Рақамли технологияларнинг назарий ва амалий масалалари Том 8 № 2 (2025) · с. 17-36
Mathematical Model and Numerical Algorithm for the Study of the Hydrodynamic Process of In-Situ Leaching
Равшанов, Н., Усмонов, Л., Курбонов, Н.М.
Аннотация
This article presents a mathematical model and numerical algorithms for solving a three-dimensional fluid filtration problem in a porous medium, using the hydrodynamic process of in-situ leaching (ISL) as an example. The developed mathematical framework enables a comprehensive analysis of ore body development parameters, optimal placement of injection and production wells, estimation of fluid flow rates, and consideration of groundwater protection from contamination sources. Since the formulated problem is described by a system of multidimensional quasilinear partial differential equations, obtaining an analytical solution is challenging. For numerical integration, an algorithm based on a finite-difference scheme with component-wise splitting and streamline sweeping methods is constructed. The proposed mathematical approach can serve as an effective tool for analyzing and forecasting the parameters of ore deposit development and mineral extraction.
подземное выщелачиваниематематическое моделированиефильтрациядиффузиякинетикаполезная компонентачисленные методыin-situ leachingmathematical modelingfiltration
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