By Larry W Lake
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2-26) can be construed as a constraint on the mass fraction ω i j , phase pressures Pj, and saturations Sj. 2-11) is a multiphase version of Darcy’s law for flow in permeable media (Collins, 1976). The single-phase version of Darcy’s law is actually a volumeaveraged form of the momentum equation (Slattery, 1972; Hubbert, 1956). The form given in Eq. 2-11) assumes creeping flow in the permeable medium with no fluid slip at the solid phase boundaries. Corrections to account for non-Darcy effects appear in standard references (Collins, 1976; Bear, 1972).
1-11) is the differential or “strong” form for the component conservation equation in each phase. It applies to any point (actually an REV) within the macroscopic dimensions of the permeable medium independent of the boundary conditions. From left to right in Eq. 1-11), the terms are now the accumulation, transport, and source terms, the last consisting of two types. 10 The strong form, Eq. 1-11), is useful in developing analytic solutions, a mainstay of this text. 1-11) and its analogous conservation equations are called the strong form because they express conservation at a point (a REV) within a medium.
2-4. There are a total of N C N P equations represented by Eq. 2-4). 16 Example 2-1. Writing the conservation equations for each component and phase. Consider two-component, three-phase flow in a permeable medium, where the components are component 1 and 2, and the phases are aqueous (w), oleic (o), and the solid phase (s). Write the specific conservation equations for each component and each phase assuming the solid phase is stationary (no deformation) and dispersive transport of each component in the solid phase is negligible.