cracking rock: progress in fracture treatment design- disk 2
TRANSCRIPT
Cracking Rock: Progress in Fracture Treatment Design
COMPLETION/STIMULATION
In the 1950s, hydraulic fracturing
was a hit-or-miss proposition.
Through the 60s and 70s, better
data quality and more sophisti-
cated models of rock mechanics
improved control over the fracture
job. Today, with cost-effective,
high-power computing, two-dimen-
sional (2D) models of fracture
propagation are giving way to a
three-dimensional (3D) approach.
Fracture treatment design has
never before been so powerful or
flexible a tool.
4
For their help with this article, thanks to Larry Behrmann,Schlumberger Perforating Center, Rosharon, Texas, USA;Simon Bittleston, Schlumberger Cambridge Research,Cambridge, England; CJ de Pater, Delft Technical Univer-sity, The Netherlands; Cor Kenter and Jacob Shlyapober-sky Koninklijke/Shell Exploratie en Produktie Laborato-rium, Rijswijk, The Netherlands; Paul Martins, BPExploration (Alaska) Inc., Anchorage, USA; and GeorgeK. Wong, Shell Bellaire Research, Houston, Texas, USA.In this article, NODAL, DataFRAC and ZODIAC (ZonedDynamic Interpretation Analysis and Computation) aremarks of Schlumberger. VAX is a mark of Digital Equip-ment Corp. and Sun is a mark of Sun Microsystems, Inc.
Barry BradyJack ElbelMark MackHugo MoralesKen NolteTulsa, Oklahoma, USA
Bobby PoeHouston, Texas, USA
The idea of hydraulically creating cracks ina pay zone to enhance production wasdeveloped in the 1920s by R.F. Farris ofStanolind Oil and Gas Corp. He evolved theconcept following a study of pressuresencountered during squeezing of cement,oil and water into formations. In 1947,Stanolind (now Amoco Production Co.) per-
formed the first experimental hydraulic frac-ture in the Klepper #1 gas well in GrantCounty, Kansas, USA. Deliverability of thewell did not improve appreciably, but thetechnique showed promise, and the follow-ing year Stanolind presented a paper on the“Hydrafrac” process.1 Halliburton Oil WellCementing Company obtained a license tothe process and, in 1949, performed the firstcommercial fracturing treatments, raisingproduction of two wells “outstandingly.”2
Oilfield Review
4. Warpinski NR: “Invited Paper: Rock Mechanics Issuesin Completion and Stimulation Operations,” in Tiller-son JR and Wawersik WR (eds): Proceedings of the33rd US Symposium on Rock Mechanics. Santa Fe,New Mexico, USA (June 3-5, 1992): 375-386.
1. Clark JB: “A Hydraulic Process for Increasing the Pro-ductivity of Wells,” Transactions of the AIME 186(1949): 1-8.
2. Waters AB: “History of Hydraulic Fracturing,” pre-sented at the SPE Hydraulic Fracturing Symposium,Lubbock, Texas, USA, 1982.
3. Veatch RW Jr, Moschovidis ZA and Fast CR: “AnOverview of Hydraulic Fracturing,” in Gidley JL,Holditch SA, Nierode DE and Veatch RW Jr (eds):Recent Advances in Hydraulic Fracturing, Monograph12. Richardson, Texas, USA: Society of PetroleumEngineers (1989): 1-38.
The method took off. By 1955, treatmentsreached 3000 wells per month, and by1968, more than a half-million jobs hadbeen performed. Today, hydraulic fracturingis used in 35 to 40% of wells, and in theUnited States, where the procedure is mostwidespread, it has increased oil reserves by25 to 30%.3 Interest in hydraulic fracturingshows no signs of abating.4 Application ofthe technology is expanding from mainly
5October 1992
North Americanactivity declines;gas deregulation
Middle Eastimports to North America
Removedamage
Tight gas;goal of 10×increase
Improvedmaterials,understanding
Year
Frac
ture
trea
tmen
ts/y
r
OPEC supply restrictions
Moderate/highperm; goalof 2×increase
0
1000
2000
3000
4000
1950 1960 1970 1980 1990 2000
nChanging motivation for hydraulic fracturing. The three parts of the graph with posi-tive slope indicate three motivations: initially, to remove damage, then to improve ten-fold the productivity of tight gas sands, and today, to double productivity of medium-to high-permeability formations.
low-permeability reservoirs to medium-tohigh-permeability settings (above).
Hydraulic fracturing is the pumping of flu-ids at rates and pressures sufficient to breakthe rock, ideally forming a fracture with twowings of equal length on both sides of theborehole. If pumping were stopped after thefracture was created, the fluids would grad-ually leak off into the formation. Pressureinside the fracture would fall and the frac-ture would close, generating no additionalconductivity. To preserve a fracture once ithas been opened, either acid is used to etch
6
nA typical pumping scheduhydrofrac in a gas well in eahoma, USA. Each unit of fluirepresents a change in propconcentration or flow rate orcalled a stage; a specific seof stages is called a pumpinschedule. This is a pumpingule to produce a 909-foot [27fracture. The pad fractures tand helps transport the propwhich holds the fracture opepressure is released. A majoponent of fracture design is lishing the volume and chempad and slurry. Generally, t
Stage Name
Pad
Slurry
Slurry
Slurry
Slurry
Slurry
Pump Ratebbl/min.
35
35
35
35
35
35
the faces of the fracture and prevent themfrom fitting closely together, or the fractureis packed with proppant (usually sand) tohold it open. This article concentrates onthe latter technique.
Today, a typical fracturing treatment usesthickened fluids pumped in stages. The firststage is a “pad” of water, a polymer andadditives. Then comes the slurry, which ispad plus proppant—generally sand—in sus-pension. Different concentrations of prop-pant and volumes of slurry are pumped asthe job progresses (below).
le for ast Okla-
d thatpant both isquenceg sched-7-m]he rockpant,n afterr com-estab-
istry ofhe pad
is the largest stage, accounting fo30 to 50% of fluid, and, rarely, up 70%. Ideally, to optimize thepropped fracture length, the pad icompletely leaked off at themoment the fracture reaches itsintended length. If the pad leaks otoo soon, the fracture will be tooshort; if too late, the fracture is noteffectively propped. In this well, fislurry stages with different proppaconcentrations and volumes areused, but as many as 17 or 20 slurstages may be used in large fracjobs. The later slurry stages havehigher proppant concentrationsthan earlier stages because theslurry fluid leaks off as it travelsalong the fracture. Therefore, a
Job Description InformationFluid Name
YF140
YF140
YF140
YF140
YF140
YF140
Stage FluidVolume
gal
5000
9000
14,000
23,000
15,000
13,200
ProppantConcentration
lbm/gal
0
2
4
6
8
0
Pressure exerted by the pad initiates andpropagates the fracture. The slurry helpsextend the fracture and transports proppant.The fracture gradually fills until the prop-pant packs into the fracture tip (next page).At this point, the fracture treatment is fin-ished and pumping stops. As pressurewithin the fracture declines, the fracturecloses on the proppant pack, ensuring that itremains in place, providing a conduit forhydrocarbons. Productivity would be inhib-ited by viscous fluid in the pad and slurrythat remains in the formation. However,when the fluid’s high viscosity is no longerneeded, the high temperature of the forma-tion or special oxidizers cause the fluid“break” to a lower viscosity, allowing it tobe produced back.5
Hydraulic fracturing lies at the interface offluid mechanics and rock mechanics. In the45 years since the first fracture job, fluid sci-ence has advanced significantly. Treatmentfluids have been diversified to handle manytemperature, chemical and permeabilityconditions (see “Rewriting the Rules forHigh-Permeability Stimulation,” page 18).Additives control a range of fluid properties,such as viscosity, pH, stability and loss offluid to the formation, called leakoff.6 Manyproppants have been developed, from thestandard silica sand to high-strength prop-pants, like sintered bauxite and zirconiumoxide particles, used where fracture closurestress would crush sand.
