Hydraulic Fracture

Hydraulic FracturingHydraulic FracturingShort Course, Short Course,

Texas A&M UniversityTexas A&M UniversityCollege StationCollege Station

20052005

Modeling, Monitoring, Post-Job Evaluation, Improvements

FractureModeling+

2

3D3D

FractureModeling+

3

P3D and 3D Models

FracPro (RES, Pinnacle Technologies)

FracCADE (Dowell)

Stimwin (Halliburton) and PredK (Stim-Lab)

TerraFrac

StimPlan

MFrac

FractureModeling+

4

Dimensionless Form of Nordgren Model

204

201w

x t -+

w

tD

D D D

D

D

w

x

i

iD

D

04

0

dx

dt

w

xfD

D

D

D

4

303

xD = 0 (wellbore) xD = xfD (tip)

D(xfD) : inverse of xfD(tD)

w D0 0

FractureModeling+

5

Propagation Criterion of the Nordgren Model

Net pressure zero at tip

Once the fluid reaches the location, it

opens up immediately

Propagation rate is determined by “how

fast the fluid can flow

FractureModeling+

6

Other Propagation Criteria

(Apparent) Fracture Toughness

Dilatancy

Statistical Fracture mechanics

Continuum Damage mechanics

FractureModeling+

7

Fracture Toughness Criterion

KI

xf

hf pn

KIC

(Rf)

Stress Intensity Factor KI =pnxf1/2

FractureModeling+

8

CDM

dD

dt= C n

n 1- D

dD

dt= C

1- D

What is the time needed for D to start at D = 0 and grow to D = 1 ?

FractureModeling+

9

CDM Propagation Criterion

u =Cl x

l + xwf

H,

2

f

f

x=x2

f

2 1 2

min

/

Cl 2Combined Kachanov parameter:

FractureModeling+

10

P3D

Pseudo 3 D Models: Extension of

Nordgren’s differential model with height

growth

Height criterion

Equilibrium height theory

or Assymptotic approach to equilibrium

Plus some “tip” effect

FractureModeling+

11

3D (Finite Element Modeling)

x

ywellbore element

tip element

FractureModeling+

12

Fracture Toughness Criterion

pn

KIC

Fluid flow in 2 DFluid loss according to local opening timePropagation: Jumps

Stress Intensity Factor KI > KIC ?

FractureModeling+

13

Data Need for both P3D and 3D:

Layer data

Permeability, porosity, pressure

Young’s modulus, Poisson ratio, Fracture

toughness

Minimum stress

Fluid data

Proppant data

Leakoff calculated from fluid and layer data

FractureModeling+

14

Design Tuning Steps

Step Rate test

Minifrac (Datafrac, Calibration Test)

Run design with obtained min (if needed)

and leakoff coefficient

Adjust pad

Adjust proppant schedule

FractureModeling+

15

Step rate test

Time

Bot

tom

hole

pre

ssur

e

Inje

ctio

n ra

te

FractureModeling+

16

Step rate test

Injection rate

Bot

tom

hole

pre

ssur

e

Propagation pressure

Two straight lines

FractureModeling+

17

Fall-off (minifrac)

1st

inje

ctio

n cy

cle

2nD

inje

ctio

n cy

cle

flow-backshut-in

1

2

34

5

68

7

Injection rate

Time

Bot

tom

hole

pre

ssur

e

Inje

ctio

n ra

te

3 ISIP

4 Closure

5 Reopening

6 Forced closure

7 Pseudo steady state

8 Rebound

FractureModeling+

18

Pressure fall-off analysis(Nolte)

eLeDpeitt tC2AtgS2AV=Ve

,

eD ttt /

eLDpi

tt tCtgSA

Vw

e2 ,2-

e

eA

FractureModeling+

19

g-function

where F[a, b; c; z] is the Hypergeometric function, available in the form of tables and computing algorithms

dimensionless shut-in time

area-growth exponent

D

t

A

D

DD

D dAdtAt

tgD

D

1

0

1

/1/1

1,

21

1;1;,2/1124,

1

DDDD

tFtttg

FractureModeling+

20

g-function

FractureModeling+

21

Pressure fall-off

,2-2-/ DeLfpfeifCw tgtCSSSAVSpp

p b m g tw N N D ,

eLeDpeitt tC2AtgS2AV=Ve

,

eD ttt /

,22- e

DeLpi

tt tgtCSA

Vw

e

wSp fnet Fracture stiffness

FractureModeling+

22

Fracture Stiffness(reciprocal compliance)

