https://doi.org/10.15255/KUI.2023.001
Published: Kem. Ind. 72 (7-8) (2023) 443–453
Paper reference number: KUI-01/2023
Paper type: Original scientific paper
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Calculation of the Optimal Cooling Temperature Profile of the Batch Crystalliser

J. Sacher, M. Sejdić, M. Gavran, N. Bolf and Ž. Ujević Andrijić

Abstract

The aim of this work was to create a computer program that can be used to calculate the optimal cooling temperature profile of the batch crystalliser. Potassium nitrate dissolved in water was used as a model system for process research. To create a mathematical model of the process, population balances were used, i.e., their moment transformation. To obtain the optimal temperature profile, a discretisation of the temperature profile was performed using a global optimisation algorithm. A genetic algorithm was used for the optimisation, while a system of ordinary differential equations was solved using the Runge-Kutta 4,5 method. The objective function was to minimise the ratio between the third moment of crystals produced by secondary nucleation, and the third moment of seed crystals at the end of the process. Firstly, the influence of the stopping conditions of the genetic algorithm on the computation time and the value of the objective function was tested. After the optimal stopping condition was determined, the influence of the number of discretisation points of the temperature profile on the value of the objective function and the required computation time was investigated. It was found that the optimal stopping condition was when fifteen members of a generation had objective function values that did not differ by more than the tolerance. It is shown that the optimal solution was achieved by dividing the temperature profile into eight parts. To check the repeatability of the calculation for optimal conditions, the calculation was repeated nine times. The optimal temperature profile was compared to a linear cooling of the same duration to determine the benefits of optimisation. The results of the simulation experiments indicate a significant improvement in the process when using the optimal temperature profile compared to the linear profile.

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Keywords

crystallisation, moment model, optimisation, genetic algorithm