A coupled formulation based on non-equilibrium thermodynamics, Biot’s elasticity is derived to model thermal-osmotic flow in very low permeability rock. Darcy’s law has been modified by incorporating thermal effects from the dissipation process by using standard arguments of non-equilibrium thermodynamics. The relationship of chemical potential of water and pore water pressure has been analysed. Helmholtz free energy is used to construct the structure of the mechanics model. The derived coupled equations can be validated by comparing with those from Mechanics approach. Finally, finite elements are used to solve the governing equations. The numerical results show the thermal-osmosis has an important effect on water transport in very low permeability porous media.
Chen, X., Pao, W., & Li, X. (2013). Coupled thermo-hydro-mechanical model with consideration of thermal-osmosis based on modified mixture theory. International Journal of Engineering Science, 64, 1-13. https://doi.org/10.1016/j.ijengsci.2012.12.005