spe 56487 analysis and interpretation of well test performance at arun field, indonesia authors: t....
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SPE 56487
Analysis and Interpretation ofWell 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 conden-sate 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
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Arun FieldLocated in Northern part of
Sumatra, IndonesiaRetrograde 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
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.
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
Bounded Reservoirwith Multiple Wells
pD(xD,yD,tDA) = qD,iu(tDA – tsDA,i)i = 1
nwell
pD,i(xD,yD,[tDA – tsDA,i],xwD,i,ywD,i)
Analytical Solution Matches Numerical Solution
10-1
100
101
102
103
Dim
en
sio
nle
ss
Pre
ss
ure
, pD
10-6
10-5
10-4
10-3
10-2
10-1
100
101
Dimensionless Time, tDA (Based on Drainage Area)
Legend:
Numerical SimulationAnalytical Solution
pD
pD'
Regional Pressure Decline Model
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.
Issues:
Regional Pressure Decline Model
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.
Assumptions:
Regional Pressure Decline Model
Pressure at focus well:
pwD(tDA) = pD,1([xwD,1 + ],[ywD,1 + ],tDA,xwD,1,ywD,1)
+ 2tDA(D – 1)
D =Vpct
q1Bdpdt
=Vpct
q1Bwhere:
Regional Pressure Decline Model
Pressure buildup analysis relations:
psD(tDA) + 2(D – 1)tDA = 12
ln 4etDAe
Arw
2+ s
Vs.
Straight line on semilog plot
Regional Pressure Decline Model
Pressure buildup analysis relations:
Vs.
Straight line on Cartesian plot
tDAedpsD
dtDAe= 1
2– 2 (D – 1)
tDA2
tDAe
Simulated CaseR
ate,
q
Time, t
Offset wells are producedat the same flowrate.
Focus well is shut-in
Focus well is put on production
Focus well is shut-in
Offset wells are kepton production.
Multiwell Response is Different than Single Well Response
-2.0
-1.8
-1.5
-1.3
-1.0
-0.8
-0.5
-0.3
0.0
0.3
0.5
psD
', [p
ws-p
wf(t=
0)]
fo
rma
t
40x10-3
3020100
tDA
Legend:
Multiwell, Single Well
, tpDA=1x10-2
, tpDA=1x10-3
, tpDA=1x10-4
, tpDA=1x10-5
p sD' [
p ws
- p w
f(t=
0)]
form
at
tDA
Pressure builds up to pbar
(closed boundary)
pbar continues to decline.
Straight Line on Cartesian Plot
-2.00
-1.75
-1.50
-1.25
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
psD
e',
[pw
s-p
wf(t=
0)]
form
at
40x10-3
3020100
tDA
2/tDAe
Legend:
tpDA=1x10-2
tpDA=1x10-3
tpDA=1x10-4
tpDA=1x10-5
psDe' = 0.5psDe' = 0.5 - 2(D - 1) tDA
2/ tDAe
p sD
e' [
p ws
- p w
f(t=
0)]
form
at
tDA2/ tDAe
Regional Pressure Decline Signature May Not Be Unique
-5
-4
-3
-2
-1
0
1
psD
e',
[pw
s-p
wf(t=
0)]
fo
rma
t
10-5
10-4
10-3
10-2
10-1
100
101
102
tDA
2/tDAe
Legend:
tpDA=1x10-2
tpDA=1x10-3
tpDA=1x10-4
tpDA=1x10-5
p sD
e' [
p ws
- p w
f(t=
0)]
form
at
psDe' = 0.5psDe' = 0.5 - 2(D - 1) tDA
2/ tDAe
This portion may be falselyinterpreted as regional pressure decline effect.
tDA2/ tDAe
Analysis Procedures for Multiwell Reservoirs
To analyze pressure buildup tests taken in multiwell systems, we recommend the following procedures:
Step 1: Plot te(dpws/dte) versus t2/te 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:
k = 70.6qBb ch
Analysis Procedures for Multiwell Reservoirs
Step 2: The Horner plot [(pws+mct) 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 + mct) t=1hr.
s = 1.1513(pws +mc t)t=1hr – pwf,t = 0
msl
– 1.1513 logtp
tp+1+ log k
ctrw2
– 3.22751
And the skin factor is calculated using:
k = 162.6qBmslh
Permeability is estimated using:
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:
tedpws
dte cor
= tedpws
dte+ mc
t2
te
pws,cor = pws + mct
10-1
100
101
102
103
Ps
eu
do
pre
ss
ure
Fu
nc
tio
ns
, ps
i
10-4
10-3
10-2
10-1
100
101
Effective Shut-in Pseudotime, tae, hrs
Well C-I-18 (A-096) [Test Date: 28 September 1992]
Condensate bankingregion.
