Generalized solutions for advection-dispersion transport equations subject to time- and space-dependent internal and boundary sources

Advection-dispersion equations with first-order decay reactions are widely used to describe the fate and transport of reactive contaminants, contributing to effective site contamination prediction and management. Previous related studies typically address the role of only a single type of source, which discourages the understanding of the interaction mechanisms between various types of sources and the precise inversion of the complex source zone. Thus, this study develops a novel analytical solution for a reactive contaminant transport model associated with time- and space-dependent internal and boundary sources. Transient solutions for the multi-type source model were derived using Laplace transform, Fourier cosine transform, variable substitution method, and coordinate transformation techniques, verified against numerical results in the time and spatial domains. Results that the previous prediction model with the Neumann inlet boundary condition would underestimate the area of the contaminated region in a transport system subject to multiple types of sources. The interaction between internal sources and boundary sources can give rise to a rebound in the downstream contaminant concentration. Moreover, several fitting functions are suggested to quantify the influence of the spatial and temporal characteristics of the sources on the area of the contaminated region and the peak downstream concentration.