In this project, the diffusion of fluid in complex porous media was simulated using D3Q27 model of Lattice Boltzmann method (LBM) in the presence of gravity force and at different temperatures and porosities. Also, the second-discretization version of LBM with Double Relaxation Times (DRT) was utilized for simulations. For better understanding of the paper regarding the order of steps of LBM calculations, a picture was drawn using a special web software to illustrate these steps in a detailed but completely regular and clear flowchart. The model of vessel (canal) including soil-like porous medium was constructed through image processing in three-dimensional space with randomly selected pixels colored as black for fixed obstacles and white pixels for fluid. For increase of accuracy, the nodes of LBM were taken as coincident on pixels of image. The entire pixels of porous medium were examined for not forming any “lake.” Furthermore, the critical point of calculation of exact value of gravity acceleration in LBM scale in various conditions and for different fluids was introduced. The mathematical programs were validated using density, velocity and pressure of fluid, and the excellent consistency in calculation of pressure from mechanics formula and thermodynamics formula was illustrated, and also, the satisfaction of valid equation of continuity was presented. For ensuring pure-diffusion regime for fluid (water vapor), the Péclet number Pe was assigned a value below 0.01. For taking into account the effect of presence of porous medium on diffusion coefficient of fluid, the tortuosity concept entered into calculations and a related equation in two forms was used and the comparison was made between them, with the Troeh etal. equation as a fundamental criterion in this regard. Because of existence of two main equations for tortuosity, velocity-based and streamline-based, both of them were used in this research, with results compared with each other. Also, the effects of temperature of fluid and the porosity of porous medium on fluid diffusion coefficient were examined thoroughly. Besides, the activation energies of diffusion in porous medium at different temperatures were evaluated using a general method beyond Arrhenius equation and the method was compared with Arrhenius equation. Also, the best criterion for investigation of sensitivity of diffusion coefficient to temperature was established.

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