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A patchy-saturated rock physics model for tight sandstone based on microscopic pore structures

  • Borehole geophysics and rock properties
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Abstract

The wave-induced local fluid flow mechanism is relevant to the complex heterogeneity of pore structures in rocks. The analysis of the local fluid flow mechanism is useful for accurately describing the wave propagation characteristics in reservoir rocks. In the exploration and production of hydrocarbon reservoirs, the real stratum may be partially saturated with a multi-phase fluid mixture in general. Therefore, it is of great significance to investigate the wave velocity dispersion and attenuation features in relation to pore structures and fluids. In this work, the characteristics of fabric microstructures are obtained on the basis of pressure dependency of dry rock moduli using the effective medium theory. A novel anelasticity theoretical model for the wave propagation in a partially-saturated medium is presented by combining the extended Gurevich squirt-flow model and White patchy-saturation theory. Numerical simulations are used to analyze wave propagation characteristics that depend on water saturation, external patchy diameter, and viscosity. We consider a tight sandstone from the Qingyang area of the Ordos Basin in west China and perform ultrasonic measurements under partial saturation states and different confining pressures, where the basic properties of the rock are obtained at the full gas saturation. The comparison of experimental data and theoretical modeling results shows a fairly good agreement, indicating that the new theory is effective.

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References

  • Amalokwu, K., Papageorgiou, G., Chapman, M., and Best, A. I., 2017, Modelling ultrasonic laboratory measurements of the saturation dependence of elastic modulus: New insights and implications for wave propagation mechanisms: International Journal of Greenhouse Gas Control, 59, 148–159.

    Article  Google Scholar 

  • Ba, J., Carcione, J. M., and Nie, J. X., 2011, Biot-Rayleigh theory of wave propagation in double-porosity media: Journal of Geophysical Research: Solid Earth, 116, B06202.

    Article  Google Scholar 

  • Ba, J., Yan, X. F., Chen, Z. Y. et al., 2013, Rock physics model and gas saturation inversion for heterogeneous gas reservoirs: Chinese Journal of Geophysics (in Chinese), 56(5), 1696–1706.

    Google Scholar 

  • Ba, J., Zhang, L., Sun, W. T., and Hao, Z. B., 2014, Velocity field of wave-induced local fluid flow in double-porosity media: Science China: Physics, Mechanics and Astronomy, 57, 1020–1030.

    Google Scholar 

  • Ba, J., Zhao, J., Carcione, J. M. et al., 2016, Compressional wave dispersion due to rock matrix stiffening by clay squirt-flow: Geophysical Research Letters, 43(12), 6186–6195.

    Article  Google Scholar 

  • Ba, J., Ma, R. P., Carcione, J. M., and Picotti, S., 2019, Ultrasonic wave attenuation dependence on saturation in tight oil siltstones: Journal of Petroleum Science and Engineering, 179, 1114–1122.

    Article  Google Scholar 

  • Batzle, M., and Wang, Z., 1992, Seismic properties of pore fluids: Geophysics, 57 (11), 1396–1408.

    Article  Google Scholar 

  • Berryman, J. G., 1995, Mixture theories for rock properties, A Handbook of Physical Constants: Washington, D. C: American Geophysical Union, 205–228.

    Google Scholar 

  • Biot, M. A., 1956a, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range: The Journal of the Acoustical Society of America, 28(2), 168–178.

    Article  Google Scholar 

  • Biot, M. A., 1956b, Theory of propagation of elastic waves in a fluid- saturated porous solid. II. Higher frequency range: The Journal of the Acoustical Society of America, 28(2), 179–191.

    Article  Google Scholar 

  • Biot, M. A., 1962, Generalized theory of acoustic propagation in porous dissipative media: The Journal of the Acoustical Society of America, 34(9A), 1254–1264.

    Article  Google Scholar 

  • Brie, A., Pampuri, F., Marsala, A. F., and Meazza, O., 1995, Shear sonic interpretation in gas-bearing sands: SPE Annual Technical Conference and Exhibition, October, Dallas, USA, SPE 30595, 701–710.

