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Finite‐element methods for steady‐state population balance equations
Author(s) -
Nicmanis M.,
Hounslow M. J.
Publication year - 1998
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.690441015
Subject(s) - population balance equation , discretization , finite element method , galerkin method , mathematics , population , steady state (chemistry) , collocation (remote sensing) , discontinuous galerkin method , balance (ability) , mathematical analysis , physics , computer science , thermodynamics , chemistry , medicine , demography , machine learning , sociology , physical medicine and rehabilitation
A finite‐element algorithm is developed to solve the population balance equation that governs steady‐state behavior of well‐mixed particulate systems. Collocation and Galerkin methods are used to solve several test problems in which aggregation, breakage, nucleation and growth (and combinations of these phenomena) occur. It is shown that the Galerkin method must be used in growth problems to obtain a well‐conditioned system. In all the cases investigated, density distributions and their moments are accurately predicted by the method. In a direct comparison with the discretized population balance (DPB) of Litster et al. (1995) the finite‐element method proves capable of predictions that are typically two orders of magnitude more accurate than those of the DPB. These results were obtained using smaller systems of equations and with considerably less computational power.