Rock Physics Models for Marine Gas Hydrates

Darrell A. Terry, Camelia C. Knapp, and James H. Knapp Earth and Ocean Sciences University 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

1.5

2 4 4.5

5

Comparisons with Jenkins’ Update

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

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

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996) Smooth Sphere (Walton, 1987) Alpha = 0.2 (Jenkins, 2005) 4.5

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996) Smooth Sphere (Walton, 1987) Alpha = 0.8 (Jenkins, 2005) 4 3.5

3 2.5

2 1.5

0 3 2.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Gas Hydrate Saturation (nondimensional) 0.8

0.9

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

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996) Smooth Sphere (Walton, 1987) Alpha = 0.2 (Jenkins, 2005) 1 3.5

3 2.5

2 1.5

0 3 2.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Gas Hydrate Saturation (nondimensional) 0.8

0.9

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

Rough Sphere (Walton, 1987; Dvorkin & Nur, 1996) Smooth Sphere (Walton, 1987) Alpha = 0.8 (Jenkins, 2005) 1 2 1.5

1 0.5

0 0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

Gas Hydrate Saturation (nondimensional) 0.8

0.9

1 1 0.5

0 0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

Gas Hydrate Saturation (nondimensional) 0.8

0.9

1

Baseline Model

• Hertz-Mindlin theory (Jenkins et al, 2005) • Effective dry-rock moduli (Helgerud, 2001)

Baseline Model

• Gassmann’s equations • Poisson’s ratio • Velocity equations • 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 GH GR

Model Configurations

• Pore-Fluid • Rock Matrix

Well Log Data

Track 19 (1) • • Mallik 2L-38 JIP Wells – Keathley Canyon – Atwater Valley 850 900 950 1000 1050 1000 1050 850 900 950 Track 19 (2) 1100 1100 1150 2 3 4 Compressional Velocity (km/s) 5 1150 0.5

1 1.5

Shear Velocity (km/s) (Data Digitized from Collett et al, 1999) 2

Well Log Data: Crossplot

Crossplot: P-Wave vs S-Wave 6 • • • • 5.5

Mallik 2L-38 5 4.5

Other logs for crossplots – Porosity 4 3.5

3 – Resistivity 2.5

2 – Gas Hydrate Saturation 1.5

0.5

Crossplots with third attribute Generate probability distribution functions (PDFs) 1 Shear Velocity (km/s) 1.5

2

MC-118 Stacking Velocities

WesternGeco Stacking Velocity, Profiles with Velocity Reversals WesternGeco Stacking Velocity, Profile Chart 28.89

28.88

28.87

28.86

28.89

28.88

28.87

28.86

• 28.85

28.85

28.84

28.84

28.83

-88.53 -88.52 -88.51

-88.5

-88.49 -88.48 -88.47 -88.46 -88.45

Longitude, degrees W 28.83

-88.53 -88.52 -88.51

-88.5

-88.49 -88.48 -88.47 -88.46

Longitude, degrees W -88.45

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

MC-118 Stacking Velocities

2 4 0 WesternGeco Stacking Velocities, Profile 63, Lon -88.4936, Lat 28.8479

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

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

2 4 2 4 6 8 6 8 6 8 10 10 10 12 1500 2000 2500 RMS, m/s 3000 3500 4000 12 1500 2000 2500 RMS, m/s 3000 3500 4000 12 1500 2000 2500 RMS, m/s 3000 3500 4000

Future Directions: Synthetic Seismic Models

Velocity Model 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 X (m) 600 700 800 900 1000 Synthetic CSG with Shot at 960 m 0.2

0.4

0.6

0.8

1 1.2

1.4

100 200 300 400 500 X (m) 600 700 800 900 1000 Reflectivity Model 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 X (m) 600 700 800 900 1000 Stacked Image for 96 Shot Gathers 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 X (m) 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

References

Dai, 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