1. SPE 56487 Analysis and Interpretation of
Well Test Performance at Arun Field, Indonesia
Authors:
T. Marhaendrajana, Texas A&M U.
N.J. Kaczorowski, ExxonMobil (Indonesia)
T.A. Blasingame, Texas A&M U.

2. Summary
A comprehensive field case history of the analysis and interpretation of well test data from the Arun Gas Field (Sumatra, Indonesia).
2-zone radial composite reservoir model is effective for diagnosing the effects of conden-sate banking at Arun Field.

3. Summary
Development and application of a new solution for the analysis and interpretation for wells that exhibit "well interference" effects.

4. Outline Introduction Well Test Analysis Strategy Multiwell Model
Regional Pressure Decline
Analysis Procedure
Field Example
Conclusions

5. Arun Field N Field Description
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 N

6. Major Phenomena in Arun
Liquid accumulation near wellbore (conden-sate banking)
Need to know radial extent of condensate banking for the purpose of well stimulation.
Well interference effect
This well interference effect tends to obscure the radial flow response, and hence, influence our analysis and interpretation efforts.

7. Well Test Analysis Strategy
Condensate banking phenomenon
2-zone radial composite reservoir model is used, where the inner zone represents the "condensate bank," and the outer zone represents the "dry gas reservoir." (Raghavan, et al, (1995) and then by Yadavalli and Jones (1996) )
Well interference effect
Developed a new method for the analysis of well test data from a well in multiwell reservoir where we treat the "well interference" effect as a "Regional Pressure Decline."

8. Multiwell Model
Bounded Reservoir
with Multiple Wells

9. Analytical Solution Matches Numerical Solution

10. Regional Pressure Decline Model
Issues:
Arun Field has been produced for over 20 years and currently in "blowdown" mode.
Drawdown and buildup tests induce local transient effects.
Most of the well tests performed at Arun Field are relatively short (< 5 hours producing time), and the pseudosteady-state flow condition is not established in the area of investigation given such short produc-tion times.

11. Regional Pressure Decline Model
Assumptions:
All of the wells in the reservoir are at pseudosteady-state flow conditions at the time the "focus" well is shut-in.
Any rate change at the focus well (including a drawdown/buildup sequence) cause transient flow conditions only in the vicinity of the focus well–not in the entire reservoir.

12. Regional Pressure Decline Model
Pressure at focus well:
where:

13. Regional Pressure Decline Model
Pressure buildup analysis relations:
Vs.
Straight line on semilog plot

14. Regional Pressure Decline Model
Pressure buildup analysis relations:
Vs.
Straight line on Cartesian plot

15. Simulated Case Rate, q Time, t Offset wells are kept
Focus well is shut-in
Offset wells are kept
on production.
Offset wells are produced
at the same flowrate.
Focus well is shut-in
Rate, q
Focus well is put on production
Time, t

16. Multiwell Response is Different than Single Well Response
pbar continues to decline.
Pressure builds up to pbar
(closed boundary)
psD' [pws - pwf(Dt=0)] format
DtDA

17. Straight Line on Cartesian Plot
psDe' = p(aD - 1) DtDA2/ DtDAe
psDe' = 0.5
psDe' [pws - pwf(Dt=0)] format
DtDA2/ DtDAe

18. Regional Pressure Decline Signature May Not Be Unique
This portion may be falsely
interpreted as regional
pressure decline effect.
psDe' = p(aD - 1) DtDA2/ DtDAe
psDe' = 0.5
psDe' [pws - pwf(Dt=0)] format
DtDA2/ DtDAe

19. Analysis Procedures for Multiwell Reservoirs
To analyze pressure buildup tests taken in multiwell systems, we recommend the following procedures:
Step 1: Plot Dte(dpws/dDte) versus Dt2/Dte on a Carte-sian scale. From the straight-line trend we obtain the slope mc and intercept bc. We calculate permeability using the intercept term as:

20. Analysis Procedures for Multiwell Reservoirs
Step 2: The Horner plot [(pws+mcDt) versus log((tp+Dt)/Dt)] can also be used to estimate formation properties. From the straight-line trend observed on the Horner plot, we obtain the slope msl as well as the intercept term, (pws + mcDt) Dt=1hr.
Permeability is estimated using:
And the skin factor is calculated using:

21. Analysis Procedures for Multiwell Reservoirs
Step 3: In order to use standard single-well type curves for type curve matching, we must make the appropriate "corrections". These relations are:
Pressure function:
Pressure derivative function:

22. [Test Date: 28 September 1992]
Well C-I-18 (A-096)
[Test Date: 28 September 1992]
Infinite acting Reservoir Model
(Does not include non-Darcy flow)
Improvement on
pressure derivative.
Pseudopressure Functions, psi
Condensate banking
region.
Higher mobility
region.
Closed boundary at 160 ft?
(includes non-Darcy flow).
Effective shut-in pseudotime, hrs

23. [Test Date: 28 September 1992]
Well C-I-18 (A-096)
[Test Date: 28 September 1992]
Condensate banking
region.
Higher mobility
region.
Shut-in Pseudopressure, psia
Horner pseudotime, hrs (tp = 1.56 hr)

