based on PKN 2-D fracture modelling, the basicprincipals can be very helpful when pressure matching. For instance, a gradual rise in thenext pressure plot indicates fracture containment, whilst a decline probably means apreferential height growth and possibly a radial fracture (or GDK fracture geometry,sometimes found when fracturing coal seams).





19.2 Well Testing for Fracture Evaluation

Well testing is sometimes used both to assess the effect of the treatment and to helpdetermine the size and shape of the fracture. To do this, well tests have to be performed bothbefore and after the treatment. Data that is collected before the treatment is used to helpevaluate the fracture geometry afterwards.

Both pre- and post-treatment tests should be performed at constant rate (or as near aspossible), rather than at constant drawdown, and should be followed by a shut in (or pressurebuild-up) period, lasting for at least as long as the flow time. In practice, it is possible tomonitor the pressure build-up real-time and see when the build-up can be terminated. Thepost-treatment well test can take some time, as treatment fluids must be recovered first, andthe well must reach some kind of relatively steady flow.

Figure 19.2a illustrates the basic anatomy of a drawdown / build-up well test.

Figure 19.2a – Anatomy of a drawdown / build-up well test (after Agarwal, 1980)

In Figure 19.2a, there are several variables that are often referred to in well test analysis,which can be broken down into two groups – time and pressure. All pressures refer to BHpressure. At the start of the well test t = 0, and the BHP = P i, which ideally will be the reservoirstatic pressure. Sometimes this is not the case, if the well has not been left static for a longenough period. However, this can be allowed for in well test analysis. As the well is producedat a constant rate, the length of time the well has produced for is called t and the flowing BHPis referred to as P wf. Because this variable is dependent upon t (the longer the well is

produced, the lower the BHP), it is said to be a function of t , and so the notation P wf(t ) is usedto denote this. The difference between the initial pressure (P i) and the actual flowing pressure(P wf(t )) is referred to at the drawdown, or ∆P drawdown. The well is flowed at a constant rate(which may require the varying of chokes) until it is shut in. At this point, t is said to equal theproducing time, t p (which is a constant, for any given test). After the well is shut in, the

nomenclature ∆t is used to describe the shut in time, such that at the point of shut in t = t p and∆t = 0. Thereafter, time is described as t p + ∆t , with t p fixed and ∆t increasing as the build-upprogresses. At the point of shut in, the BHP pressure is referred to as P wf(t p) – well flowing

wellbore pressure at t p – or as P ws(∆t = 0), the static wellbore pressure at ∆t = 0. These twopressures are identical. After shut in, during the pressure build-up, the now static BHP isreferred to as P ws(t p+∆t ) – this means that the wellbore static pressure (P ws) is a function ofshut in time (t p+∆t ). Finally, the difference between the shut in pressure (P wf(t p) or P ws(∆t =0))and the wellbore static pressure (P ws(t p+∆t )) during the build-up is referred to as the build-uppressure, or ∆P build-up.

B H P

CONSTANT RATE DRAWDOWN BUILD-UP

∆∆∆∆P drawdown

∆∆∆∆P build-up

P wf(t )

P ws(t p+∆∆∆∆t )

P wf(t p) = P ws(∆∆∆∆t = 0)

t ∆∆∆∆t 0 t p

P i





Figure 19.2a illustrates the most basic type of well test, the constant rate drawdown and staticbuild-up test. This type of test can be applied to the well both before and after the treatment,as discussed below. There are many other and more complex types of well test performed,designed to get more accurate data under specific circumstances. A full discussion on thecurrent state of well testing and well test data analysis is beyond the scope of this manual andthe reader is invited to consult the references for further information.

Infinite or Finite Conductivity Fractures

From a pressure transient analysis perspective, propped hydraulic fractures fall into twocategories, infinite conductivity and finite conductivity. The pressure transient behaviour ofthese two types of fracture is significantly different.

Infinite Conductivity fractures have no significant pressure drop as the fluid passes downthe fracture. Therefore, pressure transients happen outside of the fracture, either in thewellbore or in the formation. With this type of fracture, the productivity of the well-fracture-formation system is limited by the ability of the formation to deliver formation fluids to thefracture, rather than by the ability of the fracture to transport the fluids. This type of fracture istypical of low permeability and/or tight gas fracturing.

Finite Conductivity fractures have a significant pressure drop as the fluid passes down thefracture. Therefore pressure transients occur inside the fracture, as well as in the wellboreand the formation. With this type of fracture, the productivity of the well-fracture-formationsystem is limited by the ability of the fracture to transport formation fluids to the wellbore, i.e.by the fracture conductivity. This type of fracture is typical of high permeability fracturing.

Pressure Transient Analysis

When a well is flowing, it can be in one of three states – Steady, Pseudo or Transient. Thedifference between these three states was discussed in Section 12 of this manual. During welltesting, the flow is usually in the transient state, which is the most complex of all to analyse,

and occasionally in pseudo-steady state. Put basically, steady state flow behaves as perDarcy’s Equation, with a constant r e and P i, whilst transient flow behaves like there is no outerboundary to the reservoir (so that the radius of investigation, r d, is continually increasing).Pseudo-steady state is halfway between the two, with a constant r e and reservoir pressurethat declines with production (i.e. a bounded reservoir). In reality, steady state Darcy radialflow very rarely exists. The difference between transient and pseudo-steady state can beseen from constant rate drawdown and pressure build-up tests, as shown in Figure 19.2b.

The basic Equation for pressure transient analysis is relatively easy to comprehend (althoughits derivation is very complex).

P i – P

r, t=

q B o µ

4π kh

1 - e

φµ cr 2

4kt ............................................ (19.1)

where P i is the static reservoir pressure, P r, t is the pressure at radius r after time t , q is thestabilised flow rate, B o is the oil formation volume factor (a factor used to correct surface

volumes to bottom hole volumes) in rbbls/stb, µ is the viscosity of the produced fluid or fluids(at bottom hole conditions), k is the permeability, h is the net height, φ is the porosity of theformation and c is the overall compressibility of the formation and fluids (also called c t).





Figure 19.2b – Graphs illustrating the deviation from transient flow caused by a reservoirboundary (i.e. pseudo-steady state flow)

Under constant rate drawdown Equation 19.1 can be simplified to:-

P i - P wf =

q B o µ

4π kh

loge k t

φµ cr w2 + 0.809 ................................... (19.2)

In field units (pressure in psi, flow rate in bbls per day, viscosity in cp, distances in ft,compressibility in psi-1, permeability in mD, time in hours and porosity expressed as afraction):-

P i - P wf = 162.6 q B o µ kh

log10

k t φµ cr w

2 - 3.23 ........................... (19.3)

So for transient flow, during a constant rate drawdown, a plot of P wf against log t will producea straight line of gradient equal to (162.6q µ / kh ). From this, if the flow rate, viscosity, volumefactor and net height are all known, the permeability can be evaluated by measuring thegradient of the straight line portion of the curve, as shown in Figure 19.2c. This is a verycommon method for evaluating permeability, but is dependent upon the well being producedat a constant – or nearly constant - rate. The permeability value produced by the test is muchmore useful for Frac Engineers than permeability derived from log or core analysis. First, thisvalue is an "average" Figure for the whole net height being produced. Second, well testanalysis is the only investigative method that penetrates deep into the reservoir and so theresults are not influenced by irrelevant near wellbore effects.

The radius of investigation of the test, r d, can be evaluated using Equation 19.4. This allowsthe distance at which a boundary is observed (see Figure 19.2b) to be estimated, by settingthe value of t (in hours) to be when the drawdown semi-log plot starts to deviate from thestraight line.

r d =2

0.00105 k t

φµ c ........................................................... (19.4)

B H P

t

Transient

Pseudo-Steady State

B H P

t

Transient

Pseudo-Steady State

Constant Rate Drawdown Pressure Build Up





Figure 19.2c – Constant rate drawdown semi-log plot. The straight line section can be used toevaluate the permeability. The deviation from the straight line at late time, is due to boundary

effects of the reservoir, as the transient flow changes to pseudo-steady state flow.

r d =2

0.00105 k t

φµ c ........................................................... (19.4)

After shut-in, the pressure in the well starts to build up, as illustrated in Figure 19.1a. TheEquation defining the behaviour of the pressure is as follows, in field units:-

Figure 19.2d – Example Horner plot, showing extrapolation of the straight line portion to obtainP *, the average static reservoir pressure. Once again, deviation from the straight line is caused

by a change from transient flow to pseudo-steady state flow.

P w s

( t p + ∆ ∆∆ ∆ t )

log10

162.6 q B o µ µµ µ

kh slope = m =

t p + ∆∆∆∆t

∆∆∆∆t

t p + ∆∆∆∆t

∆∆∆∆t

INCREASING ∆∆∆∆t

P* (Transient)

0

P* (Pseudo-

Steady State)

P w f

log10 t

162.6 q B o µ µµ µ

kh slope =





P i – P ws(t p+∆t ) =

162.6 q B o µ kh

log10

t p+∆t

∆t ....................................... (19.5)

Therefore, a plot of P ws(t p+∆t ) against log10[(t p+∆t )/ ∆t ] will produce a straight line for transientflow, which will have a slope equal to (162.6q µ / kh ). This plot is often referred to as a Hornerplot and is a widely used tool in pressure transient analysis. An example is illustrated in

Figure 19.2d. Note that as ∆t tends to infinity, (t p+∆t )/ ∆t tends to 1 and hence log10[(t p+∆t )/ ∆t ]tends to 0. Therefore, by extrapolating the Horner plot back to where the x-axis equals zero,an estimate for the static reservoir pressure can be made. This means that the pressure build-up portion of the well test can be more useful than the drawdown phase, and that the welldoes not need to be shut in for a long time prior to the well test, in order to get an accurateFigure for P i.

So from the drawdown test, we can get reliable data for the average reservoir pressure and k (or often, kh , as the net height may be unknown). We can also get the skin factor S (seeSection 2.5) from the build-up data by applying the API Skin Factor Equation, in field units:-

S = 1.151

P ws(∆t = 1)-P wf(t p)

m - log10

k

φµ cr w2 + 3.23 ..... (19.6)

where P ws(∆t = 1) is the static wellbore pressure 1 hour after the well is shut in, and m is theslope from the Horner plot, as shown in Figure 19.2d.

Once the skin is known, the pressure drop due to the skin, ∆P skin can easily be calculated:-

∆P skin = 141.2

q B o µ

2π kh S (field units) ................................... (19.7)

Which can be worked back into Equation 19.3:-

P i - P

wf=

162.6 q B o µ

kh

log10

k t

φµ cr w2 - 3.23 + S ................. (19.8)

Diagnostic Plots

Diagnostic plots are standard plots used to determine the characteristics of the reservoir.Usually, the diagnostic plot will consist of a log-log plot of the change in wellbore pressure,∆P , against shut in time, ∆t , for the pressure build-up. Sometimes, semi-log plots (∆P plottedagainst log ∆t ) are also used.

In addition, the derivative of the pressure build-up, ∆P ’, is also plotted alongside the pressuredata. This is a slightly different derivative than that used in minifrac pressure decline analysis,and is generally calculated as follows:-

∆P ’ = ∆t

∆P

∆t .................................................................... (19.9)

Usually, this will produce a very noisy derivative plot, and it is common practice to use somekind of smoothing or averaging algorithm to produce a clear derivative trend. Moderncomputer-based analysis makes this easy.

Example diagnostic plots for fractured and non-fractured wells are shown in Figures 19.2e to19.2h, below (after Economides et al , 1994):-





Gas Well Testing

Gas well testing is an order of magnitude more complex than oil/water well testing, due to thefact that the above theory assumes that the produced fluid is incompressible. Obviously, thisis not the case for gas wells. To compensate for this, Equation 19.8 is modified as follows:-

P i2 - P wf

2=

1639 Q µ iz iTB gkh

log10

k t

φµ icr w2 - 0.351 + 0.87S (19.10)

This Equation is in field units, were Q is the gas flow rate in scf/d, µ i is the gas viscosity atstatic reservoir conditions, z i is the z-factor at static reservoir conditions (the z-factor is adimensionless factor used to correct the ideal gas Equation to allow for real gas behaviour,and is calculated or measured for each reservoir), T is the reservoir absolute temperature inrankine and B g is the gas formation volume factor (this is a factor used to correct surfacevolumes to reservoir volumes, with units of cuft/scf).

Usually, this Equation is rearranged so that it is more conveniently used:-

m(P i) – m(P wf) =

1639 QTB g

kh (log10t D – 0.351 + 0.87S) .................. (19.11)

Figure 19.2e – Log-log diagnostic plot withderivative for the pressure build-up of an

infinite-acting reservoir (i.e. no boundariesand no pseudo-steady state flow).

Figure 19.2f – Log-log diagnostic plot withderivative for the pressure build-up of

reservoir with a partial boundary (e.g. asealing fault).

log10 t log10 t

∆∆∆∆P

∆∆∆∆P'

∆∆∆∆P

∆∆∆∆P'

Figure 19.2g – Log-log diagnostic plotwith derivative for the pressure build-u of an infinite conductivit fracture

Figure 19.2h – Log-log diagnostic plotwith derivative for the pressure build-

u of a finite conductivit fracture

log10 t log10 t

∆∆∆∆P

∆∆∆∆P'

∆∆∆∆P

∆∆∆∆P'





where

m(P i) =P i

2

µ i z i ........................................................................... (19.12)

m(P wf) = P wf2

µ i z i ........................................................................... (19.13)

and

t D =2.634 x 10

-4kt

φµ icr w2 ........................................................... (19.14)

Note that in Equation 19.14, r w is in feet. m(P ) is referred to as the gas pseudo-pressure.

By using Equation 19.11 for the drawdown, similar techniques can be used as for oil welltesting. However, this time m(P wf ) is plotted on the y-axis, and the slope of the straight lineportion is equal to 1639 QTB g / kh .

For the pressure build-up, the transformation from incompressible to compressible is similar:-

m(P i) – m(P ws) =

1639 QTB g

kh log10

t p+∆t

∆t ..................................... (19.15)

For the Horner plot, the x-axis remains unchanged, but the y-axis plots m(P ws). The straightline portion can be extrapolated back to where the x-axis = 0, to give m(P i).

Type Curve Matching

Figure 19.2i – Type curves for a single well in an infinite reservoir, with wellbore storage and skindamage (after Agarwal, Al-Hussainy and Ramey, 1970).

S = 20

S = 10

S = 5

S = 0

S = -5

C D =

1 0 5

C D = 0

C D =

1 0 4

C D =

1 0 3

C D =

1 0 2

102 103 104 105 106 107 108

10-1

1

10

102

P w D

t D





Type curve matching is a technique that involves matching field generated data curves toexperimentally or numerically derived type curves. The field data is moved over the typecurve, until the type curve that most closely matches the field data is found. This techniquehas become very popular recently, as it is very easily performed by computers.

Usually, there will be several different type curves available, for wells with differentcharacteristics such as skin, wellbore storage (see below), number of wells and reservoirboundaries. A typical set of type curves is shown in Figure 19.2i, which is for a single well inan infinite system (i.e. no boundaries), with wellbore storage and skin damage.

