Stochastic analysis and modeling of pharmaceutical screw feeder mass flow rates

Screw feeders, as the initial operation in continuous manufacturing of drug product processes, greatly influence the mass flow rate of pharmaceutical powders downstream. Existing flowsheet models can quickly simulate the average powder mass flow rate while custom Discrete Element Method models require prohibitively long times to simulate a minute of realistic, high-variance particle flow. We propose a hybrid deterministic-stochastic feeder flowsheet model that leverages time series analysis and an Autoregressive Moving Average (ARMA) model to quantify and simulate the observed non-random variation in feeder powder flow. To allow for improved process and controller design, our approach is quick-to-solve, high-variance, and has a low experimental overhead. By examining the deterministic model errors of three different volumetrically fed excipients, we demonstrate that the errors are leptokurtic, heavy-tailed, and display a linear dependence on their prior two seconds of state. These errors are all reasonably modeled by an ARMA(2,1) model and are parametrically distinct from each other. Furthermore, we show that refilling the feeder online significantly alters the error distribution, autocorrelation structure, and ARMA parameters. These findings lay the groundwork necessary to model and predict the realistic feeder dynamics of a much broader range of powders and operating conditions.