Embed Size (px)
Citation preview
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 1
SPE 71517
Decline Curve Analysis Using Type Curves —Evaluation of Well Performance Behavior
in a Multiwell Reservoir System
T. Marhaendrajana, SchlumbergerT.A. Blasingame, Texas A&M U.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 2
Motivation
Outline
Objectives
Multiwell model Model assumptions
Validation using a numerical simulator
Decline type curve analysis Methodology
Validation using a numerical simulator
Field application (Arun Field, Indonesia)
Conclusions
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 3
Note that the well interference causes the data to deviate from the "p/z" straight line.
A Typical p/z Plot in Arun Field (Well A-015)
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 4
Decline Type Curve Analysis (Well A-015)
Note that the late time data show well interference effects.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 5
p/z Plot for Arun Field (Total Field Performance)
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 6
Objectives
To develop an analytical solution for a multiwell system Correctly models all flow regimes Completely general formulation (constant rate,
constant pressure, variable rate/pressure)
To develop a method for the analysis of production data from a multiwell system Estimate the original oil/gas-in-place
Estimate the local flow capacity (permeability-thickness product)
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 7
Multiwell Model — Model Assumptions
A bounded rectangular reservoir Homogeneous
Isotropic
Uniform thickness
Multiple vertical wells produce at arbitrary prescribed pressures (or rates) which are functions of time
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 8
Multiwell Model — Data Used for Validation
16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
ire
cti
on
, ft
16
00
0
14
00
0
12
00
0
10
00
0
80
00
60
00
40
00
20
000
X-Direction, ft
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
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]
Bo
tto
m H
ole
Flo
win
g P
res
su
re, p
si
Time, Days
Homogeneous boundedsquare reservoir with nineproducing wells.
Bottomhole flowing pressureis arbitrary for each well and is function of time.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 9
Multiwell Model — Validation
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
103
104
10008006004002000
Legend:
Numerical Simulation Analytical Solution
102
103
104
10008006004002000
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
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 10
Analytical Solution Matches Numerical Solution
Oil
Rat
e, S
TB
/D
Time, Days
Well [1,2]
Variable pwf
Final pwf
Initial pwf
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 11
Decline Type Curve Analysis — Methodology
qk(t)(p i – pwf)
= 1
1Nct
1qk(t)
q i(t)i = 1
nwell
dt0
t+ c(t)
Production Data(Pressure & Rate)
Total MaterialBalance Time
ttot =Np,fieldqwell
c(t) becomes constant at long times
Results from this work: A general formulation of the "Arp's Exponential Decline." A single well decline type curve can be used to analyze a
well performance in a multiwell system.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 12
Decline Type Curve Analysis — Methodology
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 13
Homogeneous Reservoir Example (Oil Case)
16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
ire
cti
on
, ft
16
00
0
14
00
0
12
00
0
10
00
0
80
00
60
00
40
00
20
000
X-Direction, ft
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
5000
4000
3000
2000
1000
010008006004002000
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]
Bo
tto
m H
ole
Flo
win
g P
res
su
re, p
si
Time, Days
Homogeneous boundedsquare reservoir with nineproducing wells.
Bottomhole flowing pressureis arbitrary for each well and is function of time.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 14
Homogeneous Reservoir Example (Oil Case)
The performance data for all 9 wells are shown on this plot.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 15
Homogeneous Reservoir Example (Oil Case)
Comparison of single and multiwell analysis.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 16
Homogeneous Reservoir Example (Gas Case)16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
ire
cti
on
, ft
16
00
0
14
00
0
12
00
0
10
00
0
80
00
60
00
40
00
20
000
X-Direction, ft
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
5000
4000
3000
2000
1000
040003000200010000
Time, Days
Bo
tto
mh
ole
Flo
win
g P
ress
ure
, psi 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]
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 17
Regionally Heterogeneous Reservoir Example16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
ire
cti
on
, ft
160
00
140
00
120
00
100
00
800
0
600
0
400
0
200
00
X-Direction, ft
2520151050
Permeability, mD
2000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
0
2000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
0
2000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
0
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]
Bo
tto
m H
ole
Flo
win
g P
ress
ure
, psi
Time, Days
Can we analyze multiwell performance?
Accuracy of results? In-place volume kh product
Uniqueness of the analysis?
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 18
Regionally Heterogeneous Reservoir Example
Decreasing PermeabilityMaterial Balance
Trend
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 19
Regionally Heterogeneous Reservoir Example
Multiwell analysis for a regionally heterogeneous oil case — this example confirms the viability of the approach.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 20
Regionally Heterogeneous Reservoir Example
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]
22.75.1
10.15.1
13.89.9
14.2
18.9
255.0105.010151015
20
22.7
9.8
OOIP (Input) 4,278 MMSTBOOIP (Calc.) 4,278 MMSTB
16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
ire
cti
on
, ft
160
00
140
00
120
00
100
00
800
0
600
0
400
0
200
00
X-Direction, ft
2520151050
Permeability, mD
[ 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]
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 21
Randomly Heterogeneous Reservoir Example
Can we analyze multiwell performance?
