Abstract
In this paper we consider an integrated model for single-phase fluid flow in elastic porous media. The model and mathematical formulation consist of mass and momentum balance equations for both fluid and porous media. We propose a mixed finite element scheme to solve simultaneously for the porous media displacement, fluid mass flux, and pore pressure. A prototype simulator for solving the integrated problem has been built based on a finite element object library that we have developed. We will present numerical and sensitivity results for the solution algorithm.
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References
Biot, M. A., ‘Nonlinear and semilinear rheology of porous solids’, J. Geophy. Res. 73 (1973), 4924–4937.
Biot, M. A. and Willis, D. G., The elastic coefficients of the theory of consolidation, J. Appl. Mech. 24 (1957), 594–601.
Biot, M. A., General theory of three-dimensional consolidation, J. Appl. Mech. 25 (1956), 91–96.
Biot, M. A., General theory of three-dimensional consolidation, J. Appl. Phys. 12 (1941), 155–164.
Chen, H. Y., Teufel, L. W., and Lee, R. L., Coupled fluid flow and geomechanics in Reservoir Study—I. Theory and governing equations, presented in The Proceding of SPE Annual Technical Conference & Exhibition, Dallas, Oct. 1995, 22–25.
Ewing, R. E., Problems Arising in the Modeling of Processes for Hydrocarbon Recovery, (Ewing, ed.) The Mathematics of Reservoir Simulation, 1983, SIAM, Philadelphia, PA, pp. 3–34.
Fatt, I. and Davis, D. H., Reduction in permeability with overburden pressure, Trans AIME 195 (1952), 329–341.
Holt, R. M., Permeability reduction induced by a nonhydrostatic stress field, SPEFE Dec. (1990), 444–448.
Jones, F. O. and Owens, W. W., A laboratory study of low-permeability gas sands, JPT Sept. (1980), 1631–1640.
Koutsabeloulis, N. C., Numerical modeling of soft reservoir behavior during fluid production, Geotechnical Engineering in Hard Soil-Soft Rocks, 1993.
Koutsabeloulis, N. C., Heffer, K. J., and Wong, S., Numerical geome-chanics in reservoir engineering, Computer Methods and Advances in Geomechanics, 1994.
Lewis, R. W. and Sukirman, Y., Finite element modeling of three-phase flow in deforming saturated oil reservoirs, Int. J. Num. & Analy. Methods Gemech. 17 (1993), 577–598.
Morita, N., et al., Rock-property changes during reservoir compaction, SPEFE Sept. (1992), 197–205.
Osorio, J. G., Numerical modeling of coupled fluid-flow/geomechanical behavior of reservoirs with stress-sensitive permeability, Ph.D dissertation, New Mexico Institute of Mining and Technology, Socorro, NM, 1998.
Raviart, P. A. and Thomas, J. M., A Mixed Finite Element Method for 2nd Order Elliptic Problems, Lecture Notes in Math. 606, Springer-Verlag, Berlin, 1977.
Rhett, D. W. and Teufel, L. W., Effect of reservoir stress path on compressibility and permeability of sandstones, paper SPE 24756 presented at the SPE Annual Technical Conference and Exhibition Washington, DC, Oct. 4–7, 1990.
Sun, T., Ewing, R. E., Chen, H., Lyons, S. L. and Qin, G., Object-oriented programming for general mixed finite element methods, Object Oriented Methods for Interoperable Scientific And Engineering Computing; The Proceeding of the 1998 SIAM Workshop, 1998.
Terzaghi, K., Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungsercheinungen, Akademi der Wissenschaften in Wien, Sitzungsherichte, Mathematisch-naturwissenschaftliche Klasse Part IIa, 1923.
Zienkiewicz, O. C., Basic formulation of static and dynamic behavior of soil and other porous media, Numerical Methods in Geomechanics, 1982.
Zimmerman, R. W., Somerton, W.H. and King, M.S., Compresibility of porous rocks, Journal of Geophysical Research 91 (1986), 12765–12777.
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Chen, H., Ewing, R.E., Lyons, S.L., Qin, G., Sun, T., Yale, D.P. (2000). A Numerical Algorithm for Single Phase Fluid Flow in Elastic Porous Media. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_6
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DOI: https://doi.org/10.1007/3-540-45467-5_6
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