Search

A new presentation of tensors of relative phase permeabilities for anisotropic porous media is considered. The relation between the tensors of absolute and phase permeabilities is supposed to be represented by a tensor of 4th rank. It is shown that in this case the relative phase permeabilities depend not only on the saturation, but also on the ratios of major values of an absolute permeability tensor. The obtained relations for phase permeabilities are used for analyzing the results of numerical modeling of two-phase flow in the orthotropic porous medium. The versions of complex studies for obtaining phase permeabilities in anisotropic porous media from the results of laboratory measurements are discussed.

Numerous experimental studies have established not only the possibility of using the Darcy law but also limits of its applicability. In the proces of these investigations, the Darcy law was shown to be valid for both isotropic and anisotropic media, but it is fulfilled merely within a certain range of flow velocities. Thus, the upper and lower boundaries for the applicability of the Darcy law can be indicated. The upper boundary is caused by the manifestation of inertial forces at high velocities, while the lower one, by physicochemical effects for interaction of a fluid with a solid skeleton and by non-Newtonian rheological properties of the fluid. In this study, we consider the generalizations of the Darcy law with isotropic filtration properties at high filtration rates.

Modern methods of oil and gas fields development are based on the classical theory of nonmixing fluid filtration developed in the researches of Muskat M., Jeverett M. and their followers. The base of that theory is hypothesis of capillary pressure and relative phase permeabilities as universal equilibrium, stationary functions of instant saturation.