Modelling and analysis of die filling and tablet compaction with Altair EDEM
Altair Employee1. Introduction
Tableting is a fundamental unit operation in the pharmaceutical solid oral dose manufacturing process and has a significant influence on tablet quality attributes such as weight, dosage, structural integrity, and dissolution rate. Reliably meeting the associated quality standards requires optimal operation for a given formulation but the effects of operational parameters on the mechanics of the tableting process are still not fully understood and process optimisation is primarily conducted empirically. Consequently, achieving high degree of reliability in tableting operations is challenging and time consuming for new formulations, leading to economic losses. Employing simulation based digital twins to gain insight into the mechanics of the tableting process beyond the one obtainable through experiments alone has significant utility in this context.
A tutorial on modelling a tableting process in EDEM can be found here:
A discrete element method based digital twin of the tableting process can be developed in Altair EDEM and used to evaluate the effect of operational parameters on process performance. Benefits of simulation analysis of this process include:
- Increased filling efficiency and fill uniformity
- Decreased size segregation
- Increased compaction uniformity
In addition to improving the mechanistic understanding of the tableting process the obtained insight can be used to inform optimal process operation.
Both the die filling stage and subsequent compaction stage can be modelled as demonstrated in this case study which was produced in collaboration with Novo Nordisk. Example simulations for the die filling and compaction stages are shown below.
| Die filling: | Tablet compaction: |
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2. Methodology
The bulk solid is modelled in EDEM via a meso-scopic approach, in which numerical particles of an intermediate scale between the physical particle scale and the scale of the system of interest are used to achieve practical computational times. The physical particle morphology is approximated in the model using the multi-sphere approach and the Edinburgh Elastic-Plastic-Adhesive contact model is used to model the visco-elastic-plastic-cohesive behaviour of the powder. The particle to particle interaction parameters are calibrated against uniaxial confined compression stress-strain measurements for Micro-Crystalline Cellulose (MCC) and the particle to die wall interaction parameters are calibrated against wall yield locus measurements of MCC sliding against stainless steel. The model details are summarised in Figures 1 and 2.
Figure 1 Particle morphology and size distribution
Figure 2 Contact model parameters and calibration results
3. Results
The effect of blade speed, die diameter and number of blade passes on the material flow rate and distribution in the die prior to compaction can be evaluated using the model and the results are shown in Figure 3. The mass added per pass decreases with blade velocity and die size. The results can be usefully represented in the normalised v/D, m/D2 space where v is the blade velocity, D is the die diameter and m is the filled mass. An approximately linear relationship between blade pass time (v/D) and die level of fill (m/D2) can be observed and this relationship can be used to inform tableting operation by providing the number of requisite passes for a given die and blade speed combination.
Figure 3 Effect of blade speed, die diameter and number of blade passes on mass in the die
Another important phenomenon during die filling is particle size segregation, which may translate into mixture component segregation as well as non-uniform compaction. The propensity for segregation as a function of die size and blade speed can be examined with the digital twin. In this case the size segregation is quantified by the standard deviation of the mean particle diameter in an EDEM Grid Bin Group. A decreased segregation with die size and increased segregation with blade speed can be observed as shown in Figure 4. These trends can be usefully examined in terms of the blade pass time where all cases apart from the extreme combination of smallest die and highest blade speed collapse onto a single curve. This curve can be used in combination with the previous fill level – blade speed curve to minimise the segregation for a given required production rate.
Figure 4 Effect of blade speed and die diameter on particle size segregation during filling
It is also useful to examine the stress state in the tablet at peak compaction – a result that is important with respect to homogeneous compaction but difficult to obtain experimentally. The consolidating stress and solid fraction fields at the peak of consolidation can be computed from the discrete particle data using EDEM’s continuum analysis functionality and a significant spatial variation can be observed for both as shown in Figure 5. This has a bearing on the propensity for tablet chipping due to the low strength of under consolidated regions, especially in the tablet corners where stress concentrations during tablet impact are high. The simulation results reveal that the under consolidated regions in the corners are a result of non-uniform distribution of material in the die prior to compaction which can be mitigated by increasing the die diameter and/or decreasing the blade speed.
Figure 5 Stress and solid fraction fields at peak compaction and corresponding initial states for the blade speed and die diameter extremes
4. Conclusions
A DEM based digital twin can be used to perform a parametric analysis of the tableting process in-silico and reveals useful trends such as:
- Increased filling efficiency and fill uniformity with blade pass time
- Decreased size segregation with blade pass time
- Increased compaction uniformity with blade pass time
In addition to improving the mechanistic understanding of the tableting process the obtained insight can be used to inform optimal process operation.