Multiscale modeling of nonlinearly adsorbing solute transport

We focus our investigations on hydrologic subsurface transport processes of a solute dissolved in groundwater. Moreover, the solute adsorbs nonlinearly on the soil matrix. Starting with transport in homogeneous media, we introduce a new methodology to identify transport parameters from dissolved solute concentration data. Transport in heterogeneous media is investigated by using a stochastic modeling approach. For mildly heterogeneous media we construct a perturbation theory around the homogeneous nonlinear theory and derive explicit expressions for asymptotic and transient large-scale transport parameters. Asymptotically, we find that the large-scale parameters are exactly the same as for linearly adsorbing transport. Differences between transport with linear and nonlinear adsorption become apparent for transient times. The characteristic time or length scales to reach the asymptotic regime depend on the grade of the nonlinearity: the smaller the Freundlich exponent p, the larger the characteristic time or travel distance. The theoretical results are verified in a semianalytical approach. Ensemble and effective dispersion coefficients are obtained from integral expressions by means only of homogeneous concentration data. We found an excellent agreement between the analytical predictions and the semianalytical results.