8 RWP PTA Infinite Acting Reservoirs 2013 UWA

P. Behrenbruch Reservoir and Well Performance

8 PTA: Infinite Acting Reservoirsp 1

4-6 April, 6-8 June 2012

Presentation Outline

Reservoir and Well Performance Pressure Transient Analysis: Infinite Acting Reservoirs

Drawdown Response

Drawdown Analysis

Type Curves

Pressure Build-up Response

Horner Analysis

Non-dimensional Horner

Build-up Type Curve Analysis

Prof Peter Behrenbruch

Model Response

First Drawdown after Stabilisation

Time from start of drawdown

Ref: Gringarten



4-6 April, 6-8 June 2012

Pressure Drawdown Response



4-6 April, 6-8 June 2012

Drawdown Response - General Solution Example of pD(tD) Function

Example: Interference Test in an Infinite Reservoir

with Homogeneous Behaviour:

Ref: Gringarten



4-6 April, 6-8 June 2012

Infinitive Reservoir, General Line Source Solution

10-2

10-1

10-1

1

10 104 105 106 107 108 109

1 10 102 103 104

5.0 ; 202

D

DD

r

tr

25 ; 1 DD tr

)(00708.0

,triD ppBq

khp

20Dr

0.1DrDimensionless Parameters

22

000264.0

rc

kt

r

t

tD

D

Valid for

2

D

D

r

t

Dp



4-6 April, 6-8 June 2012

Drawdown Type Curves Example of Independent Variables*

Ref: Gringarten

Dimensionless parameters, non-unique match

Independent variables, unique match

* oilfield units



4-6 April, 6-8 June 2012

Pressure Drawdown Analysis



4-6 April, 6-8 June 2012

Pressure Transient Analysis

Logarithmic Approximation of Pressure Drawdown

fwwoot cScScc

100 4

ln2

1~

2D

D

DD t

r

tp

at the wellbore

valid for

or

2

4ln

4 wiwt

cr

kt

kh

qpp

and in field units

23.3log)log(

6.1622

wt

iwtrc

kt

kh

qBpp

where



4-6 April, 6-8 June 2012

Single Rate Transient Drawdown Analysis Including Afterflow and Skin

Equations (field units):

23.3log

k gives /6.162

2

w

iihr

cr

k

m

pps

cyclepsikh

Bqm

Analysis Plot (Drawdown)

10-1 1 10 102

lhrp

ip

wp

Wellbore Storage

Effects

Slope m

Time (hrs)

m is negative!



4-6 April, 6-8 June 2012

Identification of Correct Analysis for Semi-log Analysis Log-log Drawdown Response and 1 Log Cycle Rule

1000

100

10

Dp

psia

t, hours 0.01 0.1 1 10

1 log cycles

End of unit

slope line

Expected start of

semi-log straight line

* Ref: Horne, Modern Well Test Analysis



4-6 April, 6-8 June 2012

Semi-log (Horner) Analysis

3000

4000

5000

5000

p, psia

t, hours 0.01 0.1 1 10

p1hr

Start of semi-log

straight line




4-6 April, 6-8 June 2012

Type Curves



4-6 April, 6-8 June 2012

Wellbore Storage (1) Rate Response

0.01 0.1 1 10 100 0

500

1000

1500

2000

2500 Flowrate, stb/d

CD = 10,000

CD = 1,000

Time, hours * Ref: Horne, Modern Well Test Analysis



4-6 April, 6-8 June 2012

Wellbore Storage (2) Pressure Response

Time, hours

0.01 0.1 1 10 100

3000

4000

5000

7000 Pressure. psia

CD = 10,000 CD = 1,000

6000




4-6 April, 6-8 June 2012

Wellbore Storage (3) Characteristic on Log-log Plot: 45o Slope

45o slope

Dt, hours 0.01 0.1 1 10 100

100

1000

10000

Dp, psi




4-6 April, 6-8 June 2012



4-6 April, 6-8 June 2012

Drawdown Type Curves Examples of Independent Variables*

* oilfiled units

Ramey

Gringarten

Ref: Gringarten



4-6 April, 6-8 June 2012



4-6 April, 6-8 June 2012

Analysis Process Model Identification, Parameter Calculation, Model Verification

Ref: Gringarten



4-6 April, 6-8 June 2012

Drawdown Type Curves Examples of Dimensionless Variables*

* oilfiled units

Ref: Gringarten



4-6 April, 6-8 June 2012

Log-log Analysis

Ref: Gringarten



4-6 April, 6-8 June 2012

Model Response in the First Drawdown

Ref: Gringarten



4-6 April, 6-8 June 2012



4-6 April, 6-8 June 2012

Type Curve Matching (2) Gringarten Curves

Ref: Gringarten



4-6 April, 6-8 June 2012

Match point: )p(Bq2.141

kh)p(

DD

kh

D

C

tkh000295.0

C

t

D

D

Type curve selected: 2

22 8936.0

wt

SS

Dhrc

CeeC

C

S

Type Curve Matching (3) Summary of Analysis Results



4-6 April, 6-8 June 2012

Differential Type Curves Homogeneous Reservoir



4-6 April, 6-8 June 2012

Time, hrs

td/cd

Infinite Acting Radial Flow Straight Line on Semi-log Plot

Flat Region on Derivative Plot




4-6 April, 6-8 June 2012

Wellbore Storage Unit Slope Line on Log-log Plot

Unit Slope Line plus Hump* on

Derivative Plot

* The hump on a derivative plot is characteristic

of a damaged well (positive skin)

