Acceleration of Numerical Modeling of Uranium In Situ Leaching: Application of IDW Interpolation and Neural Networks for Solving the Hydraulic Head Equation

The application of In Situ Leaching (ISL) has significantly boosted uranium production in countries like Kazakhstan. Given that hydrodynamic and chemical processes occur underground, mining enterprises worldwide have developed models of reactive transport. However, modeling these complex processes demands considerable computational resources. This issue is particularly significant in the context of numerical analyses of mining processes or when modeling production scenarios in uranium mining by the ISL technique, given that a substantial portion of computational resources is allocated to solving the hydraulic head equation. This work aims to explore the applicability of PINNs to accelerate hydrodynamic simulations of the ISL process. The solution of the Poisson equation is accelerated by generating an initial approximation for the iterative method through the application of the Inverse Distance Weighting (IDW) interpolation and PINNs. The impact of various factors, including the computational grid and the spacing between wells, on both the accuracy and efficiency of initial approximation and the overall solution of the elliptic equation are explored. Employing the hydraulic head distribution obtained through PINNs as the initial approximation led to a significant reduction in computation time and a decrease in the number of iterations by a factor of 2.8 to 7.10.