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

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.