Contributions to Theoretical/Experimental Developments in Shock Waves Propagation in Porous Media

S. Sorek, A. Levy, G. Ben-Dor, D. Smeulders

Research output: Contribution to journalConference articlepeer-review

11 Scopus citations

Abstract

Macroscopic balance equations of mass, momentum and energy for compressible Newtonian fluids within a thermoelastic solid matrix are developed as the theoretical basis for wave motion in multiphase deformable porous media. This leads to the rigorous development of the extended Forchheimer terms accounting for the momentum exchange between the phases through the solid-fluid interfaces. An additional relation presenting the deviation (assumed of a lower order of magnitude) from the macroscopic momentum balance equation, is also presented. Nondimensional investigation of the phases' macroscopic balance equations, yield four evolution periods associated with different dominant balance equations which are obtained following an abrupt change in fluid's pressure and temperature. During the second evolution period, the inertial terms are dominant. As a result the momentum balance equations reduce to nonlinear wave equations. Various analytical solutions of these equations are described for the 1-D case. Comparison with literature and verification with shock tube experiments, serve as validation of the developed theory and the computer code. A 1-D TVD-based numerical study of shock wave propagation in saturated porous media, is presented. A parametric investigation using the developed computer code is also given.

Original languageEnglish
Pages (from-to)63-100
JournalTransport in Porous Media
Volume34
Issue number1-3
DOIs
StatePublished - 1 Jan 1999
EventProceedings of the 1997 EUROMECH Colloquium 366, 'Porous Media - Theory and Experiments' - Essen, Germany
Duration: 23 Jun 199727 Jun 1997

Keywords

  • 1-D numerical simulation
  • Compaction waves
  • Forchheimer terms
  • Mass
  • Momentum and energy balance equations
  • Saturated and multiphase porous media
  • Shock tube experiments

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