Analytical Modelling of Contaminant Transport in One-Dimensional Porous Medium Domains: The Fourier-FFT Approach

Analytical solutions for contaminant transport in porous media are important for understanding subsurface processes and validating numerical models. However, conventional Laplace-transform-based approaches often face difficulties in handling realistic transient boundary conditions and typically result in challenging inverse formulations that require computationally intensive convolved integration. To address these limitations, this paper presents a Fourier-FFT analytical framework for solving the well-established one-dimensional advection–dispersion–reaction (ADR) equation in homogeneous and heterogeneous porous domains. The proposed Fourier-FFT approach enables straightforward mathematical formulation, rapid computation, and incorporation of realistic transient boundary conditions beyond idealized step or impulse inputs. Verification against a Laplace-based analytical solution for a homogeneous domain and a finite element solution for a dual-permeability domain show good agreement, confirming the accuracy of the method. Parametric analyses further demonstrate that the framework captures the expected physical behaviour of contaminant transport under varying hydrogeological and reaction conditions.