Simulation of the process of plane-radial filtration of fluid in a porous medium considering the migration

¹ Research Institute for the Development of Digital Technologies and Artificial Intelligence, Tashkent, Uzbekistan
² “TIIAME” NRU, Department of “Information Technologies”, 100000, Qori Niyoziy street, 39, Tashkent, Uzbekistan

^* Corresponding author: abdullaevv.zafar@gmail.com

Abstract

Modeling plane-radial fluid filtration in a porous medium is considered in the article, taking into account the condition of fluid flow to a perfect well with a constant flow rate drilled in the center of the formation; the problem of identifying the parameters, entering the mathematical formulation to the problem, is solved. Solving the problem, the values of the following parameters were determined: T - the coefficient of water conductivity, which ranges from 15% to 27%, and μ^∗− the coefficient of water loss (water filtration), which ranges from 22% to 31% relative to the exact values used in solving the forward problem. In the course of the study, it was revealed that one of the main parameters in the process of ground and underground water filtering in porous media is the identification of evaporation parameters. To identify their values, the following methods were applied in the study: the method of barycentric coordinates; the least squares method; and the gradient method. Numerical experiments were conducted at a time when the critical depth of groundwater was a known value, while q₀, n were the unknown parameters. The analysis of the studies showed that the “discrepancy” takes the minimum value when the found parameters (taken as zero approximations) are used in the least squares method.