Investigations of Interfacial Coupling Phenomena and its Impact on Recovery Factor
Authors: Zhang X.Y. , Bentsen R.G. , Cunha L.B. 
Published: March 2010

Abstract
Interfacial coupling phenomena in multiphase flow through porous media and its impact on the recovery factor have been of interest for sometime, especially in the SAGD process and in fractured reservoirs. In this study, a numerical simulator that takes into account inlet end effects was developed to solve the modified transport equations proposed by Bentsen(1, 2), Ayub and Bentsen(3), Ayub(4) and Ayodele(5) to account for interfacial coupling phenomena and hydrodynamic effects. Moreover, the simulator was validated using experimental data. Finally, sensitivity analysis studies were carried out with the simulator to show the effect of interfacial coupling phenomena on the recovery factor.

Introduction
It is well known that Darcy's equation was developed on the basis of experiments involving single-phase flow through porous media. To account for multiphase flow, Darcy's equation was modified by Muskat et al.(6) into a form that has been widely used in petroleum reservoir engineering. However, as pointed out by several researchers(1, 3, 7–13), the modified equation can not give accurate recovery predictions when used to simulate multiphase flow in petroleum reservoirs. This is because, in multiphase flow, the presence of one fluid affects the flow of the other fluids; that is, interfacial coupling effects (viscous and capillary coupling effects) influence the flow. The viscous coupling effect, first identified by Yuster(14), refers to the coupling that arises due to the viscous drag exerted by one fluid on the other when they flow through the same porous medium, and it is usually associated with the mobility of the fluids(5). The capillary coupling effect, recently postulated by Babchin and Yuan(15) and by Bentsen(16), refers to the coupling that arises due to coupling, through the capillary function(2), of pressure across the interfaces of the fluids. Moreover, counter-current experimental data(17–19) has been used to show that Muskat's extension of Darcy's equation does not correctly describe the physics of multiphase flow through porous media, because the magnitude of the relative permeabilities for a given phase obtained from counter-current flow is always less than that acquired from a co-current experiment conducted in the same porous medium.
To closely capture the physics of flow, Bentsen(1, 2), Ayub and Bentsen(3), Ayub(4) and Ayodele(5) developed a set of modified transport equations that incorporate interfacial coupling and hydrodynamic effects. In the following sections, a one-dimensional form of these modified transport equations is solved numerically by developing an Interfacial Coupling Simulator (ICS). Simulation results are compared with immiscible displacement experimental data and some conclusions are drawn as well.

Mathematical Formulation
To describe the one-dimensional immiscible displacement flow by using the fractional flow concept, two governing equations, the fractional flow equation and the frontal advance equation, are needed.
Fractional Flow Equation
With the assumption that two immiscible and incompressible fluids flow through a homogenous and isotropic water-wet porous medium, Bentsen(1, 2), Ayub and Bentsen(3), Ayub(4) and Ayodele(5) developed a set of modified transport equations whose one-dimensional form is as follows:
V1 = Equation 1 Available In Full Paper
V2 = Equation 2 Available In Full Paper
The definitions for the relat