A comparison between drop size distributions derived from the probability distribution functions and maximum entropy principle. Case study; pilot plant Scheibel extraction column

•Mean drop size and size distribution is measured in Scheibel extraction column.•Gamma, Inverse Gaussian, Weibull functions was used for drop size distributions.•Empirical correlations are proposed to predict Sauter mean drop size.•Maximum entropy method reconstructs accurately the drop size distributions.

A new model for prediction of drop size distribution is proposed in an eleven stage Scheibel extraction column by the maximum entropy density approximation technique. In addition, the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the drop size distribution. The experimental procedures were carried out by three different systems such as toluene-water, n-butyl acetate-water and n-butanol-water. The drop size distribution was measured with an image analysis technique as a function of the operating conditions and physical properties of the liquid-liquid systems. The results show that the agitation speed has the main effect on the drop size distribution in the column. However, the effects of phase flow rates are not significant. An empirical correlation is proposed for estimation of the Sauter mean drop diameter in terms of operating variables, column geometry and physical properties. The results show that the maximum entropy function describes the drop size distribution better than the conventional probability distribution functions. The Shannon maximum entropy method provided a novel prediction method for the drop size distributions in the liquid-liquid extraction columns. The latter that could be used for modeling approaches.

Graphical abstractDownload high-res image (223KB)Download full-size image