A new matrix for multiphase couplings in a membrane porous medium

The empirical Darcy's law of water transport in porous media, Fick's law of chemical diffusion, and Fourier's law of thermal transport have been widely used in geophysics/geochemistry for over 150 years. However, the strong couplings between water, temperature, and chemicals in a membrane porous medium have made these laws inapplicable and present a significant hurdle to the understanding of multiphase flow in such a material. Extensive experiments over the past century have observed chemical osmosis and thermal osmosis, but a model for understanding their underlying physicochemical basis has remained unavailable, because of the highly cross‐disciplinary and multiscale‐multiphase nature of the coupling. Based on the fundamental principles of nonequilibrium thermodynamics and mixture coupling theory, a rigorously theoretical and mathematical framework is proposed and a general model accounting for all of the coupled influences is developed. This leads to a simple and robust mathematical matrix for studying multiphase couplings in a membrane porous medium when all chemical components are electrically neutral

Mathematical model of coupled dual chemical osmosis based on mixture-coupling theory

Very low permeability soils and rocks can act as a semi-permeable osmotic membrane, which will generate osmotic flow. Such complexities have been extensively studied, but dual chemical osmosis, the influence of sorption on chemical osmotic flow and the consequent influence on the stress/stain change remains unclear. This study extends mixture-coupling theory, by including chemical sorption entropy and chemical potential, and provides a new-coupled formulation for chemical transport in very low permeability rock. The classical Darcy's Law and Fick's Law have been modified to include the influence of chemical potential and sorption under relevant conditions, and dual chemical osmosis. The mechanical deformation has been coupled with the water and chemical flows using Helmholtz free energy. Finally, a coupled unsaturated hydro-mechanical-chemical model which considers dual chemical osmosis and sorption is presented. This mathematical model provides the possibility of using dual chemicals to control osmotic flow and chemical transport, which leads to important engineering applications such as those in the field of nuclear waste disposal