Analytical model for steady-state solute diffusion in non-isothermal fractured porous media

Mass transfer in non-isothermal fractured porous media have a wide application in many natural phenomena and engineering processes. The current study focuses on developing alternative formulations of steady-state analytical modelling for thermally induced solute diffusion in fractured porous media. The proposed analytical frameworks are validated by two set of experimental data. The varied examples of coupled heat transfer and solute diffusion are evaluated by the proposed solution to discuss the effects of thermal diffusion, flow operational conditions, geometry and thermal properties of fracture and matrix on the overall transport of solute in a fractured porous media. It is found that thermal-diffusion process, or explicitly as a “Soret effect (S_T)”, is a non-negligible part for investigating solute transport in non-isothermal fractured porous media. For example, increasing S_T from 10^-3 K⁻¹ to 10^-2 K⁻¹ leads to a reduction of solute concentration by a factor of 1.2. We demonstrate that a larger Peclet number ensures the temperature of the solute along the fracture decreasing while its concentration along the fracture increasing. However, an increase of the temperature difference between the entry and the output shows an opposite trend. An increase in fracture aperture or matrix thickness leads to temperature decreasing and concentration increasing along the fracture and matrix as a larger amount of solute are injected from the inlet boundary. The presented analytical solutions may also serve as a benchmark test tool for alternative numerical studies of coupled heat transfer and solute diffusion in fractured porous media.