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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 1
4-6 April, 6-8 June 2012
Presentation Outline
Reservoir and Well Performance Pressure Transient Analysis: Infinite Acting Reservoirs
Drawdown Response
Drawdown Analysis
Type Curves
Pressure Build-up Response
Horner Analysis
Non-dimensional Horner
Build-up Type Curve Analysis
Prof Peter Behrenbruch
Model Response
First Drawdown after Stabilisation
Time from start of drawdown
Ref: Gringarten
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P. Behrenbruch Reservoir and Well Performance
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Pressure Drawdown Response
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P. Behrenbruch Reservoir and Well Performance
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Drawdown Response - General Solution Example of pD(tD) Function
Example: Interference Test in an Infinite Reservoir
with Homogeneous Behaviour:
Ref: Gringarten
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Infinitive Reservoir, General Line Source Solution
10-2
10-1
10-1
1
10 104 105 106 107 108 109
1 10 102 103 104
5.0 ; 202
D
DD
r
tr
25 ; 1 DD tr
)(00708.0
,triD ppBq
khp
20Dr
0.1DrDimensionless Parameters
22
000264.0
rc
kt
r
t
tD
D
Valid for
2
D
D
r
t
Dp
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 5
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Drawdown Type Curves Example of Independent Variables*
Ref: Gringarten
Dimensionless parameters, non-unique match
Independent variables, unique match
* oilfield units
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Pressure Drawdown Analysis
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P. Behrenbruch Reservoir and Well Performance
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Pressure Transient Analysis
Logarithmic Approximation of Pressure Drawdown
fwwoot cScScc
100 4
ln2
1~
2D
D
DD t
r
tp
at the wellbore
valid for
or
2
4ln
4 wiwt
cr
kt
kh
qpp
and in field units
23.3log)log(
6.1622
wt
iwtrc
kt
kh
qBpp
where
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P. Behrenbruch Reservoir and Well Performance
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Single Rate Transient Drawdown Analysis Including Afterflow and Skin
Equations (field units):
23.3log
k gives /6.162
2
w
iihr
cr
k
m
pps
cyclepsikh
Bqm
Analysis Plot (Drawdown)
10-1 1 10 102
lhrp
ip
wp
Wellbore Storage
Effects
Slope m
Time (hrs)
m is negative!
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P. Behrenbruch Reservoir and Well Performance
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Identification of Correct Analysis for Semi-log Analysis Log-log Drawdown Response and 1 Log Cycle Rule
1000
100
10
Dp
psia
t, hours 0.01 0.1 1 10
1 log cycles
End of unit
slope line
Expected start of
semi-log straight line
* Ref: Horne, Modern Well Test Analysis
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P. Behrenbruch Reservoir and Well Performance
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Semi-log (Horner) Analysis
3000
4000
5000
5000
p, psia
t, hours 0.01 0.1 1 10
p1hr
Start of semi-log
straight line
* Ref: Horne, Modern Well Test Analysis
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 11
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Type Curves
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P. Behrenbruch Reservoir and Well Performance
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Wellbore Storage (1) Rate Response
0.01 0.1 1 10 100 0
500
1000
1500
2000
2500 Flowrate, stb/d
CD = 10,000
CD = 1,000
Time, hours * Ref: Horne, Modern Well Test Analysis
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Wellbore Storage (2) Pressure Response
Time, hours
0.01 0.1 1 10 100
3000
4000
5000
7000 Pressure. psia
CD = 10,000 CD = 1,000
6000
* Ref: Horne, Modern Well Test Analysis
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Wellbore Storage (3) Characteristic on Log-log Plot: 45o Slope
45o slope
Dt, hours 0.01 0.1 1 10 100
100
1000
10000
Dp, psi
* Ref: Horne, Modern Well Test Analysis
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Drawdown Type Curves Examples of Independent Variables*
* oilfiled units
Ramey
Gringarten
Ref: Gringarten
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P. Behrenbruch Reservoir and Well Performance
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Analysis Process Model Identification, Parameter Calculation, Model Verification
Ref: Gringarten
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Drawdown Type Curves Examples of Dimensionless Variables*
* oilfiled units
Ref: Gringarten
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P. Behrenbruch Reservoir and Well Performance
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Log-log Analysis
Ref: Gringarten
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Model Response in the First Drawdown
Ref: Gringarten
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Type Curve Matching (2) Gringarten Curves
Ref: Gringarten
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Match point: )p(Bq2.141
kh)p(
DD
kh
D
C
tkh000295.0
C
t
D
D
Type curve selected: 2
22 8936.0
wt
SS
Dhrc
CeeC
C
S
Type Curve Matching (3) Summary of Analysis Results
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P. Behrenbruch Reservoir and Well Performance
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Differential Type Curves Homogeneous Reservoir
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Time, hrs
td/cd
Infinite Acting Radial Flow Straight Line on Semi-log Plot
Flat Region on Derivative Plot
* Ref: Horne, Modern Well Test Analysis
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Wellbore Storage Unit Slope Line on Log-log Plot
