Adsorption processes have already been considered as an appealing technology for carbon capture and climate change mitigation. Accordingly, this work investigated the capacity of shaped MIL-160(Al) as a water stable bioderived Al dicarboxylate microporous metal-organic framework for separation of carbon dioxide and nitrogen concerning postcombustion application. First, breakthrough experiments of carbon dioxide and nitrogen were accomplished at 313 K and 4.0 bar. Then, a set of equations/relations were considered to model the dynamic fixed-bed tests, in which the outcomes proved the capacity of the developed model for such a purpose. Next, a pressure swing adsorption (PSA) process with five steps, including pressurization, feed, rinse, blowdown, and purge, was planned and validated using performed experiments in a laboratory-scale PSA setup. In the end, an industrial PSA process was designed to attain a better grasp of the capacity of MIL-160(Al) for postcombustion application. The results indicated an exciting potential of this adsorbent for postcombustion carbon capture, with the purity and recovery of carbon dioxide around 67.3 and 99.1%, respectively.