Grey-Box Approach for the Prediction of Variable Residence Time Distribution in Continuous Pharmaceutical Manufacturing

Abstract

Axial dispersion models are used for the prediction of residence time distribution (RTD) of the flow occurring in various processes. Such models are essential for the understanding of the flow dynamics allowing monitoring, control and material tracing specially in the scope of continuous pharmaceutical manufacturing. However, RTDs are most usually dependent on the process variables (PVs), indicating that a single constant parameter dispersion model would not be capable of capturing this variability. In this contribution a variable parameter axial dispersion model is proposed, where the dependency on the process variables are captured from experimental data using Gaussian Process Regression (GPR) models. The method is illustrated with an example of a Vibrated Fluidized Bed Dryer (VFBD), in which a number of tracer experiments are performed at diferent values of the drying process air flow rate and vibration acceleration. The axial dispersion model parameter values are identifed for each experiment. Manifolds for the axial dispersion model parameters are then constructed by the regression of the GP models on the identifed values. Comparisons between the experiments and model predictions for an example validation case are drawn showing that the proposed model is capable of producing accurate RTD predictions and certainty bounds even for points not explicitly included in regression dataset. Insight about the advantages of the method in model based controller design is given.