Hybrid modeling of liquid-liquid pulsed sieve tray extraction columns

Accurate models for pulsed sieve tray extraction columns (PSEs) are commonly based on population balance models (PBMs) incorporating semi-empirical sub-models to account for extractive phenomena. However, the submodels' parameters must be adjusted for every new application, e.g., new operating conditions and changes in feed composition. Within this work, we want to limit the need for repeated parametrization by introducing datadriven parameter estimator models (PEM) for key phenomena in PSEs. The focus lies on drop breakage and coalescence since these phenomena determine the drop diameter which is the most important property in PBMbased models. In our previous work on drop breakage, we developed a hybrid modeling approach combining data-driven PEMs with a physically motivated model basis, thus achieving a successful trade-off between validity range and accuracy. In this work, we adjusted our hybrid modeling approach to coalescence in PSEs. For this purpose, a database of 270 column experiments was retrieved from the literature. Additionally, a framework was developed that enables the extension of column data by an individual coalescence parameter that poses the target feature of the PEM. The prediction of the coalescence parameter was bisected into a coalescence classifier model that distinguishes between coalescing and coalescence-inhibited data sets and the PEM that predicts the coalescence parameter. Finally, the hybrid breakage and coalescence models were incorporated into a PBM-based PSE model. The validation based on the 270 column experiments showed that the PSE model is versatile enough to predict the mean drop diameter over a wide range of operating conditions with high accuracy.