Where P wD is dimensionless pressure:-

P wD =kh (P i - P wf)

141.2 q B o µ (Oil Wells)................................. (19.16)

P wD =kh [m(P i)-m(P wf)]

1424 Q B gT (Gas Wells)............................... (19.17)

and t D is as defined in Equation 19.14.

Wellbore Storage

Wellbore storage is a measure of how much the volume of liquid and gas contained in thewellbore effects the flow of the well. For instance, the pressure transient theory outlinedabove, assumes that there is an instantaneous change from flowing to not flowing, when thewell is shut in and vice versa . This assumption is probably valid for a drill stem test (DST),where the valve being opened and closed is located downhole. However, for most well tests,the controlling valve will be at the surface. When the well is shut in, there will be some flowfrom the reservoir into the wellbore, otherwise the pressure in the wellbore would not rise. Theonly way this can happen is if the wellbore expands. Similarly, when the well is opened, andthe pressure drops, the wellbore contracts. This storage effect is greatest when the wellborevolume is largest (i.e. flow through casing) or when the fluids are compressible (i.e. gas wellsor wells with significant associated gas production).

The wellbore storage coefficient, C , is defined as follows, with volume measured in bbls andpressure in psi:-

C = ∆V

∆P ............................................................................ (19.18)

So that C is a measure of how much change in volume is produced for a given change inpressure. Dimensionless wellbore storage, C D, as used in the type curves, is defined as

follows:-

C D =5.6146C

2πφ chr w2 ................................................................... (19.19)

Type Curve Matching

Type curve matching is performed as follows.

1. Select a set of type curves which most closely suit the well and reservoir situation, basedon items such as reservoir boundaries, skin factor, wellbore storage, number of wells andwhether or not the well has a hydraulic fracture.

2. Produce a log-log plot of ∆t against ∆P (or ∆m(P ) for gas wells) for the well test data. Thiscan be for a constant flow rate drawdown, a constant drawdown flow or for a build-up. An





example is illustrated in Figure 19.2j. When constructing this plot, make sure the axes areof the same scale as the axes used in the type curves. This is a critical component of thetype curve matching process, and is made very easy by computer-based methods.

3. Move the log-log plot of the test data over the type curves, until the data matches up withone of the type curves. This process can often be very difficult – especially if the data isnoisy - as several type curves may have very similar shapes. Once the curves have been

matched, the type curves will yield (as in the case of Figure 19.2i) the dimensionlesswellbore storage coefficient and the skin factor.

4. The final step is to obtain the match pressure and match time. With the test data curvestill positioned at its curve match, pick a point on the test data plot. This can be any point,and does not necessarily have to be anywhere near the data. In fact, it is often easier topick a point where two major axes cross. Note the value of ∆t and ∆P at this point (thesevalues are referred to as ∆t M and ∆P M). Then note the corresponding values for this pointon the type curve, to give t DM and P wDM, the dimensionless match time and pressure. Thisprocess is more easily visualised if we imagine we have two hard copies of the plots. Thetype curve plot is on paper, whilst the test data log-log plot is on a transparency. Thetransparency has been moved over the type curve to obtain the match. Then, we haveselected a point on the test data plot, and pushed a pin through both plots to make asmall hole in each. ∆t M and ∆P M are the coordinates of the pin hole in the test data plot,

and t DM and P wDM are the coordinates of the pin hole in the type curve plot.5. The match pressures and times can now be used to obtain reservoir data. The match

pressures are substituted into Equations 19.16 and 19.17, in order to determine thepermeability-thickness (kh or conductivity) of the formation, as shown in Equations 19.20and 19.21. If the net height is known, the permeability can easily be found.

kh = 141.2qB o µ

P wDM

∆P M (for oil wells) ........................... (19.20)

kh = 1424QB gT

P wDM

∆m(P )M (for gas wells) ........................ (19.21)

Figure 19.2j – Example of a log-log plot of ∆∆∆∆t against ∆∆∆∆P , used for type curve matching.

10-2 10-1 1 10 102 1031

10

102

103

∆ ∆∆ ∆ P ( p s i )

∆∆∆∆t (hours)





Figure 19.2k – Post-treatment log-log plot of well test data for a finite conductivity fracture in agas well. An infinite conductivity fracture would have a half slope.

Similarly, Equation 19.14 can be re-arranged to yield the porosity-compressibility product,which is another variable that will be useful in future analysis:-

φ c =

2.637x10-3

k µ r w

2 ∆t Mt DM

.................................................. (19.22)

Post-Treatment Well Testing

Once the well has been fractured, and the fracturing fluid has been recovered, the well can betested again, to assess the performance of the fracture. Usually, this test will consist of a shutin for one hour, a constant rate flow period of about 24 hours and finally a shut-in period ofabout 48 hours. These numbers are typical for oil wells. Gas wells are a little more complex,as the flow is much more affected by non-Darcy flow in the fracture and wellbore storage. Forgas wells, it is advisable to rely on previous experience, and where that is not available, beprepared to change the well test plan on location.

Basically, for a fractured gas well, the log-log plot of the test data should look something likeFigure 19.2k. With reference to this Figure (which is also applicable to oil wells, with DP asthe vertical axis), flow from a fractured well should fall into 5 distinct regimes, in chronologicalorder:-

• Wellbore storage dominated flow.• Fracture linear flow, in which the flow is dominated by liner flow down the fracture to the

wellbore. This is usually characterised by a half slope on the log-log test data plot. Thisperiod of flow will also not last very long.

• Bilinear flow, in which fluid flow along the fracture and through the formationperpendicular to the fracture faces are both significant. This flow regime is characterisedby a quarter slope on the log-log plot and should be a prominent feature of the test, if the

treatment has been successful. This is the most useful portion of the test data.

10-2 10-1 1 10 102 103106

107

108

109

∆ ∆∆ ∆ m ( P ) ( p s i 2 / c p )

∆∆∆∆t (hours)

14 Slope





• Formation linear flow, where the test data is dominated by linear flow through theformation, perpendicular to the fracture faces.

• Pseudo-radial flow. This flow regime comes last and is characterised by a combination oflinear flow perpendicular to the fracture faces, and by radial flow from the formationbeyond the fracture tip.

For a gas well, the test should continue until significant data has been obtained for the bilinearflow data, whether for drawdown or build-up. The best way to assess this is to plot the log-logplot real time and watch for the quarter slope.

A typical set of post-treatment type curves is shown in Figure 19.2l.

In Figure 19.2l, the x-axis variable is the fractured well dimensionless time, defined asfollows:-

t Dxf =

2.634x10-4

kt

φµ cx f2 ........................................................... (19.23)

Where x f is the fracture half-length. It should be noted that this style of type curve is only valid

if the fracture half-length is significantly less than the reservoir’s radial extent.

Matching the test data log-log plot to the type curve is easier than for the pre-fracture test.When the match is performed, the quarter slope portion of the test data log-log plot ismatched within the shaded area of Figure 19.2l. As all the variables for the dimensionlesspressure are already known, the type curve match is used to obtain the dimensionlessfracture conductivity, C fD, and the match times. The match times are used to find the fracturehalf length, as follows in Equation 19.24.

Figure 19.2l – Type curves for a well with a finite conductivity, vertical fracture (after Agarwal et al , 1979 and Economides et al , 1987).

1

10

t Dxf

P w D

10-5 10-4 10-3 10-2 10-1 110-2

10-1

Region of Bilinear Flow

C fD =

0. 1

0. 5

1. 0

5. 0

1 0

1 0 0

5 0

5 0 0





x f =2

2.634x10

-4 k

µφ c

∆t M

t Dx f M

................................... (19.24)

As k and φ c where obtained in the pre-fracture well test, the fracture half-length can be quicklydetermined. Once x f has been found, the value for dimensionless fracture conductivity can be

used to obtain the fracture conductivity from Equation 10.1.

Taking this one step further, if the permeability of the proppant, k p is known (remembering toallow for proppant damage, non-Darcy flow and multi-phase flow), then the average width ofthe fracture, w ¯ , can also be obtained.

Quarter Slope versus Half Slope

According to the theory, as the well starts to flow the system passes through five distinctphases of flow:- wellbore storage; fracture linear flow; bilinear flow; formation linear flow; andfinally pseudo-radial flow. In practice, wellbore storage occurs at very early time, and fracturelinear flow only occurs for a very short period of time. For the majority of the well test period,the data will be dominated by bilinear flow or formation linear flow.

If the fracture has a finite conductivity, the flow will spend a considerable amount of time inthe bilinear flow regime, as characterised by a quarter slope on the plot of Log ∆P against Log∆t (the log-log plot). However, if the fracture has infinite conductivity, then the flow quicklymoves from bi-linear to formation linear, which has a half slope on the log-log plot. In fact,often the quarter slope section will not be detected.

Spotting the difference between the two is easy. Bi-linear flow (finite fracture conductivity)produces a straight line on a plot of ∆P (or ∆m(P )) against ∆t

0.25, whilst formation linear flow

(infinite fracture conductivity) produces a straight line on a plot of ∆P (or ∆m(P )) against ∆t .Useful information regarding the fracture dimensions can be obtained from these plots, asfollows:-

Finite conductivity fracture (field units):-

k p w =

44.1qB µ h m bf

2

1φµ c t k

(oil wells)................................. (19.25)

k p w =

444.8q z i T

h m bf

2

1φµ c t k

(gas wells) .......................... (19.26)

Infinite conductivity fracture (field units):-

x f =4.064 q B

h m lf

µ

k φ c t (oil wells)....................................... (19.27)

x f =40.925 q z i T

h m lf

µ

k φ c t (gas wells) ............................... (19.28)

where m bf is the slope of the straight line portion of the bi-linear flow plot (i.e. ∆P against∆t

0.25), whilst m lf is the slope of the straight line portion of the linear flow plot (i.e. ∆P against∆t ). Therefore, by using these plots, the average propped fracture width (w ¯ ) can be foundfor finite conductivity fractures, and propped fracture half length (x f) can be found for finiteconductivity fractures, provided an accurate proppant permeability is known, under theproducing conditions.





A Word of Caution

Type curve methods for obtaining the fracture geometry from well test data are notorious forbeing non-unique. A glance at Figure 19.2h will show that all the curves in the bilinear flowarea have similar gradients. Additionally, the analysis is very sensitive to the quality andreliability of the data obtained. Formation permeability, for instance, is not a constant. It willchange with fluid saturations, so if the well shows a change in GOR, GLR or WOR betweenthe pre-and post-treatment tests, the permeability will be suspect. Therefore, be aware of thelimitations and risks associated with relying entirely upon this type of analysis.

19.3 Other Diagnostic Techniques.

Tiltmeters

Tiltmeters are extremely sensitive devices for measuring changes in orientation from thevertical. Surface and downhole tiltmeters are used to measure the azimuth and geometry ofthe fracture versus time, as illustrated in Figure 19.3a.

Surface tiltmeters measure the deflection of the earth at the surface. Usually, they are placedin 30 to 40 ft deep bore holes, and placed around the wellbore, from a distance of as little as100ft, to as great as half a mile. These tiltmeters are used to measure the fracture azimuth, orthe direction of the fracture relative to north. Because the determination of fracture azimuthcan often be performed on a qualitative basis, the accuracy of the data required is less thanthat for determining fracture geometry. Therefore, fracture azimuth can be quite reliablydetermined from these devices, if used correctly. However, surface tiltmeters cannot provideany useful data regarding the fracture geometry, as they are usually too far away from thefracture and located on the wrong plane. Subsurface tiltmeters are placed in wells adjacent tothe well being treated, at the same vertical depth. Because they are often much closer to thefracture than the surface tiltmeters, and they are located perpendicular to the most likelyplane of fracture propagation, it is possible to obtain fracture height, width and length fromthem, against time.

Figure 19.3a – The principle of tiltmeter fracture diagnostics (after Cipolla and Wright, 2000).

The accuracy of fracture geometry determination is controlled by a number of factors. Themost important factor is the number of tiltmeters used, which in turn is controlled by thenumber of available observation wells. Obviously, the fewer the number of tiltmeters, the lessaccurate the analysis is. Unfortunately, many candidate wells do not observation wellsconveniently positioned, or else the operator is unwilling to shut these wells in for the durationof the set up, treatment and rig down (sometimes several days). Another major factor

affecting the quantitative analysis required in order to obtain fracture geometry, is the qualityof the data on the rock mechanical properties of the affected formations. The tiltmeter is

Fracture-inducedsurface trough

Surface tiltmeters

Downhole

tiltmeters inoffset wells

Fracture D e p t h





basically measuring the angular deflection of the rock at a particular point. The magnitude ofthis deflection will depend upon the distance between the fracture and the tiltmeters, andupon the mechanical properties of the rock between them (chiefly Young’s modulus andPoisson’s ratio). If these rock properties are unknown – or worse still if the formations areheterogeneous – then the accuracy of the measurements will be significantly reduced.

Microseismic

Microseismic fracture diagnostics rely on the use of several highly accurate seismographs,similar in principle to the seismographs used to detect and measure earthquakes. Essentially,as the fracture propagates through the earth’s surface, it does not grow in a smooth,homogenous fashion. Instead, the fracture will tend to propagate in short bursts, each one ofwhich produces a small seismic shock wave that can be detected and measured. As thesemicroseismic events occur mostly at the fracture tip, it is possible, by using 3 or moremicroseismographs positioned in 3-D space around the well, to map the position of each ofthe microseismic events and hence the position of the fracture tip against time. It should beremembered that the fracture tip encompasses the entire perimeter of the fracture, and thatthe fracture (or fractures) could well be propagating all the way along this perimeter.Therefore, the technique can measure fracture height, length and the overall shape of thefracture.

As with tiltmeters, this technique requires the use of measuring devices positioned inobservation wells. If there are no suitable observation wells, then the technique cannot beapplied.

It should be remembered that any seismic device measures time, not distance. In order toconvert time into distance, the velocity of the shock wave through the rock formation(s) mustbe known. This can often be obtained from acoustic logs, but is highly dependent upon theformation bulk density, which in turn is dependent upon the porosity and the relativesaturations of liquids and gases. These factors, coupled with heterogeneity in the formation,tend to limit the resolution and accuracy of the results. However, provided enough suitablylocated measuring devices are used, this technique can be used to give a good overall idea ofthe fracture geometry and to detect multiple fractures.

Radioactive Tracers

Radioactive tracers are soluble radioactive isotopes that are added to the fracturing fluidsduring the treatment, on the fly. After the treatment, the well is logged using a tool fitted with aGeiger-Müller detector that can identify and quantify the presence of the isotope. The ideabehind this is to see where the fracturing fluid has gone.

The capabilities of this technique are further enhanced by the use of three differentradioactive isotopes, Scandium-46 (46Sc), Antimony-124 (124Sb) and Iridium-192 (192Ir). Theseare run at different times during the treatment. By logging the well with a tool that can tell the

difference between the isotopes, it is possible to see if different sections of the treatment wentin different directions.

