Non-isothermal transport of multi-phase fluids in porous media. The entropy production

Abstract

We derive the entropy production for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in pressure, temperature, and chemical potentials. Thermodynamic extensive variables on the macro-scale are obtained by integrating over a representative elementary volume (REV). Using Euler homogeneity of the first order, we obtain the Gibbs equation for the REV. From this we define the intensive variables, the temperature, pressure and chemical potentials and, using the balance equations, derive the entropy production for the REV. The entropy production defines sets of independent conjugate thermodynamic fluxes and forces in the standard way. The transport of two-phase flow of immiscible components is used to illustrate the equations.

arXiv comment25 pages, 7 figures, Talk at Interpore, New Orleans, 2018

References in corpus (6)

• New Derivatives on Fractal Subset of Real-line
• A geometric state function for two-fluid flow in porous media
• Macroscopic Equations of Motion for Two Phase Flow in Porous Media
• History-independence of steady-state in simultaneous two-phase flow through porous media
• Effective Rheology of Bubbles Moving in a Capillary Tube
• Stable and efficient time integration of a dynamic pore network model for two-phase flow in porous media

Cited by in corpus (6)

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• Nanothermodynamic description and molecular simulation of a single-phase fluid in a slit pore
• Local Statistics of Immiscible and Incompressible Two-Phase Flow in Porous Media