Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs
48
Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs Taufan Marhaendrajana Ph.D. Candidate Texas A&M University SPE International Paper Contest 5 October 1999
description
Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs. Taufan Marhaendrajana Ph.D. Candidate Texas A&M University. SPE International Paper Contest 5 October 1999. 10 Second Summary. - PowerPoint PPT Presentation
Transcript of Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs
Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs
Taufan MarhaendrajanaPh.D. Candidate
Texas A&M University
SPE International Paper Contest5 October 1999
10 Second Summary
Developed a new method to estimate the original oil/gas-in-place by analyzing production data from only one well.
This method can also be used to esti-mate the permeability-thickness product in the drainage area for a particular well.
These developments are based on an analytical solution for a multiwell model.
Why is this work important?
Multiwell Solution Accurate Rigorous and robust Very fast solution (can be run on a PC)
Multiwell Analysis Approach Can be based on single-well decline type curve "Total Material Balance Time" system volume Easy-to-apply
Validation Homogeneous reservoir case Heterogeneous reservoir case Field Cases (Arun Gas Field, Indonesia)
OutlineOutline
Introduction Objectives Physical Model and Analytical Solution Decline Type Curve Analysis Field Application (Arun Field, Indonesia) Conclusions Recommendations for Extensions of This Work
IntroductionIntroduction
Bounded Reservoirwith Multiple Wells
Current Multiwell Models Rodriguez and Cinco-Ley (1993) Camacho et al (1996)
– Constant pressure only– Pseudosteady-state only– Does not provide a mechanism
for analyzing production data
Modeling of Individual Well Performance?Current Multiwell Models Valko et al (1998)
– Pseudosteady-state only– Does not provide a mechanism
for analyzing production data
Single Well Model (Well-by-well analysis)
Production Data Analysis?
Is a single well model satis-factory?
1.To Develop an Analytical Solution for a Single Well or Multiple Wells in a Multiwell Reservoir System Correctly models all flow regimes. Completely general formulation (constant rate, constant
pressure, or variable-rate/pressure).
2.To Develop a Method for the Analysis of Production Data from a Multiwell SystemEstimate the original oil/gas-in-place.Estimate the local flow capacity (permeability-thickness
product).
ObjectivesObjectives
Homogeneous, Closed ReservoirSlightly Compressible FluidFully Penetrating Wells
Assumptions:
(0,0,0) xe
ye
ze
Physical ModelPhysical Model
Well Pressure Solution (Convolution Form)Well Pressure Solution (Convolution Form)
i = well counterk = well index (well location where pressure is evaluated)
Constant Rate Solution For Single Well in A Closed
Rectangular Reservoir
Accuracy Speed Formulation
pD([xwD,k + ],[ywD,k + ],tDA) =
qD,i()dpD,cr(tDA – )
d k,id
0
tDA
i = 1
nwell
+ qD,k(tDA) sk
Initial PressureInitial Pressure ::5,000 psi5,000 psiPermeabilityPermeability ::5 md5 mdPorosityPorosity ::0.20.2Total Comp.Total Comp. ::3x103x10-6-6 1/psia 1/psiaThicknessThickness ::500 ft500 ftAreaArea ::16,86016,86022 ft ft22
No. of WellsNo. of Wells ::NineNineOil ViscosityOil Viscosity ::0.8 cp0.8 cpFVFFVF ::1.184 RB/STB1.184 RB/STBOOIPOOIP ::4,278 MMSTB
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irect
ion,
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Numerical Simulation Model (Base Case)Numerical Simulation Model (Base Case)
[3,1] [3,2] [3,3]
[2,1] [2,2] [2,3]
[1,1] [1,2] [1,3]
Permeability :5 md
OOIP :4,278 MMSTB
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Well [1,1] Well [1,2] Well [1,3]
Well [2,1] Well [2,2] Well [2,3]
Well [3,1] Well [3,2] Well [3,3]
Bot
tom
Hol
e Fl
owin
g Pr
essu
re, p
si
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Numerical Simulation Analytical Solution
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Legend:
Numerical Simulation Analytical Solution
