Pore-scale modeling and continuous time random walk analysis of dispersion in porous media

[1] 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, DL, 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 DL Pe with d = 3 b 1.2, where b is an exponent characterizing the distribution of transit times between pores, (2) the crossover to a linear regime DL Pe for Pe > Pe 400 is due to a transition from a diffusioncontrolled late time cutoff to transport governed by advective movement, and (3) the transverse dispersion coefficient DT Pe for all Pe 1.