Method of Characteristics for the Efficient Simulation of Population Balance Models

Xiaoxiang Zhu, Lifang Zhou and Richard D. Braatz ()
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Xiaoxiang Zhu: Massachusetts Institute of Technology
Lifang Zhou: Massachusetts Institute of Technology
Richard D. Braatz: Massachusetts Institute of Technology

A chapter in Optimization of Pharmaceutical Processes, 2022, pp 33-51 from Springer

Abstract: Abstract Model-based optimization is increasingly applied in pharmaceutical manufacturing. Particulate processes are especially ubiquitous in pharmaceutical manufacturing, which are modeled by population balance models (PBMs), which are described by coupled nonlinear ordinary and hyperbolic partial differential equations. A substantial literature has investigated ways to reduce the computational cost of simulating these equations, to enable their direct incorporation into dynamic optimization. This paper describes the implementation and applications of a particular simulation method – the method of characteristics (MOCH) – for efficient simulation of coupled population balance models and mass conservation in particulate processes by transforming the PBM into a system of differential-algebraic equations (DAEs). This DAE formulation of MOCH approach is especially advantageous for the simulation of complicated multidimensional systems with size-dependent growth and/or dissolution. Numerical examples were presented and demonstrated the high accuracy and computational efficiency. The MOCH approach enables online applications of parameter estimation, state estimation, and real-time optimization-based control based on population balance models.

Keywords: Method of characteristics; Population balance models; Particle size distribution; Pharmaceutical crystallization; Pharmaceutical manufacturing (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-90924-6_2

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DOI: 10.1007/978-3-030-90924-6_2

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