In this study, we first report the development of a robust and efficient finite volume based adsorption process simulator, essential for rigorous optimization of a transient cyclic operation without resorting to any model reduction. We present a detailed algorithm for the common boundary conditions encountered in nonisothermal and nonisobaric adsorption process simulations. A comprehensive comparison of the high-resolution total variation diminishing (TVD) schemes, namely, van Leer and Superbee, with the weighted essentially nonoscillatory (WENO) finite volume scheme is performed, and trade-off plots are presented to identify the numerical scheme most suitable for attaining speed and accuracy at the same time. The simulator is then used to perform rigorous optimization of a four-step process for postcombustion CO2 capture from dry flue gas on zeolite 13X. The aim is to identify operating conditions at which the purity and recovery demands are met and to calculate corresponding energy consumption and process productivity. The purity-recovery and energy-productivity Paretos are generated using multiobjective optimization. It is shown that, for a strict vacuum swing adsorption (VSA) process, an evacuation pressure of 0.02 bar is required to satisfy regulatory demands of attaining a CO2 purity and recovery of 90%. It is also quantitatively shown that pressurizing the flue gas is detrimental to the energy consumption of process, although offering improvement in productivity.