Table 5.5 Proportionality constant, Sf and suggested for basic fracture geometries

PKN KGD Radial

4/5 2/3 8/9

Sf 2E

hf

'

E

xf

'

3

16

ERf

'

wSp fnet Pa/m

FractureModeling+

23

Shlyapobersky assumption

No spurt-loss

,2-2- DeLfpfe

ifCw tgtCSSS

A

VSpp

Ae from intercept

g

pw

bN mN

g=0

FractureModeling+

24

Nolte-Shlyapobersky

PKN KGD Radial

Leakoffcoefficient,

CL

N

e

f mEt

h

'4

N

e

f mEt

x

'2

N

e

f mEt

R

'3

8

FractureExtent CNf

if

pbh

VEx

2

2 CNf

if

pbh

VEx

3

8

3

CN

if

pb

VER

FractureWidth

eL

ff

ie

tC

hx

Vw

830.2

eL

ff

ie

tC

hx

Vw

956.2

eL

f

ie

tC

R

Vw

754.2

22

FluidEfficiency

i

ffee

V

hxw

i

ffee

V

hxw

i

fe

eV

Rw2

2

Vi: injected into one wing

FractureModeling+

25

7 Calculate

(fluid efficiency)

3 Calculate Rf

(fracture extent -radius)

4 Calculate CLAPP

(apparent leakoff coeff)

5 Calculate wL

(leakoff width)

6 Calculate we

(end-of pumping width)

RE V

b pfi

N C

3

83

CR

t EmLAPP

f

eN

8

3 '

w g C tL LAPP e ( , )08

92

wV

Rwe

i

fL 2 2 /

w

w we

e L

1: g-function plot of pressure2: get parameters bN and mN

FractureModeling+

26

Computer Exercise 3-1 Minifrac analysis

FractureModeling+

27

Example

Permeable (leakoff) thickness, ft, 42

Plane strain modulus, E' (psi), 2.0E+6

Closure Pressure, psi, 5850

21.8 9.9 0.0 1 0

21.95 0.0 7550.62 0 0

22.15 0.0 7330.59 0 0

Time,

min

BH Injection

rate, bpm

BH Pressure,

psi

Include into inj

volume

Include into

g-func fit

0.0 9.9 0.0 1 0

1.0 9.9 0.0 1 0

FractureModeling+

28

Output

Slope, psi -4417

Intercept, psi 13151

Injected volume, gallon 9044

Frac radius, ft 39.60

Average width, inch 0.4920

5

Fluid efficiency 0.1670

8

Apparent leakoff coefficient (for total area),

ft/min^0.5

0.0159

2

Leakoff coefficient in permeable layer, ft/min^0.5 0.0247

9

FractureModeling+

29

From "apparent" to "real“ (radial)

64.0)arcsin()1(2

53.06.39*2

42

2

5.02

xxxr

R

hx

p

f

p

ft/min 0.024 ft/min 0.64

0.015 m/s

0.214

1085.5

ft/min 0.015 m/s1085.5

0.50.50.55

,

0.50.55,

TrueL

AppL

C

C

FractureModeling+

30

Redesign

Run the design with new leakoff

coefficient

(That is why we do minifrac analysis)

FractureModeling+

31

Monitoring

Calculate proppant concentration at bottom (shift)

Calculate bottomhole injection pressure, net pressure

Calculate proppant in formation, proppant in well

Later: Add and synchronize gauge

pressure

FractureModeling+

32

Nolte-Smith plot

Log net pressure

Log injection time

Normal frac propagation

Tip screenout

Wellbore screenout

Unconfined

height growth

FractureModeling+

33

Post-Job Logging

Tracer Log

Temperature Log

Production Log

FractureModeling+

34

Radius of penetra

tion

Available Techniques for Width and Height

Measured Directly Formation Micro Scanner

Borehole Televiewer

Based on Inference Temperature Logging

Isotopes (fluid, proppant)

