1

SPE Distinguished Lecturer Program

Primary funding is provided by

The SPE Foundation through member donations

and a contribution from Offshore Europe

The Society is grateful to those companies that allow their

professionals to serve as lecturers

Additional support provided by AIME

Society of Petroleum Engineers

Distinguished Lecturer Programwww.spe.org/dl

The Determination of Minimum Tested Volume and

Future Well Production from the Deconvolution of

Well Test Pressure Transients

Tim WhittleBg Group

Society of Petroleum Engineers

Distinguished Lecturer Programwww.spe.org/dl

3

Well Test Objectives

• Fluid Characterisation (PVT)

• Well Performance (Flow)

• Reservoir Description (Model)

• Reservoir Deliverability (Flow)

• Flow Assurance (Facilities)

• Clean Up (Production)

4

Types of Well Test

Fluid

Characterisation

Well

Flow

Reservoir

Description

Reservoir

Flow

Exploration

Appraisal

Extended

(EWT)

Production

Primary objectives depend on the type of test

5

Wireline Formation Tests

Objective WT WFT

Fluid

Small Volume

Large Volume

Well Flow

Reservoir Flow

Reservoir Description

Versus Depth

Formation

Boundaries

WFT and WT are not equivalent

6Pressure, p and Flowrate, q

pwf

qtest

Flow rate, q

Pre

ssure

, p

00

Operating Point

wfr

test

pp

qPI

Productivity Index

AOFP

PI

pr

SurfaceFlow, qtest

Reservoir

Well

Bottom hole

prpwf

Well Performance

7

How to Improve Well Performance?

Flow rate, q

Pre

ssure

, p

00

pr

Outflow 1 to Outflow 2 Change in completion (tubing, choke, artificial lift…)

Inflow 1 to Inflow 2 Change in well/reservoir (perfs, acid, frac, well type…)

Need to understand Inflow to see if improvement is possible…

∆q ∆q ∆q

8

Reservoir Deliverability

t1

Flow rate, q

Pre

ssure

, p

00

pr

t2

t3

t3> t2 > t1

• Reservoir constrained

– Complex boundaries

(e.g. channel sands)

– Low permeability

2000

4000

Pre

ssure

[psi

a]

TH

P [

ps

ia]

0

20

40

Gas

Rate

Pro

du

cti

on

[M

Ms

cf/

D]

07-Nov-2008 09-Nov-2008 11-Nov-2008 13-Nov-2008 15-Nov-2008

Pressure [psia], Gas Rate [MMscf/D] vs Time [ToD]

9

-1000

0

1000

2000

3000

4000

5000

6000

22-Apr 23-Apr 24-Apr 25-Apr

Pre

ssu

re (

psia

)

Elapsed time (Date)

0

1000

2000

3000

4000

5000

6000

7000

8000

Oil

Ra

te (

ST

B/D

)

Pressure History

t1

Flow rate, q

Pre

ssu

re, p

00

pi

t2

t3

t3> t2 > t1

• Depletion

• Hopefully not seen in a

well test!

Reservoir Deliverability

pi

Depletion

10

Pressure Transient Analysis

Flow, q, Pressure, p, and Time, t

Pre

ss

ure

, p

Time, t

q(t)

Ra

te

0

pi

Δp

Δt

Δq

p(t)Steady state

Pseudo-steady state

Transient

11

Log-log Diagnostic Plot

Early Time Middle Time Late TimeNear WellStorage

Skin

Fractures

Partial Completion

ReservoirHomogeneous

2-Porosity

Multi-layer

BoundariesNo-Flow

Constant Pressure

Permeability thickness,

kh, and skin, S

Stabilisation

Infinite Acting

Radial Flow

½ Slope

Linear Flow

Channel

Unit Slope

Well Storage

Unit Slope

Depletion

Assuming single constant rate drawdown...

