HR: 16:35h
AN: H34E-03    [Abstracts]
TI: Upscaling Flow and Transport Through Block Permeability Inclusions by an Analytical Approach
AU: * Sviercoski, R
EM: rsvier@lanl.gov
AF: Los Alamos Nat. Laboratory, Los Alamos, Los Alamos, NM 87545, United States
AU: Travis, B
EM: bjtravis@lanl.gov
AF: Los Alamos Nat. Laboratory, Los Alamos, Los Alamos, NM 87545, United States
AB: Numerical simulation of flow and transport in natural porous media becomes very challenging when one takes into account the multi-scale heterogeneity of geological formations. Instead of obtaining the fine-scale solution numerically, which may be computationally expensive, another approach is to derive an up-scaled equation that provides the averaged solution and an approximation to the small scale dynamics. We present an analytical method to obtain the up-scaled coefficient when the heterogeneous coefficients (e.g., permeability) are periodic and rapidly oscillating and can be defined locally as step functions describing inclusions in a primary matrix. The new contribution involves deriving an analytical approximation for the solution of the periodic cell-problem, obtained by a two-scale asymptotic expansion of the governing heterogeneous equation. The analytical approximation also provides a lower bound of the generalized Voigt-Reiss' inequality. By defining a corrector to the approximation, the up-scaled coefficient is obtained as well as an analytical basis function that is used to derive the first-order term of the two-scale expansion. The known analytical results in the literature, such as the geometric average for a checkerboard geometry, are derived as particular cases and a comparison with some numerical results from the literature is presented. We demonstrate the convergence properties numerically, for linear and nonlinear problems of interest for flow in porous media. Further, we apply these results to special cases of transport and multi-scale diffusion, for a range of inclusion surface areas.
DE: 1839 Hydrologic scaling
DE: 1847 Modeling
DE: 1869 Stochastic hydrology
DE: 1875 Vadose zone
SC: Hydrology [H]
MN: 2007 Fall Meeting