Hydrodynamic dispersion and mixing under two-phase flow can be found in many natural, industrial, and engineering processes such as the modified salinity water flooding (MSWF). In MSWF the injected water displaces the formation brine and will interact with the crude oil and rock to improve the oil recovery. We show throughout numerical simulations that access of the injection water to the available pore space is not homogeneous, even in homogeneous porous media, and it is controlled by the saturation topology and pore-scale velocity field.Under the steady-state two-phase flow in a homogeneous porous medium, the velocity field has a bimodal distribution. The bimodal distribution of pore-scale velocity dictates two different transport time scales spatially distributed over the stagnant and flowing regions at a given saturation topology. These distinctly different transport time scales lead to a non-Fickian transport, which cannot be captured using the conventional advection-dispersion equation.Using the volume-of-fluid method implemented in the OpenFOAM (ver. 4.0), we simulated pore-scale two-phase flow and the hydrodynamic transport at different saturations. We have investigated the impact of stagnant saturation and the tortuosity of flow pathways on the dispersion coefficient and the mass exchange rate -as the two major parameters controlling transport and mixing -under steady-state two-phase flow. At the Darcy scale, different theories such as the mobile-immobile (MIM) theory have been proposed to capture the non-Fickian transport and mixing in two-phase flow through porous media. Based on the simulation results, we assess the validity of the assumptions employed in MIM to define the stagnant saturation and mass exchange rate coefficient. The results of this research provide fresh insights into the potential impact of saturation topology on mixing between the modified salinity water and the formation brine under steady-state flow conditions, which has not been investigated and reported in the literature.Hydrodynamic dispersion and mixing in two-phase flow through porous 2 media are found in many natural, industrial, and engineering processes such 3 as contaminant transport in the vadose zone where the infiltrated water car-4 ries the contaminants and mixes with the resident water, while air has filled 5 some part of the pore space [37,4,23]. Another example is the modified-6 (or low-) salinity water flooding (MSWF) as one of the enhanced oil recovery 7 techniques, in which injection water with a tuned chemical composition is 8 injected into the reservoir filled originally with the formation brine and the 9 crude oil [31, 1,29,42]. The performance of MSWF depends on many pore-10 scale physio-chemical factors such as crude oil chemistry, formation brine and 11 injection water chemistry, temperature, and rock mineralogy, which have 12 been extensively studied [33, 2,25]. However, the larger-scale mechanical 13 factors such as transport and mixing of the modified-salinity water have not 14 been extensively studied. ...

Low salinity waterflooding has proven to accelerate oil production at core and field scales. Wettability alteration from a more oil-wetting to a more water-wetting condition has been established as one of the most notable effects of low salinity waterflooding. To induce the wettability alteration, low salinity water should be transported to come in contact with the oil-water interfaces. Transport under two-phase flow conditions can be highly influenced by fluids topology that creates connected pathways as well as dead-end regions. It is known that under two-phase flow conditions, the pore space filled by a fluid can be split into flowing (connected pathways) and stagnant (deadend) regions due to fluids topology. Transport in flowing regions is advection controlled and transport in stagnant regions is predominantly diffusion controlled. To understand the full picture of wettability alteration of a rock by injection of low salinity water, it is important to know i) how the injected low salinity water displaces and mixes with the high salinity water, ii) how continuous wettability alteration impacts the redistribution of two immiscible fluids and (ii) role of hydrodynamic transport and mixing between the low salinity water and the formation brine (high salinity water) in wettability alteration. To address these two issues, computational fluid dynamic simulations of coupled dynamic two-phase flow, hydrodynamic transport and wettability alteration in a 2D domain were carried out using the volume of fluid method. The numerical simulations show that when low salinity water was injected, the formation brine (high salinity water) was swept out from the flowing regions by advection. However, the formation brine residing in stagnant regions was diffused very slowly to the low salinity water. The presence of formation brine in stagnant regions created heterogeneous wettability conditions at the pore scale, which led to remarkable two-phase flow dynamics and internal redistribution of oil, which is referred to as the "pull-push" behaviour and has not been addressed before in the literature. Our simulation results imply that the presence of stagnant regions in the tertiary oil recovery impedes the potential of wettability alteration for additional oil recovery. Hence, it would be favorable to inject low salinity water from the beginning of waterflooding to avoid stagnant saturation. We also observed that oil ganglia size was reduced under tertiary mode of low salinity waterflooding compared to the high salinity waterflooding.

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