Higher mobilityregion.
Closed boundary at 160 ft?(includes non-Darcy flow).
Pse
ud
opre
ssu
re F
unc
tion
s, p
si
Effective shut-in pseudotime, hrs
Infinite acting Reservoir Model(Does not include non-Darcy flow)
Improvement onpressure derivative.
Well C-I-18 (A-096)[Test Date: 28 September 1992]
1160
1140
1120
1100
1080
1060
1040
1020
Sh
ut-
in P
se
ud
op
res
su
re, p
pw
s, p
sia
100
101
102
103
Horner Pseudotime, (ta+tpa)/ta (tpa=tp=1.56 hr), hr
Well C-I-18 (A-096) [Test Date: 28 September 1992]
Condensate bankingregion.
Higher mobilityregion.
Well C-I-18 (A-096)[Test Date: 28 September 1992]
Sh
ut-i
n P
seu
dop
ress
ure
, psi
a
Horner pseudotime, hrs (tp = 1.56 hr)
1150
1149
1148
1147
1146
1145
1144
1143
1142
Sh
ut-
in P
seu
do
pre
ssu
re,
pp
ws, p
sia
1086420
dppws/dta, psi/hr
Well C-I-18 (A-096) [Test Date: 28 September 1992]
Well C-I-18 (A-096)[Test Date: 28 September 1992]
pp,bar = 1148.6 psia
Onset of boundarydominated flow.
"Transient flow"
Data deviate from the "Muskat line"--indicating an interference effect
from surrounding wells.
Shu
t-in
pse
udop
ress
ure,
psi
a
dppws/dta, psi/hr
-15
-10
-5
0
5
10
15
(p
p')
t a
e, p
si
302520151050
ta
2/tae, hrs
Well C-I-18 (A-096) [Test Date: 28 September 1992]
Well C-I-18 (A-096)[Test Date: 28 September 1992](
p p')
tae,
psi
ta2/ tae
100
101
102
103
Ps
eu
do
pre
ss
ure
Fu
nc
tio
ns
, p
si
10-4
10-3
10-2
10-1
100
101
Effective Shut-in Pseudotime, tae, hrs
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Closed boundary at 150 ft?(includes non-Darcy flow).
Ps
eud
op
res
su
re F
un
ctio
ns,
psi
Effective shut-in pseudotime, hrs
Infinite-acting Reservoir Model(Does not include non-Darcy flow)
Improvement onpressure derivative.
Example 3: Log-log Summary Plot
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Raw dataCorrected
2100
2000
1900
1800
1700
1600
1500
1400
1300
1200
Sh
ut-
in P
seu
do
pre
ssu
re,
pp
ws, p
sia
100
101
102
103
Horner Pseudotime, ( ta+tpa)/ta (tpa=tp=1.62 hr), hr
Well C-IV-11 (A-084) [Test Date: 5 January 1992]S
hu
t-in
Ps
eud
op
res
su
re, p
sia
Horner pseudotime, hrs (tp = 1.62 hr)
Example 3: Horner (Semilog) Plot
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Raw dataCorrected
1922
1920
1918
1916
1914
1912
1910
Sh
ut-
in P
seu
do
pre
ssu
re,
pp
ws, p
sia
20151050
dppws/dta, psi/hr
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Sh
ut-
in p
seu
do
pre
ss
ure
, psi
a
dppws/dta, psi/hr
pp,bar = 1920 psia
Onset of boundarydominated flow.
"Transient flow"
Example 3: Muskat Plot (single well pavg plot)
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
25
20
15
10
5
0
-5
(p
p')
t a
e
2520151050
ta
2/tae, hrs
Well C-IV-11 (A-084) [Test Date: 5 January 1992](
pp')
ta
e, p
si
ta2/ tae
Example 3: "Well Interference" Plot (radial flow only)
Well C-IV-11 (A-084) [Test Date: 5 January 1992]
Intercept is used tocalculate permeability.
Slope is used in thepressure correction.
