Continuous mixing technology: Validation of a DEM model

Abstract

Continuous powder mixing is an important technology used in the development and manufacturing of solid oral dosage forms. Since critical quality attributes of the final product greatly depend on the performance of the mixing step, an analysis of such a process using the Discrete Element Method (DEM) is of crucial importance. On one hand, the number of expensive experimental runs can be reduced dramatically. On the other hand, numerical simulations can provide information that is very difficult to obtain experimentally. In order to apply such a simulation technology in product development and to replace experimental runs, an intensive model validation step is required. This paper presents a DEM model of the vertical continuous mixing device termed CMT (continuous mixing technology) and an extensive validation workflow. First, a cohesive contact model was calibrated in two small-scale characterization experiments: a compression test with spring-back and a shear cell test. An improved, quicker calibration procedure utilizing the previously calibrated contact models is presented. The calibration procedure is able to differentiate between the blend properties caused by different API particle sizes in the same formulation. Second, DEM simulations of the CMT were carried out to determine the residence time distribution (RTD) of the material inside the mixer. After that, the predicted RTDs were compared with the results of tracer spike experiments conducted with two blend material properties at two mass throughputs of 15 kg/h and 30 kg/h. Additionally, three hold-up masses (500, 730 and 850 g) and three impeller speeds (400, 440 and 650 rpms) were considered. Finally, both RTD datasets from DEM and tracer experiments were used to predict the damping behavior of incoming feeder fluctuations and the funnel of maximum duration and magnitude of incoming deviations that do not require a control action. The results for both tools in terms of enabling a control strategy (the fluctuation damping and the funnel plot) are in excellent agreement, indicating that DEM simulations are well suited to replace process-scale tracer spike experiments to determine the RTD.

Introduction

Continuous manufacturing is increasingly applied in the pharmaceutical industry, replacing traditional batch production processes. Its advantages include smaller footprints of processing units and intermediate product storage, faster turnaround times and better control of quality parameters (Plumb, 2005, Aigner et al., 2017). The simplest set-up for a continuous tableting line is the continuous direct compression (CDC) process, consisting of three main unit operations: feeding of raw material, mixing of individual component streams and compressing the blends into the tablet dosage form (Ervasti et al., 2015, Van Snick et al., 2017). Several critical quality attributes (CQAs) of the final product, e.g., the content uniformity, are affected by the mixing step (Yu, 2008). In addition, the tensile strength of final tablet depends on the extent of powder lubrication in the mixing device (Kushner and Moore, 2010).

Fig. 1 provides an overview of a vertical continuous mixing device termed Continuous Mixing Technology (CMT). CMT features two rotating impellers stacked on top of each other in a cylindrical vessel with a conical section at the bottom. The top impeller rotates inside a de-lumping screen in the top half of the CMT and breaks up agglomerates that may have formed during the upstream process. After de-lumping, the particles fall into the mixing zone and are agitated by the bottom impeller. The CMT is placed on load cells to continuously measure the hold-up mass contained within the mixer. A control system constantly adjusts the opening of the motor-driven exit valve to control the outflow and to keep the hold-up mass within the CMT constant (Blackwood et al., 2019). The DEM model controls the exit valve in a similar manner. The hold-up mass in the simulation is simply the sum of the masses of the individual particles in the system.

This work is a continuation of an investigation of (Toson et al., 2018), with the same methodology (DEM simulations) and implementation. The initial study analyzed the operating space of CMT at a low throughput (10 kg/h) with a free flowing blend and a formulation with a low API concentration. The residence time distribution obtained from the DEM simulations were successfully validated in tracer experiments. The aim of this work is to extend the applicability of the previously presented DEM model of the CMT to more cohesive powder blends with a new API and formulation as well as higher throughputs and a more comprehensive validation of model predictions. Two mass throughputs are considered in this work: 15 kg/h and 30 kg/h. Furthermore, two blends of the same formulation were experimentally characterized and calibrated. The only difference between the two blends is the particle size of the API. Two API grades are considered in this work, corresponding to the minimum and maximum in-spec sizes. This allows to extend the DEM model to capture the effect of variations in the material properties on the process outcome.

Due to the sheer number of particles in the order of >10¹² in the CMT it is necessary to scale-up the particle size to reduce the number of particles in the simulation domain (Coetzee, 2018, Thakur et al., 2016). The particle size was chosen based on performance (particle number, process time, simulation time) and geometric (e.g., resolution of clearances in the CMT) considerations. The contact model calibration ensures that the bulk flow behavior is correctly reproduced in the DEM simulations. This calibration method is known as the bulk calibration approach and is widely applied in the pharmaceutical field and beyond (Dai et al., 2019, Ghodki et al., 2019, Madlmeir et al., 2019, Orefice and Khinast, 2019, Roessler and Katterfeld, 2018). The bulk calibration approach has been applied to model vastly different types of granular media with different flow behavior by adjusting the contact parameters (Coetzee, 2017, Paulick et al., 2015, Yeom et al., 2019, Zhu et al., 2007, Zhu et al., 2008). This implies that the change in flowability due to a different API particle size can also be modeled using different contact parameters, without the need to change the DEM particle size.

The calibration routine reproduces small-scale characterization experiments: a compression and spring-back test for the plastic deformation and elastic recovery of the powder bed, and a shear cell test to measure the flowability, as already demonstrated in (Toson et al., 2018). Because previously calibrated contact models are available, the new formulations can be calibrated quickly by adjusting a limited set of contact parameters. This workflow is applicable as long as there are no fundamental changes in the powder behavior, e.g. a segregation tendency or electrostatic charging.

The obtained contact parameters are subsequently used in DEM simulations of the CMT, replicating the experiments published by (Lee et al., 2021). For validation, the raw residence time distributions (RTD) and the resulting predicted damping of feeder fluctuations in the DEM and tracer experiments were compared.