An Improved Permeation Model for Solution–Diffusion-Based Hollow Fiber Gas Separation Membrane: Implementation and Analysis

Dense polymeric hollow fiber membrane–based gas separation modules are becoming increasingly important in various industrial fields due to their higher efficiency compared to other gas separation processes. Modeling the membranes gas separation process and analyzing the governing mathematical equations such as the solution–diffusion model are crucial for optimizing module performance and making the process cost-effective. Herein, we introduce an improved methodology for solving the mathematical model of polymeric hollow fiber gas separation membranes focusing on a simpler and more accurate solution strategy. Unlike previous solving methods, the model characteristic functions (feed flow, permeate flow, feed composition, permeate composition within the porous support layer, and bulk permeate composition) better adhere to boundary conditions at the module inlet and closed-end. The improved solving algorithm provides a more accurate solution, with a maximum mean squared error of 7.3441 × 10⁻⁵ and minimum $R^2$ of 0.8853, outperforming previous complex methods. The corrected algorithm also features improved speed, completing calculations in under 0.015 s, faster than any reported values. The model's response to changes in geometric and operating conditions is evaluated through an extensive sensitivity test, which is conducted by statistical analysis and numerical solutions. Numerical solution approach allows for a wider range of possibilities of interactions compared to statistical analysis and enables inspection of a wider response surface. Additionally, the response equation is estimated for permeate purity, stagecut, and retentate purity, and the process is optimized for different goals. Performance of membrane gas separation is highly sensitive to the membrane sizing and feed concentration, as these factors significantly influence the separation driving force. Therefore, this study presents an improved solving strategy and a detailed description of the effect of various parameters on the model response, along with a comprehensive comparison to statistical analysis and process optimization possibilities.