Oilfield Review
rto
s
ff
vent
ry
slurry concentration that starts at thewellbore as 2 lb of proppant per gal-lon of fluid [240 kg/m3], may end upas 8 lbm/gal [960 kg/m3] at the endof pumping, and 44 lbm/gal [5270kg/m3] when the fracture closes. Inthis job, one proppant size is used(20/40 refers to a standard sievemesh size that permits passage of aparticle with an average diameter of0.63 mm [0.025 in.] ). A larger prop-pant is sometimes used near the well-bore to minimize turbulent flow,which would decrease hydrocarbonflow rate.
Proppant Type+ Mesh
INTERPROP + 20/40
INTERPROP + 20/40
INTERPROP + 20/40
INTERPROP + 20/40
INTERPROP + 20/40
—
Estimated SurfacePressure
psi
5630
4610
3760
3080
2460
6170
25% slurry volume pumped
Hei
ght,
m
30
15
0
50% slurry volume pumped
75% slurry volume pumped
Distance, m
0 50 100
Hei
ght,
m
30
15
0
Hei
ght,
m
30
15
0
nAn investigational proppant transportmodel, showing variation of proppantconcentration at three times during frac-turing. This simulation, by Simon Bittle-ston at Schlumberger CambridgeResearch in England, predicts the finaldistribution of proppant, used for quanti-fying fracture conductivity. Yellow is noproppant, green to dark blue is low tohigh proppant concentrations, respec-tively, and red is packed proppant. Slurryis denser than pad so it tends to slump,called gravity current. After 50% of theslurry volume is pumped, a shower of set-tling proppant appears as a light blue fognear the tip of the propagating slurry.Falling proppant results in a packed bed(red) along the bottom of the fracture. Thispacked bed restricts downward growth ofthe fracture. As a result of this proppantdistribution modeling, the pumpingschedule can be modified to optimizefracture design. Although still a researchtool, it may later be integrated into frac-ture design programs.
5. Gulbis J, Hawkins G, King M, Pulsinelli R, Brown Eand Elphick J: “Taking the Brakes off Proppant-PackConductivity,” Oilfield Review 3, no. 1 (January1991): 18-26.
6. Overviews of fracturing fluids:Constien VG: “Fracturing Fluid and Proppant Charac-terization,” in Economides MJ and Nolte KG (eds):Reservoir Stimulation, 2nd ed. Englewood Cliffs, NewJersey, USA: Prentice Hall (1989): 5-1–5-23.Ely JW: “Fracturing Fluids and Additives,” in GidleyJL, Holditch SA, Nierode DE and Veatch RW Jr (eds):Recent Advances in Hydraulic Fracturing, Monograph
Initialfracturegeometryat wellbore
Pro
ppan
t con
cent
ratio
n, v
ol %
0
5
10
15
20
25
30
3565
Until recently, advances in rock mechan-ics lagged somewhat behind those in fluidtechnology. In the 1950s, there was no needfor a rigorous theory of fracture propagation,the backbone of fracture treatment design.Low-volume, low-rate and low proppantconcentration fracture stimulation suc-ceeded without careful design. But as treat-ments grew in size and complexity, opera-tors needed more control. Today more thanever, the expense of hydraulic fracturingrequires that the operator knows how theformation will respond to treatment, andwhether the treatment design—the selectionof pump rates, fluid properties, pumpingschedule and fracture propagation model—will create the intended fracture (see “ToFrac or Not to Frac?” next page).
Pivotal to designing the treatment—and todeciding whether to do one at all—is cost-benefit analysis, relating cost of the fracturejob to increased well productivity. The morefracture length for a given fracture conduc-tivity, the more productivity, but also themore costly the fracture job. This analysis,called net present value, is done with simu-lators that find the optimum fracture lengthand conductivity for a given payback sched-ule. Too short a fracture, or too low a con-ductivity, and the increase in well produc-tivity won’t cover the cost of the fracturetreatment; too long, and the extra fracturelength will add significantly to cost but neg-ligibly to production. Some simulatorsmodel fracturing economics in longer terms;they tell, for example, for a well with agiven deliverability, amortized at a certainrate, how much should be spent onhydraulic fracturing given a future oil price.
In the past few years, improvements infracture design have come from develop-ments in several areas:•Fracture geometry modeling. Mathemati-
cal models today can better predict howin-situ rock responds to fracturing.
•Relationship of perforation design andfracture initiation (see “The Shape of Per-foration Strategy,” page 54). Carefuldesign of perforations can minimize pres-sure drop at the borehole.
•Fracture treatment evaluation. Mathemati-cal advances have also made evaluationtools more powerful. There is a growingpractice of testing the validity of the frac-ture geometry model against postfracturewell test data, then refining the model.This “back analysis” permits prediction offracture parameters, particularly fracturelength and conductivity, to be comparedwith independent field measurements.
12. Richardson, Texas, USA: Society of PetroleumEngineers (1989): 130-146.
7October 1992
Maximum benefit achieved forrecompletions only?
Maximum benefit achieved aftermatrix treatment only?
Is maximum benefit achievedafter fracturing only?
Is maximum benefit achieved afterfracturing with recompletion?
No
No
No
No
No
Perform recompletion.
Perform recompletion.
Perform recompletion.
Yes
Yes
Yes
Yes
Yes
Determine if the well is providing the maximum benefit, indicatedby return on investment and net present value.
Determine benefit using NODALanalysis for variouscombinations of:•Recompletions (tubing size,
perforations, surfaceequipment, artificial lift)
and•Matrix treatments(different materials and sizes)
or•Fracture treatments (different material and sizes).
Perform matrixtreatment (see “Trends in MatrixAcidizing,” page 24).
Perform fracturetreatment.
Evaluate permeability and skin (near well damage) from well test.
