Abstract
In connection with the increasing share of low-permeability oil and gas reservoirs, of particular scientific and practical interest is the study of the characteristics of the flow of filtration processes in reservoirs characterized by non-linear filtration laws. The article presents the results of an analytical study of the features of capillary impregnation of low-permeability reservoirs characterized by non-linear filtration laws. Mathematical modeling of the impregnation processes was carried out under the assumption that the dependence of the filtration rate on the pressure gradient modulus near the zero point can be represented by a power function. It was established that, in contrast to capillary impregnation processes under the traditional linear Darcy law, the intensity of impregnation of low-permeability layers of a productive formation in a nonlinear case depends on the longitudinal pressure gradient in the formation - the larger this gradient, the higher the intensity of impregnation. It was also shown that for nonlinear filtration laws, the capillary impregnation front in a porous medium with a fluid at rest can propagate at a finite speed, which is impossible with linear filtration laws.
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