With an increased emphasis on reduced carbon emissions, many research efforts focused on various carbon capture techniques have concurrently expanded in application. Pressure swing adsorption (PSA) is one of the key processes for carbon capture and storage (CCS). During the natural gas sweetening operation of PSA processes, a high volume of carbon dioxide is included in the waste flow (heavy product). To improve the CO2 purity of the waste flow, this work first performs the dynamic optimization of a general four-step dual PSA process. The objective of the rectifying unit is to maximize methane recovery while the objective of the stripping unit is to maximize carbon dioxide purity for CCS. In brief, decision variables for the rectifying unit are the step times, P/F ratios, and feeding velocities of each unit; the length of the bed is added as a decision variable for the stripping unit. Optimization results indicate that carbon dioxide purity increases from 41.4% to 76.3% and methane recovery increases from 78.5% to 95.4%.