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

Few analytical or semi-analytical models simulating the transport of sequentially decaying reaction products affected by nonequilibrium sorption in the groundwater have been presented considering decay or degradation reaction occurring exclusively in the dissolved phase in the literature. However, the process of decay in the sorbed phase, which is important for the transport of decaying contaminants, has been neglected in previously developed analytical models. This study is thus designed to develop a novel semi-analytical model for simulating the multispecies transport of decaying contaminants subject to a nonequilibrium sorption process simultaneously coupled in both the dissolved and sorbed phases. For this purpose, a set of first-order reversible kinetic sorption reaction equations that respectively represent the nonequilibrium sorption processes between the dissolved and sorbed phases, are coupled to a set of advection-dispersion equations, to illustrate the decay process which occurs in both the dissolved and the sorbed phases. By including the decay in the sorbed phase both the parent sorbed concentration and daughter sorbed concentration coexist in a set of first-order reversible kinetic sorption reaction equations, which absolutely complicate the theoretical derivation of the analytical solution.
 Recursive analytical solutions are derived to account for the concentration distribution of arbitrary transformation products with the aid of the Laplace transform and generalized integral transform. The correctness of the solutions is confirmed through a comparison of our newly derived recursive analytical solution with an existing model which considers an equilibrium sorption process. The newly developed recursive analytical solution is then applied to investigate how the decay in the sorbed phase affects the nonequilibrium transport of a four-member radionuclide decay chain. The result clearly predicts a lower radioactivity concentration of the first nuclide (238Pu), with decay in the sorbed phase, than the simulated results obtained using a model without decay in the sorbed phase. For other daughter elements (234 U, 230 Th, 226 Ra) of the radionuclide decay chain, neglect of decay in the sorbed phase leads to overestimation of the radioactivity concentrations. The result of large differences found in dissolved radioactivity concentration between the decay and no decay in sorbed phase may alter the decision of health risk assessment in the performance of radioactive waste disposal site. The implication is that the decay reactions of contaminants in the sorbed phase are important mechanisms that should be taken into accounts for accurately simulating and assessing the nonequilibrium multispecies transport of decaying contaminants.