Stochastic Analysis and Modeling of Pharmaceutical Screw Feeder Mass Flow Rates

Screw feeders serve as the critical first unit operation in a continuous manufacturing of drug product (CMDP) processes, influencing the mass flow rate of active pharmaceutical ingredients and excipients downstream. There is great industrial interest modeling the behavior of screw feeders accurately. Existing flow sheet models focus on deterministically simulating the powder mass flow rate [2]–[4]; however, these models only capture the average mass flow rate, and lack the stochastic behavior of the mass flow. The use of custom Discrete Element Method (DEM) models provide highly realistic simulations of particles’ residence time and by extension mass flow, but prohibitively require long computation times to simulate only minutes of operation [5]. In the pursuit of designing better processes and improved controllers, there is a need for a computationally quick-to-solve flow sheet model that can simulate the stochastic nature of a real screw feeder. This is precisely the gap addressed in the present paper.

This work presents the novel characterization and modeling of the stochastic nature of a screw feeder’s mass flow rate using statistical time series analysis and a deterministic flowsheet model. First, a battery of experiments was performed using different powders and a variety of operating speeds on a Coperion K-tron KT20 screw feeder. Then, for each experiment, the parameters of a hybrid mechanistic-empirical screw feeder model, based upon the work of [4], were estimated. After, the stochastic element of the mass flow is isolated by subtracting the flowsheet model’s deterministic mass flow rate from the feeder-reported instantaneous mass flow rate. Next, each experiment had an autoregressive moving average model (ARMA) [6] fit to its stochastic remainder, characterizing its mass flow variation. Finally, the set of ARMA models was used to develop a predictive model, relating the flow rate stochasticity to powder properties and operating conditions. This predictive model was integrated into the current deterministic feeder model, yielding a novel hybrid mechanistic-empirical-stochastic flow sheet model that simulates a realistic, high variance mass flow rate and is suitable for the development of CMDP processes and controllers.

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[2] Y. Yu, “Theoretical modelling and experimental investigation of the performance of screw feeders,” PhD thesis, 1997.

[3] F. Boukouvala, V. Niotis, R. Ramachandran, F. J. Muzzio, and M. G. Ierapetritou, “An integrated approach for dynamic flowsheet modeling and sensitivity analysis of a continuous tablet manufacturing process,” Computers & Chemical Engineering, vol. 42, pp. 30–47, 2012.

[4] D. Bascone, F. Galvanin, N. Shah, and S. Garcìa-Muñoz, “A hybrid mechanistic-empirical approach to the modelling of twin screw feeders for continuous tablet manufacturing,” Industrial & Engineering Chemistry Research, 2020.

[5] P. Toson and J. G. Khinast, “Particle-level residence time data in a twin-screw feeder,” Data in brief, vol. 27, p. 104672, 2019.

[6] G. E. P. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, Time series analysis: Forecasting and control. John Wiley & Sons, 2015.