Characterizing and Modeling Pharmaceutical Twin Screw Feeder Mass Flow Rates Using Statistical Time Series Analysis

Screw feeders are the critical first unit operation in continuous manufacturing of drug product (CMDP) processes, influencing the mass flow rate of pharmaceutical powders downstream. Thus, industrial leaders are keen on accurately modeling feeders. Existing flowsheet models simulate the average mass flow rate [1]–[3], neglecting the stochastic behavior of the mass flow. Custom Discrete Element Method models realistically simulate particles’ behavior but require prohibitively long computation times to simulate minutes of operation [4]. To better design processes and controllers, a quick-to-solve flowsheet model that can simulate the stochastic nature of real screw feeders is necessary. This is precisely the gap addressed by this work.

This work describes 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, experimental data was used to estimate the parameters of a hybrid mechanistic-empirical screw feeder model, based on Bascone et al. 2020 [3]. Next, the stochastic residual of the mass flow was isolated by subtracting the flowsheet model’s deterministic mass flow from the feeder-reported mass flow. Then, each experiment's stochastic residual was fit to an autoregressive moving average model (ARMA) [5], characterizing the mass flow variation. Finally, a predictive model mapping powder properties and operating conditions to ARMA model parameters was developed. This predictive model was integrated with our deterministic feeder model, yielding a novel mechanistic-empirical-stochastic flowsheet model that simulates realistic, high-variance mass flows and is suitable for the development of CMDP processes and controllers.

Research Interests: Dynamic Systems, Multivariate Analysis, Constrained Regression, Optimization, and Technical Software Development

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

[2] 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.

[3] 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.

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

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