An extended 3-compartment model for describing step change experiments in pharmaceutical twin-screw feeders at different refill regimes.

Residence time distributions (RTDs) are a valuable tool for product tracking in the unit operations of a continuous line for manufacturing pharmaceutical oral solid dosage (OSD) and the integrated system itself. The first unit operation in such a continuous line in which extended intermixing can occur, is typically a feeder. The RTD of a feeder can be obtained by performing tracer experiments with a tracer material. A physical interpretation can be given to the observed tracer concentration responses by fitting a tanks-in-series (TIS) or compartmental model to it. Consequently, the internal mixing behaviour inside the feeder hopper can be rationalized. However, typically, a constant volume is assumed for the tanks or compartments in these models. This has led to several publications where the experimental set-up does not violate the constant volume assumption, i.e. one performs refills at a high hopper fill level. Here, we step away from this assumption and develop a set of differential equations for a 3-compartment model in order to account for a non-constant volume of the compartments. Moreover, the model distinguishes between a bypass trajectory formed by the agitator inside the feeder and an inner mixing volume, in which the tracer concentration lags on the tracer concentration in the bypass volume. This compartmentalization was inspired by the results obtained in a previous study using a spatial sampling method to assess the tracer concentration throughout the feeder hopper for different experimental runtimes. The developed model successfully describes the step responses for different refill regimes: the standard smooth first order plus dead time response (FOPDT) for a high refill regime and the more complex step response, including dips in the rising phase of the curve, for the low refill regime. As a consequence, a more thorough understanding of the complex mixing behaviour inside the feeder is obtained, which allows for an improved traceability. Next to that, the model delivers enhanced knowledge on the interaction between the residence time and the refill regime. The developed model was fitted to a data set, containing step change experiments for different pharmaceutical materials (Tablettose 80 (T80), Microcelac 100 (MCL), and Avicel PH101 (MCC)), different mass flow rates, and refill regimes. The experimentally observed phenomena could be reliably described by the proposed model. The model showed an improved transferability compared to typical TIS models.