fluid substitution for an hti medium
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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
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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
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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.
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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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