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Abstract Diffusion is an important mass transfer mode of tight sandstone gas. Since nano-pores are extensively developed in the interior of tight sandstone, a considerable body of research indicates that the type of diffusion is mainly molecular diffusion based on Fick’s law. However, accurate modeling and understanding the physics of gas transport phenomena in nano-porous media is still a challenge for researchers and traditional investigation (analytical and experimental methods) have many limitations in studying the generic behavior. In this paper, we used Nano-CT to observe the pore structures of samples of the tight sandstone of western of Sichuan. Combined with advanced image processing technology, three-dimensional distributions of the nanometer-sized pores were reconstructed and a tight sandstone digital core model was built, as well the pore structure parameters were analyzed quantitatively. Based on the digital core model, the diffusion process of methane molecules from a higher concentration area to a lower concentration area was simulated by a finite volume method. Finally, the reservoir’s concentration evolution was visualized and the intrinsic molecular diffusivity tensor which reflects the diffusion capabilities of this rock was calculated. Through comparisons, we found that our calculated result was in good agreement with other empirical results. This study provides a new research method for tight sandstone digital rock physics. It is a foundation for future tight sandstone gas percolation theory and numerical simulation research.