Abstract
Pore structure and mineral matrix elastic moduli are indispensable in rock physics models. We propose an estimation method of pore structure and mineral moduli based on Kuster-Toksöz model and Biot’s coefficient. In this technique, pore aspect ratios of five different scales from 100 to 10−4 are considered, Biot’s coefficient is used to determine bounds of mineral moduli, and an estimation procedure combined with simulated annealing (SA) algorithm to handle real logs or laboratory measurements is developed. The proposed method is applied to parameter estimations on 28 sandstone samples, the properties of which have been measured in lab. The water saturated data are used for estimating pore structure and mineral moduli, and the oil saturated data are used for testing these estimated parameters through fluid substitution in Kuster-Toksöz model. We then compare fluid substitution results with lab measurements and find that relative errors of P-wave and S-wave velocities are all less than 5%, which indicates that the estimation results are accurate.
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References
Ament, W. (1953), Sound propagation in gross mixtures, J. Acoustic Soc. Am. 25, 638–641, DOI: 10.1121/1.1907156.
Anselmetti, F., and G.P. Eberli (1999), The velocity-deviation log: A tool to predict pore type and permeability trends in carbonate drill holes from sonic and porosity or density logs, AAPG Bull. 83, 3, 450–466.
Bakhorji, A., H. Mustafa, S. Aramco, and P. Avseth (2012), Rock physics modeling and analysis of elastic signatures for intermediate to low porosity. In: 82nd Annual International Meeting, SEG, Technical program expanded abstracts, 1–5.
Berryman, J. (1980), Long-wavelength propagation in composite elastic media, J. Acoust. Soc. Am. 68, 1809–1831.
Berryman, J. (1995), Mixture theories for rock properties. In: T.J. Ahrens (ed.), Rock Physics and Phase Relations: A Handbook of Physical Constants, American Geophysical Union, Washington, D.C., 205–228, DOI: 10.1029/RF003p0205.
Budiansky, B. (1965), On the elastic moduli of some heterogeneous materials, Mech. Phys. Solids 13, 4, 223–227, DOI: 10.1016/0022-5096(65)90011-6.
Cleary, C., G. Coates, and J. Dumanoir (1984), Theoretical and experimental bases for the dual-water model for interpertation of shaley sands, Soc. Petrol. Eng. J. 24, 153–168, DOI: 10.2118/6859-PA.
Eshelby, J. (1957), The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. London A241, 1226, 376–396, DOI: 10.1098/rspa.1957.0133.
Gassmann, F. (1951), Elastic waves through a packing of spheres, Geophysics 16, 4, 673–682, DOI: 10.1190/1.1437718.
Hadley, K. (1975), Comparison of calculated and observed crack densities and seismic velocities in westerly granite, J. Geophys. Res. 81, 20, 3484–3494, DOI: 10.1029/JB081i020p03484.
Hashin, Z., and S. Shtrikman (1963), A variational approach to the elastic behavior of multiphase materials, Mech. Phys. Solids 11, 2, 127–140, DOI: 10.1016/0022-5096(63)90060-7.
Hill, R. (1952), The elastic behavior of crystalline aggregate, Proc Phys. Soc. 65, 389, 349–354, DOI: 10.1088/0370-1298/65/5/307.
Hill, R. (1965), A self-consistent mechanics of composite materials, Mech. Phys. Solids 13, 4, 213–222, DOI: 10.1016/0022-5096(65)90010-4.
Jensen, E.H., C.F. Andersen, and T.A. Johansen (2011), Estimation of elastic moduli of mixed porous clay composites, Geophysics 76, 1, 9–20, DOI: 10.1190/1.3511351.
Johansen, T.A., E.H. Jensen, G. Mavko, and J. Dvorkin (2013), Estimate rock physics modeling for reservoir quality prediction, Geophysics 78, 2, 1–18, DOI: 10.1190/geo2012-0215.1.
Krief, M., J. Garat, J. Stellingwerff, and J. Ventre (1990), A petrophysical interpretation using the velocities of P and S waves (full-waveform sonic), The Log Analyst 31, 6, 355–369.
Kuster, G., and M. Toksöz (1974), Velocity and attenuation of seismic waves in two-phase media: Part 1–Theoretical formulations, Geophysics 39, 5, 587–606, DOI: 10.1190/1.1440450.
