Mathematical Model of Solute Transport in Macroscopic Inhomogeneous Porous Medium Based on Multi-Stage Deposition Kinetics

Source abstract

This study develops a mathematical model for solute transport in a two-dimensional macroscopic inhomogeneous porous medium consisting of mobile and stagnant or low-mobility zones. The model accounts for solute exchange between the zones and incorporates multistage deposition kinetics, including deposition and release of suspended particles during transport. The governing system of equations describes advective–diffusive transport in the mobile region, diffusive mass transfer in the low-mobility region, and the evolution of deposited material. An efficient numerical algorithm based on the finite difference method is developed for solving the resulting coupled problem. The pressure-gradient and permeability fields are determined as part of the numerical procedure, and the resulting transport equations are solved using an implicit difference scheme and the progonka method. Numerical experiments are performed to investigate the influence of medium inhomogeneity, deposition and release coefficients, and diffusion parameters on the spatial and temporal evolution of solute concentration and deposition. The results demonstrate that exchange between mobile and low-mobility regions substantially affects the concentration distribution, while increasing the deposition rate reduces the penetration and spatial spreading of the solute and leads to greater accumulation of deposited material. The simulations also demonstrate characteristic features associated with multistage deposition kinetics, including changes in the concentration-profile behavior. The proposed model provides a numerical framework for describing solute transport and deposition processes in heterogeneous porous media.