Two phase flow including interfacial area as a variable
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Based on the procedure of (Gray & Hassanizadeh 1998) we state macroscale conservation equations for multi phase flow in porous media including interfacial area as a variable. The phases we consider are a solid phase, a wetting phase and a non-wetting phase. Some modeling work is done to decide the functionality of the coefficients in the equations. In particular we construct constitutive relationships for the interfacial area as a function of saturation and capillary pressure, and the resistance terms. The final set of equations is reduced to a 2 x 2 system with the saturation and the interfacial area as independent variables. Some preliminary numerical experiments are reported.