Article

Transport in Porous Media

, Volume 1, Issue 2, pp 105-125

First online:

Flow in porous media II: The governing equations for immiscible, two-phase flow

  • Stephen WhitakerAffiliated withDepartment of Chemical Engineering, University of California

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Abstract

The Stokes flow of two immiscible fluids through a rigid porous medium is analyzed using the method of volume averaging. The volume-averaged momentum equations, in terms of averaged quantities and spatial deviations, are identical in form to that obtained for single phase flow; however, the solution of the closure problem gives rise to additional terms not found in the traditional treatment of two-phase flow. Qualitative arguments suggest that the nontraditional terms may be important whenμ β /μ γ is of order one, and order of magnitude analysis indicates that they may be significant in terms of the motion of a fluid at very low volume fractions. The theory contains features that could give rise to hysteresis effects, but in the present form it is restricted to static contact line phenomena.

Key words

Volume averaging interfacial phenomena closure