Evolution of governing mass and momentum balances following an abrupt pressure impact in a porous medium
✍ Scribed by Shaul Sorek; Jacob Bear
- Publisher
- Springer Netherlands
- Year
- 1990
- Tongue
- English
- Weight
- 544 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0169-3913
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✦ Synopsis
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. Key words. Compressible fluid, porous media, abrupt pressure change, time and spatial averaging, mass and momentum balance equations, nondimensional forms.