Establishing Patterns Correlation from Time Lapse Seismic

Jianbing Wu[1], Andre Journel[1], Tapan Mukerji[2]

[1] Stanford Center for Reservoir Forecasting[2] Stanford Department of Geophysics

2

Objective

• Establish patterns correlation between seismic and water saturation variables

• Predict the water saturation field (future work)

3

Outline• The challenge of 4D seismic• The Stanford V reservoir• Flow simulation• Seismic amplitude simulation• Point-to-point correlation• Pattern correlation• Conclusions and future work

4

• 4D seismic can be used to detect fingering, monitor fluid movement, improve recovery and locate new wells

• Success stories are limited to clastic reservoirs, shallow reservoirs, some carbonate reservoirs and reservoirs with great density differentiation

• This study aims at establishing correlation between seismic and water saturation variables in intermediary less favorable cases

The challenge of 4D seismic

5

The challenge of 4D seismic (cont.)

t1=Jan.1, 2000 t2=Jan.1, 2002Overall correlation: -0.11yet excellent visual pattern correlation

Seismictimelapse

Watersaturationtimelapse

. . .

6

The Stanford V reservoir (Layer 2)

Clastic fluvial channels

Facies Proportion

mudstone 47%

sandstone 45%

crevasse 8%

injectorproducer

7

Introduction to Stanford V reservoir (cont.)

10130100 stratigraphic grid

t op

st r at i gr aphi ccoor di nat es

s=0

s=1

613m

1097m

283m

60m

dept h( t r ue coor di nat es)

0m

600m

1100m

Layer 2

bot t om of r eser voi r envel ope

t op of r eser voi r envel ope

dz=10m

10sub- l ayer sz( x, y, j )

z( x, y, i )

50130100 true depth grid

8

The Stanford V reservoir (cont.)

(md)

Channel sand 0.27 648

Crevasse 0.24 521

Mudstone 0.07 1.5

All layer 0.17 314

K

9

Flow simulation

Oil density 45API0

Pressure 1100psiTemperature 1800FWater viscosity 0.325cPGOR 850scf/STB

Reservoir parameters:

Initial water saturation:15.0Sw30.0Sw

in sandstone and crevasse

in mudstone

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Flow simulation (cont.)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

krw kro

rela

tive

pe

rme

ab

ility

water saturation0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

krw kro

rela

tive

pe

rme

ab

ility

water saturation

Relative permeability curves:

mudstone sandstone & crevasse

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Oil saturation field on Dec. 29, 2013 (before breakthrough)

Vertical Section at x=20

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Normal incidence 1D convolution model

with Fresnel zone lateral averaging

Seismic amplitude simulation

Seismic amplitude should be able to

distinguish velocity difference when

saturated with 100% brine vs. 100% oil

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Forward simulate seismic amplitude (cont.)

Sandstone Crevasse

Mudstone

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Fresnel zone: 225m

Horizontal resolution

Vertical resolution: 15m

Vertical section X=1 Initial ( Jan. 1, 2000)

lithofacies

Layer 2 mean thickness: 152m

Forward simulate seismic amplitude (cont.)Impedance

Amplitude

MudstoneCrevasseSandstone

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• Different volume supports

Seismic amplitude: Fresnel zone

Saturation: grid node

• Seismic amplitude shows vertical impedance contrast

Point-to-point correlation

. . .

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Point-to-point correlation (cont.)

L

l l

L

l ll SwSw

1

1

u

1,,,,,, kjiSwkjiSwkjiSwd

Colocated correlation between seismic amplitude and a vertical contrast of spatially averaged saturation values.

399 L total nodes within a moving window

with:

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Point-to-point correlation (cont.)

(Jan. 1, 2000)

seismic amplitude

vertical water contrast

Overall 3D colocated correlation: -0.20 poorbut excellent visual pattern correlation

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Spatial pattern correlation

Principal component analysis (PCA)Canonical analysis (CA)

1. Well understood, easy to apply

2. Linear combinations of data within 3D moving windows

3. PCA aims at max. within-window variance contribution

4. CA aims at defining pairs of max. correlated linear combinations

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Spatial pattern correlation (cont.)

Template sizes:

Seismic: only vertical

W 1(u,1)W 1(u,2)

W 1(u,7)

k-3k-2

k+3

Z

Water saturation: 3D

X

Y

Z

W 2(u,1),W 2(u,2),W 2(u,3)

W 2(u,4),W 2(u,5),W 2(u,6)

k-1

k

k+1W 2(u,7),W 2(u,8),W 2(u,9)

X

Y

u(i,j) i+2i-2

j+2

j-2

W (u,1): va lue a t

W (u,2): m ean va lue over

W (u,3): m ean va lue over

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Spatial pattern correlation (cont.)

3D correlation (space only) :

PCA applied to data recorded on Jan. 1, 2000:% within-template variance explained by 1st seismic PC: 84% 1st saturation difference PC: 84%Overall colocated correlation 0.39

PCA repeated on data recorded on Jan.1, 2002:correlation is 0.32

Correlation values improve, but still low!

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Spatial pattern correlation (cont.)

4D correlation:

PCA and CA performed on time lapse data:

time difference of seismic amplitude:

time difference of water saturation vertical contrast:

1212 ,,,,,,,,,, tkjiseistkjiseisttkjiseis

1212 ,,,,,,,,,, tkjidSwtkjidSwttkjisw

tkjiSwtkjiSwtkjidSw ,1,,,,,,,, with:

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Spatial pattern correlation (cont.)

1st PCseis

1st PCsw

t1=Jan.1, 2000 t2=Jan.1, 2004

Overall 4D correlation: 0.78 !! Significant

. . .

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Spatial pattern correlation (cont.)

1st CCseis

1st CCsw

t1=Jan.1, 2000 t2=Jan.1, 2004

Overall 4D correlation: 0.82 !! Significant

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seis

sw

t1=Jan.1, 2000 t2=Jan.1, 2004

Overall 4D correlation: 0.34

4D colocated point-to-point correlation

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• Colocated point-to-point correlation between seismic amplitude and water saturation variables is low because of different resolutions

Conclusions

• 1st PC and 1st CC can capture the spatial patterns of seismic and saturation time lapse variables

• High correlation between PC’s or CC’s can be used towards predicting saturations from time lapse seismic data

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Available data:

• Water saturation at well locations (hard) :

• Time lapse of seismic amplitude (soft) :

• Water saturation at present time obtained from a flow simulator :

Saturation prediction (Future work)

2,tSw u

tseis ,u

1,tSw u

ttt 12

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• Use as an external drift for kriging water saturation time lapse

21*

1021 ,,,, ttaattE SwSw uuuu with

1221 ,,,, tSwtSwttSw uuu

21*

12* ,,,, tttSwtSw Sw uuu

• Predict water saturation

Saturation prediction (Future work), cont.

• Predict time lapse by regression from known tseis ,u

tSw ,* u

*Sw

2121* ,,,, tttt SwSw uu locationswell:,

28

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amplitude diff. impedance diff.

Sw diff. pressure diff. (Mpa)

4 year time lapses of amp, imp, Sw and Pres. at vertical section X=20

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seis

sw

t1=Jan.1, 2000 t2=Jan.1, 2004

Original 1st PC 2nd PC

Correlation: 0.34 0.78 0.55