PLUME DEVELOPMENT OF A NONLINEARLY ADSORBING SOLUTE IN HETEROGENEOUS POROUS FORMATIONS

Transport of nonlinearly adsorbing solutes in homogeneous and heteroge neous porous formations is considered. Initially, a fixed amount of so lute is assumed to be present in the domain. Transport is characterize d in terms of the first and second spatial moments. Nonlinear equilibr ium adsorption is described by the Freundlich isotherm, with the Freun dlich exponent n, 0 < n < 1. By asymptotic balancing we derive first-o rder approximations of the limiting behavior of the plume position and plume growth as a function of time for the homogeneous case. In the h eterogeneous case we consider random variation of a physical (log cond uctivity) and a chemical (log adsorption coefficient) parameter, both with an isotropic exponential covariance function. Expected behavior o f the relevant spatial moments is obtained by applying a Monte Carlo a pproach. Individual realizations are solved numerically with a particl e-tracking scheme in which nonlinear adsorption is accounted for by a time-dependent retarded velocity. We assess the effects of varying cer tain transport parameters, such as the degree of physical and chemical heterogeneity, degree of nonlinearity, the adsorption coefficient, an d the degree of correlation between hydraulic conductivity and adsorpt ion coefficient. Results of the homogeneous case for a strong degree o f 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 long itudinal direction. For the heterogeneous case the analytical expressi ons predict well the time dependence of the growth rate of the spatial moments. Variation of the transport parameters demonstrates a dominat ing effect of the degree of nonlinearity on the plume dimensions, whic h 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.