GRAVITATIONAL FORCES IN DUAL-POROSITY SYSTEMS .1. MODEL DERIVATION BYHOMOGENIZATION

We consider the problem of modeling flow through naturally fractured p orous media. In this type of media, various physical phenomena occur o n disparate length scales, so it is difficult to properly average thei r effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish th is through the mathematical technique of formal two-scale homogenizati on. This technique enables us to average the single-porosity, Darcy eq uations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We con sider three flow situations, the flow of a single component in a singl e phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.