Evolution of governing mass and momentum balances following an abrupt pressure impact in a porous medium

Shaul Sorek, Jacob Bear

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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.

Original languageEnglish
Pages (from-to)169-185
Number of pages17
JournalTransport in Porous Media
Volume5
Issue number2
DOIs
StatePublished - 1 Apr 1990

Keywords

  • Compressible fluid
  • abrupt pressure change
  • mass and momentum balance equations
  • nondimensional forms
  • porous media
  • time and spatial averaging

ASJC Scopus subject areas

  • Catalysis
  • General Chemical Engineering

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