Rock Physics Models for Marine Gas Hydrates

Darrell A. Terry, Camelia C. Knapp, and James H. Knapp

Earth and Ocean SciencesUniversity of South Carolina

Long Range Research Goals

• Further develop statistical rock physics to associate seismic properties with lithology in marine gas hydrate reservoirs

• Investigate AVO and seismic attribute analysis in a marine gas hydrate reservoir

• Analyze anistropic seismic properties in a marine gas hydrate reservoir to delineate fracture structures and fluid flow pathways

Outline

• What is Rock Physics?• Models Used by JIP• Brief Theoretical Background• Recent Updates Suggested for Models• Candidate Models to Use• Role of Well Log Data• Future Directions

What is Rock Physics?

• Methodology to relate velocity and impedance to porosity and mineralogy

• Establish bounds on elastic moduli of rocks– Effective-medium models – Three key seismic parameters

• Investigate geometric variations of rocks– Cementing and sorting trends– Fluid substitution analysis

• Apply information theory– Quantitative interpretation for texture, lithology, and

compaction through statistical analysis

Models Used by JIP

(from Dai et al, 2004)

Models Used by JIP

(from Dai et al, 2004)

Theoretical Background

Effective-medium models for unconsolidated sediments

• Mindlin, 1949 (Hertz-Mindlin Theory)• Digby, 1981; Walton, 1987• Dvorkin and Nur, 1996• Jenkins et al, 2005• Sava and Hardage, 2006, 2009• Dutta et al, 2009

Theoretical Background

(from Walton, 1987)

(from Mindlin, 1949)

Theoretical Background

Modifications for saturation conditions and presence of gas hydrates

• Dvorkin and Nur, 1996• Helgerud et al, 1999; Helgerud, 2001

Why Use Jenkins’ Update?

• Hertz-Mindlin theory often under predicts Vp/Vs ratios in comparison with laboratory rocks and well log measurements (Dutta et al, 2009) for unconsolidated sediments.

• A similar problem is noted in Sava and Hardage (2006, 2009).

• Additional Degree-of-Freedom

Comparisons with Jenkins’ Update

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.5

2

2.5

3

3.5

4

4.5

5 Critical Porosity = 0.4, n = 8.5, Pressure = 2 MPa, Porosity = 0.4

Gas Hydrate Saturation (nondimensional)

Sat

-roc

k P

-wav

e V

eloc

ity (

km/s

)

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996)

Smooth Sphere (Walton, 1987) Alpha = 0.2 (Jenkins, 2005)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.5

2

2.5

3

3.5

4

4.5

5 Critical Porosity = 0.4, n = 8.5, Pressure = 2 MPa, Porosity = 0.4

Gas Hydrate Saturation (nondimensional)

Sat

-roc

k P

-wav

e V

eloc

ity (

km/s

)

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996)

Smooth Sphere (Walton, 1987) Alpha = 0.8 (Jenkins, 2005)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3 Critical Porosity = 0.4, n = 8.5, Pressure = 2 MPa, Porosity = 0.4

Gas Hydrate Saturation (nondimensional)

Sat

-roc

k S

-wav

e V

eloc

ity (

km/s

)

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996)

Smooth Sphere (Walton, 1987) Alpha = 0.8 (Jenkins, 2005)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3 Critical Porosity = 0.4, n = 8.5, Pressure = 2 MPa, Porosity = 0.4

Gas Hydrate Saturation (nondimensional)

Sat

-roc

k S

-wav

e V

eloc

ity (

km/s

)

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996)

Smooth Sphere (Walton, 1987) Alpha = 0.2 (Jenkins, 2005)

Baseline Model

• Hertz-Mindlin theory (Jenkins et al, 2005)

• Effective dry-rock moduli (Helgerud, 2001)

Baseline Model

• Gassmann’s equations

• Velocity equations

• Poisson’s ratio

• Bulk density

Model Configurations

• Gas Hydrate Models (for solid gas hydrate)– Rock Matrix (Supporting Matrix / Grain)– Pore-Fluid (Pore Filling) Rock Matrix Pore-Fluid

GH

GR

GR GR

GR

GR GR

GR

GH

Model Configurations

• Pore-Fluid • Rock Matrix

Well Log Data

• Mallik 2L-38• JIP Wells

– Keathley Canyon– Atwater Valley

(Data Digitized from Collett et al, 1999)

2 3 4 5

850

900

950

1000

1050

1100

1150

Track 19 (1)

Compressional Velocity (km/s)

Dep

th (

m)

0.5 1 1.5 2

850

900

950

1000

1050

1100

1150

Track 19 (2)

Shear Velocity (km/s)

Dep

th (

m)

Well Log Data: Crossplot

• Mallik 2L-38• Other logs for crossplots

– Porosity– Resistivity– Gas Hydrate Saturation

• Crossplots with third attribute• Generate probability

distribution functions (PDFs)

0.5 1 1.5 21.5

2

2.5

3

3.5

4

4.5

5

5.5

6 Crossplot: P-Wave vs S-Wave

Shear Velocity (km/s)

Com

pres

sion

al V

eloc

ity (

km/s

)

