Statistical Modelling and Correlation of Membrane Distillation Data
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Membrane distillation (MD) is a process in which the driving force for mass transfer is a temperature gradient rather than conventional gradients based on density, static pressure, chemical nature, affinity, or freezing point differences. A complete set of experimental data on air gap membrane distillation will be analyzed using the methods of statistical experimental design and will be correlated using an artificial neural network. The data involves a study of the effects of salt concentration (at pre-set conditions of feed temperature, coolant temperature, and flow rate) and membrane porosity on permeate flux for four inorganic salts (MgCl2, NaCl, Na2CO3, and Na2SO4) using three different commercial membranes (TF-200, TF-450 and TF-1000). The data will be used in performing a statistical analysis study in terms of hypothesis testing, where different hypotheses regarding the mean permeation flux of the three membranes will be tested. Several statistical techniques, i.e., F-test, Fisher LSD test, Bonferroni and Tukey's test are applied. The F-test predicts that all membranes handle salts at their low concentration levels in a comparable manner with no significant differences in permeate fluxes, but significant differences result at higher concentrations. Two-level and three-level factorial experimental designs are then applied to investigate the influence of the main operating parameters on water permeation flux. The objective here is to gain an idea about the main effects of the involved factors and their interactions. Based on analysis of the 22 and 32 factorial designs, membrane porosity is found to be the most influential factor with a direct relationship with the permeation flux. Interaction terms are found to be statistically insignificant. Finally, the experimental data are correlated using an artificial neural network (ANN). By using the ANN toolbox in MATLAB©, the permeate flux is correlated to salt concentration and membrane porosity for all salts and membranes. A good agreement between ANN predictions and the experimental data was obtained for NaCl, MgCl2, and Na2SO4, but not for Na2CO3.