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A Gaussian quadrature method for solving batch crystallization models
Author(s) -
Qamar Shamsul,
Mukhtar Safyan,
Ali Qasim,
SeidelMorgenstern Andreas
Publication year - 2011
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.12264
Subject(s) - quadrature (astronomy) , population balance equation , mathematics , nucleation , gaussian quadrature , normalization (sociology) , gaussian , nyström method , population , statistical physics , mathematical analysis , thermodynamics , chemistry , physics , computational chemistry , integral equation , demography , sociology , anthropology , optics
The quadrature method of moments (QMOM) has been recently introduced for solving population balance models. In this article, an alternative approach of QMOM is proposed for solving batch crystallization models describing crystals nucleation, size‐dependent growth, aggregation, breakage, and dissolution of small nuclei below certain critical size. In this technique, orthogonal polynomials, obtained from the lower order moments, are used to find the quadrature abscissas (points) and weights. Several test problems with different combinations of processes are considered in this manuscript. The numerical results are compared with analytical solutions and with the finite‐volume scheme results. Excellent agreements were observed on the moment calculations in all test cases. © 2010 American Institute of Chemical Engineers AIChE J, 2011