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

ensi

onle

ss P

ress

ure,

p D

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 =Vpctq1B

dpdt =

Vpctq1B where:

Regional Pressure Decline Model

Pressure buildup analysis relations:

psD(tDA) + 2(D – 1)tDA = 12ln 4

etDAeArw

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)tDA

2

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

p sD'

, [p w

s-p w

f(t=

0)] f

orm

at

40x10-3 3020100tDA

Legend:

Multiwell, Single Well, tpDA=1x10 -2

, tpDA=1x10 -3

, tpDA=1x10 -4

, tpDA=1x10 -5

p sD' [

p ws -

pw

f(t=

0)] f

orm

at

tDA

Pressure builds up to pbar

(closed boundary)

pbar continues to decline.

Straight Line on Cartesian Plot

-2.00-1.75-1.50-1.25-1.00-0.75-0.50-0.250.000.250.500.751.00

p sD

e', [p

ws-

p wf(

t=0)

] for

mat

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 -

pw

f(t=

0)] f

orm

at

tDA2/ tDAe

Regional Pressure Decline Signature May Not Be Unique

-5

-4

-3

-2

-1

0

1

p sD

e', [p

ws-

p wf(

t=0)

] for

mat

10-5 10-4 10-3 10-2 10-1 100 101 102

tDA2/tDAe

Legend:

tpDA=1x10 -2

tpDA=1x10 -3

tpDA=1x10 -4

tpDA=1x10 -5

p sD

e' [p

ws -

pw

f(t=

0)] f

orm

at

psDe' = 0.5psDe' = 0.5 - 2(D - 1) tDA

2/ tDAeThis portion may be falsely

interpreted 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 = 70.6 qBb 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 kc trw

2 – 3.22751

And the skin factor is calculated using:

k = 162.6 qBmslh

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:

tedpwsdte cor

= tedpwsdte

+ mct2

te

pws,cor = pws + mct

10-1

100

101

102

103

Pseu

dopr

essu

re F

unct

ions

, psi

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 mobility

region.Closed boundary at 160 ft?(includes non-Darcy flow).

Pse

udop

ress

ure

Func

tions

, psi

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

Shut

-in P

seud

opre

ssur

e, p

pws,

psi

a

100101102103

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]

Shu

t-in

Pse

udop

ress

ure,

psi

a

Horner pseudotime, hrs (tp = 1.56 hr)

1150

1149

1148

1147

1146

1145

1144

1143

1142

Shut

-in P

seud

opre

ssur

e, p

pws,

psi

a

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

pseu

dopr

essu

re, p

sia

dppws/dta, psi/hr

-15

-10

-5

0

5

10

15(

p p')

t ae, p

si

302520151050ta

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

') ta

e, ps

i

ta2/ tae

100

101

102

103

Pseu

dopr

essu

re F

unct

ions

, psi

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).

Pseu

dopr

essu

re F

unct

ions

, 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

Shut

-in P

seud

opre

ssur

e, p

pws,

psi

a

100101102103

Horner Pseudotime, (ta+tpa)/ta (tpa=tp=1.62 hr), hr

Well C-IV-11 (A-084) [Test Date: 5 January 1992]Sh

ut-in

Pse

udop

ress

ure,

psi

a

Horner pseudotime, hrs (tp = 1.62 hr)

Example 3: Horner (Semilog) PlotWell C-IV-11 (A-084) [Test Date: 5 January 1992]

Raw dataCorrected

1922

1920

1918

1916

1914

1912

1910

Shut

-in P

seud

opre

ssur

e, p

pws,

psi

a

20151050dppws/dta, psi/hr

Well C-IV-11 (A-084) [Test Date: 5 January 1992]

Shut

-in p

seud

opre

ssur

e, p

sia

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

2520151050ta

2/tae, hrs

Well C-IV-11 (A-084) [Test Date: 5 January 1992](

p p')

t ae,

psi

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

Pseu

dopr

essu

re F

unct

ions

, psi

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)

Pseu

dopr

essu

re F

unct

ions

, 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

Shut

-in P

seud

opre

ssur

e, p

pws,

psi

a

100101102103

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.

Shut

-in P

seud

opre

ssur

e, p

sia

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

Shut

-in P

seud

opre

ssur

e, p

pws,

psi

a

20151050dppws/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"

Shut

-in p

seud

opre

ssur

e, p

sia

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

302520151050ta

2/tae, hrs

Well C-IV-11 (A-084) [Test Date: 4 May 1992](

p p')

t ae,

psi

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 ofmultiwell 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-po

sitio

n (re

lativ

e di

stan

ce)

5500500045004000350030002500200015001000y-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-105ST2A-106

A-107

A-108

A-109

A-110ST

100000

80000 60000

50000

50000

500

00

40000

40000

40000

400

00

40000

40000

30000

300

00

300

00

300

00

300

00

30000 200

00

20000

200

00

200

00

200

00

200

00

20000 200

00

10000

10000

100

00

100

00

100

00

100

00

100

00

100

00

10000

100

00

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-po

sitio

n (re

lativ

e di

stan

ce)

5500500045004000350030002500200015001000y-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-105ST2A-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-po

sitio

n (re

lativ

e di

stan

ce)

5500500045004000350030002500200015001000y-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-105ST2A-106

A-107

A-108

A-109

A-110ST

40

35

35

30

30

30

30

25

25

25

25

25

25

25

25

20

20

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

106103 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)

Non

-Dar

cy F

low

Coe

ffici

ent (

D, 1

/MSC

FD)

from

Wel

l Tes

t Ana

lysi

s (D

at T

ime

of W

ell T

est)

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

p sD' o

r p sD

e' or

psD

c' , [

p ws-

p wf(

t=0)

] for

mat

10-6 10-5 10-4 10-3 10-2

tDA or tDAeDim

. Pre

ssur

e D

eriv

ativ

e Fu

nctio

ns

tDA or tDAe

tpDA=10-5

tpDA=10-4 tpDA=10-3tpDA=10-2

Agarwal eff.shut-in time

Shut-in time

The "Regional Pressure Decline" Improves The Derivative

9

8

7

6

5

4

3

p sD

or p

sDc,

[pw

s-p w

f(t=

0)] f

orm

at

10-6 10-5 10-4 10-3 10-2

tDA or tDAe tDA or tDAe

p sD

or p

sDc [

p ws -

pw

f(t=

0)] f

orm

at

Agarwal effective time

MDH

tpDA=10-5tpDA=10-4tpDA=10-3tpDA=10-2