Mesoscale modeling of the crystallization parameters identification during the iron-based catalyst preparation process: the dilute concentration case

ABSTRACT

In this paper we model the mesoscale crystallization of the crystals $Fe(OH{)}_3$ in the dilute solution concentration in the sense that the microscale model is a stochastic process and meanwhile the macroscale model is a deterministic heat diffusion process. The crystallization process includes the steps of nucleation, nucleus radial growth and nuclei aggregation. In the case of the dilute solution concentration we may neglect the effect of the nuclei aggregation, i.e. the crystallization neglects the impingement. The coupled model of crystallization and heat diffusion show the mesoscale characteristic between the micro- and macro- aspect. Furthermore we reformulate the simultaneous identification of nucleation rate and crystal growth speed in the stochastic birth-growth process by the inverse approaches. The regularization strategy is adopted to implement the numerical inversion of the inverse problem. Finally, numerical examples are provided to show the effectiveness of the proposed algorithm.

KEYWORDS:

• Mesoscale heat diffusion model
• stochastic inverse problem
• crystallization
• parameter identification
• Tikhonov regularization
• nucleation rate
• radial growth speed

AMS CLASSIFICATIONS:

• 35R30
• 60D05
• 74N05
• 65M32

Acknowledgments

The first-named author are also appreciative for the discussion with Professor M. Yamamoto and Dr Y. K. Liu during the stay in the University of Tokyo in August 2017 and February 2018.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is partially supported by the National Natural Scientific Foundation of China: a key scientific project on Mathematical modeling of meso-scale behavior in the preparation process of iron-based catalysts by the ferric hydroxide precipitation method [grant number 91534113] and the NSFC project on Computable Modeling for Industrial Problems with Grant Nos. [11471287 and 11871435] and NSF project of Zhejiang Province on Computational Methods for Forward and Inverse Problems with Grant Nos. [LY18A010030, LY19A010026].