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Legend:
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Legend:
Numerical Simulation Analytical Solution
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Legend:
Numerical Simulation Analytical Solution
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Legend:
Numerical Simulation Analytical Solution
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Legend:
Numerical Simulation Analytical Solution
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Legend:
Numerical Simulation Analytical Solution
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Legend:
Numerical Simulation Analytical Solution
Well [1,1] Well [1,2] Well [1,3]
Well [2,1] Well [2,2] Well [2,3]
Well [3,1] Well [3,2] Well [3,3]
Oil
Rat
e, S
TB/D
Time, Days
Analytical Solution Matches Analytical Solution Matches Numerical SolutionNumerical Solution
Oil
Rat
e, S
TB/D
Time, Days
Well [1,2]
Initial pwf
Variable pwf
Final pwf
Decline Type Curve AnalysisDecline Type Curve Analysis
Formulation for Multiwell Decline Type Curve Analysis
Fetkovich/McCray Decline Type Curve Decline Type Curve Analysis Procedure Application to Simulated Performance Data
Production Data(Pressure & Rate)
Total MaterialBalance Time
ttot =Np,fieldqwell
c(t) includes:-Transient flow-Reservoir shape-Well location
vs
Formulation for Multiwell AnalysisFormulation for Multiwell Analysisusing Decline Type Curvesusing Decline Type Curves
Original-Oil-in-Place
c(t) becomes constant at long
times
qk(t)(p i – pwf)
= 1
1Nct
1qk(t) q i(t)
i = 1
nwell
dt0
t+ c(t)c(t)c(t)
Type Curve ConstructionType Curve Construction(Multiwell System)(Multiwell System)
tDde,bar = 0.00633k t totctA
2
ln (reD/ D ) – 0.5
qDde = 141.2Bkh
qp ln (reD/ D ) – 0.5
D= 1 D= 9 D= 25
"Total Material Balance Time" "Total Material Balance Time" Generalizes The Fetkovich/McCray Type Generalizes The Fetkovich/McCray Type
Curve Curve
10-2
10-1
100
101
Dim
ensi
onle
ss R
ate
Func
tions
, q D
de, q
Dde
i, q D
deid
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Dimensionless Time, tDde
Dim
ensi
onle
ss R
ate
Func
tions
(qD
de, q
Dde
i, q D
deid
)
Dimensionless Total Material Balance Time, tDde,bar
=1x104
800
16080 48 28 18 12 7 4
471247
1218284880
1608001x104
qDde
qDdei
qDdeidreD/ D
Model(Dimensionless
Variables)
Log-log Plot
Dataqwell/pwell
tbar,tot=Np,field/qwell
Match
Original Oil/Gas-In-Place (N or G) Flow Capacity (kh)
Decline Type Curve Analysis Procedure Decline Type Curve Analysis Procedure
All Curves Overlay Each OtherAll Curves Overlay Each Other(Homogeneous Reservoir Example)(Homogeneous Reservoir Example)
10-2
10-1
100
101
q/
p, (
q/
p)i,
(q/
p)id
, ST
B/D
/psi
100 101 102 103 104 105
Total Material Balance Time, tbar,e, Days
(q/ p)(q/ p)i
(q/ p)id
Legend:
Well [1,1]; Well [2,1]; Well [3,1] Well [1,2]; Well [2,2]; Well [3,2] Well [1,3]; Well [2,3]; Well [3,3]
q/p
, (q/
p) i,
(q/
p)id
, STB
/D/p
si
tbar,tot = Np,field/qwell, Days
(q/p)id is affected by severe rate changes(unlikely in practice)
10-2
10-1
100
101
Dim
ensi
onle
ss R
ate
Func
tions
, q D
de, q
Dde
i, q D
deid
10-3 10-2 10-1 100 101 102
Dimensionless Total Material Balance Time, tDde
reD/ D =1x104
800
16080 48 28 18 12 7 4
1x10416080048801828
412
47127
Dim
ensi
onle
ss R
ate
Func
tions
(qD
de, q
Dde
i, q D
deid
)
Dimensionless Material Balance Time, tDd,bar or
Dimensionless Total Material Balance Time, tDde,bar
Multiwell Model Is More Accurate Multiwell Model Is More Accurate Than Single Well ModelThan Single Well Model
Total material balance functions align with
correct solution
Dimensionless Material Balance Time, tDd,bar
Dimensionless Total Material Balance Time, tDde,bar
reD/ D
2520151050Permeability, mD
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0
Y-D
irect
ion,
ft
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0
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X-Direction, ft
Locally Homogeneous Reservoir ExampleLocally Homogeneous Reservoir Example
[ 25 mD ] [ 5 mD ] [ 10 mD ]
[ 15 mD ]
[ 20 mD ]
Issues: Can we analyze
multiwell performance?