Lin, K., X.J. Xiong, X. Yang, Z.H. He, J.X. Cao, Z.X. Zhang, and P. Wang (2011), Self-adapting extraction of matrix mineral bulk moduli and verification of fluid substitution, Appl. Geophys. 8, 2, 110–116, DOI: 10.1007/s11770-011-0278-0.
Markov, M., E. Kazatchenko, A. Mousatov, and E. Pervago (2013), Novel approach for simulating the elastic properties of porous rocks including the critical porosity phenomena, Geophysics 78, 4, L37–L44, DOI: 10.1190/geo2012-0260.1.
Mavko, G., and N. Saxena (2013), Embedded-bound method for estimating the change in bulk moduli under either fluid or solid substitution, Geophysics 78, 5, L87–L99, DOI: 10.1190/geo2013-0074.1.
Mavko, G., T. Mukerji, and J. Dvorkin (1998) The Rock Physics Handbook, Cambridge University Press, Cambridge.
Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller (1953), Equation of state calculations by fast computing machines, J. Chem. Phys. 21, 1087–1092, DOI: 10.1063/1.1699114.
Mori, T., and K. Tanaka (1973), Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall. 21, 5, 571–574, DOI: 10.1016/0001-6160(73)90064-3.
Norris, A., P. Sheng, and A. Callegari (1985), Effective-medium theories for two-phase dielectric media, Appl Phys. 57, 6, 1990–1996, DOI: 10.1063/1.334384.
Nur, A., G. Mavko, and J. Dvorkin (1998), Critical porosity: The key to relating physical properties to porosity in rocks, The Leading Edge 17, 357–362, DOI: 10.1190/1.1887540.
O’Connell, R., and B. Budiansky (1974), Seismic velocities in dry and saturated cracked solids, J. Geophys. Res. 79, 35, 5412–5426, DOI: 10.1029/JB079i035p05412.
Raymer, L.L., E.R. Hunt, and J.S. Gardner (1980), An improved sonic transit time-to-porosity transform. In: 21st Ann. Logg. Symp., SPWLA.
Saleh, A., and J.P. Castagna (2004), Revisiting the Wyllie time average equation in the case of near spherical pores, Geophysics 69, 1, 45–55, DOI: 10.1190/1.1649374.
Sprunt, F., and W. Brace (1974), Direct observations of microcavities in crystalline rocks, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 11, 4, 139–150, DOI: 10.1016/0148-9062(74)92874-5.
Timur, A., W. Hempkins, and R. Weinbrandt (1971), Scanning electron microscope study of pore systems in rocks, Geophysics 76, 20, 4932–4948, DOI: 10.1029/JB076i020p04932.
Toksöz, M., C.H. Cheng, and A. Timur (1976), Velocities of seismic waves in porous rocks, Geophysics 41, 4, 621–645, DOI: 10.1190/1.1440639.
Tran, D.T., and S. Chandra (2008), Changes in crack aspect-ratio concentration from heat treatment: A comparison between velocity estimation and experimental data, Geophysics 73, 123–132.
Vernik, L., and M. Kachanov (2010), Modeling elastic properties of siliciclastic rocks, Geophysics 75, 6, E171–E182, DOI: 10.1190/1.3494031.
Walsh, J. (1965), The effect of cracks on the compressibility of rock, J. Geophys. Res. 70, 2, 381–389, DOI: 10.1029/JZ070i002p00381.
Wang, Z.J. (2001), Fundamentals of seismic rock physics, Geophysics 66, 2, 398–412, DOI: 10.1190/1.1444931.
Wu, T. (1966), The effect of inclusion shape on the elastic moduli of a two phase material, Int. J. Solids Struct. 2, 1, 1–8, DOI: 10.1016/0020-7683(66)90002-3.
Zimmerman, R. (1991), Compressibility of Sandstones, Elsevier, New York.
Zimmerman, R. (1984), The elastic moduli of a solid with spherical pores: New self-consistent method, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 21, 6, 339–343, DOI: 10.1016/0148-9062(84)90366-8.
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Peng, D., Yin, C., Zhao, H. et al. An Estimation Method of Pore Structure and Mineral Moduli Based on Kuster-Toksöz (KT) Model and Biot’s Coefficient. Acta Geophys. 64, 2337–2355 (2016). https://doi.org/10.1515/acgeo-2016-0108
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DOI: https://doi.org/10.1515/acgeo-2016-0108