Stochastic analysis of transport and multicomponent competitive monovalent cation exchange in aquifers

Abstract

Most stochastic analyses of reactive transport in physically and geochemically heterogeneous aquifers have focused on the analysis of a single reactive species. Here we conduct the stochastic analysis of multicomponent competitive monovalent cation exchange. Transport equations for dissolved cations are coupled with nonlinear cation exchange terms, which, for chemical equilibrium, are described by mass-action law expressions. These equations can be effectively decoupled by assuming that the weighted sum of cation concentrations is constant. The weight of each cation is equal to the reciprocal of its selectivity. Randomness of cation exchange capacity (CEC) leads to random retardation factors. Analytical expressions for effective retardation factors, longitudinal macrodispersivities, and concentration spatial moments are derived for a chemical system made of three monovalent cations (Na1 ,K 1 , and Cs 1 ) using the stochastic analytical solution of Miralles-Wilhelm and Gelhar (1996). Our results indicate that effective retardation factor, RC,i, spatial moments, and macrodispersivities of K1 are significantly different from those of Na1 . Effective retardation factors asymptotically attain their mean values after a transient phase of cationdependent duration. They strongly depend on the correlation between log-permeability (log K) and CEC. Pre-asymptotic effective retardation factor values for a negative correlation are smaller than the mean value, regardless of the value of the coefficient of variation of CEC (CVCEC). The smaller (larger) the variance of log K, , the great2 sf er (smaller) the effective retardation factor for a negative (positive) correlation. Cation