A mathematical model is developed to simulate a gas separation process using a hollow fiber membrane module. In particular, a new numerical technique is introduced based on flash calculation. Such analysis allows identifying the required membrane properties needed to reach module performance of interest. This model is validated for six different gas separation cases taken from literature. Then, the validated model is used to investigate the effect of O-2 and N-2 permeances on O-2 recovery and O-2 mole fraction in the permeate stream. A realistic two-stage air enrichment process is also proposed for O-2 production using an industrial module with different fibers numbers. Moreover, this model is used to simulate a natural gas purification process using a single unit to determine the required membrane separation area and CH4 loss. Finally, a two-stage process is proposed to equally enhance CH4 retentate mole fraction and decrease CH4 loss. (C) 2017 American Institute of Chemical Engineers