碳酸盐岩孔隙结构参数构建与储层参数反演(英文)
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摘要
碳酸盐岩储层孔隙结构相对碎屑岩更复杂,常用的岩石物理模型不能较好的描述其孔隙结构的变化规律,且岩石孔隙结构的差异较大程度上会影响岩石的弹性性质。本文首先利用岩石薄片分析了碳酸盐岩的微观孔隙结构。然后基于Gassmann方程和Eshelby-Walsh椭球包体裂缝理论,在合理的假设前提下给出了一种新的岩石物理建模方法,并且从中提取了一个参数来表征孔隙结构的变化规律。最后,基于全波列测井数据,我们利用该方法计算了单井的孔隙度,并与用常规方法预测的结果进行了比较,同时进行了地震储层参数反演。研究结果表明,孔隙结构对岩石的弹性性质的影响较大,且新的建模方法预测的孔隙度误差仅为0.74%。因此,该方法可有效的减小孔隙结构对计算各岩石弹性参数的影响并提高孔隙度的预测精度。
With a more complex pore structure system compared with clastic rocks, carbonate rocks have not yet been well described by existing conventional rock physical models concerning the pore structure vagary as well as the influence on elastic rock properties. We start with a discussion and an analysis about carbonate rock pore structure utilizing rock slices. Then, given appropriate assumptions, we introduce a new approach to modeling carbonate rocks and construct a pore structure algorithm to identify pore structure mutation with a basis on the Gassmann equation and the Eshelby-Walsh ellipsoid inclusion crack theory. Finally, we compute a single well’s porosity using this new approach with full wave log data and make a comparison with the predicted result of traditional method and simultaneously invert for reservoir parameters. The study results reveal that the rock pore structure can significantly influence the rocks’ elastic properties and the predicted porosity error of the new modeling approach is merely 0.74%. Therefore, the approach we introduce can effectively decrease the predicted error of reservoir parameters.
With a more complex pore structure system compared with clastic rocks, carbonate rocks have not yet been well described by existing conventional rock physical models concerning the pore structure vagary as well as the influence on elastic rock properties. We start with a discussion and an analysis about carbonate rock pore structure utilizing rock slices. Then, given appropriate assumptions, we introduce a new approach to modeling carbonate rocks and construct a pore structure algorithm to identify pore structure mutation with a basis on the Gassmann equation and the Eshelby-Walsh ellipsoid inclusion crack theory. Finally, we compute a single well’s porosity using this new approach with full wave log data and make a comparison with the predicted result of traditional method and simultaneously invert for reservoir parameters. The study results reveal that the rock pore structure can significantly influence the rocks’ elastic properties and the predicted porosity error of the new modeling approach is merely 0.74%. Therefore, the approach we introduce can effectively decrease the predicted error of reservoir parameters.
引文
Avseth, P., Mukerji, T., and Mavko, G., 2005, Quantitative seismic interpretation: Cambridge University Press, UK.
Berryman, J. G., Pride, S. R., and Wang, H. F., 2002,A differential scheme for elastic properties of rockswith dry or saturated cracks: Geophysical JournalInternational, 151, 597 – 611.
Chen, Y., and Huang, T. H., 2001, Rock physics: Beijing University Press.
Chen, S. Q., Wang, S. X., Zhang, Y. G., and Ji, M., 2009a,Reservoir prediction using pre-stack inverted elasticparameters: Applied Geophysics, 6(4), 349 – 358.
Chen, Y., Huang, T. H., and Liu, E. Y., 2009b, Rockphysics: University of Science and Technology Press.
Eshelby, J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion and related problems: Proc.Royal Soc. London, A241, 376 – 396.
Gassmann, F., 1951, über die elastizit t poroser medien:Vier. Der Natur. Gesellschaft in Zurich, 96, 1 – 23.
Greenberg, M. L., and Castagna, J. P., 1992, Shear-wave velocity estimation in porous rocks: Theoreticalformulation, preliminary verification and applications:Geophysical Prospecting, 40(2), 195 – 209.
Hampson, D. P., and Russell, B. H., 2005, Simultaneous inversion of pre-stack seismic data: 75th Ann. Internat.Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1633 –1637.
Han, D. H., Nur, A., and Morgan, D., 1986, Effects of porosity and clay content on wave velocities insandstones: Geophysics, 51, 2093 – 2107.
He, Z. H., Huang, D. J., and Wen, X. T., 2007, Geophysics prediction in fractured hydrocarbon reservoir: SciencePress.
