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Thermodynamically Constrained Averaging Theory: Why Bother?

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This study simplifies the thermodynamically constrained averaging theory (TCAT) for porous medium flow. It demonstrates TCAT’s power in deriving accurate macroscale models, making complex systems more understandable for researchers.

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Area of Science:

  • Multiphysics
  • Continuum Mechanics
  • Porous Media Science

Background:

  • Macroscale models are essential for porous medium research but often lack rigorous derivation.
  • Phenomenological models are common, but thermodynamically constrained averaging theory (TCAT) offers a rigorous approach.
  • TCAT's complexity can be a barrier to its widespread adoption in porous media research.

Purpose of the Study:

  • To clarify and demonstrate the practical application of TCAT for deriving macroscale models.
  • To illustrate the derivation of macroscale models for single-fluid flow in porous media using TCAT.
  • To highlight the advantages and accessibility of TCAT for porous media practitioners.

Main Methods:

  • Derivation of an essentially exact macroscale model via rigorous scale connection.
  • Application of entropy inequalities to derive approximate macroscale models for Stokes-flow regimes.
  • Analysis of macroscale models within the transition-flow regime.

Main Results:

  • Demonstration of a rigorously derived, essentially exact macroscale model for porous media flow.
  • Successful application of TCAT principles to derive approximate models for specific flow regimes.
  • Identification of TCAT's utility across different flow regimes in porous media.

Conclusions:

  • TCAT provides a robust framework for deriving accurate macroscale models in porous media.
  • The study simplifies TCAT's application, making its benefits more evident to researchers and practitioners.
  • TCAT offers significant potential for advancing the understanding and modeling of complex porous medium systems.