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.
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 condensate banking at Arun Field.
Summary

Development and application of a new solution
for the analysis and interpretation for wells that
exhibit "well interference" effects.
Outline







Introduction
Well Test Analysis Strategy
Multiwell Model
Regional Pressure Decline
Analysis Procedure
Field Example
Conclusions
Arun Field
Field Description
 Located
Ø
in Northern part of
Sumatra, Indonesia
 Retrograde gas reservoir
 One of the largest gas fields
in the world
 Arun Field has 111 wells:
Ø
Ø
Ø
Ø
Ø
79 producers
 11 injectors
 4 observation wells
 17 wells have been abandoned

Ø
Ø
N
Ø
Ø
Ø
Ø
Major Phenomena in Arun

Liquid accumulation near wellbore (condensate 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.
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."
Multiwell Model
n well
p D(xD,y D,t DA) =
q
i=1
D,iu(t DA – t sDA,i)
 p D,i(xD,y D,[tDA – tsDA,i],xwD,i,y wD,i)
Bounded Reservoir
with Multiple Wells
Analytical Solution Matches Numerical Solution
3
10
Dimensionless Pressure, pD
Legend:
Numerical Simulation
Analytical Solution
2
10
pD
1
10
0
pD'
10
-1
10
-6
10
-5
-4
-3
-2
-1
0
10
10
10
10
10
10
Dimensionless Time,tDA (Based on Drainage Area)
1
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 production times.
Regional Pressure Decline Model
Assumptions:


All of the wells in the reservoir are at pseudosteadystate 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.
Regional Pressure Decline Model
Pressure at focus well:
p wD(tDA) = p D,1([xwD,1 + ],[y wD,1 + ],tDA,xwD,1,y wD,1)
+ 2tDA(D – 1)
Vpc t dp Vpc t

=
where:  D =
q1B dt q1B
Regional Pressure Decline Model
Pressure buildup analysis relations:
p sD(t DA) + 2( D – 1)t DA = 1 ln 4 t DAe A2 + s
2 e
rw
Vs.
Straight line on semilog plot
Regional Pressure Decline Model
Pressure buildup analysis relations:
2

dp sD
t
t DAe
= 1 – 2 ( D – 1) DA
t DAe
dt DAe 2
Vs.
Straight line on Cartesian plot
Rate, q
Simulated Case
Offset wells are produced
at the same flowrate.
Focus well is shut-in
Focus well is put on production
Time, t
Offset wells are kept
on production.
Focus well is shut-in
Multiwell Response is Different than
Single Well Response
', [p-pwf((
t=0)] format
psD' p[psDws
wsp
wf t=0)] format
0.5
0.3
0.0
-0.3
pbar continues to decline.
Pressure builds up to pbar
(closed boundary)
-0.5
-0.8
-1.0
Legend:
Multiwell, Single Well
-1.3
-1.5
-1.8
,
tpDA=1x10
,
tpDA=1x10
,
tpDA=1x10
,
tpDA=1x10
-2
-3
-4
-5
-2.0
0
10
20
ttDA
DA
30
-3
40x10
psDe
' [p
- p t=0)]
(t=0)]
psDe
', [p
format format
ws
ws-pwf(wf
Straight Line on Cartesian Plot
1.00
0.75
0.50
psDe' = 0.5 - 2(D - 1) tDA2/ tDAe
0.25
psDe' = 0.5
0.00
-0.25
-0.50
-0.75
Legend:
-1.00
tpDA=1x10
-1.25
tpDA=1x10
-1.50
tpDA=1x10
-1.75
tpDA=1x10
-2
-3
-4
-5
-2.00
0
10
20
2
2 /tDAe
tDA
tDA / tDAe
30
-3
40x10
Regional Pressure Decline Signature
May Not Be Unique
[p',ws
psDep'sDe
(t=0)]
(t=0)]
[pws--pp
formatformat
wfwf
1
0
This portion may be falsely
pinterpreted
- 2regional
(D - 1) tDA2/ tDAe
sDe' = 0.5 as
psDe' = 0.5
pressure decline effect.
-1
-2
-3
Legend:
tpDA=1x10
-4
tpDA=1x10
tpDA=1x10
tpDA=1x10
-5
-5
10
-4
10
-2
-3
-4
-5
-3
10
-2
10
-1
10
2
tDA
2 /tDAe
tDA / tDAe
0
10
1
10
2
10
Analysis Procedures for Multiwell Reservoirs
To analyze pressure buildup tests taken in multiwell
systems, we recommend the following procedures:
1: Plot te(dpws/dte) versus t2/te on a Cartesian scale. From the straight-line trend we obtain the
slope mc and intercept bc. We calculate permeability
using the intercept term as:
 Step
qB
k = 70.6
b ch
Analysis Procedures for Multiwell Reservoirs
2: The Horner plot [(pws+mct) versus
log((tp+t)/t)] 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 + mct) t=1hr.
 Step
Permeability
And the skin is
factor
estimated
is calculated
using: using:
qB– p

