Central composite design (CCD) was applied in this work to analyze the performance of poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) flat sheet membrane in the seawater desalination using direct contact membrane distillation (DCMD) process. It is the most popular in response surface method (RSM). Development on Quadratic Regression model for membrane performance as a function of the operating conditions was studied. The ranges for each operating condition were selected as follows: feed temperature (T_f): 48–58 °C, feed flow rate (Q_f): 80–180 mL/min, permeate temperature (T_p):17–22 °C and permeate flow rate (Q_p): 80–180 mL/min. The model R-squared of 0.9759 (adjusted to degree-of-freedom), Lack-of-fit test (p = 0.4764), predicted residual error sum of squared (PRESS) statistic of 10.3 suggest that the model is adequate to correlate the impact of operating conditions on permeates. ANOVA analysis showed that factors as feed flow rate, feed temperature, and permeate temperature have a valuable impact (p ≤ 0.05) on the response variable. Additionally, the interaction among feed temperature-feed flow rate, feed flow rate-permeate flow rate, and the quadratic impact of feed temperature, permeate temperature, and permeate flow rate have shown an important impact (p ≤ 0.05) on the permeate flux. Optimization of operating conditions to make the permeate flux and salt rejection high as possible was determined according to desirability function approach. A desirability of 0.969 was achieved at a feed temperature of 58 °C, feed flow rate of 180 mL/min, permeate temperature of 18.8 °C, and permeate flow rate of 145.3 mL/min in which a permeate flux of 12.56 kg/m²h and a salt rejection of 99.97% was obtained.

The performance of nanofiltration membrane process for lead retention has been modelled by the modified Donnan steric pore-flow model (DSPM). The model predictions have been used to analyse the contribution of diffusive, convective and electrical flux on ion retention. A good agreement was found between the experimental and modelling data at various operating conditions. The influence of various process parameters, such as the permeation flux, feed solution concentration and cross-velocity, on lead (Pb) ion retention, was investigated. Maximum lead ion rejection was 93.8% at permeate flux of 1.25 * 10(-5) m/s. It was found that the lead retention increases initially with permeate flux and then decreases with further increase in permeate flux due to the developed concentration polarisation layer. Furthermore, the rejection drops by similar to 80% when the uncharged membrane is used, revealing the important role of electrical potential on the performance of the nanofiltration membrane. Finally, it is confirmed that the diffusion phenomenon is the dominant mechanism for ion transfer through the membrane.

An Erratum to this paper has been published: https://doi.org/10.1134/S0040579523330060