Seismic Methods, Noise Logging

Tiltmeter techniques

Spinner survey

FractureModeling+

35

ScSb Ir

Tracerlog

FractureModeling+

36

Tiltmeter Results after Economides at al. Petroleum Well Construction

FractureModeling+

37

0 100 200 300 400

Fracture Half-Length (ft)

< 0.00.00.0 - 2.02.0 - 4.04.0 - 6.06.0 - 8.08.0 - 10.010.0 - 12.012.0 - 14.0> 14.0

FracCADE

*Mark of Schlumberger

EOJ Fracture Profile and Proppant Concentration

Texaco E&POCS-G 10752 #D-12Actual05-23-1997

-0.45 -0.30 -0.15 0 0.15 0.30 0.45

Wellbore Hydraulic Width(in)

5600 6400 7200

Stress(psi)

7300

7350

7400

7450

7500

Pressure Match with 3D Simulation

FractureModeling+

38

3D Simulation

0 50 100 150 200 250

Fracture Half-Length - ft

0

0.05

0.10

0.15

0.20

0.25P

rop

pe

d W

idth

- in

0

1000

2000

3000

4000

5000

Co

nd

uctivity (K

fw) - m

d.ftPropped Width (ACL)

Conductivity - Kfw

FracCADE

*Mark of Schlumberger

Flow Capacity Profiles

Texaco E&POCS-G 10752 #D-12

Actual05-23-1997

FractureModeling+

39

Well Testing: The quest for flow regimes

FractureModeling+

40

Design Improvement in a Field Program

Sizing

Pad volume for “generic” design

More aggressive or defensive proppant schedule

Proppant change (resin coated, high strength etc.)

Fluid system modification (crosslinked, foam) Proppant carrying capacity

Leakoff

Perforation strategy changes

Forced closure, Resin coating, Fiber reinforcement, Deformable particle

FractureModeling+

41

Example: Tortuous Flow Path

Analysis of the injection rate dependent

element of the treating pressure

Does proppant slug help?

Does limited entry help?

Does oriented perforation help?

Extreme: reconsidering well orientation:

e.g. S shaped

FractureModeling+

42

Misalignment

FractureModeling+

43

Fracture Orientation: Perforation Strategy after Dees J M, SPE 30342

max max

From overbalanced perforation

From underbalanced perforation

FractureModeling+

44

High Viscosity slugs

FractureModeling+

45

Proppant Slugs

FractureModeling+

46

Forcheimer Equation

Cornell & Katz

Case Study: Effect of Non-Darcy Flow

2vk

v

L

p

2avk

v

L

p

FractureModeling+

47

Non-Darcy Flow

Dimensionless Proppant Number is the most

important parameter in UFD

res

propfprop V

V

k

kN

2

Effective ProppantPack Permeability

FractureModeling+

48

Non-Darcy Flow

Effective Permeability

Reynolds Number

Re1 N

kk nom

eff

vk

N nomRe

keff is determined through an iterative processDrawdown is needed to calculate velocity

FractureModeling+

49

Non-Darcy Flow Coefficient

Several equations have been developed mostly from lab measurements (empirical equations)

General form of equation

where is 1/m and k is md

cbfk

ax

8101

FractureModeling+

50

SPE 90195

Optimum FractureTreatment Design Minimizes the Impact of Non-Darcy Flow Effects

Henry D. Lopez-Hernandez, SPE, Texas A&M University, Peter. P. Valko, SPE, Texas A&M University, Thai T. Pham, SPE, El Paso Production

FractureModeling+

51

Case Study: Reynolds number

FractureModeling+

52

Case Study: Proppant number

Comparison for 20/40 Norton Proppants

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Pro

ppan

t N

umbe

r

Naplite® Interprop® Sintered Bauxite

FractureModeling+

53

Case Study: Max possible JD

FractureModeling+

54

Case Study: Optimum frac length

FractureModeling+

55

Case Study: Optimum frac width

FractureModeling+

56

Summary

Increasing role of evaluation

Integration of reservoir engineering, production engineering and treatment information

Cost matters

Expensive 3D model does not substitute thinking

Still what we want to do is increasing JD