Skip to main content
Research Article

Thermodynamically Constrained Averaging Theory: Why Bother?

Authors
  • Timothy M. Weigand orcid logo (University of North Carolina)
  • William G. Gray orcid logo (University of North Carolina)
  • Cass T. Miller orcid logo (University of North Carolina)

Abstract

Porous medium researchers and practitioners usually rely on macroscale models to represent systems of concern. While macroscale models have often been formulated phenomenologically, the thermodynamically constrained averaging theory (TCAT) provides a means to rigorously derive closed macroscale models for a wide variety of systems. However, the TCAT approach can appear overwhelmingly complicated, the entry point for use unclear, and the advantages not self-evident. In response to these perceived shortcomings, we demonstrate several aspects of TCAT macroscale model formulations for single-fluid flow in a porous medium.  Specifically, we illustrate an essentially exact macroscale model derived from a rigorous connection across scales, show how an entropy inequality can be used to derive an approximate macroscale form for the Stokes-flow regime, and examine models in the transition flow regime. A special emphasis is placed upon leveraging available results, and other application opportunities are summarized.

Keywords: Model Development, Upscaling, Porous Media

How to Cite:

Weigand, T. M., Gray, W. G. & Miller, C. T., (2024) “Thermodynamically Constrained Averaging Theory: Why Bother?”, ARC Geophysical Research (1), 1. doi: https://doi.org/10.5149/ARC-GR.1362

Downloads:
Download PDF
View PDF

Funding

Name
National Institute of Environmental Health Sciences
Funding ID
P42ES03100
Name
National Science Foundation
Funding ID
ACI-1548562

444 Views

54 Downloads

Published on
2024-12-20

Peer Reviewed