Development of a Semi-Analytical Solution for Simulating the Migration of Parent and Daughter Contaminants from Multiple Contaminant Sources, Considering Rate-Limited Sorption Effects

Most existing multispecies transport analytical models primarily focus on inlet boundary sources, limiting their applicability in real-world contaminated sites where contaminants often arise from multiple internal sources. This study presents a novel semi-analytical model for simulating multispecies contaminant transport driven by multiple time-dependent internal sources. The model incorporates key transport mechanisms, including advection, dispersion, rate-limited sorption, and first-order degradation. In particular, the inclusion of rate-limited sorption addresses limitations in traditional equilibrium-based models, which often underestimate pollutant concentrations for degradable species. The derivation of this semi-analytical model utilizes the Laplace transform, finite cosine Fourier transform, generalized integral transform, and a sequence of inverse transformations. Results indicate that the concentrations of contaminants and their degradation products are highly sensitive to the variations in time-dependent sources. The model’s most significant contribution lies in its capability to simulate the contaminant transport from multiple internal pollution sources at a contaminated site under the influence of rate-limited sorption. By enabling the representation of multiple time-varying sources, this model fills a critical gap in analytical approaches and provides a necessary tool for accurately assessing contaminant transport in complex, realistic pollution scenarios.