HR: 0800h
AN: H51F-0428    [Abstracts]
TI: Pore-scale Modeling and CTRW Analysis of Dispersion in Porous Media
AU: * Bijeljic, B
EM: b.bijeljic@imperial.ac.uk
AF: Imperial College, Department of Earth Science and Engineering, South Kensington Campus, London, SW7 2AZ United Kingdom
AB: We provide a physically based explanation for the complex macroscopic behavior of dispersion in porous media as a function of Peclet number, Pe. A Lagrangian pore-scale transport model incorporating flow and molecular diffusion is applied in 2D and 3D lattices of throats with square cross-section whose radius distribution is representative of Berea sandstone. The model accurately predicts NMR, laser fluorescence and the classic breakthrough data for the experimental dependence of the longitudinal dispersion coefficient, D_L}, on Pe. We compute the probability, Ψ(t)}, that a particle moves from one throat junction to a nearest neighbor junction in a time t and fit it to the simple analytical expression that depends on the mean advective transit time, t₁, a late-time cut-off, t₂, and a parameter characterizing the porous medium heterogeneity, (β). Then, interpreting transport as a continuous time random walk (CTRW), we show: (1) that the power-law dispersion regime is controlled by the variation in average velocity between throats (the distribution of local Pe rather than by diffusion from boundary layers within throats, giving D_L ~ Pe^δ with (δ = 3- β ≈ 1.2); (2) the cross-over to a linear regime for Pe > Pe_crit(≈ 400) is due to a transition from a diffusion-controlled late-time cut-off, to transport governed by advective movement; and (3) that the transverse dispersion coefficient D_T ~ Pe for all Pe >> 1. We provide a quantitative description of both asymptotic and pre-asymptotic dispersion using CTRW with a physical interpretation of the parameters. Hence, through an analysis of experiment, numerical modeling and theory we provide a physical explanation of the subtle and surprising dependence of dispersion coefficient in porous media on Peclet number. Our demonstration that the power-law dependence of dispersion coefficient on Peclet number is due to the distribution of flow speeds in individual pores contrasts with the traditional theories of Saffman and Koch and Brady that emphasize the contribution to dispersion within pores or at pore junctions.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: Fall Meeting 2005