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Pore‐scale modeling and continuous time random walk analysis of dispersion in porous media
Author(s) -
Bijeljic Branko,
Blunt Martin J.
Publication year - 2006
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2005wr004578
Subject(s) - péclet number , random walk , dispersion (optics) , porous medium , continuous time random walk , exponent , power law , materials science , diffusion , statistical physics , mechanics , mathematics , physics , thermodynamics , statistics , porosity , optics , linguistics , philosophy , composite material
We provide a physically based explanation for the complex macroscopic behavior of dispersion in porous media as a function of Peclet number, Pe , using a pore‐scale network model that accurately predicts the experimental dependence of the longitudinal dispersion coefficient, D L , on Pe . The asymptotic dispersion coefficient is only reached after the solute has traveled through a large number of pores at high Pe . This implies that preasymptotic dispersion is the norm, even in experiments in statistically homogeneous media. Interpreting transport as a continuous time random walk, we show that (1) the power law dispersion regime is controlled by the variation in average velocity between throats (the distribution of local Pe ), giving D L ∼ Pe δ with δ = 3 − β ≈ 1.2, where β is an exponent characterizing the distribution of transit times between pores, (2) the crossover to a linear regime D L ∼ Pe for Pe > Pe crit ≈ 400 is due to a transition from a diffusion‐controlled late time cutoff to transport governed by advective movement, and (3) the transverse dispersion coefficient D T ∼ Pe for all Pe ≫ 1.