Using radioactive tracers has a couple of drawbacks:-

1. Storage and transportation of the radioactive materials, even these low activity isotopes,is governed by strict regulations in most areas and can often be more trouble than thisinformation is worth. This is especially true if the isotopes have to cross a national frontieror go offshore.

2. The rocks in the formation reduce the count measured by the detector. Therefore it is verydifficult to tell the difference between a low level of radioactivity close to the wellbore, anda high level of radioactivity some distance away from the wellbore. This means that whilstthe technique can be used to see where the fracture is located at the perforations, and to

a certain extent which perforations took fluids at which time during the treatment, it cannotbe used to detect fracture height or width.





Temperature Logs

Temperature logs are used to detect where thetreatment fluid has gone. By running atemperature log right after a treatment, andmeasuring the temperature of the well againstdepth, it is possible to see where the cold treatingfluid cooled down the hot formation as it entered.The center of this zone is the point of fractureinitiation, as illustrated in Figure 19.3b.

Figure 19.3b – Generic temperature log illustratingthat the treating fluid has entered only a small

portion of the perforated interval. The fracture will

have initiated in this small interval. However, thisdoes not necessarily mean that this is the center of

the fracture.

References

Johnson, D.E., Wright, C.A., Stachel, A., Schmidt, H., and Cleary, M.P.: “On-Site Real-TimeAnalysis Allows Optimal Propped Fracture Stimulation of a Complex Gas Reservoir”, paperSPE 25414, presented at the SPE Production Operations Symposium, Oklahoma City, March1993.

Crockett, A.R., Okusu, N.M., and Cleary, M.P.: “A Complete Integrated Model for Design andReal-Time Analysis of Hydraulic Fracturing Options”, paper SPE 15069, presented at the 56

th


Meyer, B.R., Cooper, G.D., and Nelson, S.G.: “Real-Time 3-D Hydraulic Fracturing

Simulation: Theory and Field Case Histories”, paper SPE 20658, presented at the 65th

SPEAnnual Technical Conference and Exhibition, New Orleans LA, Sept 1990.

FracPro Version 8.0+ On-Line Help, RES/Gas Research Institute, March 1998.

FracproPT Version 9.0+ On-Line Help, Pinnacle Technologies/Gas Research Institute, July1999.

Hagel, M.W., and Meyer, B.R.: “Utilizing Mini-Frac Data to Improve Design and Production”,Journal of Canadian Petroleum Technology , March 1994, pp. 26 – 35.

MFrac III Version 3.5+ On-Line Help, Meyer and Associates Inc, December 1999.

D E P T H

TEMPERATURE

PerforatedInterval

Section of Perfsthat is actuallytaking fluid





Cipolla, C.L. and Wright, C.A.: “Diagnostic Techniques to Understand Hydraulic Fracturing:What? Why? and How?”, paper SPE 59735, presented at the SPE/CERI Gas TechnololgySymposium, Calgary, Alberta, Canada, April 2000.

Economides, M.J, Hill, A.D. and Ehlig-Economides, C.: Petroleum Production Systems ,Prentice Hall, Upper Saddle River, NJ, 1994


Agarwal, R.G., Al-Hussainy, R. and Ramey, H.J., Jr.: “An Investigation of Wellbore Storageand Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment,” Soc. Pet. Eng. J. (Sept1970); Trans., AIME, 249.

Agarwal, R.G., Carter, R.D. and Pollock, C.B.: “Evaluation and Performance Prediction ofLow-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing”, paper SPE 6838,JPT , 362-372, March 1979.

Agarwal, R.G., Carter, R.D. and Pollock, C.B.: “Type Curves for Evaluation and Performance

Prediction of Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing”, paperSPE 8145, JPT , 651-656, May 1979. (Published as an accompaniment to SPE 6838, above).

Bostic, J.N., Agarwal, R.G. and Carter, R.D.: “Combined Analysis of Post Fracturing andPressure Buildup Data for Evaluating an MHF Gas Well”, paper SPE 8280, presented at theSPE 54

th Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1979.

Agarwal, R.G.: “A New Method to Account for Producing Time Effects When Drawdown TypeCurves are Used to Analyze Pressure Buildup and Other Test Data”, paper SPE 9289,presented at the SPE 55

th Annual Technical Conference and Exhibition, Dallas, Texas,

September 1980

Crafton, J.W.: “Oil and Gas Well Evaluation Using the Reciprocal Productivity Index Method”,

paper SPE 37409, presented at the SPE Production Operations Symposium, Oklahoma City,Oklahoma, March 1997.

Cramer, D.D.: “Evaluating Well Performance and Completion Effectiveness in HydraulicallyFractured Low-Permeability Gas Wells”, paper SPE 84214, presented at the SPE AnnualTechnical Conference and Exhibition, Denver, Colorado, October 2003

Archer, J.S. and Wall, C.G.: Petroleum Engineering Principals and Practices , Graham &Trotman, London, 1986.

Dake, L.P.: Fundamentals of Reservoir Engineering , Elsevier, Amsterdam, 1978

Cipolla, C.L. and Mayerhofer, M.J.: “Understanding Fracture Performance by Integrating Well

Testing and Fracture Modelling”, paper 74632, SPEPF, November 2001.

Arihara, N., Abbaszadeh, M., Wright, C.A. and Hyodo, M.: “Integration of Fracturing Dynamicsand Pressure Transient Analysis for Hydraulic Fracture Evaluation”, paper SPE 36551,presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado,October 1996.

Horne, R.N., Modern Well Test Analysis – A Computer-Aided Approach , 2nd

Edition, PetrowayInc, Palo Alto CA, 2002.

Cipolla, C.L. and Wright, C.A.: “State-of-the-Art in Hydraulic Fracture Diagnostics”, paper SPE64434, presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane,Australia, October 2000.



BJ Services’ Frac Manual20. Equipment


20. Equipment

20.1 Horsepower Requirements

Working out horsepower requirements is a relatively easy thing to do, provided you know theexpected treating pressure and slurry rate:-

HHP = STP x Slurry Rate

40.8 ......................................................... (20.1)

where STP is in psi and Slurry Rate is in bpm. The 40.8 is simply a conversion factor for theunits (in the SI system, pumping power – in kW – is directly equal to pressure (kPa) multipliedby rate (m3/sec)). This formula will tell you how many pumps of what size you need onlocation. Remember to have at least 20% excess horsepower on location and - as a minimum- mobilise at least one spare pump. This excess capacity is required in case of pump failure or

higher than expected treating pressures.

It is also worthwhile looking at the set of curves supplied with each pump – called “pumpcurves”. These curves show the maximum rate and pressure that the pump can run at in eachgear. Correctly speaking, these curves are showing maximum torque from the engine.Remember that it is quite possible to be limited by torque, rather than by horsepower. In sucha situation, the pump may not be able to run at a given rate and pressure, even though it iswithin the pump’s rated horsepower. Remember also that the reduction ratios between theengine and transmission, and between the transmission and the pump, will affect the finaltorque available. In reality, “pump curves” are in fact “pump-transmission-engine” curves.Figure 20.1a shows an example.

If a treatment is going to be close to the maximum power for a given pumping unit, it is

recommended that the pump curves be consulted in order to confirm that the pump canactually do the treatment.

Figure 20.1a – Typical pump curves. This set is for a 30-16-6 frac skid, with a 16V92TA engine, a

CLBT8962 transmission and a pacemaker pump with a 4.5 inch fluid end. Nominal rating of thepump skid is 700 HHP





20.2 Flow Lines

This section is intended as a guideline only. Full details on requirements for high andlow pressure flow lines can be found in the BJ Services Standard Practices Manual ,and it is recommend that this should be consulted before any rig-up is designed.

Suction Hoses

It is essential that sufficient suction hoses be used between the tanks and the blender. Theonly force available to move the fluid to the blender is the suction of the inlet pump andhydrostatic pressure from a difference in fluid levels. This is not much. In order to ensure thatthe suction pump receives fluid at sufficient rate, a simple rule applies;

One 4” diameter 10’ suction hose will carry up to 10 bpm of gel

If 20 bpm is required, then two hoses will be needed, and so on. In addition, longer hoses willcarry less rate. For instance, 20’ of 4” diameter hose will only carry half as much rate, i.e. 5

bpm. So if 20 bpm were required from tanks which were 20’ away, 4 x 4” flow lines would berequired.

From this it is easy to see why the blender is usually placed as close as possible to the fractanks, and why the frac tanks are often manifolded together with 8” (or larger) diameter lines.

Also consider the comparative diameter of manifolds and suctions hoses. For instance:-

An 8” manifold has a flow are of 50.26 sq inches. This corresponds to the same flow area as4 x 4 inch hoses (50.24 sq inches). Therefore, there is little point in building an 8” manifoldand then using only 3 x 4” suction hoses.

Finally, remember that there is a difference between suction and discharge hoses. Suction

hoses need to be rigid, otherwise the suction pump of the blender can suck them flat.Discharge hoses, which generally do not have to carry suction, are often made from non-rigidhoses, which collapse flat when there is no fluid in them. This makes for easier storage andmakes the hoses easier to carry. As a general rule-of-thumb, suction hoses can be used forthe discharge (provided they have the correct pressure rating) but discharge hoses cannot beused on the suction.

Discharge Hoses

The discharge hoses run from the blender to the high pressure frac pumps. Generally, onedischarge hose is required from the blender to each pump. These hoses do not need to be

rigid (see above comments on suction hoses) but must have sufficient pressure rating. Theymust also have crimped connections (similar to high pressure hydraulic hose connections)and not the old-style clamps. Discharge hoses should also be fitted with "whip-checks" ateach connection.

For rates below 5 bpm per pump, a single 3" discharge hose is required for each pump. Atrates above 5 bpm, a single 4" hose should be used - although at very high rates (15 bpm +),more than one hose may be required.

High Pressure Flow Lines

When pumping abrasive fluids – such as a frac gel with proppant – down a high pressure

treating line, there is a limit to how fast it is advisable to pump. Above this pump rate, seals on





chiksans, swivels and hammer unions start to wash out. It is generally accepted in theindustry that the velocity of the frac fluid should not exceed 40 ft sec-1. Therefore:-

Q max = 2.33 d 2 ............................................................................ (20.2)

where Q max is the maximum flow rate down any single high pressure line, in bpm, and d is the

inside diameter of the line, in inches.

Important Points

1. The actual inside diameter of high pressure flow lines is often significantly less thanthe nominal diameter. Equation 20.2 should be used with the actual diameter. This isillustrated in Figure 20.2a.

2. HP flexible lines, such as Coflexip hoses, have separate guidelines. For these, followthe manufacturer’s instructions.

Figure 20.2a – Chart showing fluid velocity against fluid rate for various nominal diameters ofFigure 1502 high pressure iron.

20.3 High Pressure Pumps

Most high pressure pumps used in hydraulic fracturing are of the triplex variety, althoughquintuplex pumps are becoming more popular. Triplex means that there are three pistonsacting to pump the fluid, quintuplex means that there are five. These pistons are driven by arotating crankshaft, as illustrated in Figure 20.3a.

Figures 20.3b and 20.3c show what happens whilst the pump is operating. Figure 20.3bshows the suction or inlet stroke of the cycle. As the plunger moves back towards the powerend, fluid is pushed through the suction valve by the blender. The spring acting to close thisvalve requires 20 to 40 psi just to lift it up, so the blender must provide a boost pressuresignificantly greater than this in order to quickly fill the fluid end.

Figure 20.3c shows the power or discharge stroke. As the plunger moves away from the

power end, the increased pressure in the fluid end causes the suction valve to close, andonce this pressure is high enough, the discharge valve to open.

Velocity ChartFigure 1502 HP Iron

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Fluid Rate, bpm

F l u i d V e l o c i t y , f t s e c - 1

1.5"

2"

3"

4"

40 ft sec-1

Max Velocity for Abrasive Fluid





Figure 20.3a – Schematic diagram of a generic frac pump

Figure 20.3b – Generic frac pump, suction stroke

Figure 20.3c – Generic frac pump, discharge stroke

Discharge Valve

Plunger

Suction Valve

Power End Fluid End





Frac pumps are usually powered by diesel engines, although some have been built withelectric motors and even gas turbines. For diesel powered units (which includes all of BJ’sfrac pumpers), there will be a transmission and a drive shaft in between the pump and theengine. The transmission allows the pump operator to select which gear the pump is in. Lowgear is for high pressure/low rate, whilst high gear is for low pressure/high rate. Thetransmission usually includes a torque converter, which amplifies the torque coming from the

engine, for a corresponding drop in rpm’s. The pump curves supplied with each pump will tellthe operator what the maximum rate and pressure is for each gear. These curves include theengine/transmission gear ratio, which is the ratio for the torque converter. For instance a 2:1engine transmission gear ration means that the torque converter reduces the input rpm’s by afactor of 2, and increases the input toque by a factor of 2.

Also included on most pumpers is a lock-up device. This is a mechanism that allows slipbetween the engine and the transmission. In the event of the pump stalling, this can preventserious damage to the transmission and engine. In order to make this device “lock up” (whichmeans that there is no “slip” in the lock up device), the engine needs to be turning at areasonable rate (usually 1700 to 1800 rpm). Below this speed, the torque converter is notlocked up. The pump is still working, but there is slippage between the engine andtransmission. It is possible to run a pumper out of lock up, but the transmission will quickly

overheat if this is maintained for too long.

Frac pumpers come in a variety of sizes, ranging from 350 HHP to 2700 HHP. Bigger pumpsare more cost effective for big treatments, but are very expensive and can be difficult to moveon roads and onto location. Smaller pumps may require more operators, more maintenance(per horsepower – maintenance per pump unit is not significantly effected by size) and takeup more space on location. Figures 20.3d to 20.3g illustrate some of BJ’s fleet of fracpumpers.

Figure 20.3d – Skid mounted 16V 92T pumpunit (700 HHP). Skid splits into two parts.

Figure 20.3e – Two views of a trailer-mountedGorilla pump unit (2700 HHP)

Figure 20.3f – Body-load Kodiak pump unit(2200 HHP)

Figure 20.3g – Skid-mounted 1200 HHPpump unit





20.4 Intensifiers

Intensifiers are devices that are used for pumping frac treatments for extended periods at highpressure and rate. They reply on conventional frac pumps to power them, and work on theprinciple that at constant power, high rate and low pressure is the same as low rate and highpressure. BJ Services no longer supplies intensifiers.

At the power fluid end of the intensifier, the frac pumps supply power fluid at high rate and(relatively) low pressure. This acts to displace a large diameter piston down the power end. Atthe other end of this piston is a smaller diameter piston, which is mounted inside thedownhole fluid end. This acts to pump the frac fluid at high pressure and (relatively) low rate,as illustrated in Figure 20.4a.

Suction Stroke – Hydraulic fluid is forced behind the power fluid piston to force the pistonback. This allows the downhole fluid end to fill with frac fluid from the blender.

