Assessing the Minimum Entropy Production Rate Principle for Multiphase Flow Using the Thermodynamically Constrained Averaging Theory Approach

The thermodynamically constrained averaging theory (TCAT) approach was used to derive a general model for multiphase flow in porous media. Additionally, an entropy inequality was derived which provides an expression for the entropy production rate of the system. Non-equilibrium thermodynamic theory aims to characterize systems away from equilibrium where irreversible processes produce entropy, while classical thermodynamics characterizes equilibrium states. The maximum entropy principle of classical thermodynamics allows equilibrium states to be described using entropy, and the minimum entropy production rate principle (MEPRP) attempts to serve the same role for non-equilibrium systems at steady-state. The MEPRP is highly debated and has not been investigated for hydrologic systems, so to serve this purpose, simplifying assumptions were applied to the multiphase flow model to arrive at a standard model for unsaturated flow: Richards' equation. Then, using two common pressure-saturation-permeability models, Richards' equation was numerically simulated and found to satisfy the MEPRP under infiltration conditions.Master of Scienc