HR: 09:35h
AN: H51K-05    [Abstracts]
TI: Non-Fickian Transport in Geological Formations: Theory and Observations
AU: * Scher, H
EM: harvey.scher@weizmann.ac.il
AF: Weizmann Institute of Science, Dept. of Environmental Sciences and Energy Research, Rehovot, 76100 Israel
AU: Berkowitz, B
EM: brian.berkowitz@weizmann.ac.il
AF: Weizmann Institute of Science, Dept. of Environmental Sciences and Energy Research, Rehovot, 76100 Israel
AB: Non-Fickian (or anomalous) transport of contaminants has been observed at field and laboratory scales, in a wide variety of porous and fractured geological formations. Over many years, advection-dispersion equation (ADE) models - and a range of variants - have been considered, developed, and applied to modeling of transport in such systems. We argue that these methods are intrinsically unsuited to account for this anomalous transport due to their averaging procedures (e.g., mean local rates). In disordered systems we demonstrate that statistically rare, slow transition rates limit transport. We retain the full range of these transitions with a pdf Ψ (r,t), where r is a transition step displacement and t is the time (inverse transition rate). Working directly with pdf's instead of mean rates is the basic approach of a continuous time random walk (CTRW) formalism. We have demonstrated CTRW to be a general and effective formulation to quantify non-Fickian transport in laboratory- and field-scale systems. We now develop the CTRW within the framework of partial differential equations (pde) and generalize its applicability to non-stationary domains (e.g., extended field sites). These pde's are non-local in time as they incorporate a memory function M(t) based on σ_r Ψ (r,t); they can be solved by conventional numerical methods in Laplace space. We show that physical models of M(t) account for effective t-dependent dispersion and the evolution to macrodispersion. In this context we exhibit recent experimental results. Specialized M(t)'s include formulations such as multirate mass transport, double-porosity, mobile-immobile, fractional derivative, and ADE models. Hence they are subsets within the CTRW framework.
DE: 1832 Groundwater transport
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: Fall Meeting 2005