Stimulation 6
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Transcript of Stimulation 6
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Stimulation design
PKN
GDK3D
P3D
Copyright, 2011
Fracturemodel
xf,hf, wf
Geometryresults
Injection rate
Fluid leakoffTotal volume
Proppant schedule
Designvariables
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Stimulation Leakoff
Carters solution for estimating fracture area accounting for fluid
leakoff.
Where Afl= fracture area exposed to fluid loss = 2h fxf(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
fx
fh
wbw
1c
fx
fhw
fV
t
0 t
d
d
fdx
LC2
dt
fdx
pS2
wbw
1c
fh
iq
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Stimulation Leakoff
Solution for fracture half length,
Where
And wwbe is maximum wellbore width at the end of pumping
Copyright, 2011
)(
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
?
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Hydraulic Fracturing design
Copyright, 2011
4*
4/1
G
fx)1(iq31.2w
4*
4/1
fGh
2f
x)1(i
q27.2w
PKN:
GDK:
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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
ptprLCLK2wfAptiq
fff hxA 2
Hydraulic Fracturing design
Copyright, 2011
Harrington (1973), with 10% error
Nolte (1979), )1(3
8L
K
8L
K
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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 Aflis fracture surface area exposed to fluid loss
Copyright, 2011
tLC
lv
flA
0
t
0 t
d
d
fldA
LC
fldAl
vL
q
Lq
injq
dt
dV
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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
Copyright, 2011
)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
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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 areaqi = 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 planepore pressure
Copyright, 2011
injq
Lq
t
w
y
yq
x
xq
)y,x(t
)p
pp(L
C2
)t,y,x(Lq
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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 heightAx = cross sectional area
Time dependent fluid loss term,
Where x) is the time at which the fracture reaches position x and hpayis
payzone thickness
Copyright, 2011
)t,x(L
Qt
)t,x(x
A
x
)t,x(Q
)x(t
payh
LC2
)t,x(L
Q
