An example of constraining well test interpretation with the help of seismic

ByHamidreza Hamdi

Patrick CorbettAndrew Curtis (Edinburgh Uni.)

Colin MacBeth

1

“Joint Interpretation of Rapid 4D Seismic with Pressure Transient Analysis”, EAGE/SPE EUROPEC 2010

Outline

• Overview of Well Testing– Information obtained from well test– Importance of Model recognition

• An integration example– Stratigraphic discontinuity detection (4D seismic)– Numerical well-test interpretation

• Deterministic approach• Inverse approach

• Conclusions

2

Information obtained from well testing

• Reservoir Description– Permeability (horizontal and

vertical)

– Heterogeneities(fractures, layering, change of properties)

– Boundaries (distance to boundaries and shape)

– Pressure (initial and average)

3

• The inverse problem

• Model recognition (S)– Well test models are

different from the geomodels in the sense that they are dynamic models and also it’s an averagemodel.

Q vs t

Reservoir

P vs t

Well test transient pressure response plot

4

wb

wb wb

DD i

BU

P P P tP P t P t

∆ =∆ = ∆ =

- ( )( ) - ( 0)

∆P’=∂P/∂SupT for General multirate∆P’= ∂P/∂(LogT) for Draw-down∆P’= ∂P/∂[(tp+∆t)/∆t] for Build-up

∂P/∂

SupT

Time, hrLog

Log

Kh

∆p S=skin

Wellbore

Reservoir

Properties Boundaries

=f(rate and time)The trend of pressure derivative curve is important :1. Slope Flow regime indicator2. Value at stabilization =f(permeability, thickness, porosity, rate, viscosity and Bo)3. The separation of ∆P and ∂P/∂SupT indication of Skin( change of permeability in very near well bore area)

Importance of model recognition

5

∂P/∂SupT

Time

Log

Log

1. Linear barrier ( Fault, pinch-out, unconformity,...) 2. Composite reservoir (Linear /radial)

Porosity, Permeability, compressibility, viscosity and thickness change across an interface

Note: Transition is ,sometimes, quite long and make it even more difficult to interpret the test

Transition K2h, S, or Fault

K1h, S

∆p

outline

• Overview of Well Testing– Information obtained from well test– Uncertainty in model recognition

• An Integration Example– Stratigraphic discontinuity detection (4D seismic)– Numerical well-test Interpretation

• Deterministic approach• Inverse Approach

• Conclusions

6

7

Static DynamicWell test 4D seismic3D seismic

Resolution +noise+ throw

Flow effect Flow effect resolution +noise +P-effect

Some issues

1.Permanent seismic2.VSP- permanent data sensors3.Short interval surface seismicmonitoring

Surface seismicRequirements

Normal faults

Reverse faults

Strike-slip faults

Meandering(connectivity)

Transient Well testing and seismic :Exploration stage - seismic helps in WT interpretation

4D seismic capability of detecting a no-flow boundary

8

∆P Pw

4D seismic detectability

∆P>200 psi

Time

Radius

∆P4D seismic

detectability∆P>200 psi

P

Fault illumination by 4D seismic with time

t1 t2 t3

r =L

9

Time lapse monitoring of transient well test response

+∞-∞

L L

L

L2f

L= distance to no-flow boundaries2f= illuminated part of the no-flow boundaries( Distinguished length of boundary by 4D signal)f=n*L , n=0,1,...,5

Active wellImage well

2

_

1 0 1 02 2 2

1 10

( , ) ( , )

( ) ( ) ( ) ( )2 (1 )2 [ ( ) ( )]

D

active well i

u t

P r t P P r t

J u Y ur Y u J urq e duT u J u Y uπ π

∞−

∆ = − =

−−

+∫

1( , ) ( , )T i

iP r t P r t

∞

=

∆ = ∆∑

w

rrr

= 2Dw

ttrη

=2

4ru

tη=

1. Single Flow boundary at distance “L”2. Single no-flow boundary at distance “L23. Two parallel no-flow boundaries (“2L”)

We then try :

Required lapsed time from base seismic to monitor in order to illuminate a specified part of the boundaries

10

56 112.37280.93

561.865

955.171

1460.85

0200400600800

1000120014001600

0 1 2 3 4 5 6

Time,hr

Illuminated section index, FIIlluminated length (ft)=FI*200

Single flow boundaryL=100ft

5.51 11.0327.07

55.15

93.75

143.397

020406080

100120140160

0 1 2 3 4 5 6

Time,hr

Illuminated section index, FIIlluminated length (ft)=FI*200

Single no-flow boundary

L=100ft

3.85.84

9.84

14.63

19.94

25.78

0

5

10

15

20

25

30

0 1 2 3 4 5 6

Time,hr

Illuminated section index, FIIlluminated length (ft)=FI*200

Parallel no-flow boundaries

2L=200ftSingle draw-downq=1500 STBDф=0.18h=100 ftμ=1.5 cpBo=1.25L=100 ft∆P=200 psia

2f=2L =200 ft

L=100 ft

FI=1Illuminated length= 0.5*1/100=200 ft

An Integration Example

∆P=200 psia

Required lapsed time from base seismic to monitor in order to illuminate a specified part

of the boundaries (sensitivity to permeability)

11

11.8 15.7 22.82 30.839.43

48.6758.5

42 46.2 52.41 59.1 65.8 72.77 80

141.6 145.25 151.35 157.65 164.1 170.42 176.9

020406080

100120140160180200

0 2 4 6 8

Time,hr

Illuminated section index, FIIlluminated length (ft)=FI*200

Parallel no-flow boundariessensitivity to permeability

K=45md

K=200md

K=700md

Single draw-downq=1500 STBDф=0.18h=100 ftμ=1.5 cpBo=1.25L=100 ft∆P=400 psia

Time Scale Practicality

<1-2 Days Inter-Survey

2 Days to 1 Month Not practical due to cost

1 to 3 Month Permanent survey

1 to 3 Years Surface seismic

Well testing and Seismic Example

• Seismic can help well test interpretation– Major Faults (3D Seismic)

– Sub-seismic faults (3D & 4D)

– Permeability baffles (4D)

• Numerical well test interpretation– Deterministic permeability profile+ seismic

– Inverse mobility and diffusivity map +seismic• Laplacian operator as a sectorization operator

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Numerical Well Testing

Is the deviation is related to Faults, Boundaries or M contrast?

