Fluid substitution effects on seismic anisotropy

Long Huang, Robert Stewart, Samik Sil, and Nikolay Dyaur

HoustonApril 2nd, 2014

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Outline Motivation Natural fractures and anisotropy, fluid effects

Theory and methods Anisotropic Gassmann’s equations, parameterize, recast Gassmann’s equations

Discussions P- & S-wave moduli and velocities, Thomsen’s parameters, azimuthal amplitude variation

Conclusions

2

X

ZY

Orthorhombic

Beautiful fractured Atoka Sandstone at Natural Dam.

(Liner, 2013)

X

YZ

HTI (http://www.rechproject.com/related-project.html)

The deformation in carbonates rocks

How to characterize these fractured rocks?How would fluid influence their physical properties?How about seismic anisotropy with different fluids?

Fractures

3

(Huang et al., 2013)

Theory

4

X

YZ

2

1 22

11 1 21 2

m fl m

1 -2

2 1/ K -K K - 1

2

drym iso N N

satN N dry

dry iso N Nm fl iso

K KC r

KK K K

11 12 13

12 22 23

13 23 331 1 2 2

44

55

66

0 0 00 0 00 0 0

( , , , , , )0 0 0 0 00 0 0 0 00 0 0 0 0

ORTij N T N T

C C CC C CC C C

C fC

CC

(Schoenberg, 1980; Schoenberg and Sayers, 1995;Bukulin et al., 2000)

Dry term Fluid term (Gassmann, 1951)

2

m fl m/ K -K K -Kmsat

m fl

K KK K

K K

3,2,1,,,,

/9C-KK-K/3/3/

pqmflmij

ji

KKCKCK

CCflm

jmimij

sat

Dry term Fluid term (Gassmann, 1951)

5

44 21satTC

55 11satTC

1 266

1 2

1 11

T Tsat

T T

C

2

1 22

11 1 21 2

m fl m

1 -2

2 1/ K -K K - 1

2

drym iso N N

satN N dry

dry iso N Nm fl iso

K KC r

KK K K

2

1 22

22 1 21 2

m fl m

1-2

2 1/ K -K K - 1

2

drym iso N N

satN N dry

dry iso N Nm fl iso

K KC r

KK K K

2

1 22 2

33 1 21 2

m fl m

1-2 2

2 1/ K -K K - 1

2

drym iso N N

satN N dry

dry iso N Nm fl iso

K KC r r

KK K K

The complete recipe

Gas to brine substitution: S-waves

Shear-wave moduli are independent of fluid type Shear-wave velocities depend on fluid type due to density change

1 20.5, 0.1T T

44 44 21sat dryTC C

55 55 11sat dryTC C

1 266 66

1 2

1 11

T Tsat dry

T T

C C

Φ=5%

Φ=25%

Red is for gasBlue is for brine

Φ=5%

Φ=5%

Φ=25%Φ=25%

6

Gas to brine substitution: P-wave

Φ=5%

Φ=25%

7

Porosity (φ) Δ C11 Δ C22 Δ C33

5% 38% 5% 2%25% 56% 23% 19%Porosity (φ) Δ Vpx Δ Vpy Δ Vpz

5% 16% 1% 0%25% 19% 6% 4%

Φ=5%

Φ=25%

Red is for gasBlue is for brine

Fluid substitution effects on P-wave are anisotropic

P-wave moduli of high-porosity sands are more sensitive to fluids

Vertical P-wave velocity of low-porosity sands is constant with fluids

X

YZ

Φ=5% Φ=5%

Φ=25%Φ=25%

gas gas

gasgas

brine brine

brinebrine

Porosity (φ) Δ ε1 Δ δ1 Δ ε2 Δ δ2

5% -22% -9% -5 % -35 %25% -30% -20% -13% -31%

Gas to brine substitution: Thomsen’s parameters

Shear-wave splitting (γ) is independent on fluids Both ε and δ are sensitive to fluids

(1)2

(1)2 2

(1)2

2 1 ,

2 [ 1 2 ],N

N T

T

g g

g g

(2)1

(2)1 1

(2)1

2 1 ,

2 [ 1 2 ],N

N T

T

g g

g g

(1)

(2)

(Bakulin et al., 2000)

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Φ=5%Φ=25%

Red is for gasBlue is for brine

X

YZ

X

ZY

(1) (1) (1), ,

(2) (2) (2), ,

YZ plane XZ plane

brine

brine

gas

gas

Porosity (φ) Δ AVAZ (30°)5% 12%25% -6%

Gas to brine substitution: AVAZ

High-porosity: gas sands have more azimuthal amplitude variations Low-porosity: wet sands have more azimuthal amplitude variations

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Shale

Sandstone

X (0°)Y (90°)P-wave reflectivity

(180°)

(Rpp calculated from Václav Vavryčuk and Ivan Pšenčík, 1998)(Azimuth versus incidence angle)

Future work: experiments with 3D printed models

Shear-wave splitting in both directions implies it’s slightly orthorhombic material.

(Huang et al., 2013)

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3D printed cube with penny-shaped cracks.

Extended Gassmann’s equations for an orthorhombic medium

Shear rigidity and splitting are independent on fluid type, but not shear-wave velocity

Fluid substitution effects are anisotropic

Vertical P-wave velocity of low-porosity sands is constant with fluids

High-porosity gas sands or low-porosity wet sands, have more azimuthal amplitude variations

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Conclusions

Acknowledgement

• Allied Geophysical Laboratories, UH

• Dr. Robert Sheriff and SEG Foundation

• UH adjunct and research professors: Dr. Leon Thomsen and Dr. Colin Sayers

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Thank you!

Questions?