Consistent thermodynamic formulations for multiscale hydrologic systems: Fluid pressures

Although averaging procedures to derive larger-scale conservation equations from their microscopic counterparts have been examined and employed in a consistent manner for a range of hydrologic problems, procedures for obtaining correspondingly averaged thermodynamic relations at the larger scale have received less attention. We examine issues related to the change of scale for intensive thermodynamic quantities, such as fluid pressures and temperatures, compare formulations based upon the underlying thermodynamic theory relied upon, and produce precise, consistent definitions for fluid pressures and capillary pressures in multiphase porous medium systems. The averaged thermodynamics approach demonstrated and advocated is applicable to a wide range of hydrologic systems beyond the two-fluid porous medium case examined in detail in this work.