AN EVALUATION OF NONLINEARITY IN SPATIAL 2ND MOMENTS OF ENSEMBLE MEANCONCENTRATION IN HETEROGENEOUS POROUS-MEDIA

The integrodifferential equation for the spatial second moments X of t he ensemble mean concentration in a heterogeneous aquifer is nonlinear due to statistical dependence of the particle displacement on X. This nonlinear equation is either linearized or quasi-linearized in previo us studies to derive the linear and quasi-linear theories of time-depe ndent macrodispersion in aquifers. In this study a fully nonlinear ana lysis is carried out by solving the integrodifferential equation for X numerically and iteratively. The effects of the variance of log hydra ulic conductivities sigma(Y)(2), the local Peclet number P-e, and the anisotropic ratio e are then investigated. Results show that in both s tatistically isotropic and anisotropic media, as compared with the lin ear theories, the effect of nonlinearity in X is to reduce the spatial longitudinal variance, X(11), and enhance the transverse spreading of a solute plume except in isotropic media with sigma(Y)(2) less than o r equal to 1, where the linear theories may underestimate the longitud inal spreading of a solute. It is also shown that the effect of local dispersion on X(11) can be neglected when P-e greater than or equal to 10 but on the transverse macrodispersion, this effect is significant for P-e as large as 100. Nevertheless, the effect of P-e on macrodispe rsion is secondary as compared with the effect of nonlinearity in X. A pplication of the nonlinear results shows good fits to the observed sp atial variances df tracer concentration in the Borden experiment and e xcellent agreement with the simulated variances from recent Monte Carl o Simulations.