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Thermodynamics-like Formalism for Immiscible and Incompressible Two-Phase Flow in Porous Media
1PoreLab, Department of Physics, Norwegian University of Science and Technology NTNU, N-7491 Trondheim, Norway.
Entropy (Basel, Switzerland)
|February 26, 2025
Summary
This study presents a thermodynamic-like framework for two-phase flow in porous media. It links fluid distribution and mobility through emergent variables like agiture and configurational entropy.
Area of Science:
- Multiphase flow dynamics
- Statistical mechanics applications
- Porous media physics
Background:
- Two-phase flow in porous media is complex, often lacking a unified theoretical framework.
- Thermodynamic analogies offer potential for deeper understanding and predictive modeling.
- Jaynes' generalization of statistical mechanics provides a powerful tool for developing such analogies.
Purpose of the Study:
- To formulate a thermodynamics-like mathematical framework for immiscible, incompressible two-phase flow in porous media.
- To interpret emergent variables (agiture, flow derivative, flow pressure) and their thermodynamic conjugates (configurational entropy, saturation, porosity).
- To explore an alternative formalism using fractional flow as the control variable.
Main Methods:
- Application of Jaynes' generalized statistical mechanics to two-phase flow.
- Derivation and analysis of emergent thermodynamic variables.
- Development of a fractional flow-based thermodynamic formalism.
Main Results:
- A thermodynamic framework is established for two-phase flow, defining conjugate variables.
- Agiture, a temperature-like variable, is conjectured to relate to the pressure gradient.
- Configurational entropy, fluid distribution, velocity, and differential mobility are shown to be interconnected.
Conclusions:
- The developed thermodynamic approach provides new insights into porous media fluid dynamics.
- The relationship between agiture, pressure gradient, and configurational entropy offers a novel perspective on fluid behavior.
- The fractional flow formalism is better suited for experimental characterization of porous media flow.
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