Estimating thermo-osmotic coefficients in clay-rocks: I. Theoretical insights

The conditions to obtain a macroscopic model for the thermo-osmotic coupling coefficient which is needed for practical calculations of fluid flow in clay-rocks subjected to temperature gradients are investigated in this paper. A theoretical expression for the thermo-osmotic coupling coefficient proportional to the hydraulic conductivity was obtained. The theoretical expression of the thermo-osmotic conductivity involves the excess Gibbs energy of the fluid between adjacent charged surfaces. The interaction energy was calculated using disjoining pressure data. Our calculations suggest a crucial role of the so-called hydration or structural energy of interaction to explain the thermo-osmotic process. The mean pore size, i.e. the mean interparticle spacing, the concentration of the equilibrium solution and the temperature are determinant variables in this process. Some exploratory comparisons between the model and the available data for pure clays are proposed.

Graphical abstractExperimental values of the ratio kγ/kkγ/k as a function of the mean half pore size, where kf=kΔH/ηiTkf=kΔH/ηiT is the thermo-osmotic permeability and ΔHΔH is the mean excess specific enthalpy of the pore fluid.Figure optionsDownload full-size imageDownload as PowerPoint slide