Analytical Solutions for Transport of Linearly Adsorbing Solutes in Heterogeneous Formations

Abstract

A new first‐order analytical solution for stochastic transport of reactive solutes in physically and chemically heterogeneous porous formations is derived and discussed. Physical and chemical heterogeneities are assumed partially correlated. The derived solution complements previous results obtained by the authors (Bellin et al., 1993). The solution proposed relies on the assumption of chemical activity described by the local linear equilibrium assumption postulating the existence of a (spatially variable) retardation factor. Retardation factors, R(x) and log permeabilities (Y(x)) modeling heterogeneities are described statistically by random space functions with assigned correlation structure. The analytical expressions derived reduce to Dagan's (1984) classic solution for the case of nonreactive solute transport and to Bellin et al.'s (1993) solutions for perfectly correlated physical and chemical heterogeneities. The main conclusion is that longitudinal dispersion may be significantly affected by different degrees of correlation between chemical and physical heterogeneities. However, such an impact vanishes progressively as the geometric mean of the partition coefficient increases and the plume behaves as in perfectly correlated cases. Transverse dispersion is not affected by either perfect or partial correlation between R and Y.