ABSTRACT
This chapter presents a system of megascopic equations for the flow of incompressible, immiscible fluid phases in porous media. It constructs the complete system of equations for compressible fluid flow and considers incompressible limit of these equations. The equations of multiphase flow in homogeneous porous media were first constructed by V. de la Cruz and T. J. T. Spanos. The equations of motion for the flow of miscible fluid phases have generally been modelled by the convection diffusion equation. This equation is based on the mixing of fluid phases at the molecular scale and completely misses the dynamic processes that occur at various other scales in porous media. Equations describing the flow of two immiscible fluid phases were constructed. It was shown that if the displacing fluid has a lower viscosity than the displaced fluid, then one of two instability processes dominate at the front separating these two fluids.
