Computational Approaches for Studying the Granular Dynamics of Continuous Blending Processes, 2 – Population Balance and Data‐Based Methods

Abstract

IntroductionPowder mixing is a crucial unit operation in the pharmaceutical industry and other solids handling industries (e.g., detergents, fertilizers) as unpredictable changes in the raw material properties or the operating conditions during operation can have a great impact on the final product quality. Recently, the promising benefits of continuous blending compared to the widely employed batch mixing has been recognized, provoking a high interest in characterization, modeling and optimization of continuous mixing processes. In literature, powder mixing has been studied both experimentally [1][2][3][4][5] and theoretically, [2,[6][7][8][9][10][11][12] resulting in the availability of a wide range of modeling techniques for predicting the behavior of processed particle mixtures. Modeling approaches for powder flow and powder process characterization are based on Monte Carlo simulations, particle-dynamic simulations, heuristic or empirical-based models, compartment method models, and kinetic theory models. A number of papers have employed discrete-element method (DEM) to study the dynamics of granular flow in different mixer geometries. The application of mechanistic models for studying a continuous blending process was described in an earlier publication. [13] This paper discusses the application of techniques with a lower computational cost, such as population balance modeling (PBM) and statistical data-driven modeling.Population balance models have become a very powerful tool for process design and control of particulate processes, The application of computationally inexpensive modeling methods for a predictive study of powder mixing is discussed. A multidimensional population balance model is formulated to track the evolution of the distribution of a mixture of particle populations with respect to position and time. Integrating knowledge derived from a discrete element model, this method can be used to predict residence time distribution, mean and relative standard deviation of the API concentration in a continuous mixer. Low-order statistical models, including response surface methods, kriging, and high-dimensional model representations are also presented. Their efficiency for design optimization and process design space identification with respect to operating and design variables is illustrated. 9 such as crystallization, granulation, and polymerization. [14] Population balances are mathematical models that describe changes in populations in which each member of the population is distributed with respect to one or more properties. The PBM framework has been described as a particle number accounting procedure, a statement of the material balance for the process at a given instance. [15] A comprehensive review of the applications of population balances in particulate systems can be found in ref. [16] Blending is the act of bringing distinct bulk material particles into intimate contact in order to produce a mixture of consistent quality. Blending of bulk solids occurs because of velocities and velocity gr...

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