| Most groundwater transport problems involve spatially heterogeneous porous media. The spatial variations occur at many scales; however, typically only the largest length scales can be represented using the limited data available. We therefore view the heterogeneities occurring on smaller scales as random fields with known statistics. From this point of view, groundwater transport through heterogeneous porous media is a stochastic process.; The stochastic process of retardation in groundwater transport of a solute through porous media may be investigated by using Monte Carlo simulations, with a suite of computational realizations associated with a length scale, to examine phenomena particular to this problem. In this dissertation, we explore the effects of retardation heterogeneity on ensemble-average contaminant plumes.; After using Monte Carlo simulations to corroborate the effects stochastic retardation in groundwater transport of a solute through porous media, we aim to develop a new “effective equation” that will incorporate the known statistics in hopes that this equation will yield these, if not exactly, then similar effects. Stochastic approaches have been extensively applied to the study of solute transport in random porous media. Two reference frames are commonly employed, eulerian and lagrangian. Henceforth, we adopt an eulerian frame of reference. The new “effective equation” obeys a nonlocal integrodifferential equation with several significant numerical implications. The integral term in the “effective equation” is actually a triple integral, one of which is with respect to time. This time integral would begin to fill up the sparse banded matrix, derived from Galerkin finite elements, as the length scale, or correlation length, increases. The integral term is integrable, but contains a singularity at the current time T.; This “effective equation” has terms that imply both increased effective velocity and enhanced contaminant spreading that one cannot model using standard Fickian assumptions. Monte Carlo simulations, using suites of computational realizations, corroborate both effects. We discuss some theoretical and numerical implications of the new model, and computationally analyze its validity. |
