An Implicit FEM Solution of a PBE Model of Gibbsite Crystallization with Constant and Nonlinear Kinetics

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• 作者：Andrey V. Bekker ; Iztok Livk
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2011
• 出版时间：April 20, 2011
• 年：2011
• 卷：50
• 期：8
• 页码：4641-4652
• 全文大小：1227K
• 年卷期：v.50,no.8(April 20, 2011)
• ISSN：1520-5045

文摘

Numerical solution for a 1-D dynamic population balance crystallization model that includes gibbsite secondary nucleation and crystal growth kinetics was developed. The implemented numerical algorithm combines an implicit Galerkin formulation of the finite element method (FEM) with Newton iterations, variable Gear-type time-step and adaptive nonuniform mesh strategies. The numerical solution of the crystallization model is compared to the analytical solution derived for the case of constant gibbsite crystallization kinetics. For this case, it is shown that the numerical solution was considerably stabilized with the introduction of the artificial diffusion term and reduction of the relative error of Newton鈥檚 iterative step. Furthermore, the numerical algorithm is tested for the case of nonlinear gibbsite crystallization kinetics demonstrating its ability to deliver consistent solutions for both nucleation and crystal growth dominant cases. In each of the cases considered, the model solution, valid for an isothermal batch homogenously mixed crystallizer, predicted evolutions of the crystal size distribution (CSD) and relative supersaturation. Using the developed modeling technique, it is also shown that the initial seed loading strongly influences the shape of the product CSD, leading in some cases to multimodal CSDs.