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Method of Characteristics for the Efficient Simulation of Population Balance Models

In: Optimization of Pharmaceutical Processes

Author

Listed:
  • Xiaoxiang Zhu

    (Massachusetts Institute of Technology)

  • Lifang Zhou

    (Massachusetts Institute of Technology)

  • Richard D. Braatz

    (Massachusetts Institute of Technology)

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.

Suggested Citation

  • Xiaoxiang Zhu & Lifang Zhou & Richard D. Braatz, 2022. "Method of Characteristics for the Efficient Simulation of Population Balance Models," Springer Optimization and Its Applications, in: Antonios Fytopoulos & Rohit Ramachandran & Panos M. Pardalos (ed.), Optimization of Pharmaceutical Processes, pages 33-51, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-90924-6_2
    DOI: 10.1007/978-3-030-90924-6_2
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