Capturing unmodelled phenomena: A hybrid approach for the prediction of the transport through ceramic membranes in organic solvent nanofiltration

Organic Solvent Nanofiltration (OSN) is widely recognized as an interesting substitute to the thermal-based separation processes traditionally used in many industries. However, its industrial implementation has been hampered by the relatively poor understanding of the complex phenomena that drive its performance. Consequently, various model formulations have been proposed in the past with various degrees of success. Unfortunately, it seems that mechanistic methodologies tend to suffer from the mentioned lack of fundamental understanding, while data-driven approaches are typically bound to have very large data requirements and their predictions are often difficult to interpret and hard to extrapolate. Accordingly, this work presents a hybrid modelling methodology focused on OSN with ceramic membranes and aimed at the engineering practice. In this approach, a mechanistic component is married with a data-driven algorithm with the objective of obtaining accurate predictions that remain interpretable and bounded by the physics of the system. Two model architectures (parallel and serial) were formulated and subsequently tested with an experimental dataset. Both options were found to offer improved predictions of total flux and solute rejection in comparison with the widely used solution-diffusion framework. The models were found to produce accurate out-of-sample predictions and it was possible to obtain a picture of the influence of the effects driving model predictions. Additionally, adequate estimations of systems in which affinity interactions are dominant were obtained. This positions the hybrid methodology presented here as a promising alternative for the prediction of the performance of OSN.