Mathematical modeling is useful for analysis of process design and performance and is widely used for membrane separation and other important technologies in the energy sector. This study presents the results of our investigations on the mathematical modeling and optimization of hollow fiber membrane permeators specifically used for air separation as well as natural gas purification. The governing equations and mathematical models are developed based on the consideration of ideal and non-ideal conditions often involved in the separation of gas mixtures using membrane permeators. The influence and consequences of adoption of two distinct numerical methods for solving governing equations are investigated in details. The results obtained by using the models as well as the effect of numerical method type are examined and compared to the experimental data. The findings highlight the important role of the solution method on the validity and accuracy of the models. Moreover, the effect of variations in the operating conditions and physical geometries of the membrane are investigated through comprehensive sensitivity analysis. Accordingly, a set of optimal input parameters is determined using an appropriate statistical method. The findings provide useful information for the design and development of high performance membrane permeators and processes particularly in the case of binary gas mixtures for energy applications.