Accuracy of results? In-place volume kh-product
Uniqueness of the analysis?
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Well [1,1] Well [1,2] Well [1,3]
Well [2,1] Well [2,2] Well [2,3]
Well [3,1] Well [3,2] Well [3,3]
Bot
tom
Hol
e Fl
owin
g Pr
essu
re, p
si
Time, Days
Well [1,1] Well [1,2] Well [1,3]
Well [2,1] Well [2,2] Well [2,3]
Well [3,1] Well [3,2] Well [3,3]
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105Oil
Rat
e, S
TB/D
Time, Days
All Curves Converge to A Single All Curves Converge to A Single Material Balance Trend Material Balance Trend
10-1
100
101
102
q/
p, S
TB
/D/p
si
100 101 102 103 104 105
Total Material Balance Time, tbar,e, Days
Legend:
Well [1,1]; Well [2,1]; Well [3,1] Well [1,2]; Well [2,2]; Well [3,2] Well [1,3]; Well [2,3]; Well [3,3]
q/p
, STB
/D/p
si
tbar,tot = Np,field/qwell, Days
Decreasing Permeability Material BalanceTrend
Locally Homogeneous Reservoir ExampleLocally Homogeneous Reservoir Example
10-2
10-1
100
101
Dim
ensi
onle
ss R
ate
Func
tions
, q D
de, q
Dde
i, q D
deid
10-3 10-2 10-1 100 101 102
Dimensionless Time, tDde
reD/ D =1x104
800
16080 48 28 18 12 7 4
471247
1218284880
1608001x104
Well [1,1]; Well [2,1]; Well [3,1] Well [1,2]; Well [2,2]; Well [3,2] Well [1,3]; Well [2,3]; Well [3,3]
Dim
ensi
onle
ss R
ate
Func
tions
(qD
de, q
Dde
i, q D
deid
)
Dimensionless Total Material Balance Time, tDde,bar
reD/ D
2520151050Permeability, mD
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14000
12000
10000
8000
6000
4000
2000
0
Y-D
irect
ion,
ft
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0
1400
0
1200
0
1000
0
8000
6000
4000
20000
X-Direction, ft
[ 25 mD ] [ 5 mD ] [ 10 mD ]
[ 15 mD ]
[ 20 mD ]
[1,1] [1,2] [1,3]
[2,1] [2,2] [2,3]
[3,1] [3,2] [3,3]Well k, calc.
