STOCHASTIC-ANALYSIS OF THE TRANSPORT OF KINETICALLY SORBING SOLUTES IN AQUIFERS WITH RANDOMLY HETEROGENEOUS HYDRAULIC CONDUCTIVITY

One of the most promising approaches for modeling solute transport in heterogeneous aquifers describes the natural variability in hydraulic conductivity by means of a stationary random field. Therefore the solute concentration distribution at a given time also becomes a random field. For the case of an inert solute, Dagan (1982, 1984) found a solution for the temporal evolution of the spatial moments of the ensemble average concentration random field; this solution describes the impact of small-scale heterogeneity upon large-scale spreading of the plume (the so-called macrodispersion phenomenon). In this paper we extend Dagan's (1982, 1984) results to the case of a reactive solute undergoing linear reversible adsorption. We assume spatially uniform kinetic rate coefficients. The solution obtained explicitly quantifies the combined effect of nonequilibrium adsorption reactions and macrodispersion, for a range of possible time scales of both processes. We show that for very large times the effects of macrodispersion and kinetics are additive, while for shorter times they are related in a nonlinear fashion. As a particular application of our solution, we demonstrate that the conditions necessary for the existence of local equilibrium depend not only on the kinetic rate coefficients but also upon the spatial structure of the conductivity field. The observed behavior of an organic solute used in the Borden field experiment appears to be consistent with the predictions of the new model.