Multiphase viscoelastic flow through porous media

Local volume averaging of the equations of continuity and of motion over each phase in a porous medium is discussed. For a Noll simple material, inertial effects may be neglected with respect to viscous effects as the product of a Reynolds number with a Weissenberg number goes to zero (in the limit of a Newtonian fluid, inertial effects may be neglected as the Reynolds number goes to zero). When inertial effects can be neglected, a resistance transformation for each phase is introduced which in part maps the local volume‐averaged velocity vector into the local force per unit volume which that phase exerts on the pore walls and the moving phase interfaces. Capillary pressure is defined through a local surface average of the jump balance for momentum. The shape of the curve denoting capillary pressure as a function of saturation in a two‐phase flow may vary with the contact angle. For an isotropic multiphase flow of incompressible materials, the functional dependence of the resistance coefficient for a Noll simple material and for a Newtonian fluid is discussed by means of the Buckingham‐Pi theorem.