Hybrid modeling of cross-flow filtration: Predicting the flux evolution and duration of ultrafiltration processes

Cross-flow ultrafiltration is a powerful tool used in bioprocesses to concentrate and separate biopharmaceuticals. However, there is a major challenge for its effective use: the fouling rate and decrease in the permeate flux vary substantially depending on the concentration and characteristics of the incoming feed, which causes variations in the process durations. We developed a hybrid model for use in predicting the flux evolution and duration of cross-flow ultrafiltration processes for various proteins, membrane types, input parameters, and filtration modes. The trained hybrid model is able to determine the process duration with an average normalized root-mean-square error of less than 6.2. It has superior adaptation to varying filtration characteristics compared to the mechanistic film theory model and can handle both batch- and fed-batch ultrafiltration using the same training set. In addition, the presented hybrid model can be used as a digital twin to simulate virtual processes with varying input parameters and different batch modes, which is a valuable tool for efficient process development or optimization.