Power Stroke – The pressure on the hydraulic fluid is released. At the same time, the inletvalve from the frac pumps is opened, allowing the power end to fill with power fluid. Thisforces the piston down the power fluid end. At the other side of the intensifier, the frac fluid isforced out of the downhole fluid end at high pressure.

One important parameter for each intensifier is the intensification ratio. This is equal to D 2 / d

2

(see Figure 20.4a). This defines by how much the intensifier converts high rate-low pressureinto low rate-high pressure. For instance, with an intensification ratio of 2.5, the fluid pressuregoing downhole will be 2.5 times the power fluid pressure, whilst the fluid rate going downhole will be 2.5 times less than the power fluid rate.

Figure 20.4b shows how the intensifier is rigged up with the other equipment, whilst Figures20.4c and 20.4d show intensifiers on location.

Figure 20.4a – Schematic diagram of a generic intensifier

SUCTIONSTROKE

POWERSTROKE

D

d

TO POWERFLUID UNIT

HYDRAULIC

FLUID IN

HYDRAULICFLUID OUT

OPEN

CLOSED

OPEN

CLOSED

FROM FRACPUMPS

FROMBLENDER

TO WELL





Figure 20.4b – Schematic diagram of the intensifier hook-up.

Figure 20.4c – Intensifier worksite. Each intensifier (A) is hooked up to three frac pumpers (B),which are pumping the power fluid. Power fluid is handled by the power fluid unit (C). Intensifiers

are rigged into a manifold (D). Note that whilst there are three intensifiers and 9 power fluidpumpers on location, there are also an additional two frac pumpers (E) rigged up to the

downhole line to provide extra horsepower.

BLENDER

FRAC PUMP

FRAC PUMP

FRAC PUMP

RESERVOIRCOOLER BOOST

PUMP

POWER FLUID UNIT

INTENSIFIER

TOWELL

A

BC

DE





Figure 20.4d – Detail of an intensifier. In the foreground, on the RHS, is the downhole fluid end.In the background, on the LHS, is the power end, complete with high pressure iron rigging it to

the frac pumpers.

20.5 Blending Equipment

The blender is the heart of the fracturing operation. Although modern blending equipment isoften highly automated, the blender operator (or Blender Tender) still retains one of the mostcritical positions on any location. Figure 20.5a shows a generic schematic diagram of a fracblender.

Figure 20.5a – Generic flow diagram for a frac blender. Note that on a blender fitted with aCondor tub (such as BJ’s Cyclone I & II blenders), the functions of the blender tub and the

discharge pump are combined into a single unit.

LIQUID ADDITIVE TANKSDRYADD.BIN

PROPPANT SILO

SUCTIONPUMP

DISCHARGEPUMP

S U C T I O N M A N I F O L D

D I S C H A R G E M A N I F O L D

BLENDERTUB

RECIRCULATION LINE

F R O M

F R A C T A N K

S

T O H I G H P R E S S U R E

P U M P S

RADIOACTIVE

DENSIMETER

SLURRY SIDEFLOW METER

CLEAN SIDEFLOW METER

T O F R A C T A N K S

LA METERINGPUMPS





The blender performs the following functions:-

i) Pre-gelling tanks.ii) Blending liquid and dry additives on the fly.iii) Blending proppant on the fly.iv) Providing supercharge for the high pressure pumps.

v) Metering and recording a variety of job critical parameters.

Figures 20.5b to 20.5e show some of BJ’s fleet of frac blenders.

When pumping a treatment the frac spread can be set up to either gel the frac tanks beforethe treatment - so that all the fluids are prepared beforehand – or to mix the gel on the fly.

Treatments with Pre-Gelled Tanks

When carrying out a treatment with tanks that are pre-gelled, considerable time and effort hasbeen invested into gelling a number of frac tanks filled with water. During this process, theblender will be used to circulate the tanks (via the suction manifold, suction pump, blendertub, discharge pump and recirculation line – see Figure 20.5a), whilst adding the necessaryingredients to produce the required gel.

Advantages of Pre-Gelling Tanks:-

Figure 20.5b – 125D Frac blender, capable of 125bpm and 35,000 lbs/min proppant rate

Figure 20.5c – Body-load mounted Cyclone IIblender, capable of 25 bpm

Figure 20.5d – Skid mounted Cyclone blender Figure 20.5e – LFC hydration unit





i) Intense quality control can be carried out on the gel, prior to each tank beingaccepted. If necessary, a tank or poor quality gel can be rejected, disposed off andthen re-blended.

ii) Fewer additives need to be mixed on the fly.iii) No need for an LFC Hydration Unit

Disadvantages of Pre-Gelling Tanks:-i) Considerable time can be taken up by blending the gel.ii) Gel properties cannot be varied on the fly.iii) Approximately 5% of the gel will be wasted as tank bottoms.iv) Bactericide must be blended with the fracturing fluid to prevent sulphate-reducing

bacteria from breaking down the gel.

Mixing Gel on the Fly

Mixing the frac gel on the fly requires less pre-job preparation, but involves the use of moreequipment and the extra cost of the LFC or XLFC (Liquid Frac Concentrate – see Section 5).LFC is an oil-based slurry of the polymer, usually mixed so that there is 4 lbs of polymer pergallon of slurry. The LFC is added to the water on the fly, allowing the gel to be prepared as itis needed. This requires an LFC hydration unit (see Figure 20.5e). This piece of equipmentconsists of an LFC storage tank, a metered LFC additive pump (usually progressing cavitytype), a hydration tank and a boost pump. Water is supplied to the LFC hydration unit, whichmeters in the LFC at a controlled ratio, to provide the required gel strength. The hydratingLFC/water mix passes into the hydration tank, which is large enough so that the gel spends 3to 4 minutes in there, before it is transferred to the blender by the boost pump. This 3 to 4minute hydration time allows the polymer to hydrate. Some LFC Hydration units are suppliedwith a QC system – consisting of a viscometer and a pH probe – to provide real time gel QCinformation.

Advantages of Mixing on the Fly:-i) No wasted gel. Only the amount of gel required is blended, so that there is no

wastage from tank bottoms or if the treatment ends prematurely.ii) Gel properties may be varied on the fly.iii) Less time and effort required for job preparation.iv) No need to use a bactericide.

Disadvantages of Pre-Gelling Tanks:-i) Extra cost of using LFC, rather than dry powder.ii) Extra cost of LFC Hydration Unit.iii) Loss of gel properties if the LFC Hydration Unit has an equipment problem.

20.6 Proppant Storage and Handling

Proppant has to be stored on location, ready for use. It has to be kept clean and dry, andmust be delivered to the blender smoothly and quickly. Figure 20.6a shows frac sand beingdelivered to the hopper of a blender:-

Figure 20.6a – Frac sand beingdelivered from a Sand King to thehopper of a blender. Note thatthere are two blenders in thispicture – one is on standby as abackup in case of equipment

failure.





There are two main methods for ensuring the smooth flow of proppant from the storage bin tothe blender. The first method is to use a gravity-feed system, which relies on the proppantbeing stored in a bin which is higher than the blender hopper. A gate valve is used to controlthe sand rate. This can be done with either large vertically mounted bins (Figure 20.6b) orfrom a dump truck (Figure 20.6c):-

The second method is to use a conveyor system to move the proppant from the bin ordumper, to the blender hopper. This method is typically used on larger frac jobs, as there isusually insufficient space around the blender hopper for all the bins to be positioned. Usually,BJ’s first option for storing large volumes of proppant is the Sand King, as shown in Figure20.6d:-

Figure 20.6d – BJ Services Sand King

The Sand King is designed to be hauled to location empty, and then filled up with proppant.BJ has two models, one with 250,000 lbs capacity and one with 400,000 lbs capacity. Theproppant is held in several separate bins along the length of the Sand King. During thetreatment, gates – positioned at the bottom of the hoppers – are opened to allow proppant to

fall onto a conveyor. This conveyor runs along the bottom of the entire length of the SandKing, and will transport the proppant to the blender hopper. When a very large treatment is

Figure 20.6b – Verticallymounted, gravity feed

proppant bins

Figure 20.6c – Trailer mounted sand dumper





planned, such that several Sand Kings have to be used, a separate Sand Belt Conveyor isused, as shown in Figure 20.6e:-

Figure 20.6e – Sand belt conveyor

This device allows several Sand Kings to be placed on either side of the belt, each onefeeding onto the main belts of the Sand Belt Conveyor. This, in turn, feed the proppant to theblender hopper.

During the treatment, it is important that the proppant system can produce a smooth,uninterrupted flow of proppant to the blender, often at quite high rates. It must also be able tokeep the proppant dry, as wet proppant can cause the blender’s proppant screws to seize up.

20.7 Treatment Monitoring

On a modern frac spread, almost every parameter can be measured, displayed and recorded.The place at which this data is displayed and recorded is the Treatment Monitoring Centre,which is usually either a van or a container, as illustrated in Figures 20.7a and 20.7b, below:-

Figure 20.7a – External view of BJ’s Stimulation Van 1800





Figure 20.7b – External view of a treatment monitoring container

The fracturing treatment will be controlled from this facility. The Frac Supervisor, the FracEngineer, the Pump Operator and the Company Man can sit in relative comfort and quiet,making treatment-critical decisions, based on the data that is being collected and displayed.

Figure 20.7c – Two internal views of treatment monitoring vans

Most modern treatment monitoring facilities also include the capability to transmit thetreatment data real time back to a specially set up remote data monitoring computer. This canbe located either in BJ’s office or in the customer’s. With this facility, Engineers no longerhave to waste productive time on location or travelling to and from the location. This isespecially significant offshore, where the costs of mobilising personnel can be significant.With the remote data transmission, the Engineers get the same data displayed via similarsoftware (typically JobMaster ), with only a second or two delay. Typically, there is also a voicelink so that the on-site Engineer can discuss various items or pass on instructions.

One other feature of most treatment monitoring containers or vans is a field lab. This will be acompact QC/QA facility, designed to ensure the quality of the fluids and proppants. On largerfrac spreads this may even be a separate piece of equipment. Sometimes these are fittedwith a fluid rheology and pH flow loop, allowing real time viscosity and pH data to bedisplayed and recorded.

20.8 The Wellhead Isolation Tool

The Wellhead Isolation Tool (WIT), often referred to as a ”Tree Saver”, is a device that allowstreatments to be pumped at a STP higher than the maximum pressure rating of the wellhead.

This allows treatments to be pumped at much higher rates than would normally be possible.The WIT does this by completely isolating the wellhead from the treating fluid, as illustrated inFigures 20.8a, b, c, and d.





The tool is used in the following manner:-

• Prior to the treatment, the WIT operator obtains data for the type and size of wellhead topflange connection, the distance from the top flange to the tubing hanger, the tubing sizeand the tubing weight. This allows the WIT operator to assemble the stinger and seal

assembly to match the wellhead.• The wellhead master valve is closed, and any pressure between the master valve and the

top flange is bled off.• The WIT is assembled to the top flange, as illustrated in Figure 20.8a. Some WIT’s are

fitted with a master valve above the stinger (below the Tee section), whilst others requireadditional valves to be fitted.

• The WIT operator applies hydraulic pressure to the lower connection on the mastercylinder, to ensure that the tool is fully extended, or stung out of the wellhead.

• The valves at the top of the WIT are closed and the tool is pressure tested.• The wellhead master valve is opened and the WIT is exposed to wellhead pressure.• The tool is stroked down by pumping hydraulic fluid into the top connection on the master

cylinder.

• The stinger and the seal assembly are sized so that the seal assembly stings into the topof the tubing, at the point when the stinger is fully stroked into the well.

• The upper section of the WIT and the master cylinder are clamped together, so thathydraulic pressure is no longer required to keep the tool stung into the tubing.

The WIT tool can be extremely useful,as it can be operated on a live well. Thisthen eliminates the need killing the welland replacing the wellhead.

Use of the WIT on a live well is a veryspecialised process, requiring a trainedoperator. The tool can be very

dangerous if not assembled or operatedcorrectly.

The WIT is generally available in twomain sizes, big and small. The small sizeis used for stinging into most tubingsizes, from 2-3/8” up to 4” or larger. Thelarge sized tool is used for stingingdirectly into casing, with no tubing in thewell.

Figure 20.8a – Generic wellhead isolationtool rigged up to wellhead. The WIT is

connected to the wellhead via thewellhead’s top flange. At this point thewellhead master and sub master valves

are closed, maintaining control of the welland allowing the frac lines and WIT to be

pressure tested.

Swab Valve

Tubing Hanger

Seal Assembly

Master Cylinder

Hydraulic Lines

Wellhead

WellheadIsolation Tool

Sub Master Valve

Master Valve

HydraulicValve





Figures 20.8b (left) and 20.8c (right) – Once the WIT has been connected to the wellhead and

pressure tested (Fig 20.8a), the next stage is to close the valves of the frac lines (not shown –note that some WIT’s have their own master valves) and open the master and sub master valveson the wellhead. One the wellhead is open, the stinger is stroked down into the top of the tubing

by pumping hydraulic fluid into the master cylinder.

Figure 20.8d – Wellhead isolation toolrigged up on location. Note the two 3”

frac lines connected to either side,

plus the remote actuated 4” plugvalve.

ClampHydraulic

Fluid

In

Out





20.9 The Frac Spread – How it Fits Together

Figure 20.9a – Schematic diagram of a frac spread

Figure 20.8a illustrates how all the various components of the frac spread fit together. All fracspreads will basically look like this, although the size and number of components may vary.Some treatments will not use an LFC hydration unit, as the gel will be batch mixed prior to thetreatment. Some treatments may use intensifiers, whilst some treatments (“batch” fracs, orLiquid Proppant fracs) may not have separate proppant handling equipment.

However, the basic process is the same, no matter what kind of treatment is being performed.Fluid (usually water) is moved from the storage tanks and is usually blended with gellingagents to increase its viscosity. It is then blended with the proppant and pumped down thewell.

Figures 20.8b to 20.8f, below, show some typical frac spreads:-

Low Pressure Lines

High Pressure Lines

Control/Data Cables

Frac Pumps

Frac Pumps

A n n u l u s P u m p

B l e n d e r

L

F C H y d r a t i o n

Fluid Tanks

P r o p p a n t

TreatmentMonitoring





Figure 20.9b – Large scale treatment, carried out on several low permeability zonessimultaneously. Note the number of Sand Kings and frac tanks on location, as well as the use oftwo blenders (one for backup in case of equipment failure). This frac spread features a separatemobile field lab (bottom left) and a third blender, just for gelling up the tanks and for pumpingfluid from the tanks that are located a significant distance from the blender (located just above

the bottom left hand row of frac tanks).

Figure 20.9c – The MV Blue Ray , a Gulf of Mexico frac boat, designed primarily for highpermeability, frac and pack treatments.





Figure 20.9d – Skin Bypass Frac spread, using the “batch” frac method. The two frac pumps arepositioned opposite each other, just below the wireline mast (the small read and yellow derrick).A third pump (with “BJ” painted on its roof) is being used as an annulus pump. The two vertical

stainless steel tanks on the RHS are for fluid storage. The two batch mixers (each with two roundbatch tanks - the blue batch mixer is 2 x 50 bbls, whilst the red one is 2 x 40 bbls), used to batch

mix the proppant into the gel, are located at the bottom of the picture.

