A Second‐Order Approach for the Modeling of Dispersive Transport in Porous Media: 1. Theoretical Development | Zendy

Tompson Andrew F. B. | Zendy; Gray William G. | Zendy

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A Second‐Order Approach for the Modeling of Dispersive Transport in Porous Media: 1. Theoretical Development

Author(s) -

Tompson Andrew F. B.,

Gray William G.

Publication year - 1986

Publication title -

water resources research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.863

H-Index - 217

eISSN - 1944-7973

pISSN - 0043-1397

DOI - 10.1029/wr022i005p00591

Subject(s) - porous medium , dispersion (optics) , dispersive partial differential equation , convection–diffusion equation , representation (politics) , balance equation , mechanics , dispersion relation , mathematical analysis , statistical physics , mathematics , physics , porosity , partial differential equation , geotechnical engineering , geology , optics , statistics , law , politics , markov model , political science , markov chain

A new approach for the treatment, of dispersive transport in a simplified porous medium is presented. Use of a volume averaging approach allows the development of a separate point macroscopic balance equation for the dispersion quantity that appears in the averaged transport equation. The new equation is a more general representation, which avoids the complications and questions that arise concerning the coefficients associated with the Fickian approximation for dispersion. Constitutive relationships are developed for a number of the source terms arising in the averaged dispersion equation. The coupled transport and dispersion equations along with Darcy's law and the macroscopic continuity equation constitute a closed, second‐order model for dispersion in a porous medium.

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