Geodesic
Simulation of multiphase fluid infiltration processes in a~layered porous medium
Matematičeskoe modelirovanie, Tome 22 (2010) no. 6, pp. 84-98.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the work multiphase fluid flows in a layered porous medium are investigated numerically taking into account capillary and gravity forces. Developed computational algorithms are approved by a number of test problems of two- and three-phase flows. The proposed approach can be employed to solve applied ecological problems connected with contamination of the soil and the ground water by petroleum products and other agents.
Keywords: two- and three-phase fluid flows, heterogeneous porous medium, capillary forces
Mots-clés : infiltration, interface conditions. 
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N. V. Isupov; M. A. Trapeznikova; N. G. Churbanova; E. V. Shilnikov. Simulation of multiphase fluid infiltration processes in a~layered porous medium. Matematičeskoe modelirovanie, Tome 22 (2010) no. 6, pp. 84-98. http://geodesic.mathdoc.fr/item/MM_2010_22_6_a7/

[1] R. Helmig., Multiphase flow and transport processes in the subsurface. A contribution to the modeling of hydrosystems, Springer, Berlin, 1997, 367 pp.

[2] Kh. Aziz, E. Settari, Matematicheskoe modelirovanie plastovykh sistem, 2-e izd., Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2004, 416 pp. | Zbl

[3] A. V. Koldoba, Yu. A. Poveschenko, E. A. Samarskaya, V. F. Tishkin, Metody matematicheskogo modelirovaniya okruzhayuschei sredy, Nauka, M., 2000, 254 pp. | Zbl

[4] R. E. Ewing (ed.), The mathematics of reservoir simulations, SIAM, Philadelphia, 1983, 186 pp. | MR | Zbl

[5] K. S. Basniev, N. M. Dmitriev, R. D. Kanevskaya, V. M. Maksimov, Podzemnaya gidromekhanika, Uchebnik dlya vuzov, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2005, 496 pp.

[6] M. Masket, Fizicheskie osnovy tekhnologii dobychi nefti, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2004, 608 pp.

[7] J. C. Parker, R. J. Lenhard, T. Kuppusami, “A parametric model for constitutive properties governing multiphase flow in porous media”, Water Resources Research, 23:4 (1987), 618–624 | DOI

[8] M. T. Van Genuchten, “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils”, Soil Sci. Soc. Am. J., 44 (1980), 892–898

[9] G. Chavent, J. Jaffre, Mathematical models and finite elements for reservoir simulation. Single phase, multiphase and multicomponent flows through porous media, Studies in mathematics and its applications, 17, Elsevier, North-Holland–Amsterdam, 1986, 375 pp.

[10] Z. Chen, R. E. Ewing, “Comparison of various formulations of three-phase flow in porous media”, J. Comp. Phys., 132 (1997), 362–373 | DOI | MR | Zbl

[11] A. N. Konovalov, Zadachi filtratsii mnogofaznoi neszhimaemoi zhidkosti, Nauka. Sib. Otd-nie, Novosibirsk, 1988, 166 pp. | MR | Zbl

[12] M. A. Trapeznikova, N. G. Churbanova, “Modelirovanie protsessa neftedobychi yavnymi i neyavnymi chislennymi metodami”, Matematicheskoe modelirovanie, 9:6 (1997), 53–66 | Zbl

[13] M. A. Trapeznikova, N. G. Churbanova, B. N. Chetverushkin, “Parallel elliptic solvers and their application to oil recovery simulation”, HPC' 2000, Grand Challenges in Computer Simulation, Proc. of Simulation Multi Conf., ed. A. Tentner, SCS, San Diego, CA, 2000, 213–218

[14] P. N. Vabischevich, V. A. Pervichko, A. A. Samarskii, V. V. Chudanov, “Nelineinye regulyarizovannye raznostnye skhemy dlya mnogomernogo uravneniya perenosa”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 40:6 (2000), 900–907 | MR

[15] R. H. Brooks, A. T. Corey, Hydraulic properties of porous media, Colorado State University Hydrology Paper, 3, Colorado State University, Fort Collins, 1964

[16] P. Bastian, Numerical computation of multiphase flows in porous media, Habilitation thesis, Christian-Albrechts-Universitaet, Kiel, 1999, 222 pp.

[17] R. Helmig, R. Huber, “Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media”, Advances in Water Resources, 21:8 (1998), 697–711 | DOI

[18] P. Bastian, R. Helmig, “Efficient fully-coupled solution techniques for two-phase flow in porous media. Parallel multigrid solution and large scale computations”, Advances in Water Resources, 23 (1999), 199–216 | DOI

[19] B. N. Chetverushkin, N. G. Churbanova, N. V. Isupov, M. A. Trapeznikova, “Simulation of NAPL Vertical Infiltration in a Heterogeneous Soil”, CD-Rom Proc. of ECCOMAS CFD 06, eds. P. Wesseling, E. Onate, J. Periaux (eds.), TU Delft, The Netherlands, 2006, track No 177

[20] B. N. Chetverushkin, N. G. Churbanova, M. A. Trapeznikova, A. A. Sukhinov, A. A. Malinovskij, “Adaptive Cartesian mesh refinement for simulating multiphase flows in porous media”, Computational Methods in Applied Mathematics, 8:2 (2008), 101–115 | MR | Zbl

[21] A. A. Sukhinov, “Postroenie dekartovykh setok s dinamicheskoi adaptatsiei k resheniyu.”, Matematicheskoe modelirovanie, 22:1 (2010), 86–98