Figure 20.9e – Coiled tubing frac spread. The wellhead is positioned directly below the CTinjector (center of picture), with the reel on the RHS. On the LHS are two nitrogen tankers. The

main part of the frac spread is positioned behind the injector, with the sand dump truck beingthe most prominent feature.





Figure 20.9f – The MV Thanh Long . This was a boat put together for a single fracturing treatment,for a customer operating offshore Vietnam. The aft deck holds the following equipment:- 4 x 1200HHP frac pumps, Cyclone II blender, 2 x 640 cu ft proppant bins, treatment monitoring container

c/w field lab, 4 x 165 bbls tanks and a 100 bbl vertical tank.

References

Standard Practices Manual, BJ Services, January 2001 onwards

Corporate Safety Standards and Procedures Manual , BJ Services, January 2001 onwards

Equipment and Technology Catalogue, BJ Services, 1990 onwards






BJ Services’ Frac Manual21. Designing Wells for Fracturing


21. Designing Wells for Fracturing

The single biggest influence on the feasibility of the hydraulic fracturing process is the designof the well, including its completion and perforations. The influence of perforations and how

they can be designed to maximise the effectiveness of hydraulic fracturing, has beendiscussed in Section 14. In this section, we will discuss the philosophy and impact on wellplanning and design of the hydraulic fracturing process. On a wider scale, we shall discussthe influence hydraulic fracturing can have on field development, whilst on the smaller scalewe shall discuss how to plan individual wells for fracturing.

21.1 How Many Wells do I Need to Drill?

The answer is, not nearly as many as you think.

Very few operating companies outside of North America plan a field development withstimulation in mind. Hydraulic fracturing is the most effective form of stimulation, but it is also

the type is most often restricted by the design of a well. Fracturing is often perceived byEngineers who do not have first hand experience with the process, as a high risk operation.Consequently, the Engineers who design the development of a field are either not aware ofthe benefits of fracturing, or not aware of the chances of a successful treatment.

If a well is planned with hydraulic fracturing in mind, it is relatively realistic to expect at leastdouble the production from the treated well, compared to the untreated well. In many cases,fracturing will produce a production increase significantly greater than this. In addition, oftenproduction targets can be met at significantly lower drawdowns, which can have atremendous impact on reservoir management and can often prevent or significantly delay theonset of water production from a WOC or gas production from a gas cap.

So if an operating company can produce at least twice as much oil from a given well, what

does this mean for reservoir development plans?

It means that the operating company needs to drill fewer wells, which can result intremendous cost savings - especially offshore, where the need for fewer wells may eveneliminate the need for entire platforms. Obviously, in highly faulted reservoirs, each “pool” willneed at least one well, but in reservoirs that would ordinarily require several wells, it is notunreasonable to expect to eliminate up to half of these.

Injection wells can also be fractured very effectively. An additional benefit to fracturing is thateach zone in an injection well can be individually treated, allowing a specific fracture, of aspecific conductivity, to be placed in each zone. This allows the Reservoir Engineer to customdesign the injectivity profile of an injection well, to meet the requirements of long termpressure maintenance.

Traditionally, the only sector of the industry that has a profound understanding of what can beachieved by fracturing, is the tight gas sector. Most tight gas wells have to be fractured -otherwise they would not be economic. In a lot of cases, these wells have to be fractured orthey would not produce at all. In these areas, the tight gas operating companies are totallydependent upon the hydraulic fracturing process for the success or failure of their fielddevelopments. Yet companies keep drilling wells, keep developing tight gas fields and keepfracturing them – so the process must be successful.

If it works for tight gas wells, why not for oil wells or even high permeability gas wells? Afterall, the basic process is the same, the equipment is the same, the proppants are the sameand the fluids are the same. The only thing that varies from well to well is the amount of eachof these items we use and the relative quantities in which they are used. Obviously, thepotential percentage production increase from fracturing a tight gas well is much greater thanfor fracturing a high permeability oil well. However, which generates the most revenue –





increasing the production from a tight gas well from 50 mscfpd to 500 mscfpd, or increasingthe production of an oil well from 5,000 bopd to 10,000 bopd? Both of these productionincreases are realistically achievable.

21.2 The Best Wells are also the Best Candidates for Fracturing

Too often, hydraulic fracturing is seen as a last-try-process, used because the company has abad well and needs to do something with it. Unfortunately, in most circumstances, hydraulicfracturing cannot turn a bad well into a good well, unless the only reason for the lowproduction is a large skin factor. In all cases, the reservoir must have some potential in orderfor the full benefits of the fracturing process to be realised.

In the late 1980’s, a company operating in the Danish sector of the North Sea, begandeveloping a new field. The oil was held in the highly same highly productive chalkformations, which were responsible for the huge Ekofisk development, just across the borderin the Norwegian sector. The traditional way to develop these reservoirs was to drill deviatedor S-shaped wells through the chalks and then perform an acid frac. However, the operatingcompany – and its partners (which included some major US operating companies) - realisedthat this may not be the best method.

Over a series of wells and a number of years, the operating company perfected a method fordeveloping their reservoirs that involved drilling long horizontal wells, each of which wouldhave between 8 and 15 fracs placed along its length, depending upon the length of theproductive section. Each of the horizontal liners was cemented in place – a bold newapproach in itself – and selectively perforated to control the point of fracture initiation (seeSection 13). These wells were also fitted with a special completion, which allowed individualaccess to each of these perforated intervals.

Then, over a period of 4 to 8 weeks, each of these zones would be hydraulically fractured. Astime progressed and the technology improved, this time decreased, but still took weeks,rather than days, to frac each well. In one well, the company successfully pumped over 13million lbs of proppant, a record for a well that has only recently been passed.

How much did this cost? A lot. Each well drilled and completed in this fashion typically cost 3times what a conventional well would cost, in a part of the world where drilling costs werealready huge. However, each well was also producing between 4 and 6 times what the typicalconventional well was producing. In addition, the conventional acid fractured wells had tohave the acid fracture repeated every 18 months to 2 years, as the highly plastic chalkformations slowly deformed into the fractures. However, this was not the case with thepropped fractures, resulting in greatly reduced future expenditure.

The point of this story is that good wells are the best candidates for fracturing. The industryshould not be limited to remedial and low-productivity applications. When selecting

candidates for fracturing look for the good wells first.

21.3 Designing Wells for Fracturing

The best time to fracture a well is right after it has been drilled and cased – before thecompletion has been run. This is another reason why it is important to consider theimplications of fracturing whilst planning the well. In general, completions act to restrict whatcan be done with a treatment, and can often eliminate the fracturing option entirely.

Completions can limit fracturing operations for the following reasons:-

i) Pressure limitations. Fractures are created by pressure, and as a result abnormally

high pressures can be generated by the treatment. Often, completions are notdesigned to withstand this loading. Although it is often possible to reduce this effect





by placing pressure on the annulus, many are completed with two or more packers,eliminating the effectiveness of annulus pressure.

ii) Temperature limitations. The pumping of a cool frac fluid will cause the completionto shrink. Sometimes, the completion can shrink so much that the tubing can sting outof packers. The effect of the extra pressure acts to make this effect even worse.

iii) Completion jewelry. Items such as sub-surface safety valves, gas lift mandrels andsliding side doors can often take significantly less differential pressure than the actualcompletion itself.

It should be noted that the above three limitations can be eliminated by the use of coiledtubing in the fracturing process.

iv) Multiple zones. Often, wells are completed with multiple sets of perforations. Whilst itis possible to treat multiple zones at the same time, it is generally a much morecomplex process, which requires more equipment and more materials (treating twoidentical zones requires twice the pump rate, and twice the volume of proppants andfluids. It may require significantly more than twice the hydraulic horsepower, as the

friction pressure will rise by significantly more than this factor).

In short, if the well can be fractured before it is completed, all the limitations imposed by thecompletion can be eliminated. However, doing this requires a degree of forward planning,faith in the fracturing process and increased up-front expenditure.

Fracturing before completion allows the perforate-stimulate-isolate method to be employed:-

1. Perforate The individual zone is perforated, allowing each zone to be fractured with theoptimum treatment. By carefully positioning the perforations, the point offracture initiation can be controlled..

2. Stimulate The fracture treatment is pumped either down the casing or through a frac

string.

3. Isolate The zone is isolated by setting either a sand fill or a bridge plug.

Repeat steps 1 to 3 as often as necessary, moving from the bottom to the top of the well.

Obviously, this process can take a lot longer than the conventional drill and complete process.However, the extra cost is more than offset by the substantially increased production fromthese wells.

If the well cannot be fractured prior to completion, then the completion should be designedwith fracturing as a potential scenario. Packers and tubing jewelry should be designed towithstand the pressures of fracturing. Seal assemblies should be long enough to cope with

the cooldown. Zones should be as isolated as possible.

Of course, all this requires substantial extra investment, which has to be justified purely on thebasis of faith in the fracturing process. However, in case after case, field development afterfield development, this initial expenditure has proved its worth.

References

Nagel, W.B, et al .: “An Integrated Team Approach for Improving Company-Wide StimulationDesign and Quality Control”, paper SPE 26142, presented at the SPE Gas Technology

Symposium, Calgary, June 1993.





Cipolla, C.L., Bernsten, B.A., Moos, H., Ginty, W.R., and Jensen, L.: “Case Study of HydraulicFracture Completions in Horizontal Wells, South Arne Field Danish North Sea”, paper SPE64383, presented at the SPE Asia-Pacific Oil and Gas Conference and Exhibition, Brisbane,October 2000.

Owens, K.A., Pitts, M.J., Klampferer, H.J., and Kreuger, S.B.: “Practical Considerations for

Well Fracturing in the ‘Danish Chalk’”, paper SPE 25058, presented at the SPE EuropeanPetroleum Conference, Cannes, France, November 1992.

Schubarth, S.K., Yeager, R.R., and Murphy, D.W.: “Advanced Fracturing and ReservoirDescription Techniques Improves Fracturing in......”, paper SPE 39777, presented at the SPEPermian Oil Basin Oil and Gas Recovery Conference, Midland TX, 1998

Voneiff, G.W., and Holditch, S.A.: “An Economic Assessment of Applying of Applying RecentAdvances in Fracturing Technology to Six Tight Gas Formations”, paper SPE 24888,presented at the SPE Annual Technical Conference and Exhibition, Washington DC, October1992.

Stewart, B.R, et al .: “Economic Justification for Fracturing Moderate to High Permeability

Formations in Sand Control Environments”, paper SPE 30470, presented at the SPE AnnualTechnical Conference and Exhibition, Dallas, October 1995.

Conway, M.W., et al .: “Expanding Recoverable Reserves Through Refracturing”, paper SPE14376, presented at the SPE Annual Technical Conference and Exhibition, Las Vegas,October 1985.

Church, D.C., and Peters, B.A.: “Improved Fracturing Technique Yields Increased ProductionPotential”, paper SPE 17045, presented at the SPE Eastern Regional Meeting, Pittsburgh,October 1997



BJ Services’ Frac Manual22. The Fracture Treatment


22. The Fracture Treatment: From Start to Finish

22.1 Frac Job Flow Chart

Obtain Well data:Logs, DST’s, Mud Logs,

Production History(if any), PVT Data,

Completion Diagram,Previous Treatments

Use NodalAnalysis or

Similar

History MatchProduction Data

Establish BaseCase Production

Input Speculative FractureGeometry into Production

Simulator

Run ProductionSimulation with Fracture

Optimum

FractureGeometry?

No

Yes

Design Treatment forOptimum Fracture Geometry

Using Fracture Simulator

1PreliminaryTreatmentSchedule

SRT ScheduleMinifrac Schedule

I N

O F

F I C E





1

Mobilise Equipment,Materials and

Personnel

Rig Up, Mix Fluids,Pressure Test

Pre-Job SafetyMeeting

Pump Step RateTest (Step Up and

Step Down)

Analyze SRT

Data

Is NWFSignificant?

Fracture ExtensionPressure, Near

Wellbore Friction

Pump

Minifrac

Pump Minifracwith Proppant Slugs

PressureRise due to Prop.

Slugs?

2

Pump ProppantSlugs as perSPE 25892

Yes

Yes

No

No

O N

L O C A T I O N

Real TimeData Modelling






Figure 22.1a – Frac job process flow diagram

2

Pressure Match Simulator

Output to Minifrac Data

E, ν, Klc, Cl,ll, lll

Pnet, Pclosure, ηfracRe-DesignTreatment

Final TreatmentDesign Load Proppant &

Additives. Mix Fluids

Pre-Job SafetyMeeting

PumpTreatment

PrematureScreenout?

Monitor Pressureuntil Fracture Closure

Shut in Well &Bleed Off Pressure

Wait for FluidSamples to Break

Flow Back Well

AnalyzeTreatment Data

Post-JobReport

O N

L O C A T I O N

O N

L O C A T I O N

O R

I N

O F F I C E

Yes

No


RigDown





The design and execution of a frac job can be broken down into 5 major steps:-

1. Data Collection

Collect as much data as possible on the well, and on treatments carried out on offset wells.This data includes, but is not limited to:-

i) Wireline logs. Useful for spotting boundaries between formations, high and lowpermeability and porosity, and also for spotting fluid contacts. Specialised logs canalso give dynamic Young’s modulus and Poisson’s ratio, stresses and the quality ofthe cement bond. Get summary or evaluated logs whenever possible – there is nopoint in doing a full log analysis when somebody else has already done this. Also – ifyou are not confident with logs - a good first step is to mark where the perforationsare, as these will be the productive intervals.

ii) Well test data. Useful for obtaining values such as reservoir pressure, permeabilityand skin factor. Again, get the report with the analysis already done. No one willexpect you to be an expert well test analyst. These reports may also containcalculated data for porosity, viscosity, fluid saturation and compressibility.

iii) Completion diagram. Essential, as this will contain all the details you will need onthe perforations, depth and sizes of tubing and casing strings etc.

iv) Wellhead diagram. Usually, all the Frac Engineer needs from this is a description ofthe top connection, so that the crew can have the appropriate crossover when theyrig up to the wellhead. However, if a wellhead isolation tool is being used, a detaileddiagram will be required.

v) Deviation survey. If the well is not vertical, the Frac Engineer will need to know MVDvs TVD for all formations, perforations and tubulars.

vi) Core data. If the well has been cored, this report may contain useful data on porosity,permeability and fluid saturation. In addition, the report may contain rock mechanicaldata and mineralogy (useful if the formation is suspected to be “water-sensitive”).

vii) Core samples. If core samples are available, get hold of them and have them testedfor Young’s modulus and Poisson’s ratio.

viii) Reservoir fluid samples. It is important to carry out compatibility testing between thefrac fluid and the reservoir fluids. Problems are rare, but when they do occur they canruin a well.

ix) Production data. Production data is useful for two reasons. First, this data is thebasis for post treatment production forecasts. Secondly, a qualitative analysis shouldbe performed to check for items such as water or gas coning and fines migration.

x) Produced sand samples. Essential if a frac and pack treatment is being designed,as a sieve analysis will be required to find the correct proppant size. However, gettinga representative sample can be difficult. Surface samples tend to have a higherproportion of fines, as these are more easily carried out of the well. Bottom holesamples tend to be the other way around – high proportions of the fines have beencarried away out of the well.

xi) Offset treatment data. Often, this is the most important and reliable source of data.Perform a complete analysis of these treatments, including a pressure match, if thedata is available. If the data is reliable enough, this may even eliminate the need for aminifrac and step rate test.

xii) Location diagram. The Frac Engineer needs to know what size the location is, toensure that all the equipment can be placed. If not, a smaller treatment needs to bedesigned. Especially important offshore, where additional factors such as cranemaximum lift and deck loading must also be considered.

xiii) Other information, such as production logs (i.e. spinner surveys), temperature logs,caliper logs, mud logs, stress surveys, core flow testing, workover reports and drillingrecords can all provide useful information.





