Derivation of vertically averaged equations describing multiphase flow in porous media

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Abstract
An extension of the REV averaging technique, used to derive balance equations for multiphase or porous media flow problems, is presented Theorems which allow a one‐step transformation from three‐dimensional point equations for a single phase to two‐dimensional point equations for multiphase systems are derived. The theorems are then applied to obtain the vertically averaged balance equations of mass, chemical species, momentum, energy, and entropy. The relation between these equations and their unaveraged predecessors is clearer than when the standard two‐step averaging procedure is applied. Furthermore, constitutive relations are more easily hypothesized for the current system of equations than for previously derived forms.