  • Carcione, J. M., 2014, Wave fields in real media. Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media, 3rd ed.: Elsevier, Amsterdam.

    Google Scholar 

  • Carcione, J. M., Helle, H. B., and Pham, N. H., 2003, White’s model for wave propagation in partially saturated rocks: comparison with poroelastic numerical experiments: Geophysics, 68(4), 1389–1398.

    Article  Google Scholar 

  • Chen, Y., Huang, T. F., and Liu, E. R., 2009, Rock Physics (in Chinese): China University of Science and Technology Press, Hefei.

    Google Scholar 

  • Cheng, W., Ba, J., Fu, L. Y. et al., 2019, Wave-velocity dispersion and rock microstructure: Journal of Petroleum Science and Engineering, 183, 106466.

    Article  Google Scholar 

  • David, E. C., and Zimmerman, R. W., 2012, Pore structure model for elastic wave velocities in fluid-saturated sandstones: Journal of Geophysical Research: Solid Earth, 117, B07210.

    Article  Google Scholar 

  • Deng, J. X., Zhou, H., Wang, H. et al., 2015, The influence of pore structure in reservoir sandstone on dispersion properties of elastic waves: Chinese Journal of Geophysics (In Chinese), 58(9), 3389–3400.

    Google Scholar 

  • Duan, C. S., Deng, J. X., Li, Y. et al., 2017, Effect of pore structure on the dispersion and attenuation of fluid-saturated tight sandstones: Journal of Geophysics and Engineering, 15(2018), 449–460.

    Google Scholar 

  • Dutta, N. C., and Odé, H., 1979, Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-Part I: Biot theory: Geophysics, 44, 1777–1788.

    Article  Google Scholar 

  • Dutta, N. C., and Seriff, A. J., 1979, On White’s model of attenuation in rocks with partial gas saturation: Geophysics, 44(11), 1806–1812.

    Article  Google Scholar 

  • Dvorkin, J., Mavkon, G., and Nur, A., 1995, Squirt-flow in fully saturated rocks: Geophysics, 60(1), 97–107.

    Article  Google Scholar 

  • Dvorkin, J., and Nur, A., 1993, Dynamic poroelasticity: a unified model with the squirt and the Biot mechanics: Geophysics, 58(4), 524–533.

    Article  Google Scholar 

  • Dvorkin, J., Nolen-Hoeksema, R., and Nur, A., 1994, The squirt-flow mechanism: macroscopic description: Geophysics, 59(3), 428–438.

    Article  Google Scholar 

  • Gassmann, F., 1951, Über die elastizität poröser medien: Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 96, 1–23.

    Google Scholar 

  • Gist, G. A., 1994, Interpreting laboratory velocity measurements in partially gas-saturated rocks: Geophysics, 59, 1100–1109.

    Article  Google Scholar 

  • Guo, M., and Fu, Y., 2006, Stress associated coda attenuation from ultrasonic waveform Measurements: Geophysical Research Letters, 34, L09307.

    Google Scholar 

  • Guo, M. Q., Fu, L. Y., and Ba, J., 2009, Comparison of stress-associated coda attenuation and intrinsic attenuation from ultrasonic measurements: Geophysical Journal International, 178, 447–456.

    Article  Google Scholar 

  • Gurevich, B., Makarynska, D., and Pervukhina, M., 2009, Ultrasonic moduli for fluid-saturated rocks: Mavko-Jizba relations rederived and generalized: Geophysics, 74(4), N25–N30.

    Article  Google Scholar 

  • Gurevich, B., Makarynska, D., de Paula, O. B. et al., 2010, A simple model for squirt-flow dispersion and attenuation in fluid-saturated granular rocks: Geophysics, 75(6), N109–N120.

    Article  Google Scholar 

  • Hill, R., 1963, Elastic properties of reinforced solids: some theoretical principles: Journal of the Mechanics and Physics of Solids, 11, 357–372.

    Article  Google Scholar 

  • Karakul, H., and Ulusay, R., 2013, Empirical correlations for predicting strength properties of rocks from P-wave velocity under different degrees of saturation: Rock Mechanics & Rock Engineering, 46(5), 981–999.

