Specific interfacial area: the missing state variable in two-phase flow equations?

Abstract

Classical Darcy's equation for multiphase flow assumes that gravity and the gradient in fluid pressure are the only driving forces and resistance to the flow is parameterized by (relative) permeability as a function of saturation. It is conceivable that, in multiphase flow, other driving forces may also exist. This would mean that such nonequilibrium effects are lumped into a permeability coefficient. Indeed, many studies have shown that the relative permeability coefficient generally depends not only on saturation but also on dynamics of the system. Through the application of rational thermodynamics, a theory of two-phase flow had been developed in which interfacial areas were introduced as separate thermodynamic entities and their macroscale effects were explicitly included. This theory includes new driving forces whose significance needs still to be established. To study new terms in the theory, we employ a dynamic pore network model called DYPOSIT. A long pore network (several representative elementary volumes connected in series) is generated, which represents as a one-dimensional porous medium column. This model provides pore scale distribution of local phase pressures, capillary pressure, interfacial area, saturation, and flow rate, which are averaged to obtain the macroscale distributions of these variables. Our analysis shows that there are discrepancies between the simulation results and the classical equations to describe the transient behavior, especially for the nonwetting phase transient permeability. The coefficients in the extended equations are quantified and parameterized. Although under the applied Dirichlet boundary conditions, flow varies significantly, there is a clear trend illustrating dependency of coefficients on saturation, independent of dynamic conditions. Furthermore, using the new coefficients, it is possible to explain either transient or steady state flow regimes, which is a new achievement.