Quantitatively, carbon dioxide is the main gas emitted from the burning of fossil fuels; thus, it is the primary contributor to global warming. However, climate change could be mitigated using "carbon capture and storage" (CCS) methods. CO2 separation by physical adsorption is a promising technology to achieve CO2 capture with minimum energy costs. Mg-MOF-74 is a distinguished adsorbent amongst porous materials owing to its high CO2 uptake under flue gas conditions. In this study, a vacuum pressure swing adsorption (VPSA) process composed of five steps (pressurization, feed, rinse, blowdown, and purge) for separating CO2 from a CO2/N-2 mixture using Mg-MOF-74 was mathematically modeled. Two- and three-dimensional computational fluid dynamics (CFD) models were developed using a user-defined-function (UDF, written in C) linked to the ANSYS Fluent program. The models have been validated against published pressure swing adsorption experimental data. The regeneration (blowdown and purge) time has been tuned to explore the performance improvement for the VPSA process. The key optimum performance indices for VPSA in terms of CO2 purity, recovery, productivity, and process power consumption were found to be 95.3%, 94.8%, 0.50 kg_CO2 h(-1) kg_MOF-1, and 68.71 kW h tonne_CO2-1, respectively. The corresponding operating carbon capture cost has been evaluated as $6.87 tonne_CO2-1 for a 500-MW post-combustion power plant. These CO2 productivity and power consumption performances represent a significant enhancement in CO2 separation using physical adsorption technology compared to those reported in the literature.