7. Hubbert MK and Willis DG: “Mechanics of HydraulicFracturing,” Transactions of the AIME 210 (1957):153-166.
8. Barree RD: “A New Look at Fracture Tip ScreenoutBehavior,” paper SPE 18955, presented at the SPEJoint Rocky Mountain Regional/Low PermeabilityReservoirs Symposium and Exhibition, Denver, Col-orado, USA, March 6-8, 1989; Journal of PetroleumTechnology 43 (February 1991): 138-143.Clifton RJ and Abou-Sayed AS: “A VariationalApproach to the Prediction of the Three-DimensionalGeometry of Hydraulic Fractures,” paper SPE/DOE9879, presented at the SPE/DOE Low-PermeabilityGas Reservoirs Symposium, Denver, Colorado, USA,May 27-29, 1981.
Fracture Geometry ModelingThe need to understand hydraulic fracturingstimulated advances in basic rock mechan-ics. A key finding was of Hubbert andWillis, in 1957, showing that fractures in theearth are usually vertical, not horizontal.7They reasoned that because a fracture is aplane of parting in rock, the rock will openin the direction of least resistance. At thedepth of most pay zones, overburden exertsthe greatest stress, so the direction of leaststress is therefore horizontal (next page,top). Fractures open perpendicular to thisdirection and are therefore vertical. In shal-low wells, or where thrusting is active, hori-zontal stress may exceed vertical stress andhorizontal fractures may form.
By the 1960s, fractures created below1000 or 2000 ft [300 to 600 m] wereaccepted as vertical. Operators then posedsome difficult questions: How high does thefracture grow? How can we prevent it fromextending into the gas or water zone? Howdoes fracture height relate to fracture widthand length? And how do we optimize frac-ture dimensions?
A major task of rock mechanics becamethe prediction of fracture height, length andwidth for a given injection rate, duration ofinjection and fluid leakoff. Needed for thisprediction is a model of how a fracturepropagates in rock.
Today, a number of models occupy a con-tinuum from 2D to pseudo-three-dimen-sional (P3D) and fully 3D. The basic differ-ence between 2D and P3D/3D models isthat in 2D models, fracture height is fixed orset equal to length (that is, a semicircularshape), whereas in P3D and 3D models,fracture height, length and width can allvary somewhat independently. Two-dimen-sional models have been around for about30 years; three-dimensional for about tenyears. Increased computing power hasrecently made pseudo-3D models practicalfor routine design. Fully 3D models have
Clifton RJ: “Three-Dimensional Fracture-PropagationModels,” in Gidley JL, Holditch SA, Nierode DE andVeatch RW Jr (eds): Recent Advances in HydraulicFracturing, Monograph 12. Richardson, Texas, USA:Society of Petroleum Engineers (1989): 95-108.Hongren G and Leung KH: “Three-DimensionalNumerical Simulation of Hydraulic Fracture Closurewith Application to Minifrac Analysis,” paper SPE20657, presented at the 65th SPE Annual TechnicalConference and Exhibition, New Orleans, Louisiana,USA, September 23-26, 1990.
9. The PKN model is from the work of Perkins and Kern,revised by Nordgren to account for flow rate gradientsin the fracture. Nordgren RP: “Propagation of a Vertical HydraulicFracture,” Society of Petroleum Engineers Journal 12(August 1972): 306-314; Transactions of the AIME 253.Perkins TK and Kern LR: “Widths of Hydraulic Frac-tures,” Journal of Petroleum Technology 13 (Septem-ber 1961): 937-949; Transactions of the AIME 222.
8 Oilfield Review
10. Khristianovic SA and Zheltov YP: “Formation of Ver-tical Fractures by Means of Highly Viscous Liquid,”Proceedings, Fourth World Petroleum Congress,Rome, Italy, section 2 (1955): 579-586.Geertsma J and de Klerk FA: “Rapid Method of Pre-dicting Width and Extent of Hydraulically InducedFractures,” Journal of Petroleum Technology 19(December 1969): 1571-1581; Transactions of theAIME 246.
11. Ahmed U: “Fracture-Height Predictions and Post-Treatment Measurements,” in Economides MJ andNolte KG (eds): Reservoir Stimulation, 2nd ed.Englewood Cliffs, New Jersey, USA: Prentice Hall(1989): 10-1–10-13.
12. Van Eekelen HAM: “Hydraulic Fracture Geometry:Fracture Containment in Layered Formations,” paperSPE 9261, presented at the 55th SPE Annual Techni-cal Conference and Exhibition, Dallas, Texas, USA,September 21-24, 1980.
Is maximum benefit achieved aftermatrix treatment with recompletion?
Fracturing not needed.
To Frac or Not to Frac?
limited use because of lengthy computationtime, but they are the way of the future.State-of-the-art fully 3D models simulatenonplanar fractures, but most commercialversions are planar.8
Most 2D models are based on three com-mon models: the Perkins-Kern-Nordgren9
(PKN) model, the Khristianovic-Geertsma-deKlerk10 (KGD) model and the radial model(below). The PKN and KGD models assumefracture height is constant along the lengthof the fracture; height is usually picked bylithologic boundaries. Fracture length andwidth are then calculated from height(which may be estimated using acoustic logdata combined with modeling of fracturemechanics and elastic properties11), Young’smodulus, fluid viscosity, injection rate andtime and leakoff. In the radial model, frac-ture length and height are equal and arejointly allowed to vary. Width is alsoallowed to vary.
The 3D approach is more realisticbecause fracture height is not determined bylithology but by vertical variation in themagnitude of least principal stresses, whichoften but not always follow lithologic units.(The greater the vertical contrast in leastprincipal stresses, the better fracture heightis contained.12)
nStresses in the earth act in three princi-pal directions, one vertical, and two hori-zontal, a maximum and a minimum. Atthe borehole wall, these are vertical, Sv,radial, S r, and tangential, S t. Verticalstress induced by overburden usuallyexceeds the two horizontal components.This means a fracture will have the leastresistance to opening along a plane nor-mal to the smallest principal stress.Because this stress is horizontal, the frac-ture will orient vertically. In areas ofactive thrusting, and in some shallowwells, a horizontal stress may exceedoverburden and the fracture will formhorizontally. Regional tectonic forcesdetermine the azimuthal orientation of theleast principal stresses and thus of thefracture wings.
The emergence of 3D models has noteclipsed 2D models. Two-dimensional mod-els work where:•The fracture grows in a formation of homo-
geneous stress and mechanical propertiesso that fracture height is small comparedto formation layer thickness. The radialmodel is appropriate in this setting.
•Stress contrasts are high between the paylayer and neighboring formations andthese contrasts follow lithologic bound-aries. The PKN or KGD models, whichassume constant height, are appropriate inthis setting.
