Dispersion modeling in pore networks: A comparison of common pore-scale models and alternative approaches

Mass transfer in porous media resulting from dispersion occurs in a wide variety of applications such as water treatment, flow batteries, flow in aquifers, enhanced oil recovery, and packed-bed reactors. The underlying mechanisms of dispersion are the molecular diffusion superimposed on the advective transport induced by the fluid flow. Modeling dispersion in pore networks can be performed at a much lower computational cost compared to that in direct numerical simulations (DNS) such as finite element or the lattice Boltzmann methods, so it can be regarded as a suitable alternative provided its accuracy is sufficient. The most common approach to model dispersion in network models is based on the first-order upwind scheme, despite its known limitations in terms of accuracy for certain flow and transport regimes. In this study, three alternative pore-scale models for dispersion, which are more accurate than the existing ones, were derived and tested in pore network simulations. These models were adopted from the CFD literature and are based on a spatial discretization of the advection-diffusion equation using the hybrid and power-law finite difference schemes and the exact solution of the one-dimensional advection-diffusion equation. Finally, considering dispersion problems over arbitrary porous structures, consisting of stick-and-ball geometries, and different flow and mass transfer arrangements, the developed models were validated. Validation was carried-out through comparisons between results obtained with DNS, using a finite element solver, and those from pore network simulations. It is shown that under a wide range of dispersion regimes (up to the onset of the dispersion power-law regime), the relative error (with respect to DNS results) introduced by the power-law and exact solution-based models is consistently below 1%, whereas the use of the upwind scheme leads to >10% of relative error, depending on the dispersion regime. All the dispersion models developed in this study were implemented as part of the open-source network modeling package, OpenPNM.