Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Dry Granulation Case Study

Abstract

We present a systematic and automatic approach for integrating tableting reduced-order models with upstream unit operations. The approach not only identifies the upstream critical material attributes and process parameters that describe the coupling to the first order and, possibly, the second order, but it also selects the mathematical form of such coupling and estimates its parameters. Specifically, we propose that the coupling can be generally described by normalized bivariate rational functions. We demonstrate this approach for dry granulation, a unit operation commonly used to enhance the flowability of pharmaceutical powders by increasing granule size distribution, which, inevitably, negatively impacts tabletability by reducing the particle porosity and imparting plastic work. Granules of different densities and size distributions are made with a 10% w/w acetaminophen and 90% w/w microcrystalline cellulose formulation, and tablets with a wide range of relative densities are fabricated. This approach is based on product and process understanding, and, in turn, it is not only essential to enabling the end-to-end integration, control, and optimization of dry granulation and tableting processes, but it also offers insight into the granule properties that have a dominant effect on each of the four stages of powder compaction, namely die filling, compaction, unloading, and ejection.

Keywords: bivariate rational functions; dry granulation; granule size distribution; reduced-order models; ribbon density; tableting.

Figure 1

The continuous solids-processing pilot plant at Purdue University involves several steps: (i) K-Tron and Schenck feeders are used to feed the APIs and excipients, respectively, ensuring a uniform blend in a Gericke GCM-250 blender; (ii) based on the manufacturing process (direct compaction or dry granulation), the powder blend is mixed with a lubricant feed from the K-Tron MT12 micro-screw lubricant feeder or fed to an Alexanderwerk WP120 roller compactor for dry granulation; and (iii) the final step involves the production of solid tablets using a Natoli NP-400 rotary tablet press.

Figure 2

Granule size distributions for different roll pressure and roll gap processing conditions estimated using the hybrid model of Huang et al. [15].

Figure 3

Diametrical compression of doubly convex tablets.

Figure 4

Stages of tablet compaction. Image courtesy of [5].

Figure 5

Contour and surface plots of $\mathit{\xi }\left(\mathrm{CPP}\right|\mathrm{CMA};\mathit{\theta })$ with $\left\{\mathrm{CPP}\right|\mathrm{CMA}\#1,\mathrm{CPP}|\mathrm{CMA}\#2\}\equiv \{x,y\}\in [0.3,1]\times [0,1]\}$ and $\mathit{\theta }=\{p1,p2,p3,p4,q1,q2,q3,r_X,r_Y\}=\{15,10,5,10,1,2,4,1,1\}$.

Figure 6

Tablet weight model.

Figure 7

Compaction force model.

Figure 8

Tablet density and elastic recovery models.

Figure 9

Tensile strength model. (a) Goodness of the tablet tensile strength prediction. (b) Predictions of the tablet tensile strength model.