When these conditions are absent, use of2D models requires estimation of fractureheight based on the user’s experience andknowledge. The consequences of underesti-mating fracture height, for example, rangefrom disastrous to troublesome but manage-able. The fracture may extend into a gas orwater leg, which can ruin a well. Underpre-dicting fracture height overpredicts fracturelength because, for a given pump rate,unanticipated doubling of fracture heightdecreases length by about 50%, dependingon leakoff. If the fracture is shorter than pre-dicted, it may not be as productive as fore-cast. The pump schedule may be inappro-priate, further cutting fracture conductivity.
9October 1992
2D Fracture Models
Fractureheight fixed
Fractureheight not
fixed
Pre
ssur
e re
quire
dto
ext
end
fract
ure
PKN
KGD
Radial
• Elliptical cross section• Width ∝ height• Width < KGD; length > KGD• More appropriate when fracture length > height
• Rectangular cross section• Width ∝ length• More appropriate when fracture length < height
• Appropriate when fracture length = height
Time
Pre
ssur
e re
quire
dto
ext
end
fract
ure
Time
Pre
ssur
e re
quire
dto
ext
end
fract
ure
Time
nThe family ofbasic 2D fracturemodels—PKN,GDK and radial.
Sv
St
Sr
Verticalstress
Min.horiz.stressMax
horiz.stress
13. Nierode DE: “Fracture Treatment Design,” in GidleyJL, Holditch SA, Nierode DE and Veatch RW Jr (eds):Recent Advances in Hydraulic Fracturing, Mono-graph 12. Richardson, Texas, USA: Society ofPetroleum Engineers (1989): 223-244.
14. Ben-Naceur K: “Modeling of Hydraulic Fractures,”in Economides MJ and Nolte KG (eds): ReservoirStimulation, 2nd ed. Englewood Cliffs, New Jersey,USA: Prentice Hall (1989): 3-1–3-31.
For example, proppant concentrations maybe excessive, causing proppant to plug thefracture before flowing its full length, andleaving some fracture length unpropped.13
The evolutionary step after 2D modelingis P3D modeling.14 When conditions areideal for a 2D model—high, known stresscontrasts—the P3D model height predictionmay be more accurate than the estimatedheight of the 2D model (below). The advan-tage of the P3D approach is that it does notrequire estimating fracture height, but it
does require input of the magnitude of mini-mum horizontal stress in the zone to befractured and in the zones immediatelyabove and below. (It calculates height usingthis stress and the fluid pressure within thefracture.) The stress values may be estimatedfrom a mechanical properties log, an indi-rect measurement.
On a small scale, the best direct stressmeasurement is from several microfracs,15
in which small fractures are created at sev-eral wellbore locations (below). Fracturingfluid is usually water without proppant. Onthe reservoir scale, determination of stressand fluid loss is accomplished by a calibra-tion treatment, in which a fracture is createdwithout proppant that is up to one-third thelength of the planned fracture. The engineeranalyzes the curve of pressure decline ver-sus time after the rock has been fractured(next page, top). Finding the fracture closure
10 Oilfield Review
15. Daneshy AA, Slusher GL, Chisholm PT and MageeDA: “In-Situ Stress Measurements During Drilling,”Journal of Petroleum Engineering 38 (August 1986):891-898.Sarda JP, Detienne JL and Lassus-Dessus J, “Recom-mendations for Microfracturing Implementationsand the Interpretation of Micro- and Pre-Fractur-ing,” Revue de l’Institut Français du Pétrole 47, no.2 (March-April 1992): 179-204.
16. Nolte KG: “Fracture Pressure Analysis: Deviationsfrom Ideal Assumptions,” paper SPE 20704, pre-sented at the 65th SPE Annual Technical Confer-ence and Exhibition, New Orleans, Louisiana, USA,September 23-26, 1990.
nA P3D fracture propagating from the borehole (top) and comparison of 2D, P3D/fully3D models for high and low contrast in minimum horizontal stress between beds. A lowstress contrast is on the order of a 100 psi [690 kilopascals (kPa)]; a high stress contrastis greater than 1000 psi [6895 kPa]. Here, if one assumes that fracture height of the 2Dmodel is selected based on lithology, not on stress contrast, then the 2D fracture modelstays within the beds. In the low-contrast case, the 2D model will probably overesti-mate fracture length and underestimate height, compared to the P3D/fully 3D models.In the low-contrast case, there would be a slight length and height difference betweenthe P3D and fully 3D models. In the high-contrast case, the P3D and fully 3D modelswould predict about the same geometry.
Wel
l dep
th, f
t
Logderived
Microfrac test
Minimum horizontal stress, psi
4200
4600
5000
5400
58002200 2600 3000 3400
nStress profile measured bymicrofrac and derived from wire-line log data. Most correlationsbetween log-derived and mea-sured stresses are linear andshow more deviation than thisexample.
Low contrast
Low contrast
High contrast
High contrast
High contrast
High contrast
Low contrast
Low contrast
2D versus P3D/3D Fracture Modelsfor Different Bed Boundary Stress Contrasts
2D
P3D/3D
P3D Fracture
17. Martins JP, Bartel PA, Kelly RT, Ibe OE and Collins PJ:“Small Highly Conductive Hydraulic Fractures NearReservoir Fluid Contacts: Application to PrudhoeBay,” paper SPE 24856, presented at the 67th SPEAnnual Technical Conference and Exhibition, Wash-ington DC, USA, October 4-7, 1992.
pressure, which equals the minimum hori-zontal stress, requires interpretation of theslopes, which is open to ambiguity.16 Thedrawback of the microfrac method is itshigh cost and insensitivity to stress variationfrom well to well and across a field. Theleakoff estimation is also complicated whenfractures grow into impermeable layers,where leakoff will not be proportional tofracture area.
P3D models assume a simplified repre-sentation of fluid flow in the fracture. Thisassumption is made mainly to shorten com-putation time, but it may result in inaccurateestimation of fracture height. This is becausepressure distribution in the fracture, whichcontrols growth of fracture height, is gener-ated by the fluid flow.
Although this problem seems simpleenough to solve, it requires the leap to fully3D modeling of fracture geometry. Fully 3Dsimulators are difficult to use—they requireaccurate stress contrast data—and so are notwidely employed, but the theory permits theclosest approximation of what fracturesreally do. The two main differencesbetween fully 3D and P3D are in how theyhandle fluid flow and pressure calculationalong the fracture. Fully 3D geometry mod-els use a fully 2D model of fluid flow,whereas P3D models approximate the 2Dfluid flow. In a fully 3D geometry model,pressure everywhere is used to calculatefracture width at any point. Width is gener-ally calculated using the “pressure integral”along the total fracture length and height. Inthe P3D model, the pressure-width relationis simplified to improve efficiency, usuallyby considering only particular shapes, suchas ellipses, or by neglecting variation ofpressure along the fracture length.
At BP, fully 3D models are not used rou-tinely because of lack of appropriate input
data. They are used to understand fracturepropagation in a particular field.17 Wherefracture containment is poor, 3D modelshave been used to assist microfrac interpre-tations and to generate simple models forroutine fracture design. These simple mod-els are refined by posttreatment evaluation.
