HR: 1340h
AN: H23D-1625    [Abstracts]
TI: Investigation of Numerical Upscaling Techniques for Mixing-Controlled Reactions in Heterogeneous Media
AU: * Valocchi, A J
EM: valocchi@uiuc.edu
AF: University of Illinois at Urbana-Champaign, Department of Civil and Environmental Engineering 205 N. Mathews, Urbana, IL 61801, United States
AU: Nakshatrala, K B
EM: nakshatr@uiuc.edu
AF: University of Illinois at Urbana-Champaign, Department of Civil and Environmental Engineering 205 N. Mathews, Urbana, IL 61801, United States
AB: Mixing of chemical species across plume boundaries has a major influence upon reactive pollutant fate in the subsurface. Small-scale heterogeneity leads to irregular plume boundaries which enhances mixing-controlled reactions through increasing the interfacial area of the plume. Therefore, it is crucial to capture this small-scale heterogeneity in order to properly model reactive transport. Unfortunately, computational limitations do not permit full resolution of the smallest scales of heterogeneity, and thus it is necessary to use a coarse numerical grid, particularly for cases with a large number of reactive species. In order to capture the sub-grid scale heterogeneity effects, we investigate the extension of multi-scale numerical techniques (which have been proved successful for diffusion and Darcy flow problems) to mixing-controlled reactive transport. The proposed upscaling technique is based on the multi-scale decomposition of the solution (which is similar to that proposed by Arbogast [1] for Darcy flow). We divide the governing system into two sub- problems – coarse-scale and fine-scale. We assume that the solute concentration has two components – coarse-scale (which is defined at the grid scale) and fine-scale (which is defined at the smallest modeled scale). The fine-scale sub-problems are solved locally by constructing numerical Green's functions, which are independent of the coarse-scale problem. The localization of fine-scale sub-problems is achieved by the closure assumption, which is enforced by prescribing appropriate boundary conditions for the fine-scale sub-problem. In this study, we investigate the effect of various closure approximations (i.e., boundary conditions for fine-scale sub- problem) on the overall accuracy of the numerical solution. We apply our multi-scale methods to several canonical problems for fast bi-molecular reactions. [1] T. Arbogast. Numerical subgrid upscaling of two-phase flow in porous media. In Z. Chen, R. E. Ewing, and Z.- C. Shi, editors, Numerical Treatment of Multiphase Flows in Porous Media, volume 552 of Lecture Notes in Physics, pages 35–49, Springer-Verlag, Berlin, 2000.
DE: 0560 Numerical solutions (4255)
DE: 1832 Groundwater transport
DE: 1847 Modeling
DE: 3225 Numerical approximations and analysis (4260)
SC: Hydrology [H]
MN: 2007 Fall Meeting