Analytical model for coupled multispecies advective dispersive transport subject to rate-limited sorption

Abstract. Mathematical models that analytically solve a set of simultaneous multispecies advection-dispersion transport equations coupled with a series of chemical reactions are cost-effective tools for predicting the plume migration of dissolved chlorinated solvents and nitrogen chains. However, few analytical solutions for coupled reactive multispecies transport equations have appeared in the literature. For convenience of mathematical derivation, most analytical models currently used to simulate multispecies transport assume instantaneous equilibrium between the dissolved and sorbed phases of the contaminant. However, research has demonstrated that rate-limited sorption process can have a profound effect upon solute transport in the subsurface environment. Making the instantaneous equilibrium sorption assumption precludes consideration of potential effects of the rate-limited sorption. This study presents a novel analytical model for simulating the migrations of plumes of decaying or degradable contaminants subject to rate-limited sorption. The derived analytical model is then applied to investigate the effects of the rate-limited sorption on the plume migration of degradable contaminants. Results show that the kinetic sorption rate constant has significant impacts on the plume migration of degradable contaminants. Increasing the kinetic sorption rate constant results in a reduction of predicted concentration for all species in the degradable contaminants while the equilibrium-controlled sorption model lead to significant underestimation of the concentrations of degradable contaminants under conditions with low sorption Damköler number, Da_i = β_iLν. The equilibrium-controlled sorption model agrees well with the rate-limited sorption model when the Damköler number is greater than 2 to 3 order of magnitude. The invalidity of the equilibrium-controlled sorption model of low Damköler number case implies that the health risk could be underestimated if such a model is used for assessing the concentrations of the degradable contaminants in the health risk model.