Unit Slope Line plus Hump* on
Derivative Plot
* The hump on a derivative plot is characteristic
of a damaged well (positive skin)
Dt, hrs
td/cd * Ref: Horne, Modern Well Test Analysis
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Pressure Build-up Responses
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 29
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Build-up Model Response after First Drawdown
Time from start of drawdown
Ref: Gringarten
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Pressure Build-up Transient Analysis
1wtp 2wtp
ipqq 1
02 q
t 1t tD 2t0 0
Rate, q Concept
Superposition
Equation: stpqpp
khDDwni 0)0()(
221
qstqpqsttqp
sttpqq
DD
DDD
DD
)()(
)( 1212
)()()(2
tpttpppq
khDDwni DD
Time, t
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 31
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Horner Analysis
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P. Behrenbruch Reservoir and Well Performance
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Pressure Build-up Analysis (Horner)
3 2 1 0
wp
*p
)( Dietzp
)log( DAAtc
ihrp
Wellbore
Storage
Effects
cyclepsikh
BqmSlope /
6.162
D
D
t
ttlog
t
t
cr
k
m
pps
w
wfhrws 1log23.3log151.1
2
1
Note:
i. If boundaries not felt at
ii. If semi-steady state before shut,
then Dietz method is valid
ipptt D* ;
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 33
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P. Behrenbruch Reservoir and Well Performance
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Determining Start of Semi-log Straight Line
2.43
1000
0.01 0.1 1 10 Dt, hours
Pwf, psia
1 log cycles
End of unit
slope line
Expected start of
semi-log straight line
* Ref: Horne, Modern Well Test Analysis
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Picking Correct Horner Line
2.44
3500
4000
4500
5000
5500
6000
psia
1 10 100 1000 (t+Dt)/Dt
p1hr
Horner time = 11.8
* Ref: Horne, Modern Well Test Analysis
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 36
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Non-dimensional Horner Analysis
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P. Behrenbruch Reservoir and Well Performance
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Model Response: Build-up after first Drawdown Horner Type Curve
Ref: Gringarten
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 38
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Horner Type Curve after Drawdown
Ref: Gringarten
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 39
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Type Curve Analysis (Gringarten)
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 40
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Drawdown and Build-up Pressure Response Superposition of Rate
q q
q
tp
tp
tp t
t t
+q
-q
+q
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8 PTA: Infinite Acting Reservoirsp 41
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Model Response: Build-up after first Drawdown Gringarten Type Curve
Ref: Gringarten
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 42
4-6 April, 6-8 June 2012
Build-up Type Curve Behaviour Difference between Drawdown and Build-up
Ref: Gringarten
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 43
4-6 April, 6-8 June 2012
Pressure Build-up Superposition Response: Argarwal Correction Factor
etD
tD
wfp
ip
wp "" pDobsersed
p""D
true
p""D
Pi - pwf
tp
pwf(Dt) pwf(tp + Dt)
pwf(tp + Dt)
tequiv = tpDt / (tp + Dt)
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P. Behrenbruch Reservoir and Well Performance
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Pressure Buid-up Derivative Response Before Argarwal Correction
3.10
100
1000
psia
P &
P
0.01 0.1 1 10 hours Time
What does this
pressure decrease
represent?
* Ref: Horne, Modern Well Test Analysis
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 45
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Build-up vs. Drawdown Pressure Response Type Curves
pDlog
tDlog
Drawdown
Buildup
Argawal Correction
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8 PTA: Infinite Acting Reservoirsp 46
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3.11
Pressure Buid-up Derivative Response After Argarwal Correction
100
1000
psia
P &
P
0.01 0.1 1 10 hours
Effective Time
All Fixed
with the
Correct Analysis!
* Ref: Horne, Modern Well Test Analysis
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 47
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Additional Handouts
(Lecture 14) Example*
* Ref: Horne, Modern Well Test Analysis
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P. Behrenbruch Reservoir and Well Performance
8 PTA: Infinite Acting Reservoirsp 48
4-6 April, 6-8 June 2012
Type Curve Matching Datum Shifting
3.21
Dt, hours
0.01 0.1 1 10 100
100
1000
10000
Dp, psi
1 minute subtracted
1 minute added
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Stimulated Well Example
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10.1
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10.2
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10.3
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10.4
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10.5
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Damaged Well Buildup
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P. Behrenbruch Reservoir and Well Performance
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10.63
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P. Behrenbruch Reservoir and Well Performance
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10.64
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10.65
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10.66