Kachanov, M., Tsukrov, I., and Shafiro, B., 1994, Effective moduli of solids with cavities of various shapes:Applied Mechanics Reviews, 47(1), S151 – S174, doi:10.1115/1.3122810.
Krief, M., Garat, J., Stellingwerff, J., and Ventre, J., 1990,A petrophysical interpretation using the velocities of Pand S waves (full waveform sonic): The Log Analyst, 31,355 – 369.
Kuster, G.. T., and Toks z, M. N., 1974, Velocity and attenuation of seismic waves in two-phase media: Part I,Theoretical formulations: Geophysics, 39, 587 – 606.
Li, H. B. and Zhang, J. J., 2010, Modulus ratio of dry rock based on differential effective-medium theory:Geophysics, 75, 43 – 50.
Markov, M., Levine, V., Mousatov, A., and Kazatchenko, E.,2005, Elastic properties of double-porosity rocks usingthe differential effective medium model: GeophysicalProspecting, 53, 733 – 754.
Mindlin, R. D., 1949, Compliance of elastic bodies incontact: Journal of Applied Mechanics, 16, 259 – 268.
Norris, A., 1985, A differential scheme for the effective moduli of composites: Mechanics of Materials, 4, 1–16.
Nur, A., Marion, D., and Yin, H., 1991, Wave velocities insediments: in Hovem, J., Richardson, M. D., and Stoll,R. D., eds., Shear waves in marine sediments: KluwerAcademic Press, 131 – 140.
Nur, A., Mavko, G., Dvorkin, J., and Gal, D., 1995, Critical porosity: The key to relating physical properties toporosity in rocks: 65th Ann. Internat. Mtg., Soc. Expl.Geophys., Expanded Abstracts, 878 – 881.
Raymer, L. L., Hunt, E. R., and Gardner, J. S., 1980, An improved sonic transit time-to-porosity transform: 21stAnnual Logging Symposium Transactions, Society ofProfessional Well Log Analysts, Paper P.
Sevostianov, I., Kachanov, M., and Zohdi, T., 2008, Oncomputation of the compliance and stiffness contributiontensors of non-ellipsoidal inhomogeneities: InternationalJournal of Solids and Structures, 45, 4375 – 4383, doi:10.1016/ j.ijsolstr.2008.03.020.
Shi, L., and Wang, C. J., 2004, The comparison of several seismic inversion software: Journal of SouthwestPetroleum Institute, 26(3), 16 – 19.
Vernik, L., 1998, Acoustic velocity and porosity systematics in siliciclastics: The Log Analyst, 39(4), 27 – 35.
Vernik, L., and Kachanov, M., 2010, Modeling elastic properties of siliciclastic rocks: Geophysics, 75, 171 –182.
Walsh, J. B., 1965, The effect of cracks on the compres sibility of rock: J. Geophys. Res., 70, 381 – 389.
Wyllie, M., Gregory, A., and Gardner, G., 1956, Elastic wave velocities in heterogeneous and porous media:Geophysics, 21, 41 – 70.
Yang, P. J., and Yin, X. Y., 2008, Non-linear quadratic programming Bayesian prestack inversion: Chinese J .Geophys. (in Chinese), 51(6), 1876 – 1882.
Zhang, J. Q., Qu, S. L., Su, J. G., Dong, N., and Yu, W. Q.,2010. A fluid substitution realization method in carbonatereservoir: OGP, 45(3), 406 – 409, 422.
Zimmerman, R. D., 1985, The effect of microcracks on the elastic moduli of brittle materials: Journal of MaterialScience Letters, 4, 1457 – 1460.
Zimmerman, R. D., 1986, Compressibility of two-dimensional cavities of various shapes: Journal ofApplied Mechanics, 53(3), 500 – 504, doi: 10.1115/1.3171802.
Berryman, J. G., Pride, S. R., and Wang, H. F., 2002,A differential scheme for elastic properties of rockswith dry or saturated cracks: Geophysical JournalInternational, 151, 597 – 611.
Chen, Y., and Huang, T. H., 2001, Rock physics: Beijing University Press.
Chen, S. Q., Wang, S. X., Zhang, Y. G., and Ji, M., 2009a,Reservoir prediction using pre-stack inverted elasticparameters: Applied Geophysics, 6(4), 349 – 358.
Chen, Y., Huang, T. H., and Liu, E. Y., 2009b, Rockphysics: University of Science and Technology Press.
Eshelby, J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion and related problems: Proc.Royal Soc. London, A241, 376 – 396.
Gassmann, F., 1951, über die elastizit t poroser medien:Vier. Der Natur. Gesellschaft in Zurich, 96, 1 – 23.