(p wsk+=m162.6
t)
t=1hr
c
wf,t = 0
s = 1.1513
h
mm
sl sl
tp
k
– 1.1513 log
+ log
– 3.22751
2
t p+1
 c tr w
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:
p ws,cor = p ws + m ct
Pressure derivative function:
dp ws
t e
dt e
cor
t 2
dp ws
= t e
+ mc
t e
dt e
Well C-I-18 (A-096)
[Test
Date:
September
1992]
Well C-I-18
(A-096)28
[Test
Date: 28 September
1992]
3
Pseudopressure Functions, psi
Functions, psi
Pseudopressure
10
2
10
Infinite acting
Reservoir
Improvement
onModel
(Does not
includederivative.
non-Darcy flow)
pressure
1
10
Condensate banking
region.
Higher mobility
region.
Closed boundary at 160 ft?
(includes non-Darcy flow).
0
10
-1
10
-4
10
-3
10
-2
10
-1
10
0
10
Effective Shut-in Pseudotime, tae, hrs
Effective
shut-in pseudotime, hrs
1
10
Pseudopressure,
Shut-in
Shut-in Pseudopressure,
ppws , psia psia
Well C-I-18 (A-096)
[Test
Date: 28 September 1992]
Well C-I-18 (A-096) [Test Date: 28 September 1992]
1160
1140
Condensate banking
region.
1120
Higher mobility
region.
1100
1080
1060
1040
1020
3
10
2
10
1
10
Horner Pseudotime, ( ta+tpa)/ta (tpa=tp=1.56 hr), hr
Horner pseudotime, hrs (tp = 1.56 hr)
0
10
pws
Shut-in
Pseudopressure, p , psia psia
pseudopressure,
Shut-in
Well C-I-18 (A-096)
[Test
Date:
1992]
Well C-I-18
(A-096)28
[TestSeptember
Date: 28 September 1992]
1150
pp,bar = 1148.6 psia
Data deviate from the "Muskat line"
--indicating an interference effect
from
surrounding
wells.
Onset
of boundary
dominated flow.
1149
1148
1147
1146
"Transient flow"
1145
1144
1143
1142
0
2
4
6
dppwsdp/d/dtat ,, psi/hr
psi/hr
pws
a
8
10
Well C-I-18 (A-096)
[Test
Date:
28 Date:
September
1992]
Well C-I-18
(A-096) [Test
28 September 1992]
15
p  ae
(p(pp')')ttae, psi
, psi
10
5
0
-5
-10
-15
0
5
10
15
2
ttaa2//tae, thrs
ae
20
25
30
psi
Functions,
Pseudopressure
Pseudopressure Functions,
psi
Example 3: Log-log Summary Plot
Well C-IV-11
(A-084)
[TestDate:
Date:55 January
January 1992]
Well C-IV-11
(A-084)
[Test
1992]
3
10
Raw data
Corrected
Improvement on
pressure derivative.
2
10
1
10
Closed boundary
atReservoir
150 ft? Model
Infinite-acting
(Does
not include non-Darcy
(includes
non-Darcy
flow). flow)
0
10
-4
10
-3
10
-2
10
-1
10
0
10
Effective Shut-in Pseudotime, tae, hrs
Effective
shut-in pseudotime, hrs
1
10
Example 3: Horner (Semilog) Plot
C-IV-11
(A-084)[Test
[TestDate:
Date: 55January
1992]
WellWell
C-IV-11
(A-084)
January
1992]
Shut-in
Pseudopressure, ppws , psiapsia
Pseudopressure,
Shut-in
2100
2000
1900
1800
1700
1600
1500
1400
Raw data
Corrected
1300
1200
3
10
2
10
1
10
Horner Pseudotime, ( ta+tpa)/ta (tpa=tp=1.62 hr), hr
Horner pseudotime, hrs (tp = 1.62 hr)
0
10
Example 3: Muskat Plot (single well pavg plot)
Shut-inpseudopressure,
Pseudopressure, ppws , psia psia
Shut-in
C-IV-11
(A-084)[Test
[Test Date:
Date: 55January
1992]
WellWell
C-IV-11
(A-084)
January
1992]
1922
pp,bar = 1920 psia
1920
Onset of boundary
dominated flow.
1918
1916
"Transient flow"
1914
1912
1910
0
5
10
dp pws
dppws
/d/dtta, ,psi/hr
psi/hr
a
15
20
Example 3: "Well Interference" Plot (radial flow only)
Well
C-IV-11
[TestDate:
Date:5 January
5 January
1992]
Well
C-IV-11(A-084)
(A-084) [Test
1992]
25
Intercept is used to
calculate permeability.
Slope is used in the
pressure correction.
15
(p ')
ae
p t
(pp')tae
, psi
20
10
5
0
Presence of multiwell
interference effects is unclear
-5
0
5
10
15
2
ttaa/2/tae, hrs
tae
20
25
psi
Functions,
Pseudopressure
Pseudopressure Functions,
psi