Commingled braided Fluvial reservoir (Complex pressure

response)

How to limit our well test interpretation based on the available seismic data?

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WELL-AX

Z

Y

0 250 500 750 1000

PERMX

Major faults

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100 1000

PRES

SURE

& P

RESS

URE

DER

IVA

TIV

E

TIME,hr

Complicated Pressure Response

Quarter Slope

Half Slope

UnitSlope

1. Channel behaviour? Too short?2. Derivative trend between 1/4 and 1/5 ? 3. Structural Framework or property effect?4. Validation of Interpretation

1

10

100

1000

0.001 0.01 0.1 1 10 100

∆P &

d∆P

/dln

t

Time,hr

Far Parallel faults

Near Parallel fault

0.5 Slope

Idea: Can seismic help in Interpretation: Synthetic seismic

14Without K-bafflesWith K-baffles

RMS amplitude map of 4D response

1. No-flow boundary2. Pressure effect on 4d seismic

A monitor as close to the end of test

To detect:

We need:

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m*=∂P/∂lnt

Ki (t)h=qμB/m*Radius of investigation

2

1 2 1( )

ri

i i rw

rdrk r k r= ∫

∆P’

t t /r

Ki

Instantaneous permeability

Deterministic well test permeability profile

Few

ft

1000

ft

0.032invt

ktrcϕµ

=

Well test composite regions

Seismic “bin”

Well test investigation radius: few ft to ∞Seismic bin size ~ 82 ft

A. Seismic Integration Into WT interpretation:Deterministic approach

P’

t

K

R

K-Map

K-Map & Seismic Structure

P’

t

GriddingSingle-Phase Sim.

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A. Seismic Integration Into WT interpretation:Deterministic approach- Matching...

1. Poor quality of match at least before fault effect2. Permeability (or M ratio)of each sector is within the range

used in the reservoir modelling (<1000 md) and obtained based on the MYA

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An Integration Example

B. Seismic Integration Into WT interpretation:Seismic Sector MAP

P’

t

P’

t

Tested well

Tested well

Sector-Map & Seismic Structure∆RSM-A

Sector-Map & Seismic Structure

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GriddingSingle-Phase Sim.

Base K =190md

1. Good quality of match2. Permeability (or M ratio)of each sector is within the range

used in the reservoir modelling (<1000 md)

B. Seismic Integration Into WT interpretation:(Seismic Sector MAP)-Matching...

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( / )( / )

t b

t i

kh cDkh c

φµφµ

=

( / )( / )

b

i

khMkh

µµ

=

50 100 150 200 250

50

100

150

200

250

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

50 100 150 200 250

50

100

150

200

250 -2

-1

0

1

2

3

4

5

B. Seismic Integration Into WT interpretation : sectorization by Laplacian

1. Laplacian is Local average operator: If Laplacian is positive then is locally less than the nearby average value.

2. Laplacian shows the front of higher changes!

3. It can be used as a reagonidentifier to be used in sector composite map (NWT)

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outline

• Overview of Well Testing– Information obtained from well test– Uncertainty in model recognition

• An Integration Example– Stratigraphic discontinuity detection (4D seismic)– Numerical well-test Interpretation

• Deterministic approach• Inverse Approach

• Conclusions

21

Conclusion

• Well test interpretation was constrained• Larger faults mapped out using 3D & 4D seismic • Permeability baffles were realized by 4D signal• Numerical well testing was performed using the information

from seismic data – reduce the uncertainty in model detection

• 4D& 3D seismic help sectorize the map used in numerical well testing software

• reasonable match obtained by integration of numerical well testing and seismic

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Acknowledgements

• Schlumberger

• Weatherford

• Kappa

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References

• Boutad de la Comb, J.L., Akinwunmi, O., 2005. Use of DST for effective dynamic appraisal: case studies from deep offshore west Africa and associated methodology, SPE 97113

• Gringarten, A., 2009. From straight lines to deconvolution - the evolution of the state-of-the-art in well test analysis, EAGE/SPE joint workshop of well testing and seismic, Berlin

• Feitosa,G.S., Lifu, C., Thompson, L.G. and Reynolds, A.C.,1994. Determination of permeability distribution from well-test pressure data, SPE 26047

• MacBeth, C., Floricich, M. and Soldo, J., 2005. Going quantitative with 4D seismic analysis, Geophysical Prospecting, 54, 303–317

• Sahni, A., Kelsch, K., Samorn, H., Boonmeelapprasert, C., 2007. Integrating pressure transient test data with seismic attribute analysis to characterize an offshore fluvial reservoir, SPE 110272

• Zheng, S.Y, Corbett, P.W.M. and Emery, A., 2003.Geological interpretation of well test analysis: case study from a fluvial reservoir in the gulf of Thailand, Journal of Petroleum Geology, Vol. 26(1)

• Zheng, S.Y, Legrand,V.M. and Corbett, P.W.M. ,2007. Geological model evaluation through well test simulation: a case study from the Wytch Farm oilfield, southern England, Journal of Petroleum Geology, Vol. 30(1), pp 41-58

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