Based upon the lattice Boltzmann method, the current paper developed a visual simulation method for the evolution of porous structure during the acid leaching process. The reliability of the model in simulating fluid flow, solute diffusion, calcite dissolution, and gypsum precipitation was validated using four benchmark tests. The model was then used to investigate the effects of calcite distribution, sulfuric acid concentration, and porous structure on reactive transport processes. Results demonstrated that simulated values closely aligned with theoretical solutions or experimental data, confirming the model's validity. Applications showed that, when calcite was distributed near the injection end, precipitation near the inlet led to a rapid permeability decline. Higher sulfuric acid concentrations caused faster permeability reduction. The porous structure distribution significantly impacted permeability evolution, especially when blockades in main flow paths greatly affected permeability and reactive transport processes. Furthermore, when pore and mineral distributions were homogeneous, permeability evolution with porosity followed a power-law relationship, but this relationship did not hold when distributions were heterogeneous. Due to the difficulty in quantifying mineral and pore heterogeneities, combining porous structure and mineral distribution images with visual simulations created a practical approach for studying dynamic reactive transport in in-situ acid leaching of sandstone uranium deposits.