Abstract This paper examines a systematic approach to determine ultimate CO2 storage capacity of two-dimensional (2D) aquifer model owing to capillary snap-off, gas dissolution, and gas compression. In our previous paper, an application of fractional flow theory was presented to evaluate CO2 storage capacity of an aquifer because of capillary snap-off and gas dissolution; we re-visit that solution and incorporate gas compression as the third mechanism by which CO2 is sequestered in geological formation. The gas compression is triggered when the pressure wave created at the injection well reaches to the physical boundaries of aquifer; beyond that point, the aquifer would realize pressure build-up (over-pressurized). Generally, numerical simulations are used to assess the CO2 storage capacity of a geological formation and evaluate various trapping mechanisms. However, the simulations are complex and time-consuming and they require detailed inputs; whereas, the presented method requires limited inputs and provides fast results in agreement with the simulation that makes the method suitable tool to compare and screen the CO2 storage potential of various formations. We study partially sealed aquifers where the build-up period starts at some point between the arrival of injection pressure wave and the injected fluid to the distant boundary; whereas, in completely sealed aquifer, the pressure build up starts immediately after the injection wave reaches to the boundary. We develop a mathematical expression to estimate the maximum CO2 storage capacity for the partially sealed aquifer. To verify the analytic solution, we incorporate the contribution of compressibility into the model we previously developed via an adjusted injection rate. The adjusted injection rate is presented as a function of the dimensionless aquifer properties through a set of plots. Gas compression yields larger immobile CO2 plume during the aquifer build-up period. However, we limit the pressure adjutant to the aquifer boundaries to the fracturing pressure/rock failure beyond which elastic deformation is not sustained. In practice, the proposed method provides an efficient screening method to assess the CO2 storage capacity of over-pressurized aquifers and significantly reduces the simulation costs while providing an interesting insight.