(196d) Towards Grey-Box Modelling in Chromatographic Separation Processes

High-fidelity (white-box) process models of separation systems are described by complex Partial Differential and Algebraic Equations (PDAEs). This often results in high computational costs that can complicate further online applications, such as optimisation and control (Pirrung et al., 2017). To overcome these limitations, hybrid (grey-box) models can be used to reduce computational complexity, while maintaining a degree of process knowledge (Narayanan et al., 2021). In this work, we are proposing a novel methodology for the development of hybrid models for separation processes and assess their potential as alternatives to the high-fidelity process models.

We focus on the Multicolumn Countercurrent Solvent Gradient Purification (MCSGP) process; a chromatographic separation process initially presented by Aumann and Morbidelli (2007). Following lumped kinetics, the model uses PADEs to describe the concentrations of each species both in the liquid and solid phase (Müller-Späth et al., 2008). Using 50 collocation points for spatial discretisation, the model comprises 3309 variables and 4119 equations (Papathanasiou et al., 2016), 805 of which are Ordinary Differential Equations (ODEs). To decrease the computational expense, we develop and assess the performance of Artificial Neural Networks (ANNs) as surrogates for the partial differential part of the model formulation.

Specifically, we eliminate the need for spatial discretisation, by training the ANNs to directly predict the process outputs, and further reduce the computational expense, by directly predicting at Cyclic Steady State (CSS). The ANNs are trained to approximate the liquid phase concentrations of the separation species, based on data generated via quasi random sampling using a validated white-box model of the process. Bayesian oprimisation is employed for the tuning of the hyperparameters of the ANNs, and different input and output strategies are investigated, based on the process knowledge and physicochemical equations maintained in the system. The resulting hybrid models are evaluated based on their prediction, interpolation and extrapolation accuracy, and computational cost, against the validated white-box model, as well as previously developed black-box models of the process. The results indicate that the developed hybrid models manage to reduce the model complexity and computational expense, while maintaining a good model accuracy, and their potential to be used in further online applications is shown.

Acknowledgements

Funding from the UK Engineering & Physical Sciences Research Council (EPSRC) for the i-PREDICT: Integrated adaPtive pRocEss DesIgn and ConTrol (Grant reference: EP/W035006/1) is gratefully acknowledged.

References

Aumann, L., & Morbidelli, M. (2007). A continuous multicolumn countercurrent solvent gradient purification (MCSGP) process. Biotechnology and Bioengineering, 98(5), 1043–1055.

Müller-Späth, T., Aumann, L., Melter, L., Ströhlein, G., & Morbidelli, M. (2008). Chromatographic separation of three monoclonal antibody variants using multicolumn countercurrent solvent gradient purification (MCSGP). Biotechnology and Bioengineering, 100(6), 1166–1177.

Narayanan, H., Luna, M., Sokolov, M., Arosio, P., Butté, A., & Morbidelli, M. (2021). Hybrid Models Based on Machine Learning and an Increasing Degree of Process Knowledge: Application to Capture Chromatographic Step. Industrial and Engineering Chemistry Research, 60(29), 10466–10478.

Papathanasiou, M. M., Avraamidou, S., Oberdieck, R., Mantalaris, A., Steinebach, F., Morbidelli, M., Mueller-Spaeth, T., & Pistikopoulos, E. N. (2016). Advanced control strategies for the multicolumn countercurrent solvent gradient purification process. AIChE Journal, 62(7), 2341–2357.

Pirrung, S. M., van der Wielen, L. A. M., van Beckhoven, R. F. W. C., van de Sandt, E. J. A. X., Eppink, M. H. M., & Ottens, M. (2017). Optimization of biopharmaceutical downstream processes supported by mechanistic models and artificial neural networks. Biotechnology Progress, 33(3), 696–707.