    Article  Google Scholar 

  • Li, D. Q., Wei, J. X., Di, B. R. et al., 2018, Experimental study and theoretical interpretation of saturation effect on ultrasonic velocity in tight sandstones under different pressure conditions: Geophysical Journal International, 212(3), 2226–2237.

    Article  Google Scholar 

  • Liu, J., Ma, J. W., and Yang, H. Z., 2010, Research on P-wave’s propagation in White’s sphere model with patchy saturation: Chinese Journal of Geophysics (in Chinese), 53(4), 954–962.

    Google Scholar 

  • Lucet, N., and Zinszner, B., 1992, Effects of heterogeneities and anisotropy on sonic and ultrasonic attenuation in rocks: Geophysics, 57(8), 1018–1026.

    Article  Google Scholar 

  • Ma, R. P., and Ba, J., 2020, Coda and intrinsic attenuations from ultrasonic measurements in tight siltstones: Journal of Geophysical Research: Solid Earth, 125, e2019JB018825.

    Google Scholar 

  • Mavko, G., and Jizba, D., 1991, Estimating grain-scale fluid effects on velocity dispersion in rocks: Geophysics, 56(12), 1940–1949.

    Article  Google Scholar 

  • Mavko, G., and Nur, A., 1975, Melt squirt in the asthenosphere: Journal of Geophysical Research, 80, 1444–1448.

    Article  Google Scholar 

  • Mavko, G., and Nur, A., 1979, Wave attenuation in partially saturated rocks: Geophysics, 44(2): 161–178.

    Article  Google Scholar 

  • Mavko, G., and Nolen-Hoeksema, R., 1994, Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks: Geophysics, 59(2), 252–258.

    Article  Google Scholar 

  • Mavko, G., and Mukerji, T., 1998, Bounds on low-frequency seismic velocities in partially saturated rocks: Geophysics, 63(3), 918–924.

    Article  Google Scholar 

  • Murphy, W. F., Winkler, K. W., and Kleinberg, R. L., 1986, Acoustic relaxation in sedimentary rocks: dependence on grain contacts and fluid saturation: Geophysics, 51 (3), 757–766.

    Article  Google Scholar 

  • Müller, T. M., and Gurevich, B., 2004, One-dimensional random patchy saturation model for velocity and attenuation in porous rocks: Geophysics, 69, 1166–1172.

    Article  Google Scholar 

  • Norris, A. N., 1993, Low-frequency dispersion and attenuation in partially saturated rocks: Journal of the Acoustical Society of America, 94(1), 359–370.

    Article  Google Scholar 

  • Ouyang, F., Zhao, J. G, Li, Z. et al., 2021, Modeling velocity dispersion and attenuation using pore structure characteristics of rock: Chinese Journal of Geophysics (In Chinese), 64(3), 1034–1047.

    Google Scholar 

  • Pang, M. Q. Ba, J. Ma, R. P., and Chen, T. S., 2020, Analysis of attenuation rock-physics template of tight sandstones: Reservoir microcrack prediction: Chinese Journal of Geophysics (In Chinese), 63, 281–295.

    Google Scholar 

  • Picotti, S., and Carcione, J. M., 2006, Estimating seismic attenuation (Q) in the presence of random noise: Journal of Seismic Exploration, 15, 165–181.

    Google Scholar 

  • Ren, S. B., Han, T. C., and Fu, L. Y., 2020, Theoretical and experimental study of P-wave attenuation in partially saturated sandstones under different pressures: Chinese Journal of Geophysics (in Chinese), 63(7), 2722–2736.

    Google Scholar 

  • Sayers, C. M., and Kachanov, M., 1995, Microcrack-induced elastic wave anisotropy of brittle rocks: Journal of Geophysical Research Solid Earth, 100(B3), 4149–4156.

    Article  Google Scholar 

  • Sun, W. T., Ba, J., Müller, T. M. et al., 2014, Comparison of P-wave attenuation models of wave-induced flow: Geophysical Prospecting, 63(2), 378–390.

