Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures

Hydrodynamic dispersion process in relation with the geometrical properties of the porous media are studied in two sets of 6 porous media samples of porosity θ ranging from 0.1 to 0.25. These two sets of samples display distinctly different evolutions of the microstructures with porosity but share the same permeability trend with porosity. The methodology combines three approaches. First, numerical experiments are performed to measure pre-asymptotic to asymptotic dispersion from diffusion-controlled to advection-controlled regime using Time-Domain Random Walk solute transport simulations. Second, a porosity-equivalent network of bonds is extracted in order to measure the geometrical properties of the samples. Third, the results of the direct numerical simulations are interpreted as a Continuous Time Random Walk (CTRW) process controlled by the flow speed distribution and correlation. These complementary modeling approaches allow evaluating the relation between the parameters of the conceptual transport process embedded in the CTRW model, the flow field properties and the pore-scale geometrical properties. The results of the direct numerical simulations for all the 12 samples show the same scaling properties of the mean flow distribution, the first passage time distribution and the asymptotic dispersion vs. the Péclet number than those predicted by the CTRW model. It allows predicting the asymptotic dispersion coefficient D* from Pe = 1 to the largest values of Pe expected for laminar flow in natural environments (Pe≈ 4,000). D*∝Pe2−α for Pe≥Pecrit, where α can be inferred from the Eulerian flow distribution and Pecrit depends on porosity. The Eulerian flow distribution is controlled by the distribution of fractions of fluid flowing at each of the pore network nodes and thus is determined mainly by the distribution of the throat radius and the coordination number. The later scales with the number of throats per unit volume independently on the porosity. The asymptotic dispersion coefficient D* decreases when porosity increases for all Péclet values larger than 1 due to the increase with porosity of both α and the flow speed decorrelation length.