Δp’ = dp/d(ln t) = t dp/dt

Deri

vati

ve, Δ

p’

Elapsed Time, Δt (hrs)

Pre

ssu

re C

han

ge, Δ

p (

psi)

0.01 0.1 1 10010 10000.1

1

10

100

12

Pressure Transient Derivative Response

0.01 0.1 1 10 100 seconds1 10 100 hours

1 10 100 days

Spherical

Radial

WellboreStorage

Horizontal/Fractured Well

ReservoirBoundaries

WFTPT

Time (k = 750 mD)

13

Scale

While

Drilling

WirelineWell Test

Pressure Test Sampling

Volumes 1-10 cc 5-50 cc 10-100 l 1-10000 m3

x-factor 1 5 10000 106-109

Times 1-5 min 1-15 min 1-5 hr 12hrs – 12days

x-factor 1 1-3 60 720-20000

(Mini-frac)

14

Scale

Radius of investigation:

k/µ = 10 mD/cp

Øct = 0.15x10-5 1/psi

h = 75 ft

While

Drilling

Wireline

Well TestPressure Test

Sampling/

Mini DST

Flow Time 5 s 10 s 15 min 12 hr

Flow Volume 5 cc 10 cc 3000 cc 40x106 cc (250 bbl)

Shut Time 30 s 3 min 5 min 24 hr

Δp/Δt (psi/min) 0.18 0.003 0.06 0.018

Theoretical ri (ft) 5 17 23 300

Practical ri* (ft) 2 4 15 250

ct

tkri

* Assuming a gauge resolution/noise of 0.03 psi

(Mini-frac)

15

Example – Low Permeability – Two Wells

kh=16 mDft

kh=2.5 mDft

kh=6 mDft

Derivative describes heterogeneity in time/space

16

Data Acquisition: Well Test Sequence of Events

Pre

ss

ure

Time0

Ra

te

Pre

ss

ure

TimeR

ate

0

Δq

Ideal Case Actual Case

Pre

ss

ure

Elapsed Time

Deri

vati

ve

, Δ

p’

Log-log Plot

Entire Test

In general, only shut-ins give sufficiently high quality pressure transients

Pre

ss

ure

Elapsed Time

Deri

vati

ve

, Δ

p’

Log-log Plot

Only Build-up

?

17

Deconvolution

Pre

ss

ure

Time

Ra

te

0

Δq

No Model

Pre

ssu

re

Time0

Ra

te

tmax

tmax

18

Deconvolution by Iteration using superposition

Pre

ss

ure

Time

Ra

te

0

Δq

Ra

te

Time0

Pre

ss

ure

Time0

Ra

te

+

Non-linear Least Squares Minimisation

tmax

tmax

tmax

Iterations

2

19

265

hrs

4750

4950

5150

0 40 80 120 160 200 240Time [hr]

0

10

20

Ga

s R

ate

, M

Ms

cf/

dP

res

su

re, p

sia

48 hrs 48 hrs

Example

20

1E-3 0.01 0.1 1 10 100

Time (hrs)

1E+8

1E+9

1E+10

Ga

s P

ote

nti

al a

nd

De

riv

ati

ve

(p

si2

/cp

)

1000

1E+11

48 hrs 265 hrs

Example - DST

Deconvolved Data

Build-up Data

Longer duration of deconvolved data larger radius of investigation?

21

Pressure Transient Analysis Workflow

Pressures

P v tDeconvolve

Model Select

Simulate

Model

Catalogue

Model

Parameters

Fit

Rates

q v t

OK?N

Another

Model?Done

YN

Y

Diagnose

With Deconvolution

Minimum

Tested

Volume

SPE 116575

22SPE 116575

Minimum Tested Pore Volume

0.001 0.01 0.1 1 10 100

Time (hrs)

1

10

100

Pre

ss

ure

ch

an

ge

an

d D

eri

va

tiv

e (

ps

i)

1000

1000

Deconvolved Data

Build-up Data

Unit

Slope

(pss)

maxp

maxt

max

max)1(

p

tq

c

SSTOIP

t

wtested

'

max

max)1(

pnm

tq

c

SGIIP

t

wtested

23

Same Principle as Reservoir Limits Test (MBH)

Flow, q, Pressure, p, and Time, t

Pre

ss

ure

, p

Time, t

q(t)

Rate

0

pi

p(t)

Pseudo-steady state

Transient

Minimum

End of Test?

