Statistical Analysis of the Operating Conditions Influencing Green Hydrogen Production by a Reversible PEM Water Electrolyser

Improving the efficiency of proton-exchange membrane (PEM) water electrolysis for green hydrogen production requires systematic optimisation of interdependent operating conditions. The present study applies a face-centred central composite design (FCCD) combined with response surface methodology (RSM) to quantify the influence of three controllable parameters on the performance of a bench-scale PEM electrolyser: applied current, stack temperature, and membrane relative humidity. A reversible two-stack configuration with 16 cm2 Nafion 117 membrane–electrode assemblies was operated across the design space (0.40–0.90 A, 18–45 °C, 50–100% RH), yielding 288 independent observations from 96 randomised runs. Four responses were evaluated: volumetric hydrogen evolution rate, Faradaic efficiency, specific electrical energy consumption, and stack voltage drift. The regression analysis identified applied current as the dominant factor governing hydrogen throughput, while membrane hydration exerted the strongest control over charge-utilisation and ohmic losses. Temperature exhibited a moderate but statistically significant positive effect, whereas feed-water resistivity emerged as a secondary practical lever for minimising energy consumption. Model adequacy was confirmed through analysis of variance and residual diagnostics, with adjusted coefficients of determination in the range 0.851–0.925 and predicted coefficients above 0.835 across all responses. Desirability profiling indicated an optimal operating window near 0.75 A, 42 °C, and 95% relative humidity, delivering a hydrogen production rate of approximately 7.4 mL min−1, a Faradaic efficiency close to 98%, and a specific energy consumption of 4.5 kWh Nm−3. These findings provide quantitative guidance for the design and operation of small-scale PEM electrolysers under constrained laboratory and educational conditions. By integrating formal uncertainty quantification with response surface modelling and jointly treating membrane hydration and feed-water resistivity, the study provides a reproducible, uncertainty-quantified benchmark and a transferable optimisation workflow.