(120f) Dynamic Reduced-Order Modeling of Particulate Systems for Pharmaceutical Unit Operations

Particulate and granular processes are of great interest within the pharmaceutical industry, as solid-based dosage forms like tablets remain among the most commonly manufactured drug products.  (1) The creation of predictive process models can play an important role in developing the requisite understanding of these processes.  Process models can be used to reduce experimental requirements, enhance process understanding, and develop control strategies. Modeling is also an important component of the Quality by Design (QbD) paradigm described by the ICH Q8 guidance for pharmaceutical development. (3)

Powder flow, compaction and other particulate phenomena have been effectively modeled with a high degree of accuracy using discrete element method (DEM) simulations. (2) However discrete and finite element models are computationally expensive to evaluate and therefore cannot be practically implemented in the context of integrated manufacturing process simulation.  Reduced order models can be used to incorporate information from these high-fidelity simulations into computationally efficient process models for simulation and optimization purposes. Previously the use of reduced-order models based on principal component analysis has been demonstrated for the incorporation of distributed state information from DEM or CFD simulations into lower order process models for systems at steady state. (4), (5)  These reduced order modeling methods rely on the reduction of the dimensionality of state data using principal component analysis (PCA) or partial orthogonal decomposition (POD). (6) State data include velocity trajectories or energy and force information for particles in the case of DEM or fluid elements in the case of CFD.  Once the state data has been projected into a lower dimensional space, a mapping between process inputs and the reduced state data is developed. This mapping can be based on fitting a response surface, neural networks, kriging, or any other appropriate technique. Once this mapping has been developed the state space can be reconstructed for any relevant set of input parameters, facilitating predictive modeling of distributed parameters in a computationally efficient manner.

Prior work has demonstrated the implementation of reduced order models for systems at steady state. (4)However, dynamic models are needed to study process response to disturbances and to implement effective control strategies for disturbance rejection. The current work thus focuses on the implementation of reduced order models for dynamic systems, specifically those pertaining to particulate processes for the manufacture of solids-based drugs. In this case, time is considered one of the inputs of interest from which the state data can ultimately be predicted. These dynamic models assume inherent time dependence for the underlying system.  A variety of order reduction techniques, including those based on principal component analysis are examined.

A case study based on a continuous convective mixer is presented to demonstrate the methods discussed. State data including average particle velocities, kinetic energies and force trajectories within the continuous mixer are readily obtained from DEM simulations. This unit operation provides an effective case study as it has been used in prior work to demonstrate the efficacy of a discrete elements reduced order modeling method for particulate systems at steady state. (4)

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