Accuracy of results? In-place volume kh product
Uniqueness of the analysis?
16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
ire
ctio
n, f
t
160
00
140
00
120
00
100
00
800
0
600
0
400
0
200
00
X-Direction, ft
1086420Permeability, mD
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]
Bo
tto
m H
ole
Flo
win
g P
ress
ure
, ps
i
Time, Days
2000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
0
2000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
0
2000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
02000150010005000
5000
4000
3000
2000
1000
0
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 22
Randomly Heterogeneous Reservoir Example
Multiwell analysis for a randomly heterogeneous oil case — note that even this extreme case works very well.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 23
Regionally Heterogeneous Reservoir Example
16000
14000
12000
10000
8000
6000
4000
2000
0
Y-D
ire
cti
on
, ft
16
00
0
14
00
0
12
00
0
10
00
0
80
00
60
00
40
00
20
000
X-Direction, ft
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
Computed permeability represents harmonic average in "well drainage area"
Observations:
1086420Permeability, mD
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 24
NØ
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Arun Field
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
Field Description
General Information — Arun Field (Indonesia)
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 25
Production Data Analysis: Arun Field
Selected wells for production data analysis: Well A-037 Well A-016 Well A-032 Well A-035 Well A-024 Well A-017 Well A-029 Well A-028 Well A-015 Well A-041 Well A-034
Expected results using multiwell analysis approach: Local kh product of the individual well Total field fluid-in-place
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 26
Arun Well A-015 — Production History
Good rate and pressure history.
150000
100000
50000
0
Gas
(To
tal W
ell S
trea
m) R
ate,
Msc
f/D
7000600050004000300020001000
Time, Days
6000
4000
2000
0
Wellh
ead P
ressure, p
si
Time, Days
Gas
(T
ota
l Wel
l Str
eam
) R
ate,
Msc
f/D
Wellh
ead P
ressure, p
si
Wellhead Pressure
Gas Rate
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 27
Arun Well A-015 — Decline Type Curve Plot
Arun Well A-015 — very good agreement of data and model.
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 28
All Selected Wells — Log-Log Plot
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 29
All Selected Wells — Decline Type Curve Plot
Good agreement of all data with single well model — validates concept. Note — data functions are not edited (raw data stream).
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 30
Summary of ResultsWell
Name[ t/tDde]MP [q/p]/
[qDde]M P
r eD / D OGIP(Tcf)
kh(md-ft)
C-II-01 18,404 95 10,000 19.8 2,946C-II-03 18,404 95 80 19.8 1,313C-II-04 21,855 80 800 19.8 1,762C-II-16 20,569 85 28 19.8 857C-III-02 19,433 90 10,000 19.8 2,791C-III-03 15,979 105 10,000 19.8 3,256C-III-04 15,894 110 800 19.8 2,422C-III-05 19,427 90 28 19.8 908C-III-06 9,202 190 10,000 19.8 5,893C-III-09 15,204 115 10,000 19.8 3,567C-III-15 13,449 130 18 19.8 1,106
Production History: (As of November 1998) Cumulative gas production (gross) = 21.3 TCF Cumulative gas reinjected = 5.2 TCF Net cumulative gas production = 21.3-5.2 = 16.1 TCF Monthly gas production (Nov. 1998) = 50 BCF (0.6 TCF/yr)
Result from a numerical study ( JPT, June 1983), OGIP = 17.1 TCF
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 31
Conclusions
Developed a general multiwell solution Accurate Provide mechanism for the analysis of
production data from a single well in a multiwell system
Developed a methodology for the analysis of production data from an individual well in a multiwell system Can estimate original fluid-in-place (total
system) and the regional permeability Can be applied for both oil and gas reservoirs
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 32
Conclusions (Continued)
Developed a total material balance time Preserves the uniqueness of the reservoir volume Allows use of the single well decline type curve
(i.e., the Fetkovich/McCray type curve)
Successfully validated our work (both the analytical solution and the data analysis method) using numerical simulation
Successfully demonstrated the application of our method for Arun Field (Indonesia)
SPE 71517...Well Performance Behavior in a Multiwell Reservoir System Slide — 33
SPE 71517
Decline Curve Analysis Using Type Curves —Evaluation of Well Performance Behavior
in a Multiwell Reservoir System
T. Marhaendrajana, SchlumbergerT.A. Blasingame, Texas A&M U.
