Guidance on Nusselt Number Correlation Selection in Membrane Distillation

Nusselt number correlations are the defacto method for estimating heat transport rates in membrane distillation (MD) models. Accurate selection and application of Nusselt number correlations, however, is complicated by a large number of available correlations, uncertainty in the correlation accuracy across module dimensions, and the fundamental mass and heat transport incongruities introduced by applying correlations developed for heat exchangers to analyze MD processes. This work analyzes the accuracy of 23 Nusselt number correlations for empty and spacer-filled channels in experimental MD systems and tests the validity of classical heuristics for their selection. The accuracy is assessed by applying the Nusselt number correlations in an MD process model to estimate the permeate flux or membrane permeability values. These values are compared to the experimentally measured permeate flux and membrane permeability in empty channels (N = 240) and spacer-filled channels (N = 80). Our results demonstrate that the best Nusselt number correlation for empty channels had an average flux error of 29 ± 32% and an average permeability error of 71 ± 161%, with accuracy being a strong function of module size. The best correlation for spacer-filled channels had an average flux error of 9 ± 11% and an average permeability error of 6 ± 8%. These findings emphasize the sensitivity of MD models to estimates of heat transfer.