Toward an improved understanding of multiphase flow in porous media

Physical description of multiphase flow in porous media ideally should be based on conservation principles. In practice, however, Darcy's law is employed as the foundation of multiphase flow studies. Darcy's law is an empirical surrogate for momentum conservation based on data obtained from experimental study of one-dimensional single-phase flow. In its original form [Darcy, 1856], Darcy's law contained a single, constant coefficient that depended on the properties of the medium. Since 1856, Darcy's relation has been heuristically and progressively altered by allowing this coefficient to be a spatially dependent, nonlinear function of fluid and solid phase properties, particularly of the quantities of these phases within the flow system. The shortcoming of this approach is that the governing flow equation is obtained by enhancing a simple empirical coefficient with complex functional dependencies rather than by simplifying general conservation principles. As a result, some of the important physical phenomena are not properly accounted for. Also, some assumptions intrinsic to the equations are overlooked, making accurate simulation more of an art than an entirely scientific exercise. A more general and more theoretically appealing approach to the derivation of conservation principles for multiphase flow has been evolving over the last 30 years. This approach employs a mathematical procedure for deriving conservation principles at the length scale of interest, followed by imposition of thermodynamic constraints to restrict the generality of these expressions. The product of this approach is a set of balance equations that provides a framework in which the assumptions inherent in a hypothesized model of multiphase flow are clearly stated. Requirements for more comprehensive and physically complete models can then be specified.