(md)k, input
(md)[1,1][1,2][1,3][2,1][2,2][2,3][3,1][3,2][3,3]
22.75.1510.15.159.7713.89.9414.218.9
255.0105.01015101520
22.7
9.77
OOIP (Input) 4,278 MMSTBOOIP (Calc.) 4,278 MMSTB
18.9
Field ApplicationField Application
Description/Layout of Arun Gas Field Analysis of Production Data (13 Wells) Comparison with Previous Results
Arun Field
N
Located in Northern part of Sumatra, Indonesia
Retrograde gas reservoirOne of the largest gas fields in the
worldArun Field has 111 wells:
79 producers 11 injectors 4 observation wells 17 wells have been abandoned
Arun Well A-015Arun Well A-016
Field Description
300000
250000
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150000
100000
50000
0
Gas
(Tot
al W
ell S
tream
) Rat
e, M
scf/D
7000600050004000300020001000Time, Days
-6000
-4000
-2000
0
2000
4000
6000
Wellhead Pressure, psi
Gas Rate
Wellhead Pressure
, Gas Rate and Wellhead Pressure for Well A-015 , Gas Rate and Wellhead Pressure for Well A-016
Gas
(Tot
al W
ell S
trea
m) R
ate,
Msc
f/D
Time, Days
Wellhead Pressure, psi
Wellhead Pressure
Gas Rate
Well Performance Data: Arun Well A-015
Type Curve Match: Arun Well A-015Type Curve Match: Arun Well A-015(Excellent Match of Data/Type Curve)(Excellent Match of Data/Type Curve)
10-2
10-1
100
101
Dim
ensi
onle
ss R
ate
Func
tions
, q D
de, q
Dde
i, q D
deid
10-3 10-2 10-1 100 101 102
Dimensionless Time, tDde
reD/ D =1x104
800
16080 48 28 18 12 7 4
471247
1218284880
1608001x104
Legend : C-III-02 (Arun A-015)
q/pp (q/pp)i (q/pp)id
Dim
ensi
onle
ss R
ate
Func
tions
(qD
de, q
Dde
i, q D
deid
)
Dimensionless Total Material Balance Time, tDde,bar
Transient Flow
TransitionBoundaryDominated
Flow
reD/ D
300000
250000
200000
150000
100000
50000
0
Gas
(Tot
al W
ell S
tream
) Rat
e, M
scf/D
7000600050004000300020001000Time, Days
-6000
-4000
-2000
0
2000
4000
6000
Wellhead Pressure, psi
Gas Rate
Wellhead Pressure
, Gas Rate and Wellhead Pressure for Well A-015 , Gas Rate and Wellhead Pressure for Well A-016
Gas
(Tot
al W
ell S
trea
m) R
ate,
Msc
f/D
Time, Days
Wellhead Pressure, psi
Wellhead Pressure
Gas Rate
Well Performance Data: Arun Well A-016
Type Curve Match: Arun Well A-016Type Curve Match: Arun Well A-016(Excellent Match of Data/Type Curve)(Excellent Match of Data/Type Curve)
10-2
10-1
100
101
Dim
ensi
onle
ss R
ate
Func
tions
, q D
de, q
Dde
i, q D
deid
10-3 10-2 10-1 100 101 102
Dimensionless Time, tDde
reD/ D =1x104
800
16080 48 28 18 12 7 4
471247
1218284880
1608001x104
Legend : C-III-04 (Arun A-016)
q/pp (q/pp)i (q/pp)id
Dim
ensi
onle
ss R
ate
Func
tions
(qD
de, q
Dde
i, q D
deid
)
Dimensionless Total Material Balance Time, tDde,bar
Transient Flow
TransitionBoundaryDominated
Flow
reD/ D
Well Flow Capacity(md-ft)
Arun A-015Arun A-016
Reservoir OGIP (TCF)
JPT (June 1983)This Study Numerical Sim.
