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Updated: Jan 20, 2026

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Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium

A S Jackson1, I Rybak2, R Helmig3

  • 1Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina, 27599-3205, USA.

Advances in Water Resources
|January 19, 2026
PubMed
Summary

This study introduces a new model for the transition zone between two- and single-fluid porous media, enhancing flow and transport modeling. The thermodynamically constrained averaging theory (TCAT) approach provides a generalized framework for multiscale systems.

Keywords:
Averaged thermodynamicsModel formulationMultiphase systemMultiscale systemsSpecies transportTCAT

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Area of Science:

  • Multiphase flow in porous media
  • Thermodynamics
  • Continuum mechanics

Background:

  • Existing models struggle with the transition region between distinct fluid phases in porous media.
  • Accurate modeling of species transport across these interfaces is crucial for various applications.
  • The thermodynamically constrained averaging theory (TCAT) provides a framework for multiscale porous media analysis.

Purpose of the Study:

  • To develop a fundamental model for the transition region between two-fluid and single-fluid porous media systems.
  • To incorporate species transport phenomena within this transition region model.
  • To establish a generalized theoretical framework guided by an entropy inequality.

Main Methods:

  • Development of a general model formulation for the transition region.
  • Application of an entropy inequality to guide the specification of closure relations.
  • Specification of a closed system based on the general model and entropy inequality.

Main Results:

  • A generalized model for the transition region between two-fluid and single-fluid porous media systems was established.
  • The model incorporates species transport and extends existing sharp interface coupling conditions.
  • The developed theoretical framework is validated through its applicability to diverse interface zones.

Conclusions:

  • The TCAT approach offers a robust method for modeling complex interface phenomena in multiscale porous media.
  • The developed transition region model provides a significant advancement over existing sharp interface models.
  • Potential applications span environmental science, geosciences, and industrial processes.