The primary complication that must be addressed in this chapter is the complex interfacial phenomena occurring between fluid phases at the pore scale and how this information enters the megascopic description. The effect of phase transitions on multiphase flow is also described. It has been observed that phase transitions can have an important stabilizing effect on displacement processes (Krueger, 1982a; 1982b; de la Cruz et al., 1985). The concept of capillary pressure in porous media as has been reviewed by a number of authors (e.g., Dullien, 1992; Barenblatt et al., 1990; Bear and Bachmatt, 1990; Lenormand and Zarcone, 1983, de Gennes, 1983). The megascopic pressure difference between phases, however, depends on the megascopic variables and thus its connection to the pore scale capillary pressure is sometimes difficult to delineate (cf. Barenblatt et al., 1990; Bear and Bachmatt, 1990; Bentsen, 1994). In the present discussion the megascopic pressure difference is described by considering the incompressible limit of the equations of compressible fluid flow through porous media. Here the equations for compressible fluid flow through porous media have been constructed from the well-understood equations and boundary conditions at the pore scale. Furthermore one may make use of the thermodynamical understanding (de la Cruz et al., 1993) of the parameters and variables described in Chapter III when considering this limit. This turns out to be an important consideration because the pressure equations for each of the fluid phases take on an
indeterminate form in this limit, and the equation which defines the process under consideration is not independent of the continuity equations in this limit. It is observed that these three equations can be combined, when taking the incompressible limit of the system of equations describing the fluid motions, to yield a single process dependent relation. This new equation is a dynamical capillary pressure equation, which completes the system of equations for incompressible multiphase flow.