Evolution of governing mass and momentum balances following an abrupt pressure impact in a porous medium |
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Authors: | Shaul Sorek Jacob Bear |
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Institution: | (1) Civil Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel;(2) Ben Gurion University of the Negev, J. Blaustein Institute for Desert Research, The Water Resources Research Center, Sede Boqer Campus, 84993, Israel |
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Abstract: | A mathematical model is developed of an abrupt pressure impact applied to a compressible fluid flowing through a porous medium domain. Nondimensional forms of the macroscopic fluid mass and momentum balance equations yield two new scalar numbers relating storage change to pressure rise. A sequence of four reduced forms of mass and momentum balance equations are shown to be associated with a sequence of four time periods following the onset of a pressure change. At the very first time period, pressure is proven to be distributed uniformly within the affected domain. During the second time interval, the momentum balance equation conforms to a wave form. The behavior during the third time period is governed by the averaged Navier-Stokes equation. After a long time, the fourth period is dominated by a momentum balance similar to Brinkman's equation which may convert to Darcy's equation when friction at the solid-fluid interface dominates. |
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Keywords: | Compressible fluid porous media abrupt pressure change time and spatial averaging mass and momentum balance equations nondimensional forms |
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