The “pressure integral” advantage of thefully 3D model has been introduced to PKNand P3D models using a method called lat-eral coupling. This is a way to introduce 3Delasticity to models that don’t include it.Mathematically, lateral coupling puts back agross approximation of the pressure integralalong the fracture length. This poor-man’sintegral couples pressures at points alongthe fracture, instead of considering them inisolation. Compared with conventional PKN
and P3D modeling, it doubles or triplescomputation time, but improves estimationof fracture height and fracture pressure dur-ing treatment (above).
A third evolutionary stage, multilayer frac-ture (MLF) modeling, takes one step back inorder to take two steps forward. The MLFsimulator is a revision of PKN modeling thatpermits describing the geometry of morethan one fracture forming in more than onelayer and then planning the appropriate
11October 1992
Bot
tom
hole
pre
ssur
e, p
si
Pressure decline
Fracture closeson proppant
ReservoirpressureClosure pressure =
minimum horizontal rock stress
9000
8000
7000
6000
500038 40 42 44 46 48 50 56 58
Time, hr
Fractureclosing
Fracturetreatment
Pre
ssur
e re
quire
d to
ext
end
fract
ure,
psi
Lateralcoupling
PKN
KGD
Time, min
300
250
200
150
100
500 20 40 60 80
nEffect of closurestress on a pres-sure/time curve. Inthis idealizedexample, interpre-tation of the slopeto find horizontalstress is straightfor-ward. Changes incurve slope are notalways so clear.
nPressure versustime for lateralcoupling com-pared with tradi-tional fracturemodels.
pumping schedule.18 (below). Multilayermodeling was needed as more reservoirswere exploited in which conventional mod-eling has limitations. This is often the casewhen stress barriers prevent the coalescingof fractures in multiple zones or where lay-ers of varying thicknesses and stress magni-tudes are to be fractured.
The MLF approach indicates whether asingle treatment or separate treatments areneeded to achieve optimum geometry offractures in multiple zones. If separate treat-ments are needed for the desired penetra-tion in each layer, the MLF simulator maybe used to determine how many arerequired. It can also help in planning lim-ited entry perforating—varying the numberof perforations in each layer, depending onlayer thickness and stress state, to achievethe desired fracture geometry. (Fewer perfo-rations in the layer taking the most fluidrestricts flow and diverts it into other layers.)
Inputs to the MLF model are the same asfor P3D: stress profile, Young’s Modulus andleakoff for each formation. The model dif-fers from existing descriptions of multilayerfracturing in that it quantifies transient fluidpartitioning during pumping as a function offracturing fluid and formation properties.Existing models calculate partitioning only
at a single time or for a limited number offormation characteristics.19
The MLF model also allows the predictionof crossflow between fractures after pump-ing stops and before all the fractures close.Matching the predicted and measured cross-flow permits a more accurate prediction ofthe parameters that determine fluid volumethat enters each zone, and the resulting frac-ture length and height.
With the arrival of the MLF model, theengineer can choose from five general typesof fracture propagation models. Selection ofthe right model is critical. Even slight differ-ences between modeled and actual fracturedimensions can translate to dramatic differ-ences in required proppant concentrationand weight, and pad volume (next page).Usually, PKN, KGD and radial models arechosen with a chain of empirical deduc-tions. The engineer estimates the shape ofthe induced fracture—if length exceedsheight, it’s PKN; if length is less than height,it’s KGD. This value is based the sand thick-ness to be fractured, proximity to gas, wateror other fractures and estimation of thestress contrast between the reservoir sectionand abutting formations, usually shales. Thestress contrast estimate is often valid whenthe well has clean sands and clean shales.
The estimate becomes tenuous in silty shale,which may have the same stress magnitudeas sand but may poorly contain fractureheight. Again, the best measurement ofstress is obtained from a microfrac.
The Perf and the Frac: What’s the Link?Field wisdom holds that the ideal perfora-tion lies in the plane normal to the mini-mum far-field stress direction. This perfora-tion links most directly with the inducedfracture, minimizing pressure drop near theborehole. Other perforations probably con-nect with the fracture indirectly, if at all. Butbecause fracture azimuth is generally notknown and because alignable perforatingguns are not readily available, conventionalguns shooting at closely spaced anglesaround 360° are generally used. These arecalled phased guns. The closer the angle(phasing) between perforations, the betterchance of having more perforations in ornear the ideal plane. Not until recently,however, were large-scale experiments per-formed to evaluate the relationship betweenperforations and hydraulic fractures.
Behrmann and Elbel of Schlumberger andDowell Schlumberger, respectively, usedfull-scale perforators on steel casingcemented into sandstone blocks placed in a
12 Oilfield Review
Gammaray Layered beds 2D P3D MLF
Per
fsP
erfs
Shale Sand
nComparison of 2D, P3D and multilayer fracture (MLF) models in a multilayer setting. In the 2D model, fractureheight is selected to be limited by the top of the upper sand and bottom of the lower sand. The fracture is consid-ered to grow simultaneously from both sands and to be of uniform length. Young’s Modulus is averaged for thetwo sands and the shale between them. In the P3D model, the fracture grows from one sand to the other, but notsimultaneously as in the 2D model. In both the 2D and P3D models, fracture lengths are equal for both the thickand thin sands. In the MLF model, which uses a modified PKN model, fracture lengths and heights are unequal.Length depends on fracture height, stress magnitude and Young’s Modulus. As with other 2D models, height isselected for each layer, here by lithologic boundaries. The next generation MLF model will adapt P3D modeling.
18. Elbel JL, Piggott AR and Mack MG: “NumericalModeling of Multilayer Fracture Treatments,” paperSPE 23982, presented at the SPE Permian Basin Oiland Gas Recovery Conference, Midland, Texas,USA, March 18-20, 1992; Journal of PetroleumTechnology 43 (May 1991): 608-615.
19. Ahmed U, Newberry BM and Cannon DE: “HydraulicFracture Treatment Design of Wells with MultipleZones,” paper SPE/DOE 13857, presented at theSPE/DOE 1985 Low Permeability Gas Reservoirs Sym-posium, Denver, Colorado, USA, May 19-22, 1985. Ben-Naceur K and Roegiers J-C: ”Design of Fractur-ing Treatments in Multilayered Formations,” SPEProduction Engineering 5 (February 1990): 21-26.
20. Berhmann LA and Elbel JL: “Effect of Perforations onFracture Initiation,” paper SPE 20661, presented atthe 65th SPE Annual Technical Conference andExhibition, New Orleans, Louisiana, USA, Septem-ber 23-26, 1990.
