Effect of momentum transfer between fluid phases on effective mobility

Conventional methods for determining effective mobilities are based on the assumption that interfacial momentum transfer may be neglected. The effect of such neglect is investigated by using fractional flow theory, in conjunction with Kalaydjianʹs transport equations and Liang and Lohrenzʹs method for calculating generalized mobilities, to construct new equations for calculating effective mobilities. With the help of these equations, it is shown that, for the sand–fluid system used in this study, neglect of viscous coupling between the two flowing phases can result in the introduction of relative errors as large as 30% into the calculated values of the effective mobilities. Because the largest errors occur only in the frontal region, and because the actual shape of the frontal region is unimportant in most practical problems, it is thought that the errors arising because of such neglect should be tolerable, provided that the displacement is stabilized. Finally, the results of this investigation are used as a basis for arguing that the cross coefficients, λ12 and λ21, which control momentum transfer between fluid phases in porous media, cannot be equal. The fact that interfacial momentum transfer should not be neglected is important to a clear understanding of multiphase flow through porous media. Thus, the results of this study should be of interest to theoreticians, people who measure effective mobility, and the people who use such information in reservoir simulation.