Fluid substitution for an HTI medium

Long Huang, Nikolay Dyaur and Robert Stewart University of Houston

Samik Sil ConocoPhillips

HoustonMay 16, 2013

OutlineMotivation 3D printed models fractured rocks, anisotropy and fluid substitution 4D time lapse seismic

Experiments 3D printed model, velocity measurements, fluid substitution experiments

Theory anisotropic Gassmann’s equations (recast for an HTI medium)

Discussion experiment results versus theoretical predictions

Conclusions2

3D printing

3

We are the first generation of geophysicists to use 3D printed models!

How it prints and where are the pores?

6

pore space

3D printed models

51 mm

51 mm

51 mm

HTI model

VTI model

5

Rotation experiments

7

VTI model

Transducer: 500 kHz horizontal componentpolarization vector

HTI model

00 4590

7

HTI model VTI model0 360 0 360

polarization polarization

TP

TS1TS2

TP

TS1TS2

180 180

time time

Velocity variation with polarization

shear wave splittingslightly splitting, slightly orthorhombic

• How velocity will change after saturation? (P-wave, S-wave?)• How can we theoretically predict the changes? (Gassmann’s equations? isotropic or anisotropic? VTI, HTI, orthorhombic? Hudson’s model? Linear slip model? GSA?)• Why do we care? (simulating 4D time lapse seismic!)

8

What if we saturate the models?

Recast Gassmann’s equations

9

21-KK-K/

12Cmflm

2

11

dryisoN

dryisoflm

dryisoN

dryisom

Nsat

KKKKKKK

21-KK-K/

22

12Cmflm

2

2

2

33

dry

isoNdryisoflm

dryisoN

dryisomNsat

KKKKKKK

satC44Dry term Fluid term TsatC 155

/9C-KK-K/

3/3/

ppqqmflmijkl dry

flm

dryklijm

dryijijmdry

ijklsat

KKCKCK

CC

(Gassmann, 1951)

linear slip model (Schoenberg and Sayers, 1995)

New!

Parameter estimation

10

21-KK-K/

12Cmflm

2

11

isoNisoflm

isoNisomN

sat

KKKKKKK

isoK，，

MZMZ NNN 1

TN ZZ 21

4455 11 CCZT

2M

,,,, 21 SSP VVV(Sil et al., 2013)(Hsu and Schoenberg, 1993)

(Sayers and Kachanov, 1995)

Well logs:

Fluid substitution experiment (HTI model)

11

air pumpwaterHTI model

vacuum

air

Fluid substitution

12

0polarization

TS1TS2

0 360polarization

time

TP

TS1TS2

180

time

180dry saturated

TP

360

Velocity measurement from sides

13

0180

90

45135

225

270

315

symmetryaxis

S1

S2

polarization vector

transmission measurements with every 45-degree azimuth

P-wave velocity measurement: 500 kHz vertical component transducerS-wave velocity measurement: 500 kHz horizontal component, polarized in two orthogonal directions

1.6

1.7

1.8

030

60

90

120

150180

210

240

270

300

330

1.6

1.7

1.8

dry saturated

We see 2% - 4.6% increase in P-wave velocity

Vp (k

m/s

)

P-wave velocity change after saturation

14

0

180

90

45

135225

270

315

S-wave velocity change after saturation

15

VS1 and VS2 before saturation

0.6

0.7

0.8

0.90

30

60

90

120

150180

210

240

270

300

330

0.6

0.7

0.8

0.9

Vs1 dry Vs2 dry

0.6

0.7

0.8

0.90

30

60

90

120

150180

210

240

270

300

330

0.6

0.7

0.8

0.9

Vs1 Satur. Vs2 Satur.

VS1 and VS2 after saturation

Vs (k

m/s

)

Black denotes fast shear-wave (VS1)Red denotes slow shear-wave (VS2)

S-wave velocity change after saturation

16

Vs (k

m/s

)

0.6

0.7

0.8

0.90

30

60

90

120

150180

210

240

270

300

330

0.6

0.7

0.8

0.9

Vs2 dry Vs2 Satur.

0.6

0.7

0.8

0.90

30

60

90

120

150180

210

240

270

300

330

0.6

0.7

0.8

0.9

Vs1 dry Vs1 Satur.

VS1 VS2

Black denotes dry Red denotes saturated

about 1.2% decrease about 1.6% decrease

Theoretical predictions for the HTI model

17

Density increases about 4% after water saturation, which contributes about 2% decrease in velocity

ConclusionsInnovative physical models - print any structure with 3D printing - cheap and fast.Rich anisotropic response - transverse isotropic symmetry - clear shear wave splittingNew equations - Gassmann’s equations for an HTI medium - predict better results for fluid substitution.

18

Acknowledgement

• Allied Geophysical Laboratories, UH

• Dr. Robert Sheriff and SEG

• ConocoPhillips

• Bode Omoboya, Tao Jiang and all the other AGL members

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