Recursive analytical solution for nonequilibrium multispecies transport of decaying contaminant simultaneously coupled in both the dissolved and sorbed phases

Multispecies transport analytical models that solve advection-dispersion equations (ADEs) are efficient tools for evaluating the transport of decaying contaminants and their sequential products. This study develops a novel semi-analytical model to simulate the multispecies transport of decaying contaminants, considering nonequilibrium sorption and decay in both dissolved and sorbed phases. First-order reversible kinetic sorption equations with decay processes are coupled to ADEs. Recursive analytical solutions, using the Laplace transform and generalized integral transform, are developed to address the mathematical complexity of the governing equations. The model's simulation results show excellent agreement with both numerical models and existing analytical solutions. Applied to a four-member radionuclide decay chain, the model reveals that including decay in the sorbed phase results in a lower concentration of the first member and avoids underestimating the radioactivity concentrations of daughter elements. These differences in dissolved radioactivity concentrations between models with and without sorbed phase decay may impact health risk assessments for radioactive waste disposal. Finally, this study provides a more sophisticated mathematical tool for analyzing multispecies transport in real field conditions where nonequilibrium sorption processes predominantly occur.