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Spatial Discretization and Kalman Filtering for Ideal Packed-Bed Chromatography

Packed-bed chromatography is ubiquitous in pharmaceutical and biotechnological manufacturing for separation of peptides, proteins, and antibiotic molecules. We investigate a mathematical model for ideal chromatography in a packed bed. The partial differential equation system that constitutes the model is linear. We discretize the mathematical model spatially using a first-order, finite-volume (FV) method as well as a high-order, discontinuous-Galerkin finite-element (DG-FE) method. We use an exact temporal discretization of the resulting system of linear equations. For the same accuracy, the DG-FE method requires far less states than the FV method. We use the resulting discrete-time, state-space model for state estimation of the packed-bed chromatographic model using a Kalman filter. By simulation, we illustrate the applications of the resulting state estimator in a monitoring and prediction system for packed-bed chromatography.