Numerical implementation of the one-dimensional microscopic model of in-situ leaching

• Main Author: А. С. Жумали
• Format: Article
• Language: English
• Published: Al-Farabi Kazakh National University 2017-11-01
• Series: Вестник КазНУ. Серия математика, механика, информатика
• Subjects: leaching; free boundary; microscopic model; numerical implementation
• Online Access: https://bm.kaznu.kz/index.php/kaznu/article/view/349/306
• ISSN: 1563-0277; 2617-4871

This publication is devoted to the numerical implementation of the mathematical model on a microscopic level of in-situ leaching process in the case of one space variable. The mathematical model is based on the common system of differential equations, when the fluid dynamics is described by the equation of motion of an incompressible fluid filling the pores of absolute solid ground skeleton, and dynamics of the active solution is described by the equation of diffusion-convection with point boundary conditions on the unknown free boundary between the fluid and the solid skeleton, expressing the conservation law of reagents. Numerical simulation by finite difference method is applied for the numerical solution of the problem. The nonlinear boundary conditions defined on the unknown free boundary is numerically solved by the iterative Newton’s method. For a more precise description of the movement of the free boundary, interpolation method is detailed. The significance of computer modelling of in-situ leaching process on a micro scales is an ability to study the basic mechanisms of the flow of physical and chemical process comprises reacting an active solutions with a solid skeleton and its movement through the capillary. The article presents the results of the problem in the case of one space variable in the form of graphs, obtained in mathematical environment Matlab.