Flow in heterogeneous porous mediums: 1. Darcian‐type description of two‐phase systems

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Abstract
Theoretical work leading to the description of fluid flow in a heterogeneous porous medium has developed slowly and somewhat sporadically, even though the areas of engineering applications predominantly involve flow in a nonhomogeneous medium. In providing a theoretically consistent basis for analysis, the special characteristics of macroscopically heterogeneous materials are discussed to provide accurate definitions. The definitions establish the functional dependence and make mathematical representation possible. The special implications of heterogeneity in Darcian‐type dynamic relationships for each of the fluid phases are considered, and the rotational velocity field resulting from nonhomogeneity is shown as a contrast to the classical irrotational case for flow in a homogeneous medium. The velocity field is also shown to be the classical complex lamellar type; hence considerable insight into the flow fields in heterogeneous mediums is immediately available. The end result of the discussion and derivation is a set of rather general Eulerian equations describing two‐phase flow in a macroscopically heterogeneous medium. These equations and their reduced forms include descriptions of some forty different flow systems. Such a variety of flow conditions is categorized through the use of a special tabular scheme, which makes it possible to write the appropriate equations efficiently. (Key words: Flow; heterogeneous porous mediums; equations)

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