Due to the unprecedented permeation properties of the recently developed thermally rearranged (TR) polymers, previous models developed for conventional less permeable membranes are no longer suitable to predict the separation performance of TR membranes. In this regard, a new mathematical model was developed taking the often-neglected shell side pressure drop and non-ideal gas behavior into account to result in a more accurate simulation for TR membrane. The model demonstrates the feasibility of using industrial size thermally-rearranged polybenzoxazole (TR-PBO) hollow fiber membrane modules in various gas separation applications. The optimal operating conditions for each application in a single-stage configuration were identified, and flue gas carbon capture was used as an example to demonstrate the substantially higher process capacity which the TR-PBO hollow fiber membranes can offer over conventional polymeric membranes. (C) 2015 Elsevier B.V. All rights reserved.