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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

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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

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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

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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

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Models Used by JIP (from Dai et al, 2004)

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Models Used by JIP (from Dai et al, 2004)

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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

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Theoretical Background (from Walton, 1987) (from Mindlin, 1949)

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Theoretical Background Modifications for saturation conditions and presence of gas hydrates Dvorkin and Nur, 1996 Helgerud et al, 1999; Helgerud, 2001

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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

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Comparisons with Jenkins Update

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

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Baseline Model Gassmanns equations Velocity equations Poissons ratio Bulk density

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

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Model Configurations Pore-Fluid Rock Matrix

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Well Log Data Mallik 2L-38 JIP Wells – Keathley Canyon – Atwater Valley (Data Digitized from Collett et al, 1999)

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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)

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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

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MC-118 Stacking Velocities

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Future Directions: Synthetic Seismic Models

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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

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References Dai, J.; Xu, H.; Snyder, F.; Dutta, N.; 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 Digby, P. J.; The effective elastic moduli of porous granular rocks. J. Appl. Mech., v. 48, p Dutta, T.; Mavko, G.; Mukerji, T.; Improved granular medium model for unconsolidated sands using coordination number, porosity and pressure relations. Proc. SEG 2009 International Exposition and Annual Meeting, Houston, p Dvorkin, J.; Nur, A.; Elasticity of high-porosity sandstones: Theory for two North Sea data sets. Geophysics, v. 61, p Helgerud, M. B.; Dvorkin, J.; Nur, A.; Sakai, A.; Collett, T.; Elastic-wave velocity in marine sediments with gas hydrates: Effective medium modeling. Geophys. Res. Lett., v. 26, n. 13, p Helgerud, M. B.; Wave Speeds in Gas Hydrate and Sediments Containing Gas Hydrate: A Laboratory and Modeling Study. Ph.D. Dissertation, Stanford University, April Jenkins, J.; Johnson, D.; La Ragione, L.; Maske, H.; Fluctuations and the effective moduli of an isotropic, random aggregate of identical, frictionless spheres. J. Mech. Phys. Solids, v. 53, pp Mindlin, R. D.; Compliance of elastic bodies in contact. J. Appl. Mech., v. 16, p Sava, D.; Hardage, B.; Rock physics models of gas hydrates from deepwater, unconsolidated sediments. Proc. SEG 2006 Annual Meeting, New Orleans, p Sava, D.; Hardage, B.; 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 Walton, K.; The effective elastic moduli of a random packing of spheres. J. Mech. Phys. Solids, v. 35, n. 2, pp

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

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