912996
19.8 17.1
Difference
?Production History: (As of November 1998)Cumulative gas production (gross) = 21.3 TCFCumulative gas reinjected = 5.2 TCFNet cumulative gas production = 21.3-5.2 = 16.1 TCFCurrent monthly gas production = 50 BCF (0.6 TCF/yr)
Results of Multiwell Analysis at Arun FieldResults of Multiwell Analysis at Arun Field
CumulativeProduction(Nov. 1998)
16.1
10-2
10-1
100
101
102
103W
ell R
ate/
Pres
sure
-Dro
p Fu
nctio
n,
q/
p p, M
scf/D
/psi
101 102 103 104 105 106 107 108
Total Material Balance Time, tbar,tot=Gp,field/qg,well, Days
Legend: Arun Gas Field
C-I-02 (A-036) C-III-02 (A-015) C-I-08 (A-027) C-III-03 (A-034) C-I-09 (A-044) C-III-04 (A-016) C-II-01 (A-037) C-III-06 (A-017) C-II-04 (A-024) C-III-09 (A-028) C-II-09 (A-021) C-III-05 (A-035) C-II-16 (A-029)
q/
p, S
TB/D
/psi
tbar,tot = Gp,field/qwell, Days
All Cases Converge to A Single All Cases Converge to A Single Material Balance Trend (Arun Field Data)Material Balance Trend (Arun Field Data)
Material BalanceTrendfor Arun Gas Field(OGIP=19.8 TCF)
10-2
10-1
100
101
Dim
ensi
onle
ss R
ate
Func
tions
, q Dde
, qD
dei,
q Dde
id
10-3 10-2 10-1 100 101 102
Dimensionless Total Material Balance Time, tDde
reD/sqrt(D) = 1x104
16048 18 7
1x1041604818
77
C-I-02 (A-036) C-II-09 (A-021) C-III-04 (A-016)C-I-08 (A-027) C-II-16 (A-029) C-III-06 (A-017)C-I-09 (A-044) C-III-02 (A-015) C-III-09 (A-028)C-II-01 (A-037) C-III-03 (A-034) C-III-05 (A-035)C-II-04 (A-024)
reD/ D
Dim
ensi
onle
ss R
ate
Func
tions
(qD
de, q
Dde
i, q D
deid
)
Dimensionless Total Material Balance Time, tDde,bar
Type Curve Match: Arun Field--13 WellsType Curve Match: Arun Field--13 Wells(Excellent Match of Data/Type Curve)(Excellent Match of Data/Type Curve)
1.Developed a Real Space Analytical Solution for a Closed Rectangular Reservoir with One or More Wells– Can serve as analytical reservoir simulator.– Completely general formulation (constant rate,
constant pressure, or variable-rate/pressure).
ConclusionsConclusions
ConclusionsConclusions
2.This Solution Provides a Mechanism for the Decline Type Curve Analysis in a Multiwell Reservoir System Conserves volume of the entire system. Rigorous and accurate approach for estima-
ting original oil/gas-in-place in the overall reservoir system and formation permeability in the local reservoir system.
Can use pressure-rate performance data for only one well to estimate original oil/gas-in-place.
Can be used for well performance monitoring. The key for the decline type curve analysis in a multiwell system is to use total material balance time.
ConclusionsConclusions
3.We Have Successfully Demonstrated the Application of the New Method to Analyze Production Data From Arun Gas Field
Recommendations for Extensions of This WorkRecommendations for Extensions of This Work
To extend this work, we recommend:
Including various reservoir outer boundary conditions other than the closed (no-flow) outer boundary.
Development and application of a method-ology to estimate the near-well skin factor.
Modeling and Analysis of Flow Behavior in Multiwell Bounded Reservoirs
Taufan MarhaendrajanaPh.D. Candidate
Texas A&M University
SPE International Paper Contest5 October 1999
1086420Permeability, mD
16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
irect
ion,
ft
1600
0
1400
0
1200
0
1000
0
8000
6000
4000
20000
X-Direction, ft
Heterogeneous Reservoir ExampleHeterogeneous Reservoir Example
Issues: Effect of a
randomly heterogeneous medium?
Accuracy of results? In-place volume kh-product
Uniqueness/meaning of the analysis?
