Abstract
The article is devoted to the calculating analysis of established filtering process. The results of calculations are presented in graphical form. Charts are provided with axis labels, and detailed explanations are given. Main hydrodynamic parameters (pressure distribution, filtration rate, pressure gradient, viscosity) of the viscoplastic oil layer in the problem of stationary filtration are calculated. It is assumed that the process of filtering is radially symmetric. The model of finite layer is used. Predetermined pressure is maintained on the boundary of the layer. Oil is considered weakly fluid and its density is determined by formula [4]. At the same time it is assumed that oil viscosity depends on pressure gradient and this dependence is approximated by the sigmoid function [2]. The proposed problem is solved by the method of finite differences using Newton's method to solve the nonlinear system of equations. The main features of hydrodynamic curves in the proposed type of modelling are distinguished and their differences from the case of constant viscosity are found. So pressure distribution curve of viscoplastic oil lies below the pressure distribution curve of conventional oil, therefore in every point of layer pressure values for viscoplastic oil are smaller than corresponding values for oil with constant viscosity. For the test, calculation basic input parameters are fixed in this paper: extent of the layer, pressure on the boundary of the layer, initial density, viscosity with maximally destroyed structure, viscosity with not destroyed structure, compressibility coefficient, while the following parameters alternately vary: values of shear gradient, smoothness with the approximation of dependence of viscosity on pressure gradient. Assessment of impact of these parameters on pressure distribution, pressure gradient, viscosity, and filtration rate in radius of the layer is conducted. In conclusion the main results of the investigation are summarized.
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