Analysis of vacuum operation on hydrogen separation from H₂/H₂O mixture via Pd membrane using Taguchi method, response surface methodology, and multivariate adaptive regression splines

The influence of vacuum pressure applied on H₂ separation from a palladium membrane is explored in this study. Three factors with three levels are considered, including the membrane chamber temperature with levels 320 °C, 350 °C, and 380 °C; the retentate-side total pressure with levels 1, 2, and 3 atm; and the permeation-side vacuum pressure with levels 0, 25, and 50 kPa. The Taguchi, response surface methodology (RSM), and multivariate adaptive regression splines (MARS) methods are employed to analyze the effects of the three parameters on hydrogen separation and predict their optimal combination. The retentate-side total pressure exhibits the highest impact on H₂ permeation, following the permeation-side vacuum pressure and then the membrane chamber temperature. The maximum H₂ flux is 0.226 mol∙s⁻¹∙m⁻², with H₂ recovery of 91 % obtained at the optimal conditions with a temperature of 380 °C, a total pressure of 3 atm, and a vacuum pressure of 50 kPa. The improvement in H₂ flux reaches 21.6 % compared with the case without the imposed vacuum pressure at the same temperature and total pressure. This result shows the imposed vacuum pressure is an efficient way to enhance H₂ permeation. The maximum relative errors between the experimental data and the predictions from the Taguchi, RSM, and MARS methods are 6.74 %, 3.37 %, and 8.08 %, respectively. The RSM method presents higher accuracy than Taguchi and MARS, perhaps due to a more precise analysis of the interaction terms. The smaller amount of input data and ignoring the temperature effect in MARS could be the reason for the lower accuracy. Nevertheless, the MARS method still demonstrates acceptable results. The cost of the Taguchi method is lower than that of the RSM method since it requires fewer experimental cases. In a word, the choice of the prediction method depends on the desired accuracy and the experimental cost.