2. Preliminary Design

This stage uses all the data gathered in step 1 to produce a preliminary frac design. The initialstep is to analyse the reservoir and production data and derive the optimum fracture geometryrequired. This step is best accomplished using nodal analysis. Then the fracture simulator isused to design a treatment to produce this fracture. Often, this design has to be tempered byconsiderations such as cost, mobilisation and equipment availability, so that the Engineermay go back and forth between the nodal analysis and the simulator several times.

Unless the Engineer has good data from offset treatments, a step rate test and a minifrac willbe required. The step rate test is pretty much standard for any well and an example isincluded below. The minifrac needs to be designed on a well by well basis. It should bepumped at the same rate as the preliminary frac design, using the same fluid and thendisplaced at the same rate using slick water. The volume of the minifrac should be at leastequal to the anticipated pad volume. The minifrac fluid volume should be large enough tocontact every formation that the actual frac will contact. This means that for tip screen outdesigns, the minifrac should be the same size as the pad, whereas for tight gas fracturing itmust be considerably larger. Remember – it is much better to pump too much fluid than toolittle.

The minifrac is exactly what its name suggests – a small frac. In fact, it should be as close aspossible to the actual treatment, in order to produce data as relevant as possible.

Remember that if minifrac and step rate tests are being performed, there is no point in doingtoo detailed a design at this stage. The real design work will be done on location after thesecalibration tests. At this stage, what is required are reasonable estimates for the expectedproduction increase, the quantity of materials and equipment that must be mobilised and thecost of the treatment.

Preliminary design work also includes designing the frac fluid. This often involves the use ofFann 50 (or similar) HPHT rheometers in order to ensure that the frac fluid has the rightcombination of stability and break.

3. Calibration Tests and Redesign

Finally, the frac spread and crew gets mobilised and is rigged up on location. The next majorstep in the design and execution process is to perform the calibration tests (minifrac and steprate test). It is vitally important to get good data from these. Whenever possible, get bottomhole pressure data, either from a gauge or from a dead string.

For the step rate test, remember the following points:-

i) Get as many low rate steps as possible. Ideally, this means 4 steps below 2 bpm,although this is not always easy with big frac pumps. However, the more steps thatcan be taken before the frac starts to initiate, the better the results will be.

ii) Don’t fiddle with the rate. When moving from one step to another, change the rateand then leave it alone. Getting a stabilised pressure is difficult enough withoutsomeone fiddling with the throttles. As long as the rate is approximately what it shouldbe, that is good enough.

iii) Use the step rate test procedure as a guideline only, especially with regard tovolumes. Getting a stabilised rate and pressure for each step is what we are after.Once this has been achieved, move on to the next step.

iv) It is important that the step rate test (step up variety) is performed on an unfracturedformation. So either do the step rate test before the minifrac, or wait for a significantperiod of time after the minifrac is finished.





v) The opposite is true for the step rate test. An open fracture is needed before the stepdown begins, and the fracture must be open throughout the entire test. It is commonto combine the two tests – step up and then step down again.

vi) Remember that the well must be full of fluid before the step rate test commences. Ifthe well has to be filled up, do it at low rate to ensure no fracture forms.

For a minifrac, the following points are important:-

i) Keep the rate constant, even if this means pumping at a different rate thanprogrammed. This makes the analysis easier and more reliable.

ii) Keep the fluid quality constant, again to make the analysis easier and more reliable. Ifnecessary, gel up a couple of frac tanks, rather than mixing on the fly.

iii) Understand the wellbore fluid. Know its fluid properties and it’s volume. Rememberthat this fluid will be injected into the fracture ahead of your carefully preparedfracturing fluid. So if you don’t know the wellbore fluid, the careful preparation of thefrac fluid is wasted. If necessary, circulate the well to completion fluid, or somethingsimilar before pumping the minifrac.

iv) Monitor the pressure decline. During this period, don’t let the frac crew do anything,except drink coffee. It is all too easy for a silly mistake to ruin data collection. The

Frac Engineer can also do his part by zero-ing out the rate on the fracturingmonitoring computer – so that any fluid pumping by the blender does not show up asan erroneous downhole rate. Remember also to collect data for long enough – if datacollection stops before closure (or closures) has happened, then the minifrac will havelost at least half of its value.

Finally, don’t forget the primary objective of the exercise – to produce a good frac design.Other objectives – such as minimising rig time or trying to get the job in the ground beforenightfall – are desirable, but secondary. The customer should be aware of the fact that aredesign can sometimes take several hours.

4. Job Execution

After all the planning and preparation has taken place, the actual treatment can sometimestake a surprisingly short period of time. During this period, the fate of the treatment no longerrests in the hands of the Frac Engineer. It is now up to the Supervisor and the rest of the fraccrew to put the job in the ground as closely as possible to the revised treatment design.

Of course, on longer treatments, real-time redesign may be performed. In which case, theFrac Engineer may still have some influence on the treatment. However, usually it is time forthe Engineer to sit back and let the crew get on with their job. Some Frac Engineers like torun the monitoring computer or check the fluid samples – both these occupations are usefuland need to be performed. It is also important that the Frac Engineer stays in close contactwith the Supervisor, just in case something unexpected happens.

5. Post Treatment Analysis

There is no such thing as the perfect frac job. Every job has room for improvement, howeverslight. This applies to the Frac Engineer’s job as well and the post treatment analysis is theway to find out what could have been done better.

Post treatment analysis comes in two parts:-

i) Analysing the pressure and rate data from the job. The best way to do this is with apressure match, although don’t spend too much time on this if you have no downholepressure data. Results obtained from this will improve the success rate of future

treatments.





ii) Assessing the production increase. Sometimes it is easy to loose sight of theobjective of the entire process – to increase production. It is vitally important to keeptrack of the production of fractured wells. Remember that production over the first fewdays doesn’t really count – we should be looking at the stabilised production severalweeks after the treatment is performed. If production does not meet or exceedexpectations, then the following three questions must be satisfied; Was the well a

good candidate (i.e. reserves and pressure)? Was the optimum fracture placed in theformation? And were the post treatment expectations realistic?

22.2 Example Treatment Schedules

Whilst BJ Services is not at liberty to publish confidential data, the example treatments wereactually pumped and all of them produced significant production increases for our customers.These designs are included so that the reader can gain some idea of the size and scale offracturing treatments.

However, remember that each treatment must be designed individually for each well – theseschedules are for guidance only and are not meant as “ready-to-use” frac designs.

Typical Step Rate Test Schedule

Rate Time Volumebpm secs gals

0.7 120 + 151.0 30 211.5 30 322.0 30 423.0 30 635.0 30 1057.0 30 1479.0 30 18911.0 30 23115.0 30 31512.0 15 1269.0 15 956.0 15 633.0 15 32Total Volume (gals) 1476

The maximum rate can be raised if desired, but this will probably not be necessary for mosttreatments. However, remember to hold the maximum rate for a few minutes to ensure that

the fracture is of sufficient volume. If the fracture is too small, it may close before the stepdown portion can be completed.

Tight Gas Fracturing

Stage Fluid Rate Clean Vol Prop. Conc.Type bpm gals ppa

1 (Pad) Linear 40 20,000 02 XLink 40 20,000 13 XLink 40 40,000 24 XLink 40 40,000 3

5 XLink 40 100,000 46 (Flush) Sl/Water 40 8,300 0





Notes Linear = Linear gel (i.e. base gel with no crosslinker)XLink = Crosslinked gelSl/Water = Slick Water

Linear gel 2.5 gpt VSP20,000 gals (75.7 m3) total

Crosslinked gel Vistar 20200,000 gals (757 m

3) total

Slick Water 2 gpt VSP8,300 gals (31.4 m3) total

Proppant 20/40 CarboLite600,000 lbs (272 tonnes) total

Treating Pressure 5,100 psi

(352 bar, 35.2 MPa)

Pumping Capacity +/- 5,000 HHP(3,730 kW)

Frac and Pack


1 (Pad) XLink 15 1,200 02 XLink 15 1,250 1

3 XLink 15 600 34 XLink 15 800 55 XLink 15 1,000 76 XLink 15 1,250 97 XLink 15 1,850 118 XLink 15 2,000 12

9 (Flush) Sl/Water 15 7,830 0

Crosslinked gel 35 ppt Viking 1D9,950 gals (37.6 m

3) total

Slick Water 4 gpt XLFC-1 in CaCl2 brine7,830 gals (29.6 m

3) total

Proppant 20/40 EconoProp70,000 lbs (31.8 tonnes) total

Treating Pressure 6,300 psi (maximum)(434 bar, 43.4 MPa)

Pumping Capacity +/- 2,300 HHP(1,716 kW)

.





Skin Bypass Fracturing


1 (Pad) XLink 8 4,000 02 XLink 8 1,300 23 XLink 8 1,100 54 XLink 8 1,050 8

5 (Flush) Sl/Water 8 2,540 0

Crosslinked gel SpectraFrac G 3500 HT7,500 gals (28.4 m

3) total

Slick Water 4 gpt XLFC-12,540 gals (9.6 m

3) total

Proppant 20/40 CarboLite16,500 lbs (8.1 tonnes) total

Treating Pressure 900 psi(62.0 bar, 6.2 MPa)

Pumping Capacity +/- 200 HHP(149 kW)

References






BJ Services’ Frac ManualNomenclature


Nomenclature

a = fracture half length (Griffith crack)

or variable used in Nolte G time analysis.A = Area, annular capacityAf = Total area of fracture (usually both wings, but for a single wing in

Nolte G-Function analysis).AR = aspect ratioB g = gas formation volume factorB o = oil formation volume factorBHA = bottom hole assemblyBHP = bottom hole pressureBHTP = bottom hole treating pressurec = total reservoir compressibil ity (also called c t)C = wellbore storage coefficientC I = viscosity controlled leakoff coefficient

C II = compressibility controlled leakoff coefficientC III = wall building controlled leakoff coefficientc b = bulk reservoir compressibility (i.e. with porosity)C c = compressibility controlled leakoff coefficientC D = dimensionless wellbore storage coefficientC eff = effective or combined leakoff coefficientc f = fracture compliance, formation compressibilityC fD = dimensionless fracture conductivity (new API notation)c r = zero porosity reservoir compressibility (i.e. rock compressibility)c t = total reservoir compressibil ity (also called c )C v = viscosity controlled leakoff coefficientC w = wall building controlled leakoff coefficientd = diameter, diameter of plastic zone at fracture tip

d p = proppant grain diameterDCF = discount factorE = Young’s modulusE’ = plane strain Young’s modulusE d = dynamic Young’s modulusf = Fanning friction factorF = forceF c = fracture conductivityF cd = dimensionless fracture conductivity (old – now C fD)9 = acceleration due to gravity (= 9.81 m/s

2 or 32.18 ft/s

2)

g (∆t D) = dimensionless loss-volume function (Nolte minifrac analysis)g (∆t cD) = g (∆t D) at fracture closureG = shear modulus,

or elastic energy release rateG (∆t D) = Nolte G timeG c = critical elastic energy release rate

or Nolte G time at fracture closureG lc = critical elastic energy release rate – failure mode lG d = dynamic shear modulusg f = frac gradientGOR = gas oil ratioGLR = gas liquids ratioh = heighth f = fracture height at wellboreH = depth, fracture height at wellboreH D = dimensionless fracture heightHH = hydrostatic headHHP = hydraulic horsepower





H ξ = characteristic length (MFrac )ISDP = instantaneous shut-down pressure (= ISIP )ISIP = instantaneous shut-in pressureIPR = inflow performance relationshipJ = original (pre-stimulation) productivity index with skinJ 0 = undamaged productivity index

J f = post-fracturing productivity indexK = bulk modulusK’ = power law consistency indexK’’ = Herschel-Buckley consistency indexK l = stress intensity factor, failure mode 1K 1c = critical stress intensity factor – failure mode 1,

or fracture toughnessk = permeabilityK d = dynamic bulk modulusk f = formation permeability, permeability to frac fluid filtratek p = proppant permeabilityk r = permeability to reservoir fluidKZD = Kristianovich, Zheltov, Daneshy – 2 dimensional frac model

L = tubing of casing length, fracture half length (also x f)m = mobility, gradient of curvem(P ) = real gas pseudo-pressureN = viscometer spring factorn’ = power law exponentn’’ = Herschel-Buckley exponentN p = dimensionless proppant number (or simply proppant number)NPV = net present valueN Re = Reynold’s numberp, P = pressureP * = average reservoir pressure from well test analysisP ’ = pressure derivativeP b = breakdown pressure

P closure = closure pressure or P cP ext = fracture extension pressureP final = post-frac surface circulation pressure (frac and packs)

P frict = friction pressure (usually ∆P frict )P i = static reservoir pressureP initial = pre-frac surface circulation pressure (frac and packs)P m = match pressure (Nolte minifrac analysis)P net = net pressure

P nwb = near wellbore friction pressure (usually ∆P nwb)P ob = pressure due to overburden

P perf = perforation friction pressure (usually ∆P perf)P r = pressure at a distance r from the wellboreP r, t = pressure at a distance r from the wellbore, after a time t .P res = reservoir pressure (also P i )P v = plastic viscosity (Bingham plastic fluids)P wb = wellbore pressure (usually bottom hole)P wD = dimensionless wellbore pressureP wDM = dimensionless wellbore match pressureP wf = flowing wellbore pressureP ws = static wellbore pressurePC = proppant concentrationPKN = Perkins, Kern, Nordgren – 2 dimensional frac modelq = pump rate, average pump rate, liquid flow rateQ = pump rate, average pump rate, gas flow rateQ L = fluid leakoff rateQ max = maximum pump rateR = frac radius (esp. radial model)r d = radius of investigation or disturbed radius





r e = reservoir radial extentr p = radius of plastic zone at fracture tip

or ratio of fracture area in permeable formation over total fracturearea (i.e. net to gross fracture area ratio) for 2-D fracture models.

