Transport of Contaminant Release by Three Different Sources: A Medium with Complex Geometry

Abstract

This study develops a mathematical model for contaminant transport from two industrial sources and one natural source through a heterogeneous aquifer featuring fracture networks with variable apertures, faults of heterogeneous width, and a complex rock matrix. Key innovations include: (1) A nonlinear Darcy’s law with concentration-dependent conductivity; (2) Three coupled advection-dispersion equations with nonlinear dispersion and reaction terms for multispecies interactions; (3) Seasonal recharge dynamics integrated into flow-transport coupling. Non-dimensional analysis reveals advection-dominated regimes governed by Péclet and Damköhler numbers. Bifurcation analysis identifies stability thresholds for ternary chemical reactions. Numerical solutions via the Crank-Nicolson scheme demonstrate fracture-controlled contaminant pathways and recharge-modulated plume evolution. The framework provides critical insights for pollution management in geologically complex aquifers.