25

Example 1 - Gas

Input:Sw = 0.15

ct = 6.62E-5 1/psi

q = 40.4 MMscf/d

pbar = 8135.32 psia

μbar = 0.032 cp

zbar = 1.247

z

p

pm

tq

c

SGIIP

t

wtested

2)1('

max

max

Δtmax= 93.6 hrs

Δm(p)’max = 2.30E8 psi**2/cp

247.1032.0

32.81352

830.2

24/6.934.40

5625.6

)15.01(

EEGIIPtested

bscfMMscf 53.33534

26

Example 2 - Oil

Input:Sw = 0.129

ct = 9.44E-6 1/psi

q = 2380 stb/d

Δtmax= 304 hrs

Δm(p)’max = 20.6 – 63.1 psi

6.20

24/3042380

644.9

)129.01(

ESTOIPtested

MMstbstb 135843,39,139

max

max)1(

p

tq

c

SSTOIP

t

wtested

1.63

24/3042380

644.9

)129.01(

ESTOIPtested

MMstbstb 1.44261,053,44

Max Min

Uncertainty in deconvolution uncertainty in connected volume

27

Example 3 - Gas

z

p

pm

tq

c

SGIIP

t

wtested

2)1('

max

max

Input:Sw = 0.1

ct = 0.00131 1/psi

q = 10.7 MMscf/d

pbar = 865.2 psia

μbar = 0.0128 cp

zbar = 0.873

Δtmax= 136 hrs

Δm(p)’max = 2.37E5 psi**2/cp

873.00128.0

2.8652

537.2

24/1367.10

331.1

)1.01(

EEGIIPtested

bscfMMscf 2.27200,27

28

Example 3b: Gas - DST versus EWT

Boundaries reduced anticipated tested volume

29

Example 4 - Oil

Input:Sw = 0.15

ct = 1.5E-5 1/psi

q = 1220 stb/d

Δtmax= 136 hrs

Δm(p)’max = 93.5 – 530 psi

5.93

24/941220

55.1

)15.01(

ESTOIPtested

MMstbstb 89.2000,894,2

max

max)1(

p

tq

c

SSTOIP

t

wtested

530

24/941220

55.1

)15.01(

ESTOIPtested

MMstbstb 51.0564,510

Max Min

Uncertainty in deconvolution uncertainty in connected volume

30

Example 5 – Oil Design

Input:Sw = 0.15

ct = 1E-5 1/psi

q = 5000 stb/d

Δtmax= 60 hrs

Δm(p)’max = 105 psi

105

24/605000

63

)15.01(

ESTOIPtested

MMstbstb 7.3333708571

max

max)1(

p

tq

c

SSTOIP

t

wtested

Design Input:k = 90 mD

h = 7 m

ø = 0.11

rw = 0.3 ft

μ = 0.5 cp

pi = 5300 psia

(rinv = 5250 ft)

No Boundaries

31

Example 5 – Oil Design

Input:Sw = 0.15

ct = 1E-5 1/psi

q = 5000 stb/d

Δtmax= 60 hrs

Δm(p)’max = 683 psi

683

24/605000

63

)15.01(

ESTOIPtested

MMstbstb 2.55182138

max

max)1(

p

tq

c

SSTOIP

t

wtested

Design Input:k = 90 mD

h = 7 m

ø = 0.11

rw = 0.3 ft

μ = 0.5 cp

pi = 5300 psia

d1 = 500 ft

d2 = 1000 ft

Channel Boundaries : Significantly reduces tested volumes

32

Elapsed Time, Δt (hrs)

Pre

ssu

re C

han

ge, Δ

p (

psi)

0.01 0.1 1 10010 10000.1

1

10

100

Coefficient of Reservoir Complexity (CRC)

Stabilisation Infinite Acting Radial

Flow

Unit Slope

PSS

Applies to deconvolved data

De

riv

ati

ve,

Δp’

maxp

intp

int

max

p

pCRC

CRC is similar to Dietz Shape Factor, CA

(inversely proportional?)

