Stimulation design

PKN

GDK

3D

P3D

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Fracture model

xf,hf, wf

Geometry results

Injection rate

Fluid leakoff

Total volume

Proppant schedule

Design variables

Stimulation Leakoff

Carters solution for estimating fracture area accounting for fluid leakoff.

Where Afl = fracture area exposed to fluid loss = 2hfxf(one wing)

CL = fluid loss coefficient, ft/(min)1/2

Sp = spurt loss, gal/ft2

Volume of one wing of fracture is:

Substitute:

Copyright, 2011

dt

fldApS

t

t

d

d

fldALCiq

dt

fdV

0

f

xf

hwb

w1c

fx

fhw

fV

t

0 t

d

d

fdx

LC2

dt

fdx

pS2

wbw1c

fh

iq

Stimulation Leakoff

Solution for fracture half length,

Where

And wwbe is maximum wellbore width at the end of pumping

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)(

2

12

8216

LerfcLeL

pS

wbew

LC

fh

iq

fx

pS

wbew

tL

C

L 8

8

wbew

4wbew

3

2*

8

3wb

w8

3w:GDK

wbew

4wbew

5

4*

16

5wb

w16

5w:PKN

?

Hydraulic Fracturing design

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4*

4/1

G

fx)1(

iq

31.2w

4*

4/1

fGh

2f

x)1(i

q27.2w

PKN:

GDK:

With a known fracture height, hf, and calculated fracture length, then,

From material balance,

where average width is from the fracture geometry models and is a function of fluid rheology, youngs modulus, injection rate, fracture height and fracture length.

rp = fluid loss area to fracture area

KL = fluid loss multiplier

pt

pr

LC

LK2w

fA

pti

q

fff hxA 2

Hydraulic Fracturing design

Copyright, 2011

Harrington (1973), with 10% error Nolte (1979), )1(

3

8L

K

8L

K

Stimulation Leakoff

Carters equation for fluid leakoff.

Where fracture width and height are assumed constant.

vl = fluid loss velocity normal to fracture face

= time at which filtration starts

Mass balance eq.

Substitute,

Where Afl is fracture surface area exposed to fluid loss

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t

LC

lv

flA

0

t

0 t

d

d

fldA

LC

fldAl

vL

q

Lq

injq

dt

dV

Stimulation Leakoff

PKN model with fluid leakoff. Continuity equation:

Where ql is the fluid loss per unit fracture length, given by:

GDK model with fluid leakoff. Based on mass balance eq:

where

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)x(t

LC

fh2

Lq

Lq

t

w

4

fh

x

q

t

0 t

d

d

dLL

Cf

h2L

q

Lq

injq

dt

dV

Stimulation Leakoff

For 3D fracture propagation models, laminar fluid flow of an incompressible power law fluid is assumed.

Where qL = volume leakoff rate per unit fracture area

qinj = volume injection rate per unit fracture area

qi = volume flow rate in i direction per unit length in j direction

Time dependent fluid loss term,

Where x,y) is the time at which the position (x,y) was first exposed to the fracturing fluid, and

Pressure difference is fracture pressure at injection plane pore pressure

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injq

Lq

t

w

y

yq

x

xq

)y,x(t

)p

pp(L

C2)t,y,x(

Lq

Stimulation Leakoff

For P3D fracture propagation models, laminar fluid flow of an incompressible power law fluid is assumed in 1D along fracture length.

Where QL = volume leakoff rate per unit length in the x direction

Q = horizontal flow rate per unit height

Ax = cross sectional area

Time dependent fluid loss term,

Where x) is the time at which the fracture reaches position x and hpay is payzone thickness

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)t,x(L

Qt

)t,x(x

A

x

)t,x(Q

)x(t

payh

LC2

)t,x(L

Q