Abstract
We describe discrete well models for 2-D non-Darcy fluid flow in anisotropic porous media. Attention is mostly paid to the well models and simplified calibration procedures for the control volume mixed finite element methods, including the case of highly distorted grids.
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References
Andreev, V. B. and Kryakvina, S. A., The fundamental solution of a one-parameter family of difference approximations of the Laplace operator in the plane, Zh. Vychisl. Mat. Mat. Fiz 13 (1973), 343–355.
Axelsson, O. and Gustaffson, I., An efficient finite element method for nonlinear diffusion problems, Bull. Greek Math. Soc. 32 (1991), 45–61.
Basniev, K. S., Kochina, I. N., and Maksimov, V. M., Underground hydromechanics, Moscow, Nedra. 1993.
Cai, Z., Jones, J. E., McCormick, S. F., and Russel, T. F., Control-Volume Mixed Finite Element Methods, Computational Geosciences 1 (1997), 289–315.
Chavent, G. and Jaffre, J., Mathematical models and finite elements for reservoir simulation, North-Holland, 1986.
Ewing, R. E., Lazarov, R., Lyons, S. L., Papavassiliou, D. V., Pasciak, J., and Qin, G., Numerical Well Model for Non-Darcy Flow through Isotropic Media, ISC Research Report ISC-98-11-MATH (1998).
Forchheimer, P., Wasserbewegung durch Boden Zeit. Ver. Deut. Ing. 45 (1901), 1781–1788.
Garanzha, V. A. and Konshin, V. N., Approximation schemes and discrete well models for the numerical simulation of the 2-D non-Darcy fluid flows in porous media Comm. in Appl. Math., Computing Center RAS, 1999.
Knupp, P. and Lage, J., Generalization of Forchheimer-extended Darcy flow model to tensor permeability case via a variational principle, J. Fluid Mech. 299 (1995), 97–104.
Peaceman, D. W., Interpretation of well-block pressure in numerical reservoir simulation, SPE Paper 6893, SPE Journal, Trans. AIME 253 (1978), 183–194.
Peaceman, D. W., Interpretation of well-block pressures in numerical reservoir simulation with non-square grid blocks and anisotropic permeability, SPE Journal (1983), 531–543.
Raviart, P. A. and Thomas, J. M., A mixed finite element method for 2nd order elliptic problems. Mathematical aspects of the finite element method. Lecture notes in Mathematics, 606, Springer, 1977.
Samarskii, A. A., Koldoba, V. A., Poveshchenko, Yu. A., Tishkin V. F., and Favorskiy, A. P., Difference Schemes on Irregular Grids, Minsk, 1996, (in Russian).
Thauvin, F. and Mohanty, K. K,, Modeling of non-Darcy flow through porous media, SPE paper 38017, presented at 1997 SPE Res. Simulation Symp., Dallas, Texas, USA, 8–11 June, 1997.
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Garanzha, V.A., Konshin, V.N., Lyons, S.L., Papavassiliou, D.V., Qin, G. (2000). Validation of Non-darcy Well Models Using Direct Numerical Simulation. 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_12
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DOI: https://doi.org/10.1007/3-540-45467-5_12
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