Ability of Single-Rate Models to Predict Solute Distribution Coefficients in Systems with Heterogeneous Sorption Kinetics

Several sorption nonequilibrium models have been developed to gain a better understanding of solute transport in porous media, among which are those that assume a single-rate behavior. In this study, two commonly used single-rate models were fitted to computer-simulated breakthrough data from hypothetical column experiments in which multirate sorption kinetics exist at the pore scale. The objective was to determine how the sorption distribution coefficient (K) predicted using these models depends on the conditions under which the data were obtained. Simulated cases covered a range of experimental conditions and involved compounds with different sorption characteristics and different degrees of sorption rate heterogeneity. Results revealed that, for a system with a multirate sorption behavior, the true K value is under-predicted if the parameter estimation is determined by curve fitting a single-rate model. The extent of deviation between the fitted and true K increases with the decrease in residence time and increase in sorption rate heterogeneity. Functional relationships were developed between the relative reduction in K and solute residence time. Analysis using the relationships developed suggests that a major potential cause of the previously reported discrepancy between batch- and column-determined K could be attributed to the use of single-rate models for parameter prediction.