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

Most analytical or semi-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. This study presents a novel semi-analytical model for simulating the migrations of plumes of degradable contaminants subject to rate-limited sorption. The derived semi-analytical model is then applied to investigate the effects of the rate-limited (nonequilibrium-controlled) 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. The equilibrium-controlled sorption model agrees well with the rate-limited sorption model when the ratio of Damköler number to the product of distribution coefficient and bulk density is greater than 2 or 3 order of magnitude.