Three-Dimensional Mathematical Model and Numerical Solution Algorithm for Monitoring and Predicting In-Situ Leaching Processes in Porous Medium

The article analyzes the hydrodynamic processes associated with underground mining, in particular, the acid extraction of precious metals from ore deposits. In order to comprehensively study, monitor and predict the behavior of the object, a mathematical model (MM) based on the filtration-convection and diffusion processes characteristic of underground fluid filtration was developed. This model includes the influence of various hydrodynamic parameters, in particular, the filtration coefficient and average porosity, which are functions of the pressure level and process kinetics. Analysis of the problem statement shows that the change in pressure in the ore deposit resulting from the pouring and extraction of the solution directly affects the permeability and porosity coefficients of the layer. The experimental results showed that the change in hydrodynamic parameters was proportional to the change in pressure, with an exponential behavior observed under high pressure and a linear behavior under low pressure. It should be noted that in the process of in-situ leaching (ISL), a chemical reaction occurred as a result of the reagent’s effect on the ore deposits, and the substance passed from one phase to another, as a result of which the hydrodynamic parameters of the pore medium (filtration and porosity coefficients) and pressure changes in the ore reservoir were observed.