An analytical model for nonlinear adsorptive transport through layered soils

Solute transport with nonlinear adsorption occurs in many situations involving inorganic chemical and metal contamination in soil and groundwater systems. The resulting isotherms can be highly nonlinear, and numerical solutions of the transport equation can encounter severe convergence difficulties. An analytical solution is developed for simulating one-dimensional transport in the layered soil column with nonlinear adsorption effects. The analytical solution is an exact solution for nondispersive transport and becomes an approximate one when dispersion effects are included. The accuracy of the solution has been examined using a numerical model under advection-dominated conditions. The derived analytical solution can be used for any form of nonlinear sorption isotherms given as closed-form functions, or tabulated data, with a general time-dependent source boundary condition. The heterogeneity of soils is handled by treating the soil column as a layered system. The resulting analytical model is suitable for estimating the leaching potential of metals or other solutes in the subsurface and for determining travel times of contaminants. Our analysis shows that the shape and nonlinearity of the sorption isotherm may have a controlling influence on transport behavior. Evaluation and application examples are provided to demonstrate applicability of the solution to solute and metal transport with both functional and tabular nonlinear isotherms.