Example 4: Log-log Summary Plot
Well Well
C-IV-11
(A-084)
[Test
May1992]
1992]
C-IV-11
(A-084)
[TestDate:
Date: 4
4 May
3
10
Raw data
Corrected
Improvement on
pressure derivative.
2
10
Condensate banking
region.
1
10
Infinite-acting Reservoir Model
Closed(Does
boundary
at
197
ft?
Higher
mobility
not include
non-Darcy
flow)
(includes non-Darcy flow).
region.
0
10
-4
10
-3
10
-2
10
-1
10
Effective Shut-in Pseudotime, t , hrs
0
10
ae
Effective shut-in pseudotime,
hrs
1
10
Example 4: Horner (Semilog) Plot
C-IV-11
(A-084)[Test
[Test Date:
Date: 44May
1992]
WellWell
C-IV-11
(A-084)
May
1992]
Shut-in
Pseudopressure, ppws , psiapsia
Pseudopressure,
Shut-in
1950
1900
1850
1800
1750
Condensate banking
region.
Higher mobility
region.
1700
1650
1600
Raw data
Corrected
1550
1500
3
10
2
10
1
10
Horner Pseudotime, ( ta+tpa)/ta (tpa=tp=1.63 hr), hr
Horner
pseudotime, hrs (tp = 1.63 hr)
0
10
Example 4: Muskat Plot (single well pavg plot)
Shut-inpseudopressure,
Pseudopressure, ppws , psia psia
Shut-in
C-IV-11
(A-084)[Test
[Test Date:
Date: 44May
1992]
WellWell
C-IV-11
(A-084)
May
1992]
1884
pp,bar = 1882.8 psia
1882
1880
Onset of boundary
dominated flow.
1878
1876
"Transient flow"
1874
1872
1870
0
5
10
dp pws
dppws
/d/dtta, ,psi/hr
psi/hr
a
15
20
Example 4: "Well Interference" Plot (radial flow only)
Well
C-IV-11
[TestDate:
Date:
4 May
1992]
Well
C-IV-11(A-084)
(A-084) [Test
4 May
1992]
40
Intercept is used to
calculate permeability.
Slope is used in the
pressure correction.
 ae
p'), tpsi
(pp')(tpae
30
20
10
(pp')tae >0, no clear indication of
multiwell interference effects.
0
0
5
10
15
2
ta / tae
ta /2tae, hrs
20
25
30
Flow Capacity (kh, md-ft)
from Well Test Analysis (Arun Field, Indonesia)
kh Map
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
16000
16000
 kh
15000
15000
10000
5000
4000
20000
10000
30000
10000
9000
40000
8000
7000
30000
A-108
6000
A-017
A-107
10000
A-097
A-070A-048
A-060
A-041
A-084
A-062
50000
50000
7000
10000
20000
A-095
11000
A-078
A-015 A-080
A-034
A-016
A-035
A-077
20000
A-099
10000
8000
A-098 40000
A-058
A-071
20000
9000
12000
A-032ST
A-032
A-061 A-021
A-024
A-106
A-082
A-105ST2A-102 A-068
A-022ST2
A-029
20000
40000
A-083
A-033
A-089 A-073
A-040
30000
A-093
10000
10000
13000
A-027
10000
A-092
A-067
20000
A-088
20000
12000
11000
14000
A-081
A-036
A-076
A-045 A-079ST
30000
A-059
A-074
A-025ST
40000
A-042
A-054
A-096
20000
A-104
30000
13000
A-101
10000
14000
30000
A-103
x-position (relative distance)
distribution appears reasonable.
 3 major "bubbles"
of kh noted, probably erroneous.
 kh shown is for the
"outer" zone (when
the radial composite model is used).
1x2 Perspective
View
A-085
10000
A-049
6000
A-110ST A-046 40000 40000
A-100
A-053
10000
60000
A-091
80000
Legend: (Well Test Analysis)
A-051
50000
5000
Flow Capacity (kh) Contour Plot
(10,000 md-ft Contours)
Arun Field (Indonesia)
A-109
100000
4000
3000
3000
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
y-position (relative distance)
Logarithm of the Non-Darcy Flow CoefficientD,
( 1/MSCFD)
from Well Test Analysis (Arun Field, Indonesia)
D (Non-Darcy) Map
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
16000
16000
1x2 Perspective
View
15000
15000
A-103
A-081
A-036
-4
A-076
A-045 A-079ST
-3.8
A-059 -3.8
A-074
A-025ST
-5 A-042
A-054A-104
A-096
-4.8
-4.6
A-088 -4.2
A-067
-4.6 A-077
A-095
-4.8
7000
A-107
A-108
5000
4000
-4
A-017
A-097
A-070A-048
A-060
A-041
-4
A-084
A-062
-3.8
6000