r w = wellbore radiusr w’ = effective wellbore radius

S = skin factorS p = spurt loss coefficientSG = specific gravitySG f = specific gravity, fluidSG p = specific gravity, proppantSTP = surface treating pressuret = timet D = dimensionless timet DM = dimensionless match timet Dx

f = fractured well dimensionless time

t DxfM = fractured well dimensionless match time

t Horner = Horner time

t ma = rock matrix compression wave transit t imet p = pump time, producing time, compression wave transit timet sma = rock matrix shear wave transit timet s = shut in time (also ∆t ), shear wave transit timeT = tensile strength, or temperatureTVD = true vertical depthU = energyU fluid = energy in the fracturing fluidU̇ = energy per unit time, work, horsepowerv = velocityv prop = fraction of fracture volume occupied by proppantV = volumeV i = total volume injected into fracture

V s = spurt loss volumeW, w = fracture widthW ¯ ,w ¯ = average fracture widthW max = maximum fracture widthWOR = water oil ratiox, y, z = mutually perpendicular directions, distancesx e = length and width of a square reservoir (such that area = x e

2)

x f = fracture half lengthx fD = dimensionless fracture half length ( = x f / r e)Y p = yield point (Bingham plastic fluids)z = gas z-factorz i = gas z-factor at static reservoir conditions

α = poroelastic constant (Biot), Nolte analysis boundary variables

β = flow capacity factor (Forcheimer Equation)or shape factor (LEFM)

β s = ratio of average to wellbore net pressures (Nolte minifrac analysis)

γ = shear rate, proppant specific gravity,or shape factor (MFrac )

∆m(P ) = real gas pseudo-pressure differential

∆m(P )M = real gas pseudo-pressure differential match∆P = pressure differential, drawdown

∆P drawdown = drawdown (= P i – P wf) ∆P build-up = build-up pressure ( = P i – P ws)

∆P frict = pressure drop due to fluid tubing friction∆P M = test data log-log plot match pressure





∆P nwb = pressure drop due to near wellbore friction∆P perf = pressure drop due to perforations∆P skin = pressure loss due to skin damage∆t = change in time, time since shut-in or shut down.∆t D = change in dimensionless time a.k.a. delta Nolte time

∆t cD = delta Nolte time at closure

∆t M = test data log-log plot match timeε = strainε 1 = strain in the vertical directionε 2,3 = strains due to the principle horizontal stresses, σ2 and σ3

ε x, y, z = strain in the x-, y- and z-directionsη = fluid efficiency, fracture efficiencyθ = angle, viscometer dial reading

µ = viscosity µ i = viscosity at static reservoir conditions

µ app = apparent viscosity

µ f = viscosity of frac fluid filtrate µ r = viscosity of reservoir fluid

ν = Poisson’s ratioν d = dynamic Poisson’s ratioπ = Pi, the ratio of a circle’s circumference to it’s radius (= 3.1415926....)

ρ = density ρ b = proppant bulk density, formation bulk density ρ gel = gel or base fluid density ρ p = proppant absolute density ρ sl = slurry densityσ = stressσ 1,2,3 = principle (i.e. mutually perpendicular) stressesσ c = critical stressσ H = horizontal stress

σ H, max = maximum horizontal stressσ H, min = minimum horizontal stressσ v = vertical stressσ xx, yy, zz = principle stresses in the x-, y- and z- directionsσ y = yield stressτ = shear stressτ ’o = initial or threshold shear stress (Herschel-Buckley fluids)φ = porosityφ p = proppant bulk porosityω = length of unwetted part of fracture (FracPro, FracproPT ),

angular velocity, viscometer rotor speed



BJ Services’ Frac ManualIndex


Index

AAbsolute volume ..................................................................................................................... 178Additives .......................................................................................... see Fluid systems, additivesAlways look..............................................................................................on the bright side of lifeAluminates ..........................................................................................................see CrosslinkersAspect ratio................................................................................................................................. 7

BBacteria..................................................................................................................................... 41Beta-factor ................................................................................................................................ 88Bilinear flow ............................................................................................................................ 202Binary foam fracturing .............................................................................................................. 39Bingham plastic fluids.......................................................................................................... 20-21

Biocides, bactericides............................................................................................................... 41Biot’s constant ........................................................................................................ 58, 62, 64, 67Blenders. blending equipment ......................................................................................... 216-218Borates ...............................................................................................................see CrosslinkersBreakers ................................................................................................................................... 41Brines............................................................................................................................. 35-36, 51Brittle fracture ........................................................................................................................... 75Buffers ...................................................................................................................................... 41Bulk modulus ............................................................................................................................ 57

Dynamic....................................................................................................................... 64

C

Calibration tests ............................................................................................................... 115-120Candidate selection ................................................................................................. 101-108, 229Cement bond .......................................................................................................................... 108Circulation tests ...................................................................................................................... 168Clay control.......................................................................................................................... 43-44Cleats................................................................................................................................ 16, 170Closure stress........................................................................................................................... 47CO2 fracturing .................................................................................................................. 39, 169Coflexip high pressure hoses ................................................................................................. 210Completions.....................................................................................................104-106, 229, 230

Jewelry........................................................................................................ 105-106, 230Compressibility ....................................................................................................................... 202

Average reservoir .......................................................................................... 10, 64, 202

Formation......................................................................................................... 8, 64, 190Compression wave ................................................................................................................... 63Conductivity

Finite ........................................................................................................... 194, 203-205Fracture .................................................................................. see Fracture, conductivityInfinite .................................................................................................165, 194, 203-205

Corrosion, tubulars ................................................................................................................. 108Crack driving force.................................................................................................................... 73Crack tip dilatency ............................................................................................................... 75-76Crack tip plasticity................................................................................................................76-77Critical energy release rate....................................................................................................... 73Critical fracture length............................................................................................................... 73Critical micellar concentration................................................................................................... 35

Critical stress intensity factor.................................................................................................... 74Constant external phase........................................................................................................... 37





Constant internal phase............................................................................................................ 37Crosslinked fluid systems ...................................... see Fluid systems, water-based, crosslinkedCrosslinkers ................................................................................................................... 31-33, 41

Aluminates.............................................................................................................. 31-32Borates ................................................................................................................... 31-32Borates, exotic ........................................................................................................ 31-32

Titanates ................................................................................................................. 31-32Zirconates ......................................................................................................... 31-32, 33

DDarcy’s Equation..................................................................................................... 9, 88, 95, 194Darcy’s law ................................................................................................... 2, 88, 109, 116, 126data collection......................................................................................................................... 235Data frac ....................................................................................................................see minifracDead string ............................................................................................................................. 121Decline curve analysis ..................................................................................................... 125-131Density...................................................................................................................................... 19

Bulk, formation............................................................................................................. 63

Bulk, formation, log-derived......................................................................................... 63Slurry, measurement of ..................................................................................... 177, 178Densometers .......................................................................................................... 176, 178, 179

Mass flowmeter density measurement ...................................................................... 177Nuclear ...................................................................................................................... 178

Derivative plots, minifrac ........................................................................................................ 131Derivative plots, well testing ............................................................................................ 197-198Desorption ................................................................................................................................ 16Discounted revenue................................................................................................................ 102Dilatency ................................................................................................................................... 75Dilatency contribution ............................................................................................................... 75Dipole sonic logs..........................................................................................................63-67, 189

EEconomics ....................................................................................................................... 101-104Elastic constants.................................................................................................................. 57-58Elastic deformation .............................................................................................................. 54-57Elastic energy release rate....................................................................................................... 73ElastraFrac ............................................................................................................................... 36Emulsifier ............................................................................................................................ 35, 43Emulsions ........................................................................................................................... 35, 42Energy..........................................................................................................5, 73, 77, 77-79, 166

Kinetic .......................................................................................................................... 89Rate of using................................................................................................................ 82

Energy balance.................................................................................................................... 77-79Enzyme breakers...................................................................................................................... 41Erosion...................................................................................................................................... 61

FFailure mode............................................................................................................................. 73FlexSan d........................................................................................................................ 50-51, 88Flow lines, high pressure................................................................................................. 209-210Flow lines, low pressure ......................................................................................................... 209Flowmeters ............................................................................................................. 176, 177, 179

Magnetic .................................................................................................................... 177Mass or inertia ........................................................................................................... 177Turbine....................................................................................................................... 177

Fluid efficiency.............................................................................................. 69, 70, 71, 128, 130

Fluid friction ......................................................................................................................... 27-28Fluid leakoff .................................................................................. 8, 12, 122, 166, 169, 187, 190





Coefficient...................................................................................................................... 8Compressibility-controlled coefficient ............................................................................ 8Dynamic......................................................................................................................... 9Harmonic ....................................................................................................................... 9Spurt loss....................................................................................................................... 9Viscosity-controlled coefficient ...................................................................................... 8

Wall-building coefficient ...................................................................................... 8-9, 190Fluid loss additives ................................................................................................................... 44Fluid loss test........................................................................................................................... 8-9Fluid mechanics................................................................................................................... 19-28Fluid systems....................................................................................................................... 29-44

Additives ................................................................................................................. 39-44Emulsion-based........................................................................................................... 35Energised................................................................................................................ 36-39Oil-based ................................................................................................................ 33-35Visco-elastic surfactant........................................................................................... 35-36Water-based, crosslinked ....................................................................................... 30-33Water-based, linear ................................................................................................ 29-30

Foam fracturing............................................................................................................36-39, 169

Proppant concentration ............................................................................................... 37Stability ........................................................................................................................ 38Quality.......................................................................................................................... 36Viscosity....................................................................................................................... 38

Foaming agents ........................................................................................................................ 42Forced closure .......................................................................................................................... 88Forcheimer Equation ................................................................................................... 88-89, 168Formation linear flow .............................................................................................................. 202Frac and Pack...............................................................................................13-14, 167-168, 239Frac job flowchart ............................................................................................................ 232-234Frac spreads.................................................................................................................... 224-227Fracture

Area ........................................................................................................................... 130

Closure time......................................................................................................... 12, 127Conductivity ....................................................7, 12, 16, 45-48, 83, 86, 95, 96, 164, 203Dimensionless conductivity ..................12, 82-83, 96, 98, 164, 166, 173, 174, 183, 203Efficiency ...........................................................................................see Fluid efficiencyGradient ............................................................................................................ 61-62, 67Half length................................................7, 13, 69, 70, 71, 83, 164, 166, 202, 203, 205Half length, dimensionless................................................................................... 97, 166Height .......................................................................................................................... 68Initiation, controlling............................................................................................ 109-111Orientation ................................................................................................ 59-60, 80, 111Relative conductivity.................................................................................................... 12

Fracture linear flow ................................................................................................................. 201Fracture mechanics ............................................................................................................. 72-79

Fracture Models........................................................................................68-71, 91-94, 165, 1862-D Models ..................................................................................................... 68-71, 1283-D models ............................................................................................................. 91-94FracPro .....................................................................................75, 91-92, 117, 183, 184FracproPT ..................................................................75, 91-92, 117, 135-147, 182, 184Geertsma and de Klerk (GDK) ............................................................................... 69-70GOHFER ..................................................................................................................... 93Kristianovich and Zheltov – Daneshy (KZD) ..................................69-70, 128, 130, 131MFrac ................................................................. 72, 92-93, 117, 151-152, 159-161, 182MinFrac ...................................................................................................................... 117Penny-shaped......................................................................................................... 68-69Perkins and Kern – Nordgren (PKN)..............................................70-71, 128, 130, 131Radial.............................................................................................. 68-69, 128, 130, 131

Stimplan ................................................................................................................. 72, 93Fracture tip diameter ................................................................................................................ 76





Fracture toughness......................................................................72-75, 116, 169, 187, 188, 190Fracturing........................................................................................................................... 1-3, 12

Batch fracs......................................................................................................... 224, 226Coal bed methane ........................................................................................ 16, 170-172Coiled tubing....................................................................................16-17, 172-173, 226High permeability...................................................12, 166-167, 167-168, 225, 228, 239

Injection wells ............................................................................................. 169-170, 228Low permeability, or tight gas................................12, 107, 168-169, 225, 228, 238-239Multiple intervals ......................................................................................... 112-113, 230Skin bypass ................................................. 15-16, 75, 98, 112-113, 165-166, 226, 240Weak or unconsolidated formations.......................................................... 107, 225, 239

Friction factor (Fanning) ...................................................................................................... 27-28

GG-function ............................................................................................................... 126, 129, 130G-function analysis .......................................................................................................... 128-131

Example.............................................................................................................. 134-138Gas contacts........................................................................................................................... 108

Gas lift....................................................................................................................................... 17Gas oil ratio (GOR)................................................................................................................... 99Gauges, pressure ................................................................................................................... 121Gel stabilisers ........................................................................................................................... 43Gelling agents................................................................................................................ 30, 39-40

Carboxymethyl guar (CMG)............................................................................. 30, 33, 40Carboxymethyl hydroxyethyl cellulose (CMHEC).................................................. 30, 40Carboxymethyl hydroxypropyl guar (CMHPG) ................................................ 30, 33, 40Cellulose...................................................................................................................... 30Guar................................................................................................................. 30, 33, 40Hydroxyethyl cellulose (HEC)................................................................................ 30, 40Hydroxypropyl guar (HPG) .................................................................................... 30, 40Oil-based fluids ...................................................................................................... 34, 40

Starch .......................................................................................................................... 30Polysaccharide ............................................................................................................ 40Xanthan ................................................................................................................. 30, 40Xanthan, derivatives of ................................................................................................ 30

Gravel pack............................................................................................................................... 14Griffith crack......................................................................................................................... 72-73Griffith failure criterion............................................................................................................... 73

HHalf length, fracture .................................................................................................................... 7Hard rocks ................................................................................................................................ 80Height ................................................................................................................................... 7, 16

Dimensionless ....................................................................................................... 15, 16Helical screw rheometer ........................................................................................................... 24Herschel-Buckley fluids ............................................................................................................ 22High pressure flow lines .................................................................see Flow lines, high pressureHooke’s law ......................................................................................................................... 58-59Horizontal wells....................................................................................................................... 112Horner plot, minifrac ........................................................................................................ 127-128Horner plot, well testing .................................................................................................. 195, 198Hugoton field......................................................................................................................... 1, 33Hydration unit................................................................................................................... 217-218Hydraulic horsepower ..................................................................................................... 2, 4, 209Hysteresis ........................................................................................................................... 55, 66

IIndependent Torpedo Company................................................................................................. 1





Inflow performance relationship (IPR) ...................................................................................... 99Injection wells .................................................................................................................. 169-170Intensifiers ....................................................................................................................... 213-216Internal rate of return .............................................................................................................. 102ISDP ................................................................................................................................... 6, 125ISIP ............................................................................................................. 6, 125, 127, 130, 192

JJob design ...................................................................................................see treatment design

KK-prime or K’.................................................................................................................. 21-22, 86Klepper No 1 well.................................................................................................................. 1, 33

LLaminar flow ....................................................................................................................... 26, 27Leakoff ...............................................................................................................see Fluid Leakoff

