Abstract
For two-phase immiscible fluid flows a generalized Darcy's law is written in invariant tensor form for crystallographic point symmetry groups and anisotropic textures. The representation of the phase permeability coefficient tensors and the structure of the expressions for the relative phase permeabilities are analyzed for all symmetry groups. The relation between the phase and absolute permeability coefficient tensors is specified by a fourth-rank tensor with the external symmetry coinciding with external symmetry of the phase permeability tensors. It is shown that the external symmetry of the phase permeability coefficient tensors can differ from the external symmetry of the absolute permeability tensor. For triclinic and monoclinic symmetry groups it is shown that the phase permeability coefficient tensors may not be coaxial with each other and with the absolute permeability tensor; moreover, the directions of the principal axes of the phase permeability coefficient tensors can depend on the saturation.
Similar content being viewed by others
REFERENCES
N. M. Dmitriev and V. M. Maksimov, “Structure of the phase and relative permeability coefficient tensors for anisotropic porous media,” Dokl. Ross. Akad. Nauk, 358, 337 (1998).
N. M. Dmitriev and V. M. Maksimov, “Determining equations of two-phase flows through anisotropic porous media,” Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 87 (1998).
V. M. Maksimov and N.M. Dmitriev, “Nonlinear tensor function methods in models of two-phase flow through anisotropic porous media”, in: Problems of Nonlinear Mechanics [in Russian], Uzd-vo MGU, Moscow (1998), P. 76.
V.V. Lokhin and L. I. Sedov, “Nonlinear tensor functions of several tensor arguments,” Prikl. Mat. Mekh., 27, 393 (1963).
Yu. I. Sirotin and M. P. Shaskol'skaya, Fundamentals of Crystal Physics [in Russian], Nauka, Moscow (1975).
A. M. Kuznetzov, “Scientific-methodical fundamentals of the investigation of the effect of the properties of reservoir rocks on the efficiency of hydrocarbon recovery,” Thesis for Degree of Doctor of Technical Sciences [in Russian], Krylov VNIIneft' Research Institute, Moscow (1998).
J. Bear, C. Braester, and P. S. Menier, “Effective and relative permeabilities of anisotropic porous media,” Transp. Porous Media, 2, 301 (1987).
K. S. Basniev, I. N. Kochina, and N.M. Dmitriev, Subsurface Hydromechanics [in Russian], Nedra, Moscow (1983).
Rights and permissions
About this article
Cite this article
Dmitriev, M.N., Dmitriev, N.M. & Kadet, V.V. Generalized Darcy's Law and the Structure of the Phase and Relative Phase Permeabilities for Two-Phase Flows through Anisotropic Porous Media. Fluid Dynamics 38, 284–292 (2003). https://doi.org/10.1023/A:1024229304312
Issue Date:
DOI: https://doi.org/10.1023/A:1024229304312