24. [Test Date: 28 September 1992]
Well C-I-18 (A-096)
[Test Date: 28 September 1992]
pp,bar = psia
Data deviate from the "Muskat line"
--indicating an interference effect
from surrounding wells.
Onset of boundary
dominated flow.
Shut-in pseudopressure, psia
"Transient flow"
dppws/dDta, psi/hr

25. [Test Date: 28 September 1992]
Well C-I-18 (A-096)
[Test Date: 28 September 1992]
(Dpp')Dtae, psi
Dta2/ Dtae

26. Example 3: Log-log Summary Plot
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Raw data
Corrected
Improvement on
pressure derivative.
Pseudopressure Functions, psi
Closed boundary at 150 ft?
(includes non-Darcy flow).
Infinite-acting Reservoir Model
(Does not include non-Darcy flow)
Effective shut-in pseudotime, hrs

27. Example 3: Horner (Semilog) Plot
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Shut-in Pseudopressure, psia
Raw data
Corrected
Horner pseudotime, hrs (tp = 1.62 hr)

28. Example 3: Muskat Plot (single well pavg plot)
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
pp,bar = 1920 psia
Onset of boundary
dominated flow.
Shut-in pseudopressure, psia
"Transient flow"
dppws/dDta, psi/hr

29. Example 3: "Well Interference" Plot (radial flow only)
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Intercept is used to
calculate permeability.
Slope is used in the
pressure correction.
(Dpp')Dtae, psi
Presence of multiwell
interference effects is unclear
Dta2/ Dtae

30. Example 4: Log-log Summary Plot
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Raw data
Corrected
Improvement on
pressure derivative.
Pseudopressure Functions, psi
Condensate banking
region.
Infinite-acting Reservoir Model
(Does not include non-Darcy flow)
Closed boundary at 197 ft?
(includes non-Darcy flow).
Higher mobility
region.
Effective shut-in pseudotime, hrs

31. Example 4: Horner (Semilog) Plot
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Condensate banking
region.
Shut-in Pseudopressure, psia
Higher mobility
region.
Raw data
Corrected
Horner pseudotime, hrs (tp = 1.63 hr)

32. Example 4: Muskat Plot (single well pavg plot)
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
pp,bar = psia
Onset of boundary
dominated flow.
Shut-in pseudopressure, psia
"Transient flow"
dppws/dDta, psi/hr

33. Example 4: "Well Interference" Plot (radial flow only)
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Intercept is used to
calculate permeability.
Slope is used in the
pressure correction.
(Dpp')Dtae, psi
(Dpp')Dtae >0, no clear indication of
multiwell interference effects.
Dta2/ Dtae

34. kh Map kh distribution ap-pears reasonable.
3 major "bubbles" of kh noted, pro-bably erroneous.
kh shown is for the "outer" zone (when the radial compo-site model is used).
kh Map

35. D (Non-Darcy) Map This map indicates a uniform distribution.
"high" and "low" regions appear to be focused near a single well.
Relatively small data set (30 points).
D (Non-Darcy) Map

36. Condensate Radius Map
Good distribution of values—"high" spots probably indicate need for individual well stimulations.
Relatively small data set (32 points).

37. D (Non-Darcy)—kh Crossplot
D-kh crossplot indi-cates an "order of magnitude" correla-tion.
Verifies that non-Darcy flow effects are systematic.
Slope = 2

38. Conclusions
The new "multiwell" solution has been successfully derived and applied for the analysis of well test data taken from a multiwell reservoir system.
The appearance of "boundary" effects in pressure buildup test data taken in multiwell reservoirs can be corrected using our new approach. Care must be taken so as not to correct a true "closed boundary" effect.

39. Conclusions
The 2-zone radial composite reservoir model has been shown to be representative for the analysis and interpretation of well test data from Arun Field (most of the wells exhibit radial composite reservoir behavior).

40. Conclusions
The effect of non-Darcy flow on pressure buildup test analysis seems to be minor for the wells in Arun Field. Although not a focus of the present study, our analysis of the pressure drawdown (flow test) data appear to be much more affected by non-Darcy flow effects.

41. SPE 56487 Analysis and Interpretation of
Well Test Performance at Arun Field, Indonesia
Authors:
T. Marhaendrajana, Texas A&M U.
N.J. Kaczorowski, ExxonMobil (Indonesia)
T.A. Blasingame, Texas A&M U.

42. The "Regional Pressure Decline" Improves The Derivative
tpDA=10-5
tpDA=10-4
tpDA=10-3
Shut-in time
tpDA=10-2
Dim. Pressure Derivative Functions
Agarwal eff.
shut-in time
DtDA or DtDAe

43. psD or psDc [pws - pwf(Dt=0)] format
tpDA=10-5
tpDA=10-3
tpDA=10-2
tpDA=10-4
psD or psDc [pws - pwf(Dt=0)] format
MDH
Agarwal effective time
DtDA or DtDAe