Greenberg, M. L., and Castagna, J. P., 1992, Shear-wave velocity estimation in porous rocks: Theoreticalformulation, preliminary verification and applications:Geophysical Prospecting, 40(2), 195 – 209.
Hampson, D. P., and Russell, B. H., 2005, Simultaneous inversion of pre-stack seismic data: 75th Ann. Internat.Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1633 –1637.
Han, D. H., Nur, A., and Morgan, D., 1986, Effects of porosity and clay content on wave velocities insandstones: Geophysics, 51, 2093 – 2107.
He, Z. H., Huang, D. J., and Wen, X. T., 2007, Geophysics prediction in fractured hydrocarbon reservoir: SciencePress.
Kachanov, M., Tsukrov, I., and Shafiro, B., 1994, Effective moduli of solids with cavities of various shapes:Applied Mechanics Reviews, 47(1), S151 – S174, doi:10.1115/1.3122810.
Krief, M., Garat, J., Stellingwerff, J., and Ventre, J., 1990,A petrophysical interpretation using the velocities of Pand S waves (full waveform sonic): The Log Analyst, 31,355 – 369.
Kuster, G.. T., and Toks z, M. N., 1974, Velocity and attenuation of seismic waves in two-phase media: Part I,Theoretical formulations: Geophysics, 39, 587 – 606.
Li, H. B. and Zhang, J. J., 2010, Modulus ratio of dry rock based on differential effective-medium theory:Geophysics, 75, 43 – 50.
Markov, M., Levine, V., Mousatov, A., and Kazatchenko, E.,2005, Elastic properties of double-porosity rocks usingthe differential effective medium model: GeophysicalProspecting, 53, 733 – 754.
Mindlin, R. D., 1949, Compliance of elastic bodies incontact: Journal of Applied Mechanics, 16, 259 – 268.
Norris, A., 1985, A differential scheme for the effective moduli of composites: Mechanics of Materials, 4, 1–16.
Nur, A., Marion, D., and Yin, H., 1991, Wave velocities insediments: in Hovem, J., Richardson, M. D., and Stoll,R. D., eds., Shear waves in marine sediments: KluwerAcademic Press, 131 – 140.
Nur, A., Mavko, G., Dvorkin, J., and Gal, D., 1995, Critical porosity: The key to relating physical properties toporosity in rocks: 65th Ann. Internat. Mtg., Soc. Expl.Geophys., Expanded Abstracts, 878 – 881.
Raymer, L. L., Hunt, E. R., and Gardner, J. S., 1980, An improved sonic transit time-to-porosity transform: 21stAnnual Logging Symposium Transactions, Society ofProfessional Well Log Analysts, Paper P.
Sevostianov, I., Kachanov, M., and Zohdi, T., 2008, Oncomputation of the compliance and stiffness contributiontensors of non-ellipsoidal inhomogeneities: InternationalJournal of Solids and Structures, 45, 4375 – 4383, doi:10.1016/ j.ijsolstr.2008.03.020.
Shi, L., and Wang, C. J., 2004, The comparison of several seismic inversion software: Journal of SouthwestPetroleum Institute, 26(3), 16 – 19.
Vernik, L., 1998, Acoustic velocity and porosity systematics in siliciclastics: The Log Analyst, 39(4), 27 – 35.
Vernik, L., and Kachanov, M., 2010, Modeling elastic properties of siliciclastic rocks: Geophysics, 75, 171 –182.
Walsh, J. B., 1965, The effect of cracks on the compres sibility of rock: J. Geophys. Res., 70, 381 – 389.
Wyllie, M., Gregory, A., and Gardner, G., 1956, Elastic wave velocities in heterogeneous and porous media:Geophysics, 21, 41 – 70.
Yang, P. J., and Yin, X. Y., 2008, Non-linear quadratic programming Bayesian prestack inversion: Chinese J .Geophys. (in Chinese), 51(6), 1876 – 1882.
Zhang, J. Q., Qu, S. L., Su, J. G., Dong, N., and Yu, W. Q.,2010. A fluid substitution realization method in carbonatereservoir: OGP, 45(3), 406 – 409, 422.
Zimmerman, R. D., 1985, The effect of microcracks on the elastic moduli of brittle materials: Journal of MaterialScience Letters, 4, 1457 – 1460.
Zimmerman, R. D., 1986, Compressibility of two-dimensional cavities of various shapes: Journal ofApplied Mechanics, 53(3), 500 – 504, doi: 10.1115/1.3171802.
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