The equations of immiscible viscous displacement in a porous medium
A statistical theory for the construction of the equations of viscous displacement in a porous medium is considered. This yields a continuum theory for immiscible displacement which can be applied to either a homogeneous or inhomogeneous porous medium. The relative motions of the fluid are considered in terms of the motion of surfaces of constant saturation which are smoothed surfaces at the macroscopic scale considered. The boundary conditions and initial conditions at the injection boundary are considered as well as the boundary conditions and breakthrough conditions at the recovery boundary and the side boundary conditions. The inertial terms are included in the equations and shown to be of importance in describing these initial conditions and the breakthrough conditions.