A Gaussian quadrature method for solving batch crystallization models



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