33

Comparison of CRC with Dietz Shape Factor, CA

(Tom Street – May 2009)

34

Comparison of CRC with Dietz Shape Factor, CA

(Tom Street – May 2009)

Coefficient of Reservoir Complexity (ref. SPE 116575) vs. Dietz Shape

Factor

y = -0.3612x + 11.852

R2 = 0.6994

y = -2.274Ln(x) + 11.743

R2 = 0.8496

0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30 35

Dietz Shape Factor

CR

C

35

Pressure Transient Analysis Workflow

Pressures

P v tDeconvolve

Model Select

Simulate

Model

Catalogue

Model

Parameters

Fit

Rates

q v t

OK?N

Another

Model?Done

YN

Y

Diagnose

Production

Forecast

SPE 122299

SPE 122299

36

Extrapolation methods for Production Forecast

10

100

1000

10000

0.001 0.01 0.1 1 10 100 1000 10000

Elapsed time, dt (hrs)

Pre

ss

ure

Ch

an

ge

an

d d

eri

va

tiv

e (

ps

i)

Unit slope

Worst

case

-1 unit slope

Best case

Most likely

Extrapolate with Different Cases

Knowing

STOIIP/GIIP

37

Example 6: Gas – Prediction from DST

-1000

0

1000

2000

3000

4000

5000

6000

01-Jan 02-Jan 03-Jan 04-Jan 05-Jan 06-Jan

Pre

ssu

re (

psia

)

Elapsed time (Date)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Ga

s R

ate

(M

Mscf/D

)

38

1

10

100

1000

10000

100000

0.0000001 0.00001 0.001 0.1 10 1000

nm

(p)

Cha

ng

e a

nd

Deri

va

tive

(p

si)

Elapsed time (yrs)

Log-Log Deconvolution - Flow Period 15

Example 6: Gas – Prediction from DST

GIIP = 150 bcf

Unit Slope

PSS

Unit Slope

WBS

Deconvolved pressure derivative extrapolation defines dynamic response

Extrapolation

2

21 years

1 1 year

?

Deconvolution

39

Production Forecast

(pwf = 1500 psi)

0

2

4

6

8

10

12

14

16

18

0 5 10 15

Time (years)

Cu

mu

lati

ve

Ga

s (

bc

f)

Ra

te (

MM

sc

f/d

)

Case 1 Rate "

Case 1 Cum

Case 2 Cum

Case 2 Rate50%

Example 6: Gas – Prediction from DST

40

Example 7: Sensitivity to Initial Pressure

0

1000

2000

3000

4000

5000

6000

0 10 20 30 40 50

Time (days)

Pre

ssu

re (

psia

)

1.00E+06

1.00E+07

1.00E+08

1.00E+09

1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03

Elapsed Time

Pseu

do

-pre

ssu

re C

han

ge a

nd

Deri

vati

ve

pi = 5495

pi = 5490

pi = 54860

20

40

60

80

100

120

140

5484 5486 5488 5490 5492 5494 5496 5498 5500 5502

Initial Reservoir Pressure (psia)

Ga

s V

olu

me

(b

sc

f)

Min Tested Volume

Recovery after ten years

(pwf = 1500 psia)

41

2850

2860

2870

2880

2890

2900

2910

2920

2930

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Pre

ssu

re (

psia

)

Elapsed time (hrs)

0

50

100

150

200

250

Ga

s R

ate

(M

Mscf/

D)

Pressure History

Example 7: Gas – Prediction from Initial Production Test

42

0.01 0.1 1 10 100

Elapsed Time (hrs)

1E+5

1E+6

1E+7

Ps

eu

do

-pre

ss

ure

Ch

an

ge

an

d D

eri

va

tiv

e (

ps

i2/c

p)

Observed Extrapolated

1E+8

1000

Worst

Most

Likely

Best

Example 7: Gas – Prediction from Initial Production Test

43

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1Time (years)

Cu

mu

lati

ve p

rod

ucti

on

(b

cf)

Best

Most likely

Worst

Actual

Example 7: Gas – Prediction from Initial Production Test

44

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

0 1 2 3 4 5 6 7 8 9

Pre

ssu

re (

psia

)

