CO2 capture and storage technology is favorable for the reduction of CO2 emissions. In recent years, a great number of research achievements have been obtained on CO2 geological storage from nano scale to oil/gas reservoir scale, but most studies only focus on the flow behaviors in single-dimension porous media. Besides, the physical experiment method is influenced by many uncertain factors and consumes a lot of time and cost. In order to deeply understand the flow behaviors in the process of CO2 geological storage in microscopic view and increase the volume of CO2 geological storage, this paper established 2D and 3D models by using VOF (Volume of Fluid) method which can track the dynamic change of two-phase interface, to numerically simulate supercritical CO2-brine two-phase flow. Then, the distribution characteristics of CO2 clusters and the variation laws of CO2 saturation under different wettability, capillary number and viscosity ratio conditions were compared, and the intrinsic mechanisms of CO2 storage at pore scale were revealed. And the following research results were obtained. First, with the increase of rock wettability to CO2, the sweep range of CO2 enlarged, and the disconnection frequency of CO2 clusters deceased, and thus the volume of CO2 storage increased. Second, with the increase of capillary number, the displacement mode transformed from capillary fingering to stable displacement, and thus the volume of CO2 storage increased. Third, as the viscosity of injected supercritical CO2 gradually approached that of brine, the flow resistance between two-phase fluids decreased, promoting the "lubricating effect". As a result, the flow capacity of CO2 phase was improved, and thus the volume of CO2 storage was increased. Fourth, the influence degrees of wettability, capillary number and viscosity ratio on CO2 saturation were different in multi-dimensional porous media models. In conclusion, the CO2-brine two-phase flow simulation based on VOF method revealed the flow mechanisms in the process of CO2 geological storage at pore scale, which is of guiding significance to the development of CCUS technology and provides theoretical guidance and technical support for the study of CO2 geological storage in a larger scale.