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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 properties 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 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 modeling of effluent concentration profiles. The disagreement between the directly estimated parameters and those obtained by the mobile-immobile-based inverse modeling 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.

Plain Language Summary Solute transport in two-phase flow through porous media is an important topic for many industrial and natural processes such as nutrient transport in partially saturated soils in agriculture, transport of chemicals in oil reservoirs for enhanced oil recovery, or in soil remediation. Modeling multiphase flow and transport in different applications is essential to improve the design and operational condition. Hence, the predictive capabilities of such models need to be improved. To evaluate the assumptions embedded in one of the most commonly used theories, referred to as the mobile-immobile theory, we have performed pore-scale simulations of these physical processes. By upscaling the simulation results, we directly estimated the transport properties and compared them with the inverse modeling results using the mobile-immobile theory. There is a significant discrepancy between the directly and indirectly estimated results that imply the potential shortcomings in the mobile-immobile theory. Moreover, it has been discussed that potentially the two-phase relative permeability data can be used as a proxy to estimate the stagnant (immobile) saturation that will link two-phase Darcy theory with the transport models.