Rock Physics Models for Marine Gas Hydrates
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Rock Physics Models for Marine Gas Hydrates
Darrell A. Terry, Camelia C. Knapp, and James H. Knapp
Earth and Ocean SciencesUniversity 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
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)
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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
• Gassmann’s equations
• Velocity equations
• Poisson’s 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
GH
GR
GR GR
GR
GR GR
GR
GH
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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)
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)
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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)
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
)
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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
-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
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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
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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
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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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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.
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Model Configurations
• Partial Gas Saturation Models (for free gas)– Homogeneous Gas Saturation– Patchy Gas Saturation