Presence of multiwellinterference effects is unclear
100
101
102
103
Ps
eu
do
pre
ss
ure
Fu
nc
tio
ns
, p
si
10-4
10-3
10-2
10-1
100
101
Effective Shut-in Pseudotime, tae, hrs
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Condensate bankingregion.
Higher mobilityregion.
Closed boundary at 197 ft?(includes non-Darcy flow).
Improvement onpressure derivative.
Infinite-acting Reservoir Model(Does not include non-Darcy flow)
Ps
eud
op
res
su
re F
un
ctio
ns,
psi
Effective shut-in pseudotime, hrs
Example 4: Log-log Summary Plot
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Raw dataCorrected
1950
1900
1850
1800
1750
1700
1650
1600
1550
1500
Sh
ut-
in P
seu
do
pre
ssu
re,
pp
ws, p
sia
100
101
102
103
Horner Pseudotime, ( ta+tpa)/ta (tpa=tp=1.63 hr), hr
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Condensate bankingregion.
Higher mobilityregion.
Sh
ut-
in P
seu
do
pre
ss
ure
, psi
a
Horner pseudotime, hrs (tp = 1.63 hr)
Example 4: Horner (Semilog) Plot
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Raw dataCorrected
1884
1882
1880
1878
1876
1874
1872
1870
Sh
ut-
in P
seu
do
pre
ssu
re,
pp
ws, p
sia
20151050
dppws/dta, psi/hr
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
pp,bar = 1882.8 psia
Onset of boundarydominated flow.
"Transient flow"
Sh
ut-
in p
seu
do
pre
ss
ure
, psi
a
dppws/dta, psi/hr
Example 4: Muskat Plot (single well pavg plot)
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
40
30
20
10
0
(p
p')
t a
e
302520151050
ta
2/tae, hrs
Well C-IV-11 (A-084) [Test Date: 4 May 1992](
pp')
ta
e, p
si
ta2/ tae
Example 4: "Well Interference" Plot (radial flow only)
Well C-IV-11 (A-084) [Test Date: 4 May 1992]
Intercept is used tocalculate permeability.
Slope is used in thepressure correction.
(pp')tae >0, no clear indication of
multiwell interference effects.
16000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
550050004500400035003000250020001500100016000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
x-p
osi
tio
n (
rela
tive
dis
tan
ce)
5500500045004000350030002500200015001000
y-position (relative distance)
A-015
A-016
A-017
A-021
A-022ST2
A-024
A-025ST
A-027
A-029
A-032A-032ST
A-033
A-034
A-035
A-036
A-040
A-041
A-042
A-045
A-046
A-048
A-049
A-051
A-053
A-054
A-058
A-059
A-060
A-061
A-062
A-067
A-068
A-070
A-071
A-073
A-074
A-076
A-077
A-078
A-079ST
A-080
A-081
A-082
A-083
A-084A-085
A-088
A-089
A-091
A-092
A-093
A-095
A-096
A-097
A-098
A-099
A-100
A-101
A-102
A-103
A-104
A-105ST2
A-106
A-107
A-108
A-109
A-110ST
100000
80000 60000
50000
50000
50
00
0
40000
40000
40000
40
00
0
40000
40000
30000
30
00
0
30
00
0
30
00
0
30
00
0
30000 20
00
0
20000
20
00
0
20
00
0
20
00
0
20
00
0
20000 20
00
0
10000
10000
10
00
0
10
00
0
10
00
0
10
00
0
10
00
0
10
00
0
10000
10
00
0
Flow Capacity (kh, md-ft)from Well Test Analysis (Arun Field, Indonesia)
Legend: (Well Test Analysis)
Flow Capacity ( kh) Contour Plot(10,000 md-ft Contours)
Arun Field (Indonesia)
1x2 PerspectiveViewkh 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
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 16000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
550050004500400035003000250020001500100016000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
x-p
osi
tio
n (
rela
tive
dis
tan
ce)
5500500045004000350030002500200015001000
y-position (relative distance)
A-015
A-016
A-017
A-021
A-022ST2
A-024
A-025ST
A-027
A-029
A-032A-032ST
A-033
A-034
A-035
A-036
A-040
A-041
A-042
A-045
A-046
A-048
A-049
A-051
A-053
A-054
A-058
A-059
A-060
A-061
A-062
A-067
A-068
A-070
A-071
A-073
A-074
A-076
A-077
A-078
A-079ST
A-080
A-081
A-082
A-083
A-084A-085
A-088
A-089
A-091
A-092
A-093
A-095
A-096
A-097
A-098
A-099
A-100
A-101
A-102
A-103
A-104
A-105ST2
A-106
A-107
A-108
A-109
A-110ST
-3
.4
-3
.6
-3
.6
-3.8
-3
.8
-3.8
-3
.8
-3
.8
-4
-4
-
4
-4
-4
-4
.2
-4.2
-4.2
-4
.2
-4
.2
-4
.4
-4
.4
-4
.4
-4.6
-4
.6
-4.6
-4.6
-4.6
-4.8
-4.8
-4.8
-5
-5
Logarithm of the Non-Darcy Flow Coefficient (D, 1/MSCFD)from Well Test Analysis (Arun Field, Indonesia)
Legend: (Well Test Analysis)
Logarithm of the Non-DarcyFlow Coefficient
(log(10) Contours)
Arun Field (Indonesia)
No Data
1x2 PerspectiveView
Good distribution of values—"high" spots probably indicate need for individual well stimulations.
