ABSTRACT
The objective of this chapter is to formulate megascopic relations for the equilibrium thermodynamics of an elastic porous matrix saturated with a compressible viscous fluid on a firm basis. It is assumed that the pores are well connected. Volume averaged equations will be used to provide the linkage to the pore scale thermodynamics rather than employing what might be called an "axiomatic" approach. Part of the motivation is to find for porosity, the new purely megascopic variable, its natural "thermodynamic" role. It will be shown that aside from its bookkeeping role (keeping track of proportions of the phases by volume), the porosity also appears in the work terms. Furthermore it is found to play a dynamic role independent of temperature thus yielding a theory of porodynamics that has analogies with thermodynamics. It is clear that a thermodynamic role for saturation in the case of compressible multiphase fluid motions can be established in an analogous fashion. Furthermore if one considers the segregation of the phases by their mass fractions (cf. Chapter VII), then the relevant thermodynamic variable becomes the megascopic concentration. The importance of the thermodynamic role that the above megascopic thermodynamic variable plays in each case occurs due to the relation between the dilational motions of the component phases and the change of these megascopic variables. This relation and how it is process dependent can be clearly seen through the description of the fluid and solid components and their interactions as described in sections ii, iii and iv.
