Correction of the Buckingham–Darcy Law for flow of high strength salts in variably saturated porous media |
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| Authors: | Erick R Burns Maria I Dragila John S Selker Ronald B Guenther Jean-Yves Parlange Noam Weisbrod |
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| Institution: | 1. Department of Geology and Geophysics, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4;2. Department of Crop and Soil Science, Oregon State University, 3017 Agriculture and Life Science Building, Corvallis, OR 97331-3002, United States;3. Department of Bioengineering, Oregon State University, 116 Gilmore Hall, Corvallis, OR 97331, United States;4. Department of Mathematics, Oregon State University, Kidder Hall 368, Corvallis, OR 97331-4605, United States;5. Department of Biological and Environmental Engineering, Cornell University, 228 Riley-Robb Hall, Ithaca, NY 14853-5701, United States;6. Department of Environmental Hydrology & Microbiology, Zuckerberg Institute for Water Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boker Campus 84990, Israel |
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| Abstract: | 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. |
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| Keywords: | Process thermodynamics Darcy Buckingham Salt Saline Unsaturated |
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