Influence of Porous Structure Heterogeneity on the Dynamics of Development of Interfacial Contacts in Two-Phase Flows with Viscous and Capillary Fingers

An investigation of the effect of capillary and viscous forces on the dynamics of the development of two types of interfacial contacts "injected fluid–ejected fluid" and "injected fluid–solid body" in the case of two-phase flows in porous media with different heterogeneities of the pore structure is carried out. The connection between the dynamics of development of interfaces, distribution of fluids in the pore space of samples and the average size of pore channels filled with the injected fluid is being established. To simulate a two-phase flow the present work resorts to the lattice Boltzmann equations together with the multirelaxation time collision operator, as well as the color field gradient model for describing the effects of interfacial interaction. The relationship between the capillary and viscous forces is controlled by flow velocity and interfacial tension. Computational experiments are carried out on artificial digital models of porous media with the use of the Monte Carlo algorithm. The heterogeneity of porous structures is described numerically with the aid of the randomness coefficient calculated as the standard deviation of local porosity measured in Voronoi′s cells. A linear law of the development of the specific length of interfacial "fluid–fluid" and "fluid–solid body" contacts has been established. The two-phase flow parameters and the heterogeneity of the pore structure exert their effect only on the dynamics of the growth of the interface length. An increase in the heterogeneity of the pore structure contributes to the growth of the mean size of pore channels filled with injected fluid. The randomness coefficient exerts an insignificant effect on the dynamics of the development of the "fluid–fluid" contact and a negative effect on the dynamics of the development of the "fluid–solid body" interface. In transition from flow with viscous fingers to a regime with capillary fingers, a significant decrease in the dynamics of development of the "fluid–fluid" contact and an increase in the dynamics of the development of the "fluid–solid body" interface are observed