A-015 A-080
A-034
A-016
A-035
8000
7000
-3.8
-3.6
-3.6
-3.4
-5
9000
-3.8
-4.8
A-099
-4.2
A-071
8000
10000
-4.2
A-098
-4.6
A-058
11000
A-078
-4
9000
12000
A-032ST
A-032
A-061 A-021
A-024
A-106
A-082
A-105ST2A-102 A-068
A-022ST2
A-029
-4.6
A-083
A-033
A-089 A-073
A-040
A-093
-4.4
10000
A-027
-4.6
A-092
13000
-4.2
12000
11000
14000
A-101
-4.2 -4
13000
No Data
-4.4
14000
x-position (relative distance)
map indicates a
uniform distribution.
 "high" and "low"
regions appear to be
focused near a single
well.
 Relatively small data
set (30 points).
-4.4
 This
A-085
A-049
A-110ST A-046
A-053
Legend: (Well Test Analysis)
A-091
Logarithm of the Non-Darcy
A-051
Flow Coefficient
(log(10) Contours)
Arun Field (Indonesia)
A-109
A-100
6000
5000
4000
3000
3000
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
y-position (relative distance)
Condensate Bank Radius (ft) from Well Test Analysis
(Arun Field, Indonesia)
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
16000
16000
Condensate Radius Map
 Good
15000
14000
13000
15000
A-103
No Data
14000
A-101
A-081
A-036
A-076
A-045 A-079ST
A-059
A-074
A-025ST
30
A-042
A-054A-104 25
A-096
13000
25
10
15
10
5
25
7000
10
20A-017
10
A-097
A-070A-048
A-060
A-041
A-084
A-062
10
7
A-108
20
25
A-107
8000
Condensate Bank Contour Plot
(Various Contours)
Arun Field (Indonesia)
20
4000
A-049
1 3
5000
A-085
3
7
5
A-110ST A-046
A-053
A-091
Legend: (Well Test Analysis)
25
A-051
7000
7
A-077
A-015 A-080
A-034
A-016
A-035
15
5
A-099
10
20
9000
A-095
6000
10000
25
8000
11000
A-078
7
5
A-098
35
A-058
A-071
3
9000
12000
15
A-032ST
A-032
A-061 A-021
A-024
A-106
A-082
A-105ST2A-102 A-068
A-022ST2
A-029
A-083
A-033
A-089 A-073
A-04030
A-093
5
10000
A-027
35
25 30
15 20
11000
25
A-092
A-067
40
12000
A-088
30
x-position (relative distance)
distribution of
values—"high" spots
probably indicate
need for individual
well stimulations.
 Relatively small data
set (32 points).
1x2 Perspective
View
A-109
A-100
6000
5000
4000
3000
3000
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
y-position (relative distance)
D (Non-Darcy)—kh Crossplot
crossplot indicates an "order of
magnitude" correlation.
 Verifies that nonDarcy flow effects are
systematic.
Non-Darcy Flow Coefficient ( D, 1/MSCFD)
from Well Test Analysis ( D at Time of Well Test)
 D-kh
Comparison of Non-Darcy Flow Coefficient ( D) from Well Test
Analysis versus Flow Capacity ( kh) from Well Test Analysis
(Arun Field -- Indonesia)
3
4
5
6
10
10
10
10
-3
6
10
10
Slope = 2
-4
5
10
10
-5
4
10
10
Legend: DWT vs. khWT
Comparison of D from Well Test Analysis
versus kh from Well Test Analysis
(Arun Field -- Indonesia)
-6
3
10
10
3
10
4
5
10
10
Flow Capacity (kh, md-ft)
from Well Test Analysis ( kh at Time of Well Test)
6
10
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.
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).
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.
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.
psDPressure
' or psDe' or pDerivative
format
Functions
Dim.
sDc' , [pws -pwf (t=0)]
The "Regional Pressure Decline"
Improves The Derivative
0
10
tpDA=10-5
tpDA=10-4 tpDA
=10-3tpDA
Shut-in
time
=10-2
-1
10
Agarwal eff.
shut-in time
-2
10
-6
10
-5
10
-4
10
tDA or tDAe
tDA or tDAe
-3
10
-2
10
psD orpsDpsDc
[p, ws
(t=0)]
(t=0)]
or psDc
[pws--pp
formatformat
wfwf
9
8
-5
-4
-3
tpDA=10-2
7
MDH
6
5
4
Agarwal effective time
3
-6
10
-5
10
-4
10
tDA or tDAe
tDA or tDAe
-3
10
-2
10