Well testing of horizontal wells
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HORIZONTAL WELL TESTING
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Gauge Placement inHorizontal Wells
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D
D
D
D
D
D
D
D
tp
zp
yp
xp
=
+
+
2
2
2
2
2
2
pBq
hkp xD =
00708.0
tLc
kett
xD =
2
4
637.2
Solve using Greens Functions,
subject to boundary conditions
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=D D
D
t x
xDDDDD
DD
D dtdxSSSba
p0
0321
2
1
)..(2
+=
=D
DD
D
n D
DD t
an
axn
axnS
2
22
0
1
1 exp)cos()cos(21
+=
=D
DD
D
m D
DD
tb
m
b
ym
b
ymS
2
22
0
1
2 exp)cos()cos(21
+=
=D
DD
D
l D
DD t
h
l
h
zl
h
zlS
2
22
0
1
3 exp)cos()cos(21
LxxD =
LaaD =
y
xD
k
k
L
yy =
y
xD
k
k
L
bb =
z
xD
k
k
L
zz =
z
xD
k
k
L
hh =
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Horizontal Model Response
1E-3 0.01 0.1 1 10 100 10001
10
100
Without Wellbore Storage
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Horizontal WellFlow Regimes
Wellbore Storage Early (vertical) Radial Flow
Early (intermediate) Linear Flow
Elliptical Flow
Late (Horizontal) Radial Flow
Boundary Dominated Flow
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Wellbore Storage
Pressure:
Derivative:
t
qB
Cpw = 24
1
t
qB
Cpw
= 24
1
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Early Radial Flow
1E-3 0.01 0.1 1 10 100 10001
10
100
Early Radial
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Vertical Radial Flow
+
=
rc
tkk
Lkk
Bqp
wt
zy
ezy
868.0227.3log6.162
2
Pressure:
Derivative:
ezy Lkk
Bq
p
6.70'
=
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Early (Intermediate) Linear Flo
1E-3 0.01 0.1 1 10 100 10001
10
100
Early Linear
1/2
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Intermediate Linear Flow
( )dcezytye
SSLkkBq
ckt
hLqBp ++=
2.141128.8
Pressure:
Derivative:
tye ck
t
hL
qB
p
064.4'
=
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1E-3 0.01 0.1 1 10 100 10001
10
100
1/3
Elliptical Flow
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Elliptical Flow
Semi-log Pressure Derivative
35.0
7241.0
=
Dy
x
D
wD
Dt
k
k
dt
dpt
35.0
' 7241.0
= t
kkCpy
xEFw
35.0
2
B893.7
=
et
h
h
EFLc
k
hk
qC
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Late (Horizontal) Radial Flo
1E-3 0.01 0.1 1 10 100 10001
10
100
Late Radial
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Late Radial Flow
( cezyet
yx
yxSLkk
Bq
Lc
tkk
hkk
Bq
p ++
=
2.141
303.2log
6.1622
Pressure:
Derivative:
hkk
Bqp
yx
6.70' =
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Boundary Dominated Flow
1. Pseudo-steady state
2. Steady State
Note:
Both similar to vertical well
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ANALYSIS PROCESS
1. Segmented Analysis2. Modeling (Regression)
3. Integrated Approach
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Plot both pressure and derivative on log-log
Select reservoir model.
Make initial estimates of reservoir parameters;kx, ky, kz, Sd, Le, height of well from base
Run reservoir model to match actual pressure
Refine model by adjusting parameters above un
a good mach is attained
Evaluate confidence on the final parameter resu
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Use both methods whenever possible
Segmented and Modeling
Segmented analysis will help to identify the
magnitude of reservoir parameters
Modeling will help to fine tune the reservoir
parameter estimates