    Article  Google Scholar 

  • Sun, Y., Carcione J. M., and Gurevich, B., 2020, Squirt-flow seismic dispersion models: a comparison: Geophysical Journal International, 222(3), 2068–2082.

    Article  Google Scholar 

  • Sun, Y., and Gurevich, B., 2020, Modeling the effect of pressure on the moduli dispersion in fluid-saturated rocks: Journal of Geophysical Research: Solid Earth, 125(12), e2019JB019297.

    Google Scholar 

  • Sun, C., Tang, G., Fortin, J. et al., 2020, Dispersion and attenuation of elastic wave velocities: impact of microstructure heterogeneity and local measurements: Journal of Geophysical Research: Solid Earth, 125(12) e2020JB020123.

    Google Scholar 

  • Sun, W. T., 2021, On the theory of Biot-patchy-squirt mechanism for wave propagation in partially saturated double-porosity medium: Physics Fluids, 33, 076603.

    Article  Google Scholar 

  • Song, L. T, Wang, Y., Liu, Z. H. et al., 2015, Elastic anisotropy characteristics of tight sands under different confining pressures and fluid saturation states: Chinese Journal of Geophysics (in Chinese), 58(9), 3401–3411.

    Google Scholar 

  • Tang X. M., Wang H. M., Sun Y. D. et al., 2021, Inversion for micro-pore structure distribution characteristics using cracked porous medium elastic wave theory. Chinese Journal of Geophysics (In Chinese), 64(8), 2941–2951.

    Google Scholar 

  • Toms, J., Müller, T. M., Ciz, R., and Gurevich, B., 2006, Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks: Soil Dynamics and Earthquake Engineering, 26(6–7), 548–565.

    Article  Google Scholar 

  • White, J. E., 1975, Computed seismic speeds and attenuation in rocks with partial gas saturation: Geophysics, 40(2), 224–232.

    Article  Google Scholar 

  • Winkler, K. W., 1985, Dispersion analysis of velocity and attenuation in Berea sandstone. Journal of Geophysical Research: Solid Earth, 90(B8), 6793–6800.

    Google Scholar 

  • Wood, A. B., 1941, A Textbook of Sound, Bell: London, UK.

    Google Scholar 

  • Wu, C. F., Ba, J., Carcione, J. M., Fu, L. Y. Chesnokov, E. M., and Zhang, L., 2020, A squirt-flow theory to model wave anelasticity in rocks: Physics of the Earth and Planetary Interiors, 301, 106450.

    Article  Google Scholar 

  • Yan, X. F., Yao, F. C., Cao, H. et al., 2011, Analyzing the mid-low porosity sandstone dry frame in central Sichuan based on effective medium theory: Applied Geophysics, 8(3), 163–170.

    Article  Google Scholar 

  • Zhang, L, Ba, J, Fu, L. Y., et al., 2019, Estimation of pore microstructure by using the static and dynamic moduli: International Journal of Rock Mechanics and Mining Sciences, 113, 24–30.

    Article  Google Scholar 

  • Zhang, L., Ba, J., Yin, W. et al., 2017, Seismic wave propagation equations of conglomerate reservoirs: A triple-porosity structure model: Chinese Journal of Geophysics (In Chinese), 60(3), 1073–1087.

    Google Scholar 

  • Zhao, H. B., Wang, X. M., Chen, S. M. et al., 2010, Acoustic response characteristics of unsaturated porous media. Science China Physics, Mechanics and Astronomy, 53(8), 1388–1396.

    Article  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant no. 41704109) and the Jiangsu Province Outstanding Youth Fund Project (Grant no. BK20200021).

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Correspondence to Jing Ba.

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Wu Chun-Fang obtained his Ph.D. degree from Hohai University in 2020. Her major is earth exploration and information technology, and her main research interests are rock physics and wave propagation theory in porous media.

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Wu, CF., Ba, J., Carcione, J.M. et al. A patchy-saturated rock physics model for tight sandstone based on microscopic pore structures. Appl. Geophys. 19, 147–160 (2022). https://doi.org/10.1007/s11770-022-0938-2

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  • DOI: https://doi.org/10.1007/s11770-022-0938-2

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