Prediction of Sauter mean diameter and droplet size distribution using different modeling approaches in uranium extraction from phosphoric acid by a pulsed sieve-plate column

The hydrodynamic behavior of reactive solvent extraction of uranium from phosphoric acid using a D2EHPA–TRPO solvent system was systematically investigated in a vertical pulsed sieve-plate column (VPSPC). Because droplet hydrodynamics govern interfacial area, phase dispersion, and mass transfer performance, the Sauter mean diameter (SMD) and droplet size distribution (DSD) were quantitatively characterized and modeled. A semi-empirical correlation based on dimensional analysis predicted SMD with an R2 of 0.9502 and an average absolute relative error (AARE) of 5.88%, while a second-order response surface model based on a central composite design (RSM–CCD) improved these values to 0.9638 and 3.10%, respectively. Two artificial neural networks, multilayer perceptron (MLP) and radial basis function (RBF), were also developed to capture nonlinear SMD behavior. The MLP provided the highest predictive accuracy (R2 = 0.9873, AARE = 1.92%), followed by the RBF model (R2 = 0.9774, AARE = 3.41%). DSD was further described using normal, log-normal, and Weibull distributions; for a representative experiment, the normal distribution showed the best agreement with the measured droplet population, with the lowest Kolmogorov–Smirnov statistic (0.2047) and binned RMSE (0.0434). Overall, the combined SMD and DSD analyses provide a quantitative framework for describing droplet-scale hydrodynamics and interfacial-area development in the VPSPC, while their application to industrial-scale design should be considered within a broader hydrodynamic and mass transfer framework.