Abstract
A microinhomogeneity-averaged model of the kinetics of the trapping process is proposed for a porous medium in which two fluids are mutually displaced. The traps are treated as a new hydrodynamic phase, and the trapping process as a phase transition. Kinetic relations for the average trapping process are obtained. The structure and quantitative values of the kinetic coefficients are obtained for a model of a porous medium in the form of a system of doublets. The dependence of the characteristic time of the process on the degree of inhomogeneity of the medium is investigated. A variant of the macroscopic model of the process of two-phase flow, in which the kinetic relations obtained are used as the closing relations, is proposed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. A. Witten and L. M. Sander, “Diffusion limited aggregation,”Phys. Rev. B,27, 5686 (1983).
V. I. Selyakov, “The forest growth model,” in:Numerical Methods of Solving Problems of Flow in Porous Media. The Dynamics of Multiphase Media: Ninth All-Union Workshop, Yakutsk, 1988 [in Russian] Novosibirsk (1989), p. 201.
G. I. Barenblatt and V. M. Entov, Nonequilibrium effects in immiscible fluid flow through porous media, in:Numerical Methods of Solving Problems of Multiphase Incompressible Fluid Flow in Porous Media [in Russian] Computing Center, Siberian Branch, USSR Academy of Sciences, Novosibirsk (1972), p. 33.
Yu. A. Zarubin, “Exchange model of displacement in porous media,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 91 (1991).
Yu. A. Buevich and U. M. Mambetov, “A theory of mutual immiscible fluid flow through a porous medium,”Inzh.-Fiz. Zh.,60, 98 (1991).
I. Chatzis, M. S. Kuntamukkula, and N. R. Morrow, “Effect of capillary number on the microstructure of residual oil in strongly water-wet sandstones,”SPE Res. Eng.,3, 902 (1988).
R. G. Larson, H. T. Davis, and L. E. Scriven, “Percolation theory of residual phases in porous-media,”Nature,268, No. 5619, 409 (1977).
L. Sylvestre, A. M. Wilhelm, and G. Casamatta, “Configuration de piégeage dans un milieu poreux à saturation rásiduelle en huile,”Rev. Inst. Franc. Pétrole.,40, 467 (1985).
I. Chatzis, N. R. Morrow, and H. T. Lim, “Magnitude and detailed structure of residual oil saturation,”Soc. Petrol. Eng. Journal,23, 311 (1983).
N. R. Morrow, I. Chatzis, and H. T. Lim, “Relative permeabilities at reduced residual saturations,”J. Canad. Petr. Technol.,24, 62 (1985).
M. B. Panfilov, “Average model of flow through strongly inhomogeneous porous media,”Dokl. Akad. Nauk SSSR,311, 313 (1990).
M. B. Panfilov and I. V. Tuvaeva, “Nonlocal models of penetrating percolation,” in:Oil and Gas Field Development: Present State, Problems, and Prospects, Zvenigorod, March 11–16, 1991 [in Russian], Proceedings of 2nd All-Union School-Workshop, Vol. 1, Oil and Gas Research Institute, USSR Academy of Sciences, Moscow (1991), p. 247.
M. B. Panfilov and I. V. Tuvaeva, “Percolation models of the processes of fluid displacement in randomly inhomogeneous media,” [in Russian], Preprint No.12, Oil and Gas Research Institute, USSR Academy of Sciences, Moscow (1991).
A. Rose, “Model of doublet for simulation of trapping in porous media,”Trans. AIME,112, No. 23, 345 (1967).
M. B. Panfilov, “Averaging of the processes of convective-diffusion transport in inhomogeneous porous media and lattice structures,” [in Russian], Preprint No.20, Oil and Gas Research Institute, USSR Academy of Sciences, Moscow (1992).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 92–101, May–June, 1995.
Rights and permissions
About this article
Cite this article
Panfilov, M.B., Panfilova, I.V. Macrokinetic model of the trapping process in two-phase fluid displacement in a porous medium. Fluid Dyn 30, 409–417 (1995). https://doi.org/10.1007/BF02282453
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02282453