(M1230-02-08) Discrete Element Method (DEM) Study of a Batch Blending Process

Purpose: When designing and developing pharmaceutical manufacturing processes, mathematical models like discrete element method (DEM) provide an alternate approach over experimental methods, of understanding the process by saving valuable resources and time. Moreover, computational simulations provide insights that would otherwise be challenging to obtain from physical means, for example, visibility into closed systems, formulation limitations, what-if scenarios, and several others. For an upstream process like blending, these savings and insights are especially noteworthy since it is a crucial step that dictates blend uniformity ahead of any further processing and dose creation. DEM is often used to simulate granular flow as it treats the particles as discrete entities. But the success of DEM models significantly depends on robust calibration, which in turn, relies on the quality of the material properties and characterization techniques. While it is very common to approximate properties from materials deemed close-enough to the actual material, the approximation can cause the simulated results to be mismatched and, therefore, reduce the usefulness of the model to the physical process being mimicked. This study showcases (i) the testing of the actual materials used in the blending process, (ii) the calibration process, and (iii) the mixing dynamics, blend homogeneity and areas of segregation within the blender.

Methods: The materials used for the study consist of a free-flowing material, sand, and a cohesive material like limestone powder, chosen due to their similarity to many oral dose ingredients. The physical blending was conducted in a batch ribbon blender and the raw materials accounted for 50% of its fill volume. Sampling was conducted at several locations and time points as the blending progressed. The properties essential to calibrate the DEM model are angle of repose, bulk density, wall friction, and cohesive strength which were determined by conducting lab tests of the individual materials and of the blend. The contact model used for the DEM simulations is a hysteresis model, developed in-house and run on an in-house built simulation platform. The simulation parameters were fine-tuned to match the physical parameters of blending rpm and fill amounts (by mass). Further, the sampling methodology employed for the simulations was consistent with the experimental methods.

Results: The properties of the individual raw materials and their blend were determined at the same conditions the physical blending was performed and at instantaneous flow. Bulk density was determined using compressibility tests at varying consolidation pressures, cohesive strength was determined using shear cell tests, wall friction was determined against one surface/finish using shear cell tests, and particle size distribution was determined by sieving and laser diffraction. Additionally, angle of repose, coefficient of restitution, dynamic friction, rolling & torsional friction, time step, shear modulus, stiffness, Poisson’s ratio, and yield stress were determined. These properties formed the inputs of the DEM simulation and were essential to the model calibration. The simulated data were compared to the data from the blending experiments for the following metrics: composition of the blend at pre-defined sampling locations, local and overall blend relative standard deviation (RSD), and stagnant zones within the blender. At around 100 revolutions a homogenous mixture had been achieved with RSD < 3% at various locations of the blend. The regions close to the blender walls and base had the most heterogeneity; although the binary mixture headed towards more uniformity as the blending revolutions increased, these interface regions never saw complete homogeneity. These regions experienced powder stagnation which not uncommon in tubular blenders. For these aforementioned outcomes, the DEM and experimental data align well.

Conclusion: A successful approach for using lab characterization results as input towards calibration of a DEM model has been demonstrated. Due to the thorough calibration, a good alignment in the results between the DEM and physical blending has been observed. In comparison to free-flowing powders, modeling of blending processes involving cohesive powders presents more challenges, which can be overcome by a representative DEM model along with accurate and relevant material properties. The mixing dynamics were assessed at preset time points (presented as revolutions) and the blending endpoint was determined as confirmed from the RSD values. Experimental values were obtained by sieving the samples extracted from the sampling locations to determine the local compositions. Additional revolutions seemed to initiate a state of demixing of the materials. Stagnant regions within the blender were also identified. In conclusion, by using mathematical models, the need for time consuming and expensive blending studies during scale up can be avoided.

Cohesive strength tests of one of the raw materials using a shear tester

DEM calibration parameters for cohesive limestone, free-flowing sand and their blend

Comparison of blend homogeneity at 75 revolutions: DEM (left), experimental (right)