21. Pearson CM, Bond AJ, Eck ME and Schmidt JH:“Results of Stress-Oriented and Aligned Perforatingin Fracturing Deviated Wells,” paper SPE 22836,presented at the 66th SPE Annual Technical Confer-ence and Exhibition, Dallas, Texas, USA, October 6-9, 1991.For details of the aligned and oriented perforatingtechnique:Yew CH, Schmidt JH and Yi L: “On Fracture Designof Deviated Wells,” paper SPE 19722, presented atthe 64th SPE Annual Technical Conference and Exhi-bition, San Antonio, Texas, USA, October 8-11, 1989.
22. de Pater CJ, personal communication, 1992.
Pro
ppan
t wei
ght,
lb ×
106
Trea
tmen
t cos
t, $
×106
Frac
ture
con
duct
ivity
, md-
ftFr
actu
re p
enet
ratio
n, ft
Fracture half-length, ft
Fracture half-length, ft
Fluid volume, gal
KGD
PKN
0
0.25
0.50
0.75
1.0
0
500
1000
1500
2000
0 750 1500 2250 3000
Fracture half-length, ft
KGD
PKN
0
0.5
1.0
1.5
2.5
0 750 1500 2250 3000
2.0
KGD
PKN
0 80,000 160,000 240,000
KGD
PKN
400
900
1400
1900
2400
2900
0 750 1500 2250 3000
nComparison of fracture properties for PKN and KGD fractures (top four graphs) and forthree fracture models (bottom).
Comparison of Fracture-Design Calculations for Different Fracturing Models
KGD Perkins-Kern Nordgren
Pad volume, bbl 750 1,350 1,650
650 350
2.5 3.5
68,350 51,000
36 36
804 845
240 185
0.17 0.16
0.16 0.16
94 85
6.5 6.5
1,250
3
157,500
36
698
486
0.22
0.20
98
7.1
Proppant-laden fluid volume, bbl
Average sand concentration, lbm/gal
Total amount of sand, lbm
Viscosity after pad, cp
Created fracture length, ft
Effective fracture length, ft
Created fracture width, in.
Effective fracture width, in.
Effective fracture height, ft
Average fracture conductivity, darcy-ft
Adapted from Veatch RW Jr, et al, reference 3.
triaxial stress cell.20 They made severalobservations about the relationship betweenperforation orientation and stress direction.They found that fractures initiate from thewellbore wall in the optimum hydraulicfracture direction, from perforations nearestthis direction, or both. Fractures tend not toform at other perforations.
The best perforation-to-fracture communi-cation is achieved when perforations arewithin 10° of the far-field minimum hori-zontal stress. This means that perforationsnot optimally oriented may result in a largepressure drop, or proppant bridging, when
October 1992
pad and slurry flow around the annulus tothe fracture. As expected, the maximumnumber of perforations in communicationwith the fracture is achieved with a perforat-ing gun having the smallest possible anglebetween shots.
Another finding of Berhmann and Elbelconcerns pump rate and viscosity of theprepad, a low-viscosity fluid sometimespumped ahead of the pad. It has been longrecognized that a prepad can increase porepressure, and thereby decrease fracture initi-ation pressure. The lower the initiation pres-sure, the lower the pressure required.Behrmann and Elbel, after cutting apart the
sandstone blocks, found that slow pumpingof low-viscosity prepad has another effect: itmaximizes the number of fractures initiatedat perforations suboptimally aligned. Morework is needed to determine whetherincreasing suboptimally aligned fracturesreduces pressure drop at the well, whichwould improve deliverability.
Pearson and colleagues at ARCO AlaskaInc. aligned perforations normal to the min-imum far-field stress in deviated wells. Theyused perforating guns with a downhole ori-entation motor in conjunction with real-time navigation tools. This enabled place-ment of larger, more productive fractures.21
Pearson and colleagues suspect that post-treatment skin damage may be associatedwith pressure drops from poor communica-tion between the main fracture and frac-tures from perforations that are not alignednormal to the minimum far-field stress.Analysis of the ARCO results by CJ de Paterand colleagues at Delft Technical Univer-sity in The Netherlands suggests that Pear-son’s results may be inconclusive.22 Pear-son and colleagues changed a number ofparameters (such as multiple zone to singlezone perforation and gun size) that mayhave equally explained their ability to placelarger treatments.
13
Conventionalpostfracture well test
ZODIAC / P3D
nPostfracture interpretation of fracturegeometry by conventional pressure tran-sient analysis and with the ZODIAC pro-gram. The main difference is that con-ventional analysis does not account forspatial variation in fracture conductivityand width, assumes fracture heightequals bed thickness, and ignores frac-ture face skin damage. The blue area isignored in the conventional analysis.
Enhanced Fracture Treatment EvaluationFracture design may be fine-tuned by care-ful postjob evaluation. This tells whether thejob went as planned, and tests the validityof the plan and the variables on which itwas based (see “Design of an Ideal FractureTreatment,” next page). Postfracture evalua-tion requires a drawdown and buildup test,which indicates fracture skin and whetherthe actual fracture length and conductivitymatch those planned. This testing is not acommon procedure because operators areusually hesitant to stop production for the10 to 14 days required for the buildup. Butin some fields, the practice is becomingmore common in a few, select wells. Forexample, in BP’s Ravenspurn South field inthe UK sector of the North Sea, an extensiveprogram of data collection and analysis wasperformed on the first six developmentwells. This included extensive pre-and post-frac well testing, logging and recording ofbottomhole pressures during job execution.The program helped optimization of jobdesign for the remainder of the field, leadingto significant reduction in the number ofwells required.23
A typical problem is that posttreatmenttransient pressure analysis shows the frac-ture is shorter than indicated by the volumeand leakoff of pumped fluid. There could beseveral reasons for the disparity. A commonreason, however, is that most postfractureevaluation models assume ideal reservoirconditions—homogeneous and isotropicformations, uniform fracture width and con-ductivity and absence of skin damage.24
To get away from assuming ideal reservoirconditions, Schlumberger has made severalimprovements to the ZODIAC ZonedDynamic Interpretation, Analysis and Com-putation program. This program improvesevaluation by accounting for variation infracture conductivity and width along thefracture length, for reservoir permeabilityanisotropy and for fracture face skin dam-
14
23. Martins JP, Leung KH, Jackson MR, Stewart DR andCarr AH: “Tip Screen Out Fracturing Applied to theRavenspurn South Gas Field Development,” paperSPE 19766, presented at the 64th SPE Annual Tech-nical Conference and Exhibition, San Antonio,Texas, USA, October 8-11, 1989.
24. Walsh DM and Leung KH: “Post Fracturing Gas WellTest Analysis Using Buildup Type Curves” paper SPE19253, Offshore Europe 1989, Aberdeen, Scotland,September 5-8, 1989.
