Plume development of a nonlinearly adsorbing solute in heterogeneous porous formations

Abstract

Transport of nonlinearly adsorbing solutes in homogeneous and heterogeneous porous formations is considered. Initially, a fixed amount of solute is assumed to be present in the domain. Transport is characterized in terms of the first and second spatial moments. Nonlinear equilibrium adsorption is described by the Freundlich isotherm, with the Freundlich exponent n, 0 < n < 1. By asymptotic balancing we derive first‐order approximations of the limiting behavior of the plume position and plume growth as a function of time for the homogeneous case. In the heterogeneous case we consider random variation of a physical (log conductivity) and a chemical (log adsorption coefficient) parameter, both with an isotropic exponential covariance function. Expected behavior of the relevant spatial moments is obtained by applying a Monte Carlo approach. Individual realizations are solved numerically with a particle‐tracking scheme in which nonlinear adsorption is accounted for by a time‐dependent retarded velocity. We assess the effects of varying certain transport parameters, such as the degree of physical and chemical heterogeneity, degree of nonlinearity, the adsorption coefficient, and the degree of correlation between hydraulic conductivity and adsorption coefficient. Results of the homogeneous case for a strong degree of nonlinearity show good agreement between the numerical calculations and the limiting analytical expressions. Nonlinear adsorption is shown to have a strong effect on the shape of the plume, especially in longitudinal direction. For the heterogeneous case the analytical expressions predict well the time dependence of the growth rate of the spatial moments. Variation of the transport parameters demonstrates a dominating effect of the degree of nonlinearity on the plume dimensions, which is hardly affected by the degree of heterogeneity, correlation, and the adsorption coefficient. The variance of the mean plume position is affected by all parameters. Although the degree of heterogeneity has a strong impact, the longitudinal and transverse variances are reduced with respect to the linear adsorption case, due to the large size of the plumes.