Gas separation polymeric membranes have gained significant attention in various industries, including gas processing, petrochemicals, and environmental applications. Accurately predicting the permeance of these membranes is crucial for optimizing their design and performance. This paper presented a numerical prediction model for the permeance of a binary gas mixture under various process conditions, using only algebraic equations to minimize the calculation effort. The model considers input parameters such as feed and permeate flow rates, feed pressure, feed and permeate mole fraction, and membrane area. It demonstrates the behavior of permeance and selectivity in this study. The study also presented two case studies that utilize predicted selectivity to model counter-current flow and compare the results with experimental data from the literature. The first case study involves recovering helium from natural gas using an asymmetric high-flux membrane. The second case study separates air using nano-porous carbon as the membrane material. The numerical analysis successfully accurately predicted the permeance of gas separation polymeric membranes. The model accounted for variations in membrane thickness, feed composition, and operating conditions, providing valuable insights into the overall performance of the membrane system. It also allowed for the optimization of membrane design and operational parameters to enhance separation efficiency and productivity. The study showcased the effectiveness of numerical techniques in accurately predicting membrane performance. The developed model can be a valuable tool for membrane designers and engineers, enabling them to optimize the design and operation of gas separation systems.