The chemical potentials governing fluid saturations in open constant volume systems

A diffusive equilibrium thermodynamic framework for two-phase capillary drainage and imbibition pressure in thin horizontal cylindrical tubes partially wetted by water is presented. The approach is based on the sum of external- and internal chemical potential for each fluid phase, which equals zero when diffusive equilibrium occurs. The difference between non-wetting and wetting phase chemical potential either externally- or internally therefore defines and generalizes the capillary pressure concept. Difference in external chemical potential is generated using e.g. pumps whereas internal difference is due to changes in interfacial areas and phase entropies. The latter is included under the assumption of non-interacting phases, which therefore give a logarithmic expression for varying fluid saturations. The assumption requires, however, fit parameters since the reference state cannot be calculated ab initio on the macroscopic level. Simple tube geometry allows for development of analytical capillary pressure expressions for drainage and imbibition. The drainage expression is compared with experimental data for homogeneous porous media and excellent match is observed considering the rough assumption related to non-interacting phases. Heterogeneities induced by pore geometry and wettability effects may induce more uncertainties and deviations in more realistic porous media. The framework is general and consistent and supported by several additional observations. Jurin’s law can e.g. be derived therefrom. It could therefore have important consequences for engineering and science disciplines where simplified tube-like geometry is a relevant representation of more complex systems.