Pore-scale modeling of dispersion in disordered porous media

We employ a direct pore-level model of incompressible flow that uses the modified moving particle semi-implicit (MMPS) method. The model is capable of simulating both unsteady- and steady-state flow directly in microtomography images of naturally-occurring porous media. We further develop this model to simulate solute transport in disordered porous media. The governing equations of flow and transport at the pore level, i.e., Navier–Stokes and convection–diffusion, are solved directly in the pore space mapped by microtomography techniques. Three naturally-occurring sandstones are studied in this work. We verify the accuracy of the model by comparing the computed longitudinal dispersion coefficients against the experimental data for a wide range of Peclet numbers, i.e., 5 × 10− 2 < Pe < 1 × 106. Solutions of full Navier–Stokes enable us to examine the impact of inertial forces at the very high Peclet numbers. We show that inclusion of the inertial forces improves the agreement between the computed dispersion coefficients with their experimental counterparts. We then investigate the impact of pore-space topology on the pre-asymptotic and asymptotic dispersion regimes by comparing solute dispersion in the three sandstones that possess different topological features. We illustrate how grain size and homogeneity of the two sandstones dictate the threshold and magnitude of the asymptotic regime.

Research Highlights
► A direct pore-level model is introduced to study solute transport in porous media.
► Pore-level transport in micro-CT images of three natural sandstones is studied.
► Computed dispersion coefficients are validated against experiments for 0.05 < Pe < 106.
► Impact of inertia on the asymptotic dispersion coefficient is investigated.
► Impact of pore-space topology on evolution of dispersion coefficient is examined.