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

doi:10.1016/j.cjche.2020.03.007

Abstract

Abstract: 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.

Key words: Cooling crystallization, Population balance model, Cell average technique, Parameter estimation, Automatic differentiation

摘要： 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.

关键词: Cooling crystallization, Population balance model, Cell average technique, Parameter estimation, Automatic differentiation

Feiran Sun, Tao Liu, Yi Cao, Xiongwei Ni, Zoltan Kalman Nagy. Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation[J]. Chinese Journal of Chemical Engineering, 2020, 28(6): 1637-1651.

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