Well [1,1] Well [1,2] Well [1,3]
Well [2,1] Well [2,2] Well [2,3]
Well [3,1] Well [3,2] Well [3,3]
Bot
tom
Hol
e Fl
owin
g Pr
essu
re, p
si
Time, Days
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Well [1,1] Well [1,2] Well [1,3]
Well [2,1] Well [2,2] Well [2,3]
Well [3,1] Well [3,2] Well [3,3]
Oil
Rat
e, S
TB/D
Time, Days
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104
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10-1
100
101
q/
p, (
q/
p)i,
(q/
p)id
, STB
/D/p
si
100 101 102 103 104 105 106
Total Material Balance Time, tbar,e, Days
Legend:
Well [1,1]; Well [2,1]; Well [3,1] Well [1,2]; Well [2,2]; Well [3,2] Well [1,3]; Well [2,3]; Well [3,3]
Decreasing Permeability
q/p
, STB
/D/p
si
tbar,e = Np,field/q, Days
All Curves Converge to a Single All Curves Converge to a Single Material Balance Trend Material Balance Trend
Material BalanceTrend
Heterogeneous Reservoir ExampleHeterogeneous Reservoir Example
10-2
10-1
100
101
Dim
ensi
onle
ss R
ate
Func
tions
, q D
de, q
Dde
i, q D
deid
10-3 10-2 10-1 100 101 102
Dimensionless Time, tDde
reD/ D =1x104
800
16080 48 28 18 12 7 4
471247
1218284880
1608001x104
Well [1,1]; Well [2,1]; Well [3,1] Well [1,2]; Well [2,2]; Well [3,2] Well [1,3]; Well [2,3]; Well [3,3]
Dim
ensi
onle
ss R
ate
Func
tions
(qD
de, q
Dde
i, q D
deid
)
Dimensionless Total Material Balance Time, tDde
reD/ D
Well k(md)
OOIP(MMSTB)
[1,1][1,2][1,3][2,1][2,2][2,3][3,1][3,2][3,3]
4.043.274.444.302.523.383.933.993.64
4,2784,2784,2784,2784,2784,2784,2784,2784,278
Calculated ResultsCalculated Results(Randomly Heterogeneous Reservoir)(Randomly Heterogeneous Reservoir)
16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
irect
ion,
ft
1600
0
1400
0
1200
0
1000
0
8000
6000
4000
20000
X-Direction, ft
1086420Permeability, mD
3.73
4.10
Well k, calc.(md)
k, input(md)
[1,1][3,3]
4.043.64
4.103.73
OOIP (Input) 4,278 MMSTBOOIP (Calc.) 4,278 MMSTB
Results:
Individual well performance appears to be "homogeneous"
Computed in-place volume is essentially exact
Computes permeability represents harmonic average in well drainage area
Observations:
Well Pressure Solution (Continued)Well Pressure Solution (Continued)
Exact Very fast (2-3 seconds/100 points)
New Single-Well Solution: (Constant Rate)
Characteristics:
pD(xD,yD,tDA) = 12 E1 amn + E1 bmn + E1 cmn + E1 dmnn = –
m = –
amn =(xD+ xwD+2nxeD)2 +(yD+ywD+2myeD)2
4tDAbmn =
(xD– xwD+2nxeD)2 +(yD+ywD+2myeD)2
4tDAcmn =
(xD+ xwD+2nxeD)2 +(yD–ywD+2myeD)2
4tDAdmn =
(xD– xwD+2nxeD)2 + (yD–ywD+2myeD)2
4tDA
Well Pressure SolutionWell Pressure Solution
+ qDi,0 [pDcr(tDA,n)]kii = 1
Nwell
pD([xwD,k + ],[ywD,k + ],tDA,n) =
+ (qDi,m – qDi,m – 1) [pD,cr(tDA,n – tDA,m – 1)]kii = 1
Nwell
m = 2
n – 1
– qDi,n – 1 [pD,cr(tDA,n – tDA,n – 1)]kii = 1
Nwell
+ qDi,n [pD,cr(tDA,n – tDA,n – 1)]kii = 1
Nwell
+ qDk(tDA,n) sk
