Correction of the Buckingham–Darcy Law for flow of high strength salts in variably saturated porous media

The Buckingham–Darcy Law is used to describe fluid flow in unsaturated porous media at low Reynolds number. In order to provide a priori corrections to this law, a process thermodynamic approach is utilized to ascertain the functional dependence. Using this knowledge, corrections to the hydraulic conductivity coefficient are proposed and compared with available data. The proposed corrections substantially predict the observed behavior of flow of high concentration (saturated) sodium chloride solutions in porous media. During the derivation, physical principles consistent with the thermodynamics of the system were utilized. A review of these principles and their results provides an alternative form of the generalized Gibbs–Duhem Relation for continuous processes, indicating that the identical equivalence to zero is unlikely to occur for dissipative processes. Further, the postulated Gibbs and Gibbs–Duhem Relations indicate that special differential operators need to be used for continuous processes rather than the usual use of a generic differential.