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--

RS. Trijana KartoatmodjoRS. Trijana Kartoatmodjo

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Estimating Reservoir PressureEstimating Reservoir Pressure

Middle Time Region MethodsMiddle Time Region MethodsMatthewsMatthews--BronsBrons--HazebroekHazebroek MethodMethod

--

Late Time Region MethodsLate Time Region Methods

ModifiedModified MuskatMuskat MethodMethod

--

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-- Based on extrapolation and correction of MTRBased on extrapolation and correction of MTR

pressure trendpressure trend AdvantageAdvantage

Use onl ressure data in the middleUse onl ressure data in the middle--timetime

regionregion Disadvanta esDisadvanta es

Need accurate fluid property estimatesNeed accurate fluid property estimates

, ,, ,location within drainage arealocation within drainage area

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-- --

Producing time prior to shutProducing time prior to shut--in,in, ttpp = 482 hr= 482 hr

,, ..

Viscosity,Viscosity, mm = 0.25 cp= 0.25 cp

Total compressibility,Total compressibility, cctt = 1.615 x 10= 1.615 x 10--

Drainage area,Drainage area, AA = 1500 x 3000 ft (a 2x1 reservoir)= 1500 x 3000 ft (a 2x1 reservoir)

2

1

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6

5

3

4

2pMBHD

1

-1

0

0.01 0.1 1 10

tpAD

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6

5

4

2pMBH

D

1

-

0

0.01 0.1 1 10

tpAD

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5

4

3

1pMBH

D

0

-

-1

0.01 0.1 1 10

tpAD

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-- --2750

p*=2689.4

2650 m=26.7

2550

Shut-in well

pressure, psia

2400

2450Step 1: Plot pressure vs. Horner time ratioStep 2: Extrapolate slope m to find p*

Horner time ratio

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a ews- rons- aze roe

Step 3: Calculate dimensionless producing timeStep 3: Calculate dimensionless producing time

0002637.0

ktt

p

AD

ct

3000150010615.125.015.0

..5

35.0

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a ews- rons- aze roe

Step 4: On appropriate MBH curve, findStep 4: On appropriate MBH curve, find ppMBHDMBHD6

4

5

2x1 rectangle

3 2.05

1

2

-1

0tpAD = 0.35

0.01 0.1 1 10

tpAD

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a ewsa ews-- ronsrons-- aze roeaze roe

Step 5: Calculate average reservoir pressure,Step 5: Calculate average reservoir pressure, pp

* pADMBHD tpm

pp

05.27.26

4.2689 303.2

.

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-- -- PlotPlot ppwsws vsvs ((ttpp++tt)/)/ttonon semilogsemilog coordinatescoordinates

Extra olate toExtra olate to tt++tt tt=1 to find=1 to find **

Calculate the dimensionless producing timeCalculate the dimensionless producing time ttppADAD Usin the a ro riate MBH chart for the draina eUsin the a ro riate MBH chart for the draina e

area shape and well location, findarea shape and well location, find ppMBHDMBHD

IfIf tt >>>>tt more accurate results ma be obtainedmore accurate results ma be obtained

a cu atea cu ate pp

by usingby using ttpsspss in place ofin place of ttpp in calculating the Hornerin calculating the Horner

time ratio andtime ratio and tt

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a ewsa ews-- ronsrons-- aze roeaze roe

AdvantagesAdvantages

well locationswell locations

Uses onl data in the middleUses onl data in the middle--time re iontime re ion

Can be used with both short and long producingCan be used with both short and long producingtimestimes

DisadvantagesDisadvantages , ,, ,

Requires accurate fluid property dataRequires accurate fluid property data

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eservo r apeseservo r apes

1

Dietz shape factor CA = 30.8828Dietz shape factor CA = 12.9851

e z s ape ac or A = .

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2

Dietz shape factor CA = 10.8374

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4

Dietz shape factor CA = 5.379

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Dietz shape factor

CA = 31.62

Dietz shape

factor CA = 19.17

Dietz shape

factor CA = 27.1

CA = 31.6

factor CA = 21.9

factor CA = 0.098

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-- ..

Step 2: Calculate dimensionless producing timeStep 2: Calculate dimensionless producing time

0002637.0 kt

ActpAD

4825.70002637.0

5

35.0

...

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--Step 3: Find the Dietz shape factorStep 3: Find the Dietz shape factor CCAA for thefor the

drainage area shape and well locationdrainage area shape and well location

pADAp tCtt

35.08.21

p

AA = .= .

