Saturation-Dependence of Non-Fickian Transport in Porous Media

In two-phase flow through porous media, the percolating pathways can be hydrodynamically split into the flowing and stagnant regions. The highly-variable velocity field in the pore space filled by the carrier fluid leads to significant differences in the transport time scales in the two regions that cannot be explained by the Fickian (Gaussian) advection-dispersion equation. In contrast with the Darcy-scale studies, up to now, relatively limited pore-scale studies have been devoted to the characterization of transport proper- ties in two-phase flow. In this paper, we report on the results of computer simulation of advection-dispersion transport in steady-state two-phase flow through porous media using a pore-network model, employed as an upscaling tool. The simulation results are upscaled to directly estimate the Darcy-scale transport coefficients and properties, namely, stagnant saturation, the mass-transfer coefficient between the flowing and stagnant regions, and the longitudinal dispersion in the flowing regions. The mobile-immobile (MIM) model, one of the most commonly used models for simulating non-Fickian transport in porous media, is used to estimate the transport properties using the inverse modelling of effluent concentration profiles. The disagreement between the directly-estimated parameters and those obtained by the MIM-based inverse-modelling implies fundamental shortcomings of the latter for describing transport in two-phase flow. The simulation results indicate that the relative permeabilities may be used to obtain accurate estimates of the stagnant saturation, which link two-phase Darcy’s law and transport.