Pore scale insights into the role of inertial effect during the two-phase forced imbibition

Abstract

Fluid inertia could significantly alter the flow paths of fluids in multiphase flow. This study aims to quantify the role of the inertia effect in fluid flow through porous media using the modified color-gradient lattice Boltzmann method. Specifically, we focused on understanding the effects of fluid inertia on two-phase distribution, pore scale events, displacement patterns, transient behaviors of fluids, and the consumption of thermodynamic energy. Results show that the effect of fluid inertia on the two-phase distribution and the final invading wetting saturation is trivial under a low viscosity ratio. However, as the viscosity ratio increases, the inertia effect becomes more pronounced and cannot be ignored in the displacement process. This observation can also be found from the dependence of the invading saturation on the injected volume when the viscosity ratio and the Ohnesorge (Oh) number are varied. In addition, we found that the contribution from the post-breakthrough stage to the total invading saturation is increasingly significant with the increasing viscosity ratio, and its contribution varies depending on the fluid inertia for a given viscosity ratio. We also used the pressure difference between the inlet and outlet to identify the direction of energy conversion in multiphase flow. It is found that for the high viscosity ratio, there is a positive relationship between the dissipated energy and the invading saturation, and both exhibit a non-monotonic change with increasing Oh. However, for low viscosity ratios, fluid inertia does not significantly affect forced imbibition. In addition, the nonwetting phase becomes less connected with the injected wetting fluid, and there exists an almost linear relationship between the invading wetting saturation and the Euler characteristic, irrespective of the Oh numbers for a given viscosity ratio. The mechanism of inertial effect is that the local fluid velocity can be several orders of magnitude larger than the mean velocity despite the low capillary number, which leads to frequent release of surface energy and notably alters the flow paths, particularly under the unfavorable displacement pattern.