63.7

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--2750

2650

-8.2665p

2550

pressure, psia

2450 HTR = 7.632400

110102103104105106

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--

PlotPlot ppwsws vsvs ((ttpp++tt)/)/ttonon semilogsemilog coordinatescoordinates

pp Find the Dietz shape factorFind the Dietz shape factor CCAA for the drainage areafor the drainage area

sha e and well locationsha e and well location

CalculateCalculate HTRHTRavgavg Extra olate middleExtra olate middle--time re ion on Horner lot totime re ion on Horner lot to

HTRHTRavgavg

ReadRead pp atat HTRHTRavgavg

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-- van agesvan ages

Applies to wide variety of drainage area shapes,Applies to wide variety of drainage area shapes,ww

Uses only data in the middle time regionUses only data in the middle time region

sa vantagessa vantages Requires drainage area size, shape, well locationRequires drainage area size, shape, well location

Requires accurate fluid property dataRequires accurate fluid property data

Requires producing time long enough to reachRequires producing time long enough to reachpseudosteadypseudosteady statestate

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---- --

region pressure trend to infinite shutregion pressure trend to infinite shut--in timein time

van agesvan ages

No need for accurate fluid property estimatesNo need for accurate fluid property estimates

No need to know drainage area shape, size, wellNo need to know drainage area shape, size, welllocation within drainage arealocation within drainage area

en o e very s mp een o e very s mp e

DisadvantageDisadvantage Require postRequire post--middlemiddle--timetime--region pressureregion pressuretransient datatransient data

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--

22

t ee

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The data points shown as dots represent data in theThe data points shown as dots represent data in theran e iven on the revious slide for the a licationran e iven on the revious slide for the a licationof the Modifiedof the Modified MuskatMuskat andand ArpsArps--Smith methods.Smith methods.

This illustrates one of the disadvantages of these twoThis illustrates one of the disadvantages of these twomethods. Many other reservoir models exhibit similarmethods. Many other reservoir models exhibit similar

, ,, ,

correct average drainage area pressure.correct average drainage area pressure.

Examples include: PSS dual porosity reservoirs duringExamples include: PSS dual porosity reservoirs duringthe early transition from fracture flow to total systemthe early transition from fracture flow to total system

, ,, ,with an inner zone mobility much lower than thewith an inner zone mobility much lower than theouter zone mobility.outer zone mobility.

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Average reservoir pressureAverage reservoir pressure

--

bt

ws

tnppn ws

btCppln

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Step 1: Assume a value for average

ws

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1000

Assumed pressure too low

p100,ws

5575

5600

5560

10

Assumed pressure too high

Time, minutes

1500 2000 2500 3000 3500 4000 4500

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o e us a e o

AdvantagesAdvantages

DisadvantagesDisadvantages

Somewhat subjective: Which data pointsSomewhat subjective: Which data pointsshould I tr to strai hten?should I tr to strai hten?

More sensitive to estimates that are tooMore sensitive to estimates that are too

Not easily automatedNot easily automated

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RecommendationsRecommendations

has been a clear deviation from thehas been a clear deviation from the

m em e-- me reg onme reg onOnce middleOnce middle--time re ion has endedtime re ion has ended

try to straightentry to straighten allalldatadata

reasonably centered in drainage areasreasonably centered in drainage areas

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--

bt

e

td

edt

dp

wsdt

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--Step 1: Assume a value for averageStep 1: Assume a value for average

,,

empirical observationempirical observation

wsppb

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--Step 2: Plot dpwsdtvspws on Cartesian scale

8

9

5

6

7

dpws/dt,

ep : a s ra g ne

through the data points

3

4

Pavg = 5575 psi

0

1

the x-intercept

Pws, psi

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rpsrps-- m e om e opt ona : st mate t e pro uct v ty n ex npt ona : st mate t e pro uct v ty n ex n

STB/D/psi from the slopeSTB/D/psi from the slope bb and theand thewellbore storage coefficientwellbore storage coefficient CC

wsppbdt

Cb24 wfppJq

B

dpCBqq w24

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-- van agesvan ages

Simple to applySimple to apply Easily automatedEasily automated

Requires data in lateRequires data in late--time region, after alltime region, after alloun ar es ave een eoun ar es ave een e

AssumesAssumes a roachesa roaches ex onentiallex onentiall Requires numerical differentiation of pressureRequires numerical differentiation of pressure

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RS. TrijanaRS. Trijana KartoatmodjoKartoatmodjo

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P** didefinisikan seba ai:P** didefinisikan seba ai:

Hasil:Hasil:

dd

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dan:dan:

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, ,, ,