25. Poe BD, Shah PC and Elbel JC: “Pressure TransientBehavior of a Finite Conductivity Fractured WellWith Spatially Varying Fracture Properties,” paperSPE 24707, presented at the 67th SPE Annual Tech-nical Conference and Exhibition, Washington DC,USA, October 4-7, 1992.
age.25 It also does not link fracture heightwith bed thickness (above), but uses a P3Dapproach to permit variation in proppedfracture height and width in the analysis.Compared to conventional postfracturepressure transient analysis, the programtakes 10 to 15% more computer time on aVAX or Sun workstation. In the future, it willinclude capabilities to model the effects ofreservoir boundaries and high-velocity flowon fracture length and conductivity esti-mates. The effects of reservoir boundariesare often observed in transient tests of longduration. These effects can be used to esti-mate the area and shape of the drainagearea of the well.
The Fracture Frontier: Rock MechanicsToday, the center of controversy in fractur-ing is a fundamental concept called fracturetoughness, a measure of energy dissipatedby fracture growth. Established thinkingholds that fracture toughness is a materialproperty that is independent of fracture size.The focus is on energy dissipated at the frac-ture tip, considered to be a very small zone.
26. Shlyapobersky J, Walhaug WW, Sheffield RE andHuckabee PT: “Field Determination of FracturingParameters for Overpressure Calibrated Design ofHydraulic Fracturing,” paper SPE 18195, presentedat the 63rd SPE Annual Technical Conference andExhibition, Houston, Texas, USA, October 2-5, 1988.Shlyapobersky J, Wong GK and Walhaung WW:“Overpressure Calibrated Design of Hydraulic Frac-turing,” paper SPE 18194, presented at the 63rd SPEAnnual Technical Conference and Exhibition, Hous-ton, Texas, USA, October 2-5, 1988.Lewis PE: “Analysis of Treatment Data Yields Cost-Effective Fracturing,” The American Oil and GasReporter 35, no. 1 (January 1992): 32-34, 36-38.Shlyapobersky J: “Energy Analysis of Hydraulic Frac-turing,” Proceedings of the 26th US Symposium onRock Mechanics, Rapid City, South Dakota, USA(June 26-28, 1985): 539-546.
Another school of thought, led by investiga-tors at Shell, mainly Jacob Shlyapobersky,maintains that fracture toughness is not amaterial property, and that it increases withfracture size.26 This point of view holds thatfracture toughness is the release of energynot at the fracture tip but within a largezone of irreversible deformation around thefracture tip. The volume of this zone isthought to increase with fracture size.
These two views lead to different explana-tions for the creation of fracture width,which is directly related to net pressure(fracture propagation pressure minus closurepressure). The size-dependent school saysfracture width is larger and only weaklyaffected by fracture fluid viscosity—that is,that net pressure is not sensitive to viscosity.This is because net pressure, in order toovercome the large, size-dependent tough-ness, creates a fracture width large enoughto make viscous flow effects negligible.According to established thinking, becausetoughness is not size-dependent and has aconventional magnitude, pressure gradientsfrom viscous flow dominate the toughnesseffect and fracturing, and create smallerfractures than those modeled by the size-dependent toughness school.
The two schools, therefore, have differentcalculations of fracture length and requiredpad volume. The size-dependent schoolmaintains that the established view willunderestimate width and therefore overesti-mate fracture length for a given fracture vol-ume. This is because net pressure, accord-ing to the established view, is determinedmainly by viscosity and not, as the sizeschool holds, by viscosity and increasingfracture toughness. The established viewmaintains that apparent error in estimationof fracture length and width does not resultfrom size-dependent toughness but from useof an inappropriate fracture geometry orreservoir model.27
Another area of investigation concerns theassumption that rock behaves as a purely
Oilfield Review
Shlyapobersky J and Chudnovsky A: “FractureMechanics in Hydraulic Fracturing,” in Tillerson JRand Wawersik WR (eds): Proceedings of the 33rdUS Symposium on Rock Mechanics. Santa Fe, NewMexico, USA (June 3-5, 1992): 827-836.
27. Elbel J and Ayoub J: “Evaluation of Apparent FractureLengths Indicated From Transient Tests,” paperCIM/AOSTRA 91-44, presented at the CIM/AOSTRATechnical Conference, Banff, Alberta, Canada, April21-24, 1991; Canadian Journal of Petroleum Tech-nology (in press).Nolte KG and Economides MJ: “Fracture LengthDetermination and Implications for TreatmentDesign,” paper SPE 18979, presented at the SPERocky Mountain Regional/Low Permeability Reser-voir Symposium and Exhibition, Denver, Colorado,USA, March 6-8, 1989; Journal of Petroleum Engi-neering 43 (September 1991): 1147-1155.
15October 1992
Design of an Ideal Fracture Treatment
Obtain stress magnitude and Young’sModulus1 versus depth from logs, cores.Also collect other well and formationinformation: lithology, natural fracturelocations, porosity. Check offset well data.
Select fluids and additives that minimizeformation and proppant damage andenvironmental impact.
If not done earlier, perform microfrac todetermine correct model, fluid losscoefficient and treatment efficiency (volumeof fluid pumped versus volume of fracture,determined mainly by leakoff).
Is well producing as expected?
Yes
Yes
Finalize pump schedule with PLACEMENTprogram. The program gives pressurerequired during job, frac length at end ofjob and distribution of proppant.
Execute job.
No
No
1. Young’s Modulus is the ratio of stress (force per unit area) to strain (displacement per unit length).
Fracture treatmentdesign is optimal.
Was bottomhole pressureduring execution as expected?
Obtain permeability and reservoir pressurefrom well test; porosity from logs.
Test for different fracturemodel or less length.
Improved or expanded stressand modulus data.
Use net present value (NPV) calculation toselect proppant, optimize pump scheduleand fracture length, and predict production.
Iteration for revisions.
Str
ess
revi
sion
.
Frac
mod
el r
evis
ion.
Flui
d r
evis
ion.
If appropriate fracture geometry model notknown, do microfrac (1/3 to 1/2 length ofactual job, no proppant) to select fracturegeometry model (2D, P3D, MLF).
Do well test and use ZODIACprogram to evaluate fracturetreatment and reservoircharacterization.
Analyze bottomhole pressureduring execution with variousfracture models.
Different fracture geometrymodel or length?
Different reservoir modelpermeability? Is reservoiranisotropic? Layered? Stress sensitive?
Fracture skin or lower fractureconductivity?
elastic continuum, meaning that deforma-tion short of fracturing is fully reversible.There is evidence that high-permeability/high-porosity formations may be elastoplas-tic, meaning they have some component ofirreversible deformation (below). Furtherwork on this is becoming possible with theincrease in computer power needed to solveequations for nonelastic behavior, which arefar more complex than those for elasticbehavior. Significant nonelastic behaviorwould affect the prediction of fracturegeometry and the analysis of fracture pres-sure data.
