Abstract
The basis of a general theory of multicomponent, multiphase displacement in porous media is presented. The theory is applicable to an arbitrary number of phases, an arbitrary number of components partitioning between the phases, and variable initial and injection conditions. Only the effects of propagation are considered; phase equilibria and dependence of fractional flows on phase compositions and saturations are required as input, but any type of equilibrium and flow behavior can be accommodated. The principal simplifying assumptions are the restriction to one dimension, local phase equilibria, volume additivity on partitioning, idealized fluid dynamic behavior, and absence of temperature and pressure effects. The theory is an extension of that of multicomponent chromatography and has taken from it the concept of "coherence" and, for practical application, the tools of composition routes and distance/time diagrams. The application of the theory to a surfactant flood is illustrated in a companion paper.1
Introduction
A key problem in modern methods of enhanced oil recovery is that of multicomponent, multiphase displacement in porous media. This term means the induced flow of any number of simultaneous, not fully miscible fluid phases consisting of any number of components. The components may partition between the phases; moreover, the physical properties of the phases (densities, viscosities, interfacial tensions, etc.) depend on composition and, therefore, on partitioning of the components.
Multicomponent, multiphase displacement may be viewed as a generalization and combination of two different and independent approaches. The first of these is the highly developed theory of multicomponent chromatrography,2 which allows for any number of components affecting one canother's distribution behavior but admits only one mobile and one stationary phase. This theory has to be extended to more than one mobile phase. The second is the fluid dynamic theory of immiscible displacement in porous media, allowing for more than one mobile phase but not for partitioning of components. This theory was developed in the 1940's for two mobile phases3 and so far has not been stated in general form for more than two phases. It has to be extended to include partitioning of the components between the phases and its effects on phase properties. A summary of the start of the art, including recent work on systems with up to three components and two phases, has been given by Pope.4
This paper describes the extension of the theory to multicomponent, multiphase displacement with partitioning and for arbitrary initial and boundary conditions. The theory concerns itself only with transport behavior. Phase equilibrium and flow properties of the phases (relative permeabilities) as a function of composition are considered as given. Application of the theory, therefore, requires as input either empirical correlations of experimental data on phase equilibria and properties or theories predicting these. Morever, the theory concentrates exclusively on multicomponent, multiphase effects and does not attempt to account for the complex fluid dynamic situation in real, three-dimensional, and nonuniform reservoirs.
Simulation of sharp interface multi-material flows involving an arbitrary number of components through an extended five-equation model
