Non-linear filtration models and the effect of nonlinearity parameters on flow rates in low-permeability reservoirs

Filtration of oil in low-permeable reservoirs is considered. The experimental data of dependence of filtration velocity on pressure gradient are analysed. It is shown that the filtration law in low-permeability reservoirs differs from the linear Darcy’s law and from the non-linear law with an initial pressure gradient. The power law of filtration in low-permeability reservoirs is experimentally substantiated. Models of nonlinear filtration influence on flow rate are proposed. The analysis of influence of nonlinear filtration parameters on flow rate in technogenically modified near-wellbore zone is carried out.

Inverse Problem For A Linear Filtration Function

The article is devoted to an important task of underground hydro-mechanics-filtration of suspension in a porous medium. One-dimensional long-term deep filtration of a monodisperse suspension in a homogeneous porous medium is considered. For a one-dimensional macroscopic model with a linear filtration function, an asymptotic solution is constructed near the concentration front of suspended and retained particles. On the basis of explicit asymptotic formulas, the inverse filtration problem is studied : finding the filtration function for a given concentration of suspended particles at the outlet of a porous medium. It is revealed that the least squares method is an effective way to determine the model parameters. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the numerical solution. The proposed numerical - asymptotic method makes it possible to calculate the linear filtration function using laboratory experiments and adjust the model to specific field conditions. It is concluded that the next stage in solving the inverse filtration problem is to determine unknown parameters of a nonlinear filtration function that depends on three or more constants. To do this, it is needed to modify the methods presented in this paper.

Capillary Impregnation with Non-Linear Filtration Laws

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.