Membrane gas separation is an energy-efficient and environmentally friendly technology for industrial gas purification and recovery. Accurate mathematical modeling is essential for predicting separation performance and optimizing process design. In this study, a mathematical model is developed for multicomponent membrane gas separation, describing the transport of gas mixtures through selective membranes under co-current flow conditions. Mass balance equations and permeation relations form the basis of the model. Numerical techniques are employed to solve the resulting system of nonlinear differential equations and simulate separation behavior. The model is applied to evaluate membrane unit performance for the separation of gases such as hydrogen and carbon dioxide from industrial gas streams. Effects of operating parameters, including feed composition, pressure difference, and membrane selectivity, on the purity and recovery of target components are investigated. Simulation results show good agreement with experimental and literature data, demonstrating the model`s capability to reliably predict performance. This approach provides a useful tool for analyzing, designing, and optimizing membrane-based gas separation processes in the chemical and energy industries.