According to stochastic and fractal features of real porous media in nature

the reconstructed stochastic porous media with fractal features were generated by random midpoint displacement algorithm (RMD) and binaryzation processing. The relationship between Hurst exponent of fractal Brown surface and box dimension of reconstructed porous media was presented. Based on the fractal reconstructed theory

the reconstruction process of porous media was carried out based on a real porous media image

and the two-point correlation function was implemented to compare the structure characteristics between real porous media image and reconstructed porous media image. A lattice Boltzmann model (LBM) which was derived from the binary gas mixture theory was introduced to simulate the gas diffusion process in stochastic porous media. The feasibility of this model was validated by comparing with the analytical solution of unsteady diffusion process. The effective diffusivity of stochastic fractal porous media reconstructed by RMD with different Hurst exponent was calculated in this paper. For a given porosity

the positive correlation between the effective diffusivity and Hurst exponent was proposed. Using thermal lattice Boltzmann model

the heat conduction process in stochastic porous media was studied

and the effect of fractal features on effective diffusivity of porous media was presented.