Process and operating temperature optimization for polysulfone hollow fiber membrane CO2/CH4 mixture separation via response surface methodology

Abstract

Membrane gas separation has gained significant interest due to its compactness, high area-to-volume ratio, and numerous advantages over traditional gas separation processes such as cryogenic distillation and adsorption towers. Optimizing operating conditions, particularly temperature, is essential to enhance process performance, thereby increasing productivity and product purity. Polysulfone is widely regarded as an ideal membrane material for natural gas treatment due to its balanced permeance for both CH₄ and CO₂. However, its permeance is temperature-dependent, necessitating careful selection of the operating temperature. Our model uniquely integrates two critical non-ideal factors: (i) Arrhenius-type temperature dependence of gas permeance, and (ii) permeate-side pressure drop, addressing limitations in existing models that typically assume isothermal conditions and neglect pressure variations. Validation against experimental data from Tranchino et al. demonstrates the model’s high predictive accuracy, with coefficient of determination (R²) of 0.9436, explained variance (EV) of 0.9463, and mean squared error (MSE) of 4.4595 × 10^− 6 across multiple operating pressures (2–7 atm). Response Surface Methodology (RSM) with Central Composite Design (CCD) was employed to systematically optimize the operating conditions, with Analysis of Variance (ANOVA) used to evaluate the statistical significance of the developed models. Through ANOVA coupled with central composite design, we systematically identified the optimal operating temperature of 348 K for CO₂/CH₄ separation using polysulfone membranes, with a consistent optimal permeate-to-feed pressure ratio (γ) of approximately 0.24. The sensitivity analysis further reveals that feed CO₂ mole fraction (\(\:{x}_{0}\)) serves as the most influential parameter for process performance, enabling flexible operation across diverse feed compositions. This integrated modeling and optimization framework provides a practical tool for process engineers to identify optimal operating windows that balance separation performance with energy consumption, and can be readily extended to other membrane materials and gas separation applications.