Effective parameters in heterogeneous and homogeneous transport models with kinetic sorption

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, i.e., 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 u eff ( t ) and the effective dispersion coefficient D eff ( t ). 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 u eff ( t ) and D eff ( t ) 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.