Dt, hrs

td/cd * Ref: Horne, Modern Well Test Analysis



4-6 April, 6-8 June 2012

Pressure Build-up Responses



4-6 April, 6-8 June 2012

Build-up Model Response after First Drawdown

Time from start of drawdown

Ref: Gringarten



4-6 April, 6-8 June 2012

Pressure Build-up Transient Analysis

1wtp 2wtp

ipqq 1

02 q

t 1t tD 2t0 0

Rate, q Concept

Superposition

Equation: stpqpp

khDDwni 0)0()(

221

qstqpqsttqp

sttpqq

DD

DDD

DD

)()(

)( 1212

)()()(2

tpttpppq

khDDwni DD

Time, t



4-6 April, 6-8 June 2012

Horner Analysis



4-6 April, 6-8 June 2012

Pressure Build-up Analysis (Horner)

3 2 1 0

wp

*p

)( Dietzp

)log( DAAtc

ihrp

Wellbore

Storage

Effects

cyclepsikh

BqmSlope /

6.162

D

D

t

ttlog

t

t

cr

k

m

pps

w

wfhrws 1log23.3log151.1

2

1

Note:

i. If boundaries not felt at

ii. If semi-steady state before shut,

then Dietz method is valid

ipptt D* ;



4-6 April, 6-8 June 2012



4-6 April, 6-8 June 2012

Determining Start of Semi-log Straight Line

2.43

1000

0.01 0.1 1 10 Dt, hours

Pwf, psia

1 log cycles

End of unit

slope line

Expected start of

semi-log straight line




4-6 April, 6-8 June 2012

Picking Correct Horner Line

2.44

3500

4000

4500

5000

5500

6000

psia

1 10 100 1000 (t+Dt)/Dt

p1hr

Horner time = 11.8




4-6 April, 6-8 June 2012

Non-dimensional Horner Analysis



4-6 April, 6-8 June 2012

Model Response: Build-up after first Drawdown Horner Type Curve

Ref: Gringarten



4-6 April, 6-8 June 2012

Horner Type Curve after Drawdown

Ref: Gringarten



4-6 April, 6-8 June 2012

Type Curve Analysis (Gringarten)



4-6 April, 6-8 June 2012

Drawdown and Build-up Pressure Response Superposition of Rate

q q

q

tp

tp

tp t

t t

+q

-q

+q



4-6 April, 6-8 June 2012

Model Response: Build-up after first Drawdown Gringarten Type Curve

Ref: Gringarten



4-6 April, 6-8 June 2012

Build-up Type Curve Behaviour Difference between Drawdown and Build-up

Ref: Gringarten



4-6 April, 6-8 June 2012

Pressure Build-up Superposition Response: Argarwal Correction Factor

etD

tD

wfp

ip

wp "" pDobsersed

p""D

true

p""D

Pi - pwf

tp

pwf(Dt) pwf(tp + Dt)

pwf(tp + Dt)

tequiv = tpDt / (tp + Dt)



4-6 April, 6-8 June 2012

Pressure Buid-up Derivative Response Before Argarwal Correction

3.10

100

1000

psia

P &

P

0.01 0.1 1 10 hours Time

What does this

pressure decrease

represent?




4-6 April, 6-8 June 2012

Build-up vs. Drawdown Pressure Response Type Curves

pDlog

tDlog

Drawdown

Buildup

Argawal Correction



4-6 April, 6-8 June 2012

3.11

Pressure Buid-up Derivative Response After Argarwal Correction

100

1000

psia

P &

P

0.01 0.1 1 10 hours

Effective Time

All Fixed

with the

Correct Analysis!




4-6 April, 6-8 June 2012

Additional Handouts

(Lecture 14) Example*




4-6 April, 6-8 June 2012

Type Curve Matching Datum Shifting

3.21

Dt, hours

0.01 0.1 1 10 100

100

1000

10000

Dp, psi

1 minute subtracted

1 minute added



4-6 April, 6-8 June 2012

Stimulated Well Example



4-6 April, 6-8 June 2012

10.1



4-6 April, 6-8 June 2012

10.2



4-6 April, 6-8 June 2012

10.3



4-6 April, 6-8 June 2012

10.4



4-6 April, 6-8 June 2012

10.5



4-6 April, 6-8 June 2012

Damaged Well Buildup



4-6 April, 6-8 June 2012

10.63



4-6 April, 6-8 June 2012

10.64



4-6 April, 6-8 June 2012

10.65



4-6 April, 6-8 June 2012

10.66

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8 RWP PTA Infinite Acting Reservoirs 2013 UWA

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