Relatively small data set (32 points).
Condensate Radius Map 16000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
550050004500400035003000250020001500100016000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
x-p
osi
tio
n (
rela
tive
dis
tan
ce)
5500500045004000350030002500200015001000
y-position (relative distance)
A-015
A-016
A-017
A-021
A-022ST2
A-024
A-025ST
A-027
A-029
A-032A-032ST
A-033
A-034
A-035
A-036
A-040
A-041
A-042
A-045
A-046
A-048
A-049
A-051
A-053
A-054
A-058
A-059
A-060
A-061
A-062
A-067
A-068
A-070
A-071
A-073
A-074
A-076
A-077
A-078
A-079ST
A-080
A-081
A-082
A-083
A-084A-085
A-088
A-089
A-091
A-092
A-093
A-095
A-096
A-097
A-098
A-099
A-100
A-101
A-102
A-103
A-104
A-105ST2
A-106
A-107
A-108
A-109
A-110ST
40
35
35
3
0
30
30
30
25
25
25
25
25
25
25
25
20
2
0
20
20
20
15
15
15
15
10
10
10
10
10
10
7
7
7
7
5
5
5
5
5
3 3
3
1
Condensate Bank Radius (ft) from Well Test Analysis(Arun Field, Indonesia)
Legend: (Well Test Analysis)
Condensate Bank Contour Plot(Various Contours)
Arun Field (Indonesia)
No Data
1x2 PerspectiveView
10-6
10-5
10-4
10-3
103
104
105
106
103
104
105
106
103
104
105
106
Comparison of Non-Darcy Flow Coefficient (D) from Well TestAnalysis versus Flow Capacity (kh) from Well Test Analysis
(Arun Field -- Indonesia)
Legend: DWT vs. khWT
Comparison of D from Well Test Analysis versus kh from Well Test Analysis
(Arun Field -- Indonesia)
No
n-D
arc
y F
low
Co
eff
icie
nt
(D,
1/M
SC
FD
)fr
om
We
ll T
es
t A
na
lys
is (D
at
Tim
e o
f W
ell
Te
st)
Flow Capacity (kh, md-ft)from Well Test Analysis (kh at Time of Well Test)
D-kh crossplot indi-cates an "order of magnitude" correla-tion.
Verifies that non-Darcy flow effects are systematic.
D (Non-Darcy)—kh Crossplot
Slope = 2
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 ofWell 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.
10-2
10-1
100
psD
' or
psD
e' o
r p
sDc' ,
[p
ws-p
wf(t=
0)]
fo
rma
t
10-6
10-5
10-4
10-3
10-2
tDA or tDAeDim
. Pre
ssur
e D
eriv
ativ
e F
unc
tion
s
tDA or tDAe
tpDA=10-5
tpDA=10-4tpDA=10-3
tpDA=10-2
Agarwal eff.shut-in time
Shut-in time
The "Regional Pressure Decline" Improves The Derivative
9
8
7
6
5
4
3
ps
D o
r p
sD
c, [
pw
s-p
wf(t=
0)]
form
at
10-6
10-5
10-4
10-3
10-2
tDA or tDAe tDA
or tDAe
psD
or
psD
c [p
ws
- p
wf(
t=0
)] fo
rma
t
Agarwal effective time
MDH
tpDA=10-5tpDA=10-4tpDA=10-3tpDA=10-2