(199b) From High-Fidelity to Data-Driven Modelling in Separation Systems: An Application to Chromatographic Separations

The growing demand of process industries towards automation has brought the development of tools that can enable end-to-end digitalisation at the forefront of scientific and industrial interest (Pirrung et al., 2017). In this context, mathematical models can be used as economic and efficient alternatives to support and accelerate the often cost- and time- intensive experiments required for process design and optimisation. Such models can be categorised into high-fidelity (white-box), hybrid (grey-box) and data-driven (black-box) models, based on the combination of prior knowledge and data used for their development (Solle et al., 2017).

In the case of chromatographic separation processes, high-fidelity models commonly comprise complex Partial Differential and Algebraic Equations (PDAEs), that describe the physicochemical phenomena taking place. This can be computationally expensive, challenging further online applications, such as optimisation and control. To overcome such limitations, data-driven or hybrid models can be used to reduce the computational complexity, while maintaining the necessary degree of process knowledge (Narayanan et al., 2021).

In this work, we present a methodology for the development of machine learning based models of chromatographic processes. We focus on the Multicolumn Countercurrent Solvent Gradient Purification (MCSGP) process (Aumann & Morbidelli, 2007). The model follows lumped kinetics and uses PDAEs to describe the liquid and solid phase concentrations of each species (Müller-Späth et al., 2008). After spatial discretisation using 50 collocation points, 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 neural networks (NNs) as surrogates for the PDE part of the formulation, eliminating the spatial discretisation of the model and predicting the process performance at cyclic steady state (CSS).

Specifically, we assess and compare two different strategies for the approximation of the liquid phase concentrations of all components: (a) by using an ANN for each component, and (b) by constructing the ANNs to predict the integrals of the outlet concentrations. The high-fidelity process model is used for data generation, via quasi-random sampling upon which dataset the ANNs are trained. Based on the decided input and output strategy, the hyperparameters of the ANNs are tuned using Bayesian optimisation and the performance of the final models is assessed. The accuracy of the ANNs is assessed against the high-fidelity process model both for the nominal conditions and within the window of measured disturbances that the model has been validated for.

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.

Solle, D., Hitzmann, B., Herwig, C., Pereira Remelhe, M., Ulonska, S., Wuerth, L., Prata, A., & Steckenreiter, T. (2017). Between the Poles of Data-Driven and Mechanistic Modeling for Process Operation. Chemie Ingenieur Technik, 89(5), 542–561.