Constitutive theory for vertically averaged equations describing steam‐water flow in porous media

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Abstract
Constitutive theory based on the Coleman and Noll method of exploitation of the entropy inequality is applied to the vertically averaged equations describing flow of two fluid phases in a porous medium. In the most general case considered the solid phase is assumed to be inert and elastic while each fluid phase is allowed to undergo phase change. For simplicity, the phases are assumed to be ideal in that the thermodynamic state within a phase depends only on the properties of that phase. However, interphase processes depend on the thermodynamics of all phases. The general constitutive forms obtained are ultimately linearized for the slow flow case to obtain equations appropriate for the description of a geothermal reservoir or other slow, two‐phase fluid flow through an elastic medium.