MC-118 Stacking Velocities

• WesternGeco: locations of stacking velocity profiles for 3D stack– 253 profiles– Spaced 40 CMPs apart, inline and crossline– Convert to interval velocities

-88.53 -88.52 -88.51 -88.5 -88.49 -88.48 -88.47 -88.46 -88.45

28.83

28.84

28.85

28.86

28.87

28.88

28.89

WesternGeco Stacking Velocity, Profiles with Velocity Reversals

Longitude, degrees W

Lat

itude

, de

gree

s N

-88.53 -88.52 -88.51 -88.5 -88.49 -88.48 -88.47 -88.46 -88.45

28.83

28.84

28.85

28.86

28.87

28.88

28.89

WesternGeco Stacking Velocity, Profile Chart

Longitude, degrees W

Lat

itude

, de

gree

s N

MC-118 Stacking Velocities

1500 2000 2500 3000 3500 4000

0

2

4

6

8

10

12

WesternGeco Stacking Velocities, Profile 81, Lon -88.4937, Lat 28.8543

RMS, m/s

Two-w

ay Tra

vel Ti

me, s

1500 2000 2500 3000 3500 4000

0

2

4

6

8

10

12

WesternGeco Stacking Velocities, Profile 63, Lon -88.4936, Lat 28.8479

RMS, m/s

Two-w

ay Tra

vel Ti

me, s

1500 2000 2500 3000 3500 4000

0

2

4

6

8

10

12

WesternGeco Stacking Velocities, Profile 101, Lon -88.4938, Lat 28.8607

RMS, m/s

Two-w

ay Tra

vel Ti

me, s

Future Directions: Synthetic Seismic Models

Velocity Model

X (m)

Y (

m)

100 200 300 400 500 600 700 800 900 1000

100

200

300

400

500

600

700

800

900

1000

Reflectivity Model

X (m)

Y (

m)

100 200 300 400 500 600 700 800 900 1000

100

200

300

400

500

600

700

800

900

1000

Synthetic CSG with Shot at 960 m

X (m)

Tim

e (s

)

100 200 300 400 500 600 700 800 900 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

X (m)

Y (

m)

Stacked Image for 96 Shot Gathers

100 200 300 400 500 600 700 800 900 1000

100

200

300

400

500

600

700

800

900

1000

Future Directions

• Create Rock Physics Templates• Amplitude Variation with Offset (AVO)• Seismic Inversion (WesternGeco data, Pre-Stack

Gathers)– Acoustic impedance– Elastic Impedance– Attribute analysis

• Assign Lithology and Estimate Gas Hydrate Probabilities Based on Information Theory

ReferencesDai, J.; Xu, H.; Snyder, F.; Dutta, N.; 2004. Detection and estimation of gas hydrates using rock physics seismic inversion:

Examples from the northern deepwater Gulf of Mexico. The Leading Edge, January 2004, p. 60-66.Digby, P. J.; 1981. The effective elastic moduli of porous granular rocks. J. Appl. Mech., v. 48, p. 803-808.Dutta, T.; Mavko, G.; Mukerji, T.; 2009. Improved granular medium model for unconsolidated sands using coordination

number, porosity and pressure relations. Proc. SEG 2009 International Exposition and Annual Meeting, Houston, p. 1980-1984.

Dvorkin, J.; Nur, A.; 1996. Elasticity of high-porosity sandstones: Theory for two North Sea data sets. Geophysics, v. 61, p. 1363-1370.

Helgerud, M. B.; Dvorkin, J.; Nur, A.; Sakai, A.; Collett, T.; 1999. Elastic-wave velocity in marine sediments with gas hydrates: Effective medium modeling. Geophys. Res. Lett., v. 26, n. 13, p. 2021-2024.

Helgerud, M. B.; 2001. Wave Speeds in Gas Hydrate and Sediments Containing Gas Hydrate: A Laboratory and Modeling Study. Ph.D. Dissertation, Stanford University, April 2001.

Jenkins, J.; Johnson, D.; La Ragione, L.; Maske, H.; 2005. Fluctuations and the effective moduli of an isotropic, random aggregate of identical, frictionless spheres. J. Mech. Phys. Solids, v. 53, pp. 197-225.

Mindlin, R. D.; 1949. Compliance of elastic bodies in contact. J. Appl. Mech., v. 16, p. 259-268.Sava, D.; Hardage, B.; 2006. Rock physics models of gas hydrates from deepwater, unconsolidated sediments. Proc. SEG

2006 Annual Meeting, New Orleans, p. 1913-1917.Sava, D.; Hardage, B.; 2009. Rock-physics models for gas-hydrate systems associated with unconsolidated marine

sediments. In: Collett, T.; Johnson, A.; Knapp, C.; Boswell, R.; eds. Natural gas Hydrates – Energy Resource Potential and Associated Geologic Hazards. AAPG Memoir 89, p. 505-524.

Walton, K.; 1987. The effective elastic moduli of a random packing of spheres. J. Mech. Phys. Solids, v. 35, n. 2, pp. 213-226.

Model Configurations

• Partial Gas Saturation Models (for free gas)– Homogeneous Gas Saturation– Patchy Gas Saturation