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Abstract:
Transport of dissolved tracers undergoing kinetic sorption in saturated porous media is described on the basis of a dual-porosity model with heterogeneous and cross-correlated sorption parameters, ie. distribution coefficient and exchange rate. The approach is a conceptual model for reactive transport in a medium with spatially varying reaction capacity, given by the distribution coefficient, and spatially varying accessibility, given by the exchange rate.

We treat the sorption parameters as a stochastic process and apply a perturbation approach. From the ensemble-averaged spatial moments of a plume, we analytically derive formal expressions for time-dependent effective transport parameters. For vanishing microdispersion, the calculations are carried out up to second order for the effective transport velocity and the effective dispersion coefficient.

For large times, the effective retardation is determined by the ensemble-averaged distribution coefficient, whereas the effective dispersion is related to the sorption parameters in a more complicated way, depending on the variability of the exchange rate and of the distribution coefficient. Effective sorption parameters are given.

For comparison, we derive exact expressions for the effective transport velocity and dispersion coefficient in a homogeneous triple-porosity model. Unlike the simpler homogeneous dual-porosity model, the triple-porosity model yields a satisfactory description of the time-dependent dispersion of the heterogeneous model. The appropriate sorption parameters for the triple-porosity model are given as functions of the stochastic parameters.