1. Decline Curve Analysis Using Type Curves —
SPE 71517
Decline Curve Analysis Using Type Curves —
Evaluation of Well Performance Behavior
in a Multiwell Reservoir System
T. Marhaendrajana, Schlumberger
T.A. Blasingame, Texas A&M U.
SPE Well Performance Behavior in a Multiwell Reservoir System

2.  Validation using a numerical simulator
Outline
 Motivation
 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 Well Performance Behavior in a Multiwell Reservoir System

3. A Typical p/z Plot in Arun Field (Well A-015)
Note that the well interference causes the data to deviate from the "p/z" straight line.
SPE Well Performance Behavior in a Multiwell Reservoir System

4. Decline Type Curve Analysis (Well A-015)
Note that the late time data show well interference effects.
SPE Well Performance Behavior in a Multiwell Reservoir System

5. p/z Plot for Arun Field (Total Field Performance)
SPE Well Performance Behavior in a Multiwell Reservoir System

6.  To develop an analytical solution for a multiwell system
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 Well Performance Behavior in a Multiwell Reservoir System

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 Well Performance Behavior in a Multiwell Reservoir System

8. Multiwell Model — Data Used for Validation
 Homogeneous bounded
square reservoir with nine
producing wells.
 Bottomhole flowing pressure
is arbitrary for each well and is function of time.
SPE Well Performance Behavior in a Multiwell Reservoir System

9. Multiwell Model — Validation
SPE Well Performance Behavior in a Multiwell Reservoir System

10. Analytical Solution Matches Numerical Solution
Initial pwf
Variable pwf
Final pwf
Oil Rate, STB/D
Well [1,2]
Time, Days
SPE Well Performance Behavior in a Multiwell Reservoir System

11. c(t) becomes constant at long times
Decline Type Curve Analysis — Methodology
Production Data
(Pressure & Rate)
c(t) becomes constant at long times
Total Material
Balance Time
 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 Well Performance Behavior in a Multiwell Reservoir System

12. Decline Type Curve Analysis — Methodology
SPE Well Performance Behavior in a Multiwell Reservoir System

13. Homogeneous Reservoir Example (Oil Case)
 Homogeneous bounded
square reservoir with nine
producing wells.
 Bottomhole flowing pressure
is arbitrary for each well and is function of time.
SPE Well Performance Behavior in a Multiwell Reservoir System

14. Homogeneous Reservoir Example (Oil Case)
The performance data for all 9 wells are shown on this plot.
SPE Well Performance Behavior in a Multiwell Reservoir System

15. Homogeneous Reservoir Example (Oil Case)
Comparison of single and multiwell analysis.
SPE Well Performance Behavior in a Multiwell Reservoir System

16. Homogeneous Reservoir Example (Gas Case)
SPE Well Performance Behavior in a Multiwell Reservoir System

17. Regionally Heterogeneous Reservoir Example
 Can we analyze multiwell performance?
 Accuracy of results?
 In-place volume
 kh product
 Uniqueness of the analysis?
SPE Well Performance Behavior in a Multiwell Reservoir System

18. Regionally Heterogeneous Reservoir Example
Material Balance
Trend
Decreasing Permeability
SPE Well Performance Behavior in a Multiwell Reservoir System

19. Regionally Heterogeneous Reservoir Example
Multiwell analysis for a regionally heterogeneous oil case — this example confirms the viability of the approach.
SPE Well Performance Behavior in a Multiwell Reservoir System

20. Regionally Heterogeneous Reservoir Example
Well
k, calc.
(md)
k, input
(md)
[3,1]
[3,2]
[3,3]
[ 20 mD ]
[1,1]
22.7
22.7 25
[1,2]
5.1
5.0
[2,1]
[2,2]
[2,3]
[1,3]
10.1 10
[ 15 mD ]
[2,1]
5.1
5.0
[2,2]
9.8 10
[1,1]
[1,2]
[1,3]
[2,3]
13.8 15
[3,1]
9.9 10
[ 25 mD ]
[ 5 mD ]
[ 10 mD ]
[3,2]
14.2 15
[3,3]
18.9 20
OOIP (Input) 4,278 MMSTB
OOIP (Calc.) 4,278 MMSTB
SPE Well Performance Behavior in a Multiwell Reservoir System

21. Randomly Heterogeneous Reservoir Example
 Can we analyze multiwell performance?
 Accuracy of results?
 In-place volume
 kh product
 Uniqueness of the analysis?
SPE Well Performance Behavior in a Multiwell Reservoir System

22. Randomly Heterogeneous Reservoir Example
Multiwell analysis for a randomly heterogeneous oil case — note that even this extreme case works very well.
SPE Well Performance Behavior in a Multiwell Reservoir System

23. Regionally Heterogeneous Reservoir Example
Well
k, calc.
(md)
k, input
[1,1]
[3,3]
4.04
3.64
4.10
3.73
OOIP (Input) 4,278 MMSTB
OOIP (Calc.) 4,278 MMSTB
Results:
Observations:
 Individual well performance appears to be "homogeneous"
 Computed in-place volume is essentially exact
 Computed permeability represents harmonic average in "well drainage area"
SPE Well Performance Behavior in a Multiwell Reservoir System

24. N General Information — Arun Field (Indonesia) Arun Field
Located in Northern part of Sumatra, Indonesia
Retrograde gas reservoir
One of the largest gas fields in the world
Arun Field has 111 wells:
79 producers
11 injectors
4 observation wells
17 wells have been abandoned
Field Description Ø N
SPE Well Performance Behavior in a Multiwell Reservoir System

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 Well Performance Behavior in a Multiwell Reservoir System

26. Arun Well A-015 — Production History
Good rate and pressure history.
SPE Well Performance Behavior in a Multiwell Reservoir System

27. Arun Well A-015 — Decline Type Curve Plot
Arun Well A-015 — very good agreement of data and model.
SPE Well Performance Behavior in a Multiwell Reservoir System

28. All Selected Wells — Log-Log Plot
SPE Well Performance Behavior in a Multiwell Reservoir System

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 Well Performance Behavior in a Multiwell Reservoir System

30. Summary of Results
Result from a numerical study ( JPT, June 1983), OGIP = 17.1 TCF
Production History: (As of November 1998)
Cumulative gas production (gross) = TCF
Cumulative gas reinjected = 5.2 TCF
Net cumulative gas production = = 16.1 TCF
Monthly gas production (Nov. 1998) = 50 BCF (0.6 TCF/yr)
SPE Well Performance Behavior in a Multiwell Reservoir System

31. Developed a general multiwell solution
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 Well Performance Behavior in a Multiwell Reservoir System

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 Well Performance Behavior in a Multiwell Reservoir System

33. Decline Curve Analysis Using Type Curves —
SPE 71517
Decline Curve Analysis Using Type Curves —
Evaluation of Well Performance Behavior
in a Multiwell Reservoir System
T. Marhaendrajana, Schlumberger
T.A. Blasingame, Texas A&M U.
SPE Well Performance Behavior in a Multiwell Reservoir System