Interfacial coupling in two-phase porous media flow was investigated analytically and numerically. Modified forms of Darcy's equation, which incorporated interfacial coupling (viscous and capillary coupling) and hydrodynamic effects, were formulated. A numerical scheme was developed to solve the equations and was codified into a standalone numerical simulator using the JavaTM programming language. From the results of the analyses carried out, the parameter that controls the amount of viscous coupling was, theoretically and experimentally, found to have maximum values of 2 and 0.001, respectively, in order to account for the effect of viscous coupling.
A comparison of analytical and experimental results shows that the transport equations give a good description of flow. The viscous coupling and capillary coupling effects are very small and can be neglected in horizontal, cocurrent flow. In horizontal, countercurrent flow, the capillary coupling was found to have a more significant effect than viscous coupling, which can be neglected. The hydrodynamic effects are found to be insignificant in horizontal, cocurrent and countercurrent flow. For vertical flow, analytical results show that viscous coupling effects are insignificant. Due to the limitations and non-availability of a complete set of vertical flow experimental data, the applicability of the capillary coupling concept could not be verified fully using the modified set of transport equations. Hence, the modified set of transport equation is yet to be verified for vertical flow.
Results of numerical studies confirm that the viscous and capillary coupling effects and hydrodynamic effects are very small in horizontal, cocurrent flow. It can be concluded that if the experimentally determined countercurrent effective permeability values are used in simulating a cocurrent flow process, the countercurrent effective permeability values would have to be divided by the interfacial coupling parameter, in order to obtain accurate predicted profiles. On the other hand, the cocurrent effective permeability values would have to be multiplied by the interfacial coupling parameter if the experimentally determined cocurrent effective permeability values are used in the numerical simulation of a countercurrent flow.
The conventional form of Darcy's equation, as modified by Muskat and Meres(1) and Muskat et al. (2) for multiphase flow has been shown to neglect the effect of interfacial coupling in porous media multiphase flow (See reference 3 to 9 and some other papers cited in these references). Ayub and Bentsen (7) provided a detailed literature review with regards to this. Despite this, the Muskat extension of Darcy's equation has been used for years to develop commercial simulators used in predicting and history matching multiphase hydrocarbon recovery. Many researchers have pointed out in multiphase flow, the presence of one fluid affects the flow of the other fluids leading to interfacial coupling effects, which may have a considerable effect on the flow of the fluids. This problem was probably first identified by Yuster. (10) when he pointed out the importance of the transfer of viscous forces across the fluidfluid interfaces. This phenomenon is also called the Yuster effect.