Understanding the dynamic displacement of immiscible fluids in porous media is important for carbon dioxide injection and storage, enhanced oil recovery, and non-aqueous phase liquid contamination of groundwater. However, the process is not well understood at the pore scale. This work therefore focuses on the effects of interfacial tension, wettability, and the viscosity ratio on displacement of one fluid by another immiscible fluid in a two-dimensional (2D) Berea sandstone using the colour gradient lattice Boltzmann model with a modified implementation of the wetting boundary condition. Through invasion of the wetting phase into the porous matrix, it is observed that the viscosity ratio plays an important role in the non-wetting phase recovery. At the viscosity ratio ( λ ) of unity, the saturation of the wetting fluid is highest, and it linearly increases with time. The displacing fluid saturation reduces drastically when λ increases to 20; however, when λ is beyond 20, the reduction becomes less significant for both imbibition and drainage. The front of the bottom fingers is finally halted at a position near the inlet as the viscosity ratio increases to 10. Increasing the interfacial tension generally results in higher saturation of the wetting fluid. Finally, the contact angle is found to have a limited effect on the efficiency of displacement in the 2D Berea sandstone.
Snap-off is a crucial mechanism for drop breakup in multiphase flow within porous media. However, the systematic investigation of snap-off dynamics in constricted capillaries with varying pore and throat heights remains limited. In this study, we conducted three-dimensional simulations of drop behavior in a constricted square capillary with non-uniform depth, employing a color-gradient lattice Boltzmann model. Our analysis encompassed a comprehensive range of parameters, including geometrical factors and physical properties, such as capillary number, initial drop size, viscosity ratio, constriction length, and the presence of soluble surfactants. Depending on these parameters, the drop exhibited either breakup or deformation as it traversed the constriction. Upon snap-off occurrence, we quantified two significant aspects: the snap-off time t̂b, which represents the time interval between the drop front passing the constriction center and the snap-off event, and the volume of the first daughter drop V̂d generated by the breakup mechanism. Consistently, we observed a power-law relationship between t̂b and the capillary number Ca. However, the variation of V̂d with Ca exhibited a more complex behavior, influenced by additional factors, such as the viscosity ratio and the presence of surfactants, which break the linear increase in V̂d with Ca. Notably, the inclusion of surfactants is able to homogenize the volume of the first daughter drop. Through our comprehensive numerical study, we provide valuable insight into the snap-off process in constricted capillaries. This research contributes to the understanding of multiphase flow behavior and facilitates the optimization of processes involving snap-off in porous media.
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