Lightning ................................................................................................................................... 32Limited entry fracturing................................................................................................ 84-85, 110Linear elastic fracture mechanics (LEFM)........................................................................... 72-75Liquid frac concentrate (LFC , XLC, GLFC , VSP ) ..................................................................... 33LiteProp ............................................................................................................................... 51-52Live annulus............................................................................................................................ 121Logistics.................................................................................................................................. 108Low surface tension modifiers .................................................................................................. 42

MMcGuire and Sikora............................................................................................................. 97-98Medallion Frac .......................................................................................................................... 32

Medallion Frac HT .................................................................................................................... 33Micelles..................................................................................................................................... 35Micro fibres .......................................................................................................................... 87-88Micro sheets ............................................................................................................................. 88Micriseismic .................................................................................................................... 186, 206Minifracs ....................................................................... 8, 115, 121-163, 167, 181-183, 236-237

Anatomy of................................................................................................................. 124Bottom hole data................................................................................................. 121-122Examples ............................................................................................................ 134-162Fluid type ................................................................................................................... 122Planning and execution ...................................................................................... 121-123Rate ........................................................................................................................... 122Volume....................................................................................................................... 122

Mobility ................................................................................................................................... 168Monobore.......................................................................................................................... 17, 170Multi-phase flow................................................................................................ 47, 164, 169, 174Multiple fractures ..................................................................................84-85, 109, 111, 133-134Mutual solvents......................................................................................................................... 43

Nn-prime or n’...................................................................................................21-22, 86, 128, 130N2 fracturing ..................................................................................................................... 38, 169Napalm ..................................................................................................................................... 33Near wellbore damage ............................................................................................................... 9Net height ....................................................................................................................... 200, 201

Net present value (NPV)..........................................................................................102-104, 174Net pressure ..................................................................................................... see pressure, netNet revenue ............................................................................................................................ 102





Newton’s law of fluids.......................................................................................................... 19-20Newtonian fluids ................................................................................................................. 20, 22Nodal analysis ................................................................................................................... 99-100Nolte analysis ................................................................................................... 82, 124, 179, 192Nolte G-function...................................................................................................................... 126Nolte G-function analysis.................................................................................................128-131

Example.............................................................................................................. 134-138Non-Darcy flow .....................................................................12, 16, 47-48, 88-89, 164, 169, 174Non-emulsifiers......................................................................................................................... 41

OOxidising breakers .................................................................................................................... 41

Pp-wave ...................................................................................................................................... 62Perforations ....................................................................................................... 81, 108, 109-114

Deviated wells..................................................................................................... 111-112Friction ................................................................................................................... 6, 116Strategy ............................................................................................................... 81, 108Vertical wells.............................................................................................................. 111

Permeability ........................................................................................................ 4, 169, 189, 194Formation........................................................................................... 7, 10, 13, 100, 164Proppant pack ....................................................................7, 12, 13, 45-48, 83, 89, 164Regained ................................................................................................................ 46-47

Pipelining ............................................................................................................................. 86-87Plane strain............................................................................................................................... 74Plastic deformation .................................................................................................. 54-55, 76, 77Plastic zone ......................................................................................................................... 76-77Plug flow ............................................................................................................................. 26, 27Poisson’s ratio ...................................................................55-56, 58, 59, 60, 62, 68, 69, 70, 191

Dynamic......................................................................................................... 63, 66, 189Polished bore receptacle .......................................................................................................... 17Poly CO2 .................................................................................................................................. 39Polyemulsion ............................................................................................................................ 35Poroelastic constant ............................................................................................... 58, 62, 64, 67Porosity........................................................................................................................... 190, 202

Formation............................................................................................................. 10, 190Power........................................................................................................................................ 77Power law fluids................................................................................................................... 21-22Pressure ..................................................................................................................................... 5

Bottom hole flowing ............................................................................... 10, 99, 100, 193Bottom hole static ...................................................................................................... 193Bottom hole treating .............................................................................. 5, 122, 124, 125Bottom hole treating, calculated ................................................ 122, 124, 176, 179, 187Breakdown......................................................................................................61-62, 191Build-up...................................................................................................................... 193Closure .......................................................................... 6, 115, 116, 125, 127, 164, 192Dimensionless ........................................................................................................... 199Dimensionless, match ............................................................................................... 200Drawdown.......................................................................................................... 193, 228Extension....................................................................................................... 6, 115, 116Fluid friction .................................................................................................... 27-28, 186Hydrostatic..................................................................................................................... 5Instantaneous shut-in (ISIP) .......................................................... 6, 125, 127, 130, 192Maximum wellhead.................................................................................................... 105Near wellbore friction............................................................................................. 6, 117

Net .................................................6, 68, 69, 70, 71, 76, 79, 82, 84, 117, 125, 166, 192Perforation friction.......................................................................................................... 6Pore ................................................................................................................. 61, 62, 67





Pseudo, gas....................................................................................................... 199, 201Reservoir ........................................................................................................... 100, 128Shut-in ....................................................................................................................... 193Surface treating ..................................................................................................... 5, 122Tubing.................................................................................................................... 5, 123Tubing friction ............................................................................................. 5, 27-28, 176

Wellhead........................................................................................................................ 5Wellhead, flowing......................................................................................................... 99

Pressure decline ..................................................................................................................... 123Decline curve analysis........................................................................................125-131

Pressure matching.............................................................................131-132, 183-184, 185-191Examples ..............................................................................135-147, 151-152, 159-161Limitations of...................................................................................................... 132, 184

Pressure transducers .............................................................................................. 176, 178-179Pressure transient analysis ............................................................................................. 194-199Production increase........................................................................................................... 95-100

Dimensionless ............................................................................................................. 98Pseudo-steady state............................................................................................... 96-98Steady state............................................................................................................ 95-96

Productivity index (PI)........................................................................................... 95, 96, 98, 166Proppant .......................................................................................................................... 4, 43-52

Average grain size....................................................................................................... 46Closure stress.............................................................................................................. 47Concentration, areal ...................................................................................................... 7Concentration, foams .................................................................................................. 37Concentration, slurry ............................................................................................ 7, 178Convection................................................................................................................... 85Grain size distribution .................................................................................................. 41Multi-phase flow........................................................................................................... 48Non-Darcy flow ....................................................................................................... 47-48Permeability............................................................................7, 12, 45-48, 83, 164, 203Pump more...............................................................................................can’t go wrong

Regained permeability ............................................................................................ 46-47Resin-coated.......................................................................................................... 47, 87Roundness................................................................................................................... 46Selection ................................................................................................................. 47-49Settling.................................................................................................................... 85-86Slugs.................................................................................................................... 81, 123Sphericity ..................................................................................................................... 46Storage and handling ......................................................................................... 218-220Substrate ..................................................................................................................... 45Transport ............................................................................................................... 37, 85Volume....................................................................................................................... 130

Proppant flowback ............................................................................................................... 86-88Causes of................................................................................................................ 86-87

Forced closure ............................................................................................................. 88Prevention of........................................................................................................... 87-88

Proppant number ............................................................................................................. 173-174Pseudo radial flow .................................................................................................................. 202Pseudo-steady state flow ................................................................................................. 97, 194Pump curves........................................................................................................................... 209Pumps, high pressure...................................................................................................... 211-213

QQuality, foams...................................................................................see Foam fracturing, quality

RRadial extent (of reservoir) ....................................................................................................... 16Radioactive tracers ................................................................................................................. 207





Radius of investigation ................................................................................................... 194, 196Rate ............................................................................................................................is my friendRe-design, treatment, on-site .......................................................................................... 181-183Re-design, treatment, real-time ....................................................................................... 183-184Relative conductivity ................................................................................................................. 97Relative fracture conductivity...................................82-83, 96, 98, 164, 166, 173, 174, 183, 203

Remote data transmission............................................................................................... 180-181Resin-coated proppant ............................................................................................................. 47Reynold’s number.......................................................................................................... 26-27, 28Roundness................................................................................................................................ 46

Ss-wave ...................................................................................................................................... 63Shear modulus..................................................................................................................... 56-57

Dynamic....................................................................................................................... 64Shear rate ................................................................................................................................. 19Shear strain .............................................................................................................................. 57Shear stress (fluids).................................................................................................................. 19

Shear stress (solids) ................................................................................................................. 57Shear-thickening fluids ............................................................................................................. 22Shear-thinning fluids................................................................................................................. 22Shear wave............................................................................................................................... 63Skin factor..................................................................... 9-11, 15, 16, 99, 100, 106-107, 196-197Sliding side door (SSD) ................................................................................................... 105,106SpectraFrac G .......................................................................................................................... 32SpectraFrac G HT ..................................................................................................................... 32Sphericity .................................................................................................................................. 46Spurt loss............................................................................................................................ 9, 200Steady state flow .................................................................................................................... 194Step down test ................................................................................................................. 116-117Step rate test .................................................................... 115-120, 121, 181-183, 236-237, 238

Examples .............................................................. 117-119, 139-140, 154-155, 158-159Step up test...................................................................................................................... 115-116Strain ................................................................................................................................... 53-54Stress........................................................................................................................................ 53

Closure ........................................................................................................................ 47Cycling ......................................................................................................................... 86Horizontal, maximum and minimum ......................................................58-59, 61-62, 81Horizontal, contrasts............................................................................................ 81, 117In-situ ...........................................................................58-59, 60-61, 126, 187, 189, 190Radial...................................................................................................................... 59-60Tangential ............................................................................................................... 59-60Vertical......................................................................................................................... 58Wellbore-related ..................................................................................................... 59-61

Logs ................................................................................................................ 63-67, 189Stress intensity factor .................................................................................................... 74-75, 76Sub-surface safety valve (SSSV) .................................................................................... 105,106Suction hoses ......................................................................................................................... 210Surface tension......................................................................................................................... 42Surfactants........................................................................................................................... 41-42

Amphoteric................................................................................................................... 41Anionic ......................................................................................................................... 41Cationic........................................................................................................................ 41Emulsifying .................................................................................................................. 42Foaming agents ........................................................................................................... 42Low surface tension modifying .................................................................................... 42Mutual solvents............................................................................................................ 42

Non-emulsifying........................................................................................................... 41Nonionic....................................................................................................................... 41





Super RheoGel .................................................................................................................... 34-35

TTemperature ...................................................................................................... 19, 121-122, 198Temperature logs.................................................................................................................... 207

Tensile strength ............................................................................................................. 52, 61-62Terminal velocity....................................................................................................................... 86Tiltmeters .................................................................................................................186, 205-206Time................................................................................................................................. 126-131

Closure .............................................................................................................. 126, 127Data ........................................................................................................................... 126Delta .......................................................................................................................... 126Delta Nolte Time ........................................................................................................ 126Dimensionless, fractured well.................................................................................... 202Dimensionless, match ............................................................................................... 200Dimensionless, minifrac..................................................................................... 126, 128Dimensionless, well testing ....................................................................................... 198Horner......................................................................................................... 126, 127-128

Nolte time................................................................................................................... 126Nolte G time....................................................................................... 126, 128, 129, 130Producing................................................................................................................... 193Pump ......................................................................................................................... 126Shut in........................................................................................................................ 126Square root time......................................................................................... 126, 126-127

Tip screenout ..........................................................................................13, 83-84, 166-167, 167Titanates .............................................................................................................see CrosslinkersTortuosity ......................................................................80-81, 111, 116, 117, 123, 132-133, 192

Controlling........................................................................................................... 111-112Curing of ...................................................................................................................... 81Example.............................................................................................................. 147-153

Tracer logs.............................................................................................................................. 207

Transient flow ........................................................................................................... 97, 193, 194Transit time............................................................................................................................... 63Compression wave (p-wave) ....................................................................................... 63Matrix ........................................................................................................................... 64Shear wave (s-wave)................................................................................................... 63

Treatment design..............................................................................................164-175, 232-238Examples ............................................................................................................ 238-240General ....................................................................................................... 164-165, 236On-site redesign ................................................................................................. 181-183Real-time redesign.............................................................................................. 183-184

Treatment monitoring....................................................................................................... 176-186Analysis and display of data ...................................................................................... 179Data processing......................................................................................................... 179

Equipment........................................................................................................... 220-221FracRT ....................................................................................................................... 143Isoplex ....................................................................................................................... 179JobMaster ................................................................................................... 179-180, 181Remote data transmission.................................................................................. 180-181

Treesaver........................................................................................... see Wellhead isolation toolTubing cooldown..................................................................................................................... 104Tubing expansion ................................................................................................................... 105Turbulent flow ..................................................................................................................... 26, 28

UUnified fracture theory ..................................................................................................... 173-172





VViking ........................................................................................................................................ 32 Viking D .................................................................................................................................... 32 Visco-elastic surfactants (VES) ........................................................................................... 35-36Viscometers ......................................................................................................................... 23-25

Brookfield ..................................................................................................................... 25Funnel.......................................................................................................................... 25Model 35 ........................................................................................................... 23-24, 25Model 50 ................................................................................................................ 24, 85

Viscosity.................................................................................................................. 10, 19, 20, 23Apparent .............................................................................................................. 25, 177Foams.......................................................................................................................... 38Fracturing fluid filtrate ............................................................................................ 8, 190Gas ............................................................................................................................ 198Measurement of...................................................................................................... 23-25Reservoir fluid.................................................................................................. 8, 10, 190

Vistar ......................................................................................................................................... 33von Mises’ yield criterion ..................................................................................................... 76-77

WWater contact.................................................................................................................. 108, 228Water cut .................................................................................................................................. 99Weak formations....................................................................................................................... 86Well testing ...................................................................................................................... 193-204

Build-up.............................................................................................................. 193, 194Constant rate ..................................................................................................... 193, 194Diagnostic plots .................................................................................................. 197-198Drawdown.................................................................................................................. 193Fractured wells .......................................................................................................... 201Gas well testing .................................................................................................. 198-199Post-treatment .................................................................................................... 202-204Pressure transient analysis ................................................................................ 194-199Type curve matching .......................................................................................... 199-202

Wellbore deviation .................................................................................................................... 80Wellbore fluid, effects of ......................................................................................................... 123Wellbore orientation.................................................................................................................. 61Wellbore radius....................................................................................................... 10, 11, 16, 98Wellbore radius, effective ......................................................................................................... 11Wellbore storage............................................................................................................. 200, 202

Dimensionless ................................................................................................... 200, 202Wellhead isolation tool.....................................................................................................221-224Wheatstone’s bridge............................................................................................................... 178Width........................................................................................................................................... 7

Average ....................................................................................... 7, 68, 69, 70, 203, 205Average propped ........................................................................................... 13, 83, 164Maximum ......................................................................................................... 68, 69, 70

Wireline logs ........................................................................................................................ 63-67

YYield point ................................................................................................................................. 76Young’s modulus .............. 13, 54-55, 68, 69, 70, 73, 80, 84, 130, 165, 167, 169, 187, 188-189,........................................................................................................................................ 190, 191

Dynamic................................................................................................... 55, 63, 66, 189Plane strain.................................................................................................. 55, 130, 191Static...................................................................................................................... 55, 66




Zz-factor.................................................................................................................................... 198Zirconates ...........................................................................................................see Crosslinkers

bj frac manual v1.0 june 2005(a4)

Documents