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

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% <i>w</i>/<i>w</i> acetaminophen and 90% <i>w</i>/<i>w</i> 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.