HR: 11:50h
AN: H32D-07    [Abstracts]
TI: A Moving Boundary Analysis of Two-Species Reaction-Diffusion with Applications to Chemical Oxidation of DNAPLs in Fractured Rock
AU: * Rajaram, H
EM: hari@colorado.edu
AF: University of Colorado, Boulder, Department of Civil Engineering Campus Box 428, Boulder, CO 80309-0428,
AB: This study was motivated by a problem arising in the context of chemical oxidation of dissolved DNAPL in a rock matrix by delivering oxidants such as permanganate through fractures. Under continuous flushing/recirculation, the concentrations of permanganate are maintained at a relatively constant level, while it diffuses into the rock matrix and reacts with the DNAPL. The permanganate-DNAPL reaction is typically described as a bimolecular reaction, based on experimental kinetic data. Due to the relatively rapid rate of the oxidation reaction, an appropriately defined Damkohler number is large. Under these conditions, a thin reaction front develops and propagates into the rock matrix at a rate controlled by diffusion. A mathematical analysis of the dynamics of this reaction front is presented. The reaction front can be described as a moving boundary by analogy with the classical Stefan problem in heat transfer with phase change. The propagation of the reaction front can be quantified using a reaction front diffusivity, which can be calculated explicitly. The reaction front diffusivity is shown to depend on the initial concentrations of DNAPL and oxidant, and their effective diffusivities. Scaling arguments are proposed to quantify the temporal dynamics of the DNAPL consumption rate and the width of the reaction zone. The results of the analysis for (i) reaction front propagation, (ii) DNAPL/oxidant consumption rate and (iii) reaction zone width, are all confirmed by numerical simulations.
DE: 1009 Geochemical modeling (3610, 8410)
DE: 1831 Groundwater quality
DE: 1832 Groundwater transport
DE: 4475 Scaling: spatial and temporal (1872, 3270, 4277)
DE: 4499 General or miscellaneous
SC: Hydrology [H]
MN: 2007 Fall Meeting