Large-scale properties for flow through a stratified medium: Various approaches

Determination of effective properties or pseudofunctions for two-phase flow through heterogeneous porous media is an important problem in petroleum reservoir engineer. The authors purpose was to compare published theories with test case studies. The test case was the waterflooding of a two-stratum heterogeneous medium. Generalized Darcy equations were solved with a black-oil reservoir simulator. Several simulations were performed by varying the filtration velocity, and the relative importance of gravity effects vs. capillary and viscous effects was studied. On the basis of an extensive literature survey, they tested two fundamental methods: a large-scale averaging method and a fine- to coarse-grid method. In the large-scale averaging method, large-scale equations and properties are obtained by averaging the Darcy-scale equations over a representative volume of the heterogeneous medium. The fine- to coarse-grid method consists of performing a simulation on the whole domain with a fine grid and then obtaining the pseudo-capillary pressure and pseudopermeabilities by averaging these results over a coarse grid. Application of the averaging techniques basically provides large-scale properties for cross sections of the stratified medium. The simulations showed three fundamental types of flow that correspond to gravity equilibrium, capillary equilibrium, and dynamic flow conditions. The ability of the two methods tomore » represent these various flow conditions properly is discussed through comparison of water-cut curves. From dimensional analysis of the descriptive equations, criteria for choosing the method are proposed« less