Elapsed time (yrs)

0

50

100

150

200

250

Me

asu

red

Ga

s R

ate

(M

Mscf/

D)

Prediction at day 142Prediction at day 379

Prediction at day 507

Example 8: Gas – Prediction from Permanent Gauge Data

45

0.1 1 10 100 1000 10000

Elapsed Time (hrs)

1E+6

1E+7

1E+8

Pse

ud

o-p

ressure

ch

an

ge

an

d D

eriva

tive

(p

si2

/cp

)

Day 142Day 379Day 507

1E+9

100000

Constrained

46

0

50

100

150

200

250

0.00 2.00 4.00 6.00 8.00 10.00

Producing Time (years)

Cu

mu

lati

ve G

as (

bcf)

Measured

Predicted at day 142

Predicted day 379

Prediction at day 507

Predicted at day 142

Constrained to GIIP

47

Limitations

• Deconvolution assumes single phase flow in the reservoir and therefore cannot be used to predict e.g. water breakthrough.

• Deconvolution currently only works for single wells; i.e. it does not take into account the influence of nearby producers and injectors.

(These limitations do not prevent the use of deconvolution but need to be considered when examining results).

48

Conclusions

• With the availability of robust deconvolution, it is possible to

extract important information from well test data quickly and

easily prior to any further analysis or models.

• Uncertainty in the deconvolution carries through to uncertainty

in results.

• The deconvolved derivative provides the signature of the

dynamic behaviour of a well which can be extrapolated to

predict future well production.

• The late time derivative response defines the long term well

and reservoir performance.

• Permanent downhole pressure gauges allow continuous

updating of the deconvolution which reduces the uncertainty in

future well performance.

49

Summary

Tested volumes and future well production can be

estimated from pressure transient data prior to

building complex models.

Use the rate normalized log-log derivative plot to

compare the response between build-ups and

between wells…

Derivative Comparison – Oil and Water

50

1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 1E+5 1E+6

Time [hr]

1E-3

0.01

0.1

1

10

100

1000

Pre

ssure

[psi]

RubyJo #4 DST #1_standard_tmw.ks3 - Diagnosis (ref)

RubyJo #4 DST #2_standard_tmw.ks3 - Diagnosis

16-29a-15_tmw.ks3 - Diagnostic

17-12-4A_Working_File_tmw.ks3 - Main BU

20-6-3-DST1_TMW.ks3 - Diagnostic

DST1aCompleteSimplified_tmw.ks3 - Diagnostic

Guara-1 DST-1 Analysis-3_tmw.ks3 - Diagnostic

Jorbaer_DST3update_tmw.ks3 - Diagnostic

Peebs #1 (core hole) DST #2_tmw.ks3 - Diagnosis

RJS-628A_BG_TW_AllRates.ks3 - PostFrac PP

Compare files: Log-Log plot (dp and dp' normalized [psi] vs dt)

Derivative Comparison - Gas

51

1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 1E+5 1E+6

Time [hr]

1E+6

1E+7

1E+8

1E+9

1E+10

1E+11

1E+12

Gas p

ote

ntia

l [psi2

/cp]

A15_July 02 2010_tmw.ks3 - No Partial Completion

Bounty_DST1a2010.ks3 - GC Main (ref)

BUpMoran27-6_tmw.ks3 - Horizontal DP

BUpOdenHeirs_tmw.ks3 - Analysis 4

ca48Canal1_tmw_new.ks3 - Channel

DST1c.ks3 - Analysis 1

Hasdrubal A1_v2.ks3 - 1-P Closed

HBH-4DST_tmw_2.ks3 - Partial Completion + Increasing h

Horseshoe-1 Interpretation_TMW.ks3 - 3 Zones

PA_v17.ks3 - Analysis 14

Endeavour_NR_v11_tmw.ks3 - homogeneous

DAP-3_CR_July2010data_5sec data_1stSept2010.ks3 - Analysis 1

Compare files: Log-Log plot (dm(p) and dm(p)' normalized [psi2/cp] vs dt)