Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

Feiran Sun, Tao Liu, Yi Cao, Xiongwei Ni, Zoltan Kalman Nagy

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
24 Downloads (Pure)


In this paper, a cell average technique (CAT) based parameter estimation method is proposed for cooling crystallization involved with particle growth, aggregation and breakage, by establishing a more efficient and accurate solution in terms of the automatic differentiation (AD) algorithm. To overcome the deficiency of CAT that demands high computation cost for implementation, a set of ordinary differential equations (ODEs) entailed from CAT based discretized population balance equation (PBE) are solved by using the AD based high-order Taylor expansion. Moreover, an AD based trust-region reflective (TRR) algorithm and another interior-point (IP) algorithm are established for estimating the kinetic parameters associated with particle growth, aggregation and breakage. As a result, the estimation accuracy can be further improved while the computation cost can be significantly reduced, compared to the existing algorithms. Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT, TRR and IP algorithms in comparison with the existing algorithms. Moreover, seeded batch cooling crystallization experiments of β form L-glutamic acid are performed to validate the proposed method.
Original languageEnglish
Pages (from-to)1637-1651
Number of pages15
JournalChinese Journal of Chemical Engineering
Issue number6
Early online date20 Mar 2020
Publication statusPublished - Jun 2020


  • Automatic differentiation
  • Cell average technique
  • Cooling crystallization
  • Parameter estimation
  • Population balance model

ASJC Scopus subject areas

  • Environmental Engineering
  • Biochemistry
  • General Chemistry
  • General Chemical Engineering


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