The Fracture Frontier: High-Angle WellsField experience in highly deviated and hor-izontal wells shows that it is possible to per-form hydraulic fracturing in these settings,but the effect on well performance is stilluncertain. Little has been published on theeffect of fracturing on deviated well perfor-mance.28 Shell investigators found thatreduced productivity is expected from afractured deviated well compared to a frac-tured vertical well.29 This is because the axisof the wellbore may not lie in the preferredfracture plane and may intersect the fractureover only a small reservoir interval. This
16
Continuoussolid
Elastic/brittle orelastoplastic
Fract
nSeveral modes of robrittle failure, disconttic yield of heavily frathey use elastic conti
results in limited communication to theborehole during fracturing and a pressuredrop that inhibits productivity. In the Prud-hoe Bay field, BP has found that fracturingcan impair the performance of highly devi-ated wells.30
Nevertheless, the increasing number ofdeviated and horizontal wells has inspiredwork on fracture modeling in these settings.Today, fracture treatment design in thesewells is largely by rule of thumb. But severalobservations have been made by Hallamand Last of BP that can enhance treatmentdesign in deviated wells:31
•When perforation tunnels are not normalto the minimum stress, fractures reorientin the preferred direction. If tunnels areshort compared to their spacing, the frac-tures will curve before linking up, result-ing in further pressure drop. Perforationlength should therefore be at least one-third to one-half tunnel separation, that is,4 to 6 in. [10 to 15 centimeters (cm)].
•Perforation densities should be 6 shots/ftat 60° phasing and 360/φ shots/ft for φ°phasing.
•A single large fracture is more productivethan several smaller ones that may notlink up. Hallam and Last constructed an
Conceptual Deformation Model
Planes ofcontinuous weakness
Db
Elastic and discontinuous plas
C O N T I N U U M
ure
ck response to stress. In rock mechanical terminuous deformation of block-jointed rock, andctured rock. Current theories of fracturing an
nuous deformation and brittle failure almost e
empirical curve showing the maximumborehole deviation that will allow devel-opment of a single fracture.
Hallam and Last made these observationsbased on studies in which they cemented orcast a liner in a block of rock, then loadedit. Work by CJ de Pater and colleaguesshows that if the block is first loaded, thenthe liner is cemented, fracture geometry willbe different.32
Work by Hugo Morales at DowellSchlumberger, using a 3D fracture simulatorthat permits curved fractures, shows thatfracture initiation pressure can be calculatedfor deviated wells, given well inclination,azimuth and direction of principal stresses.But once the fracture starts, there is not yet acalculation for propagation pressure. This isbecause fracture propagation models do notaddress how multiple fractures affect near-borehole stresses. A general recommenda-tion, however, is that flow rate should behigh enough to reduce bridging of proppantassociated with pressure drops of multiple,small fractures (next page).
An evolving capability is triaxial boreholeseismic imaging—listening from three direc-tions to sound emitted by the fracture as itcloses, then triangulating its location to find
Oilfield Review
s
iscretelocks
Randomfractures
tic Plastic
s, they are elastic continuous deformation, pseudocontinuous deformation and plas-d treatment design are limited becausexclusively.
Max.horizontalstress
Min.horizontalstress
Max.horizontalstress
Min.horizontalstress
fracture length.33 This would provide valu-able feedback in development of fracturepropagation models. Still, the weakest linkin the models is probably stress magnitudedetermination. A confident measurement ofstress, by an economical and practicalmethod, would provide the required datafor evolving a fracture propagation model.
Probably as important as technicalimprovements is a change in the engineer-ing mindset. “If only I had a fully 3D model,all my problems would go away” is perhapsjust half true. Often, the most sophisticatedfracture propagation models and fracturetreatment designs are undermined by some-thing as simple and elusive as bad perme-ability data. In 3D modeling, major limita-tions remain in input data—it is still difficultto obtain valid stress profiles, fluid-loss pro-files and fracture conductivities.
Today, fully 3D models help generate sim-pler models for routine application. Carefulpostfracture evaluation allows the engineerto tune fracture design, yielding the mostfrom the simplest approaches. Tomorrow,increased computer power may place thecurving fracture of varying height and widthwithin reach of engineers in the field. —JMK
28. One notable paper on the subject to date: Ovens J:“The Performance of Hydraulically Fractured Stimu-lated Wells in Tight Gas Sands: A Southern NorthSea Example,” paper SPE 20972, presented atEuropec 90, The Hague, The Netherlands, October22-24, 1990.An overview of fracturing horizontal wells:Soliman MY, Hunt JL and El Rabaa AM: “FracturingAspects of Horizontal Wells,” paper SPE 18542, pre-sented at the SPE Eastern Regional Meeting,Charleston, West Virginia, USA, November 1-4,1988; Journal of Petroleum Technology 42 (August1990): 966-973.Brown E, Thomas R and Milne A: “The Challenge ofCompleting and Stimulating Horizontal Wells,” Oil-field Review 2, no. 3 (October 1990): 52-62.
29. Veeken CAM, Davies DR and Walters JV: “LimitedCommunication Between Hydraulic Fracture and(Deviated) Wellbore,” paper SPE 18982, presentedat the SPE Joint Rocky Mountain Regional/Low Per-meability Reservoirs Symposium and Exhibition,Denver, Colorado, USA, March 6-8, 1989.
30. Martins JP, Dyke GC, Abel JC, Ibe OE, Stewart G,Bartel PA and Hanna RR: “Analysis of a HydraulicFracturing Program Performed on the Prudhoe BayOil Field,” paper SPE 24858, presented at the 67thSPE Annual Technical Conference and Exhibition,Washington, DC, USA, October 4-7, 1992.
31. Hallam SD and Last NC: “Geometry of HydraulicFractures From Modestly Deviated Wellbores,”paper SPE 20656, presented at the 65th SPE AnnualTechnical Conference and Exhibition, New Orleans,Louisiana, USA, September 23-26, 1990.
32. de Pater CJ, personal communication, 1992.33. Vinegar HJ, Willis PB, DeMartini DC, Shlyapobersky
J, Deeg WFJ, Adair RG, Woerpel JC, Fix JE and Sor-rells GG: “Active and Passive Seismic Imaging ofHydraulic Fractures in Diatomite,” paper SPE22756, presented at the 66th SPE Annual TechnicalConference and Exhibition, Dallas, Texas, USA,October 6-9, 1991.
nOrientation of hydraulic fractures in horizontal wells as a function of stress directions(top) and, in a deviated well, evolution of small, multiple fractures that may contributeto pressure drop at the wellbore (bottom). In the horizontal well example, only one largefracture forms if the wellbore axis is normal to the minimum horizontal stress. If thewellbore axis parallels the minimum horizontal stress, fractures form at each perfora-tion. The end fractures are highest because they are affected on only one side by thecompressive stress exerted by the opening of the neighboring fracture. Height of theseend fractures tends not to exceed 2 to 3 borehole diameters. The time-lapse view (bot-tom) shows fractures developing tails that reach up and down the wellbore. By time 3,they coalesce into one fracture. In so doing, rhomboids of rock are isolated between theperforations. Small fractures develop here that may contribute to pressure drop at thewellbore and early bridging of proppant.
17October 1992
Minimumhorizontal stress
Time 1 Time 2 Time 3