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One-group reduced population balance model for CFD simulation of a pilot-plant extraction column / Christian Drumm in Industrial & engineering chemistry research, Vol. 49 N° 7 (Avril 2010) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 49 N° 7 (Avril 2010) . - pp. 3442–3451 Titre : One-group reduced population balance model for CFD simulation of a pilot-plant extraction column Type de document : texte imprimé Auteurs : Christian Drumm, Auteur ; Menwer Attarakih, Auteur ; Mark W. Hlawitschka, Auteur Année de publication : 2010 Article en page(s) : pp. 3442–3451 Note générale : Industrial Chemistry Langues : Anglais (eng) Mots-clés : Population  Reduced  Balance  CFD  Simulation Résumé : In this work, a one-group reduced population balance model based on the one primary and one secondary particle method (OPOSPM) developed recently by Attarakih et al. (In Proceedings of the 19th European Symposium on Computer Aided Process Engineering, ESCAPE-19, Cracow, Poland, June 14−17, 2009; Jezowski, J., Thullie, J., Eds.; Elsevier: New York, 2009; ISBN-13: 978-0-444-53433-0) is implemented in the commercial computational fluid dynamics (CFD) package FLUENT 6.3 for solving the population balance equation in a combined CFD−population balance model (PBM). The one-group reduced population balance conserves the total number (N) and volume (α) concentrations of the population by directly solving two transport equations for N and α and provides a one-quadrature point for closing the unclosed integrals in the population balance equation. Unlike the published two-equation models, the present method offers accuracy improvement and internal consistency (with respect to the continuous population balance equation) by increasing the number of primary particles (sections). The one-group reduced population balance provides the possibility of a one-equation model for the solution of the PBM in CFD based on the mathematically consistent d30 instead of the classical d32 mean droplet diameter. Droplet breakage and coalescence are considered in the PBM, which is coupled to the fluid dynamics in order to describe real droplet behavior in a stirred liquid−liquid extraction column. As a case study, a full pilot-plant extraction column of a rotating disk contactor (RDC) type consisting of 50 compartments was simulated with the new model. The predicted results for the mean droplet diameter and the dispersed-phase volume fraction (holdup) agree well with literature data. The results show that the new CFD−PBM model is very efficient from a computational point of view (a factor of 2 less than the QMOM and a factor of 5 less than the method of classes). This is because the one-group reduced population balance requires the solution of only one equation (the total number concentration) when coupled to the CFD solver. It is therefore suitable for fast and efficient simulations of small-scale devices and even large-scale industrial processes. ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie901411e [article] One-group reduced population balance model for CFD simulation of a pilot-plant extraction column [texte imprimé] / Christian Drumm, Auteur ; Menwer Attarakih, Auteur ; Mark W. Hlawitschka, Auteur . - 2010 . - pp. 3442–3451. Industrial Chemistry Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 49 N° 7 (Avril 2010) . - pp. 3442–3451 Mots-clés : Population  Reduced  Balance  CFD  Simulation Résumé : In this work, a one-group reduced population balance model based on the one primary and one secondary particle method (OPOSPM) developed recently by Attarakih et al. (In Proceedings of the 19th European Symposium on Computer Aided Process Engineering, ESCAPE-19, Cracow, Poland, June 14−17, 2009; Jezowski, J., Thullie, J., Eds.; Elsevier: New York, 2009; ISBN-13: 978-0-444-53433-0) is implemented in the commercial computational fluid dynamics (CFD) package FLUENT 6.3 for solving the population balance equation in a combined CFD−population balance model (PBM). The one-group reduced population balance conserves the total number (N) and volume (α) concentrations of the population by directly solving two transport equations for N and α and provides a one-quadrature point for closing the unclosed integrals in the population balance equation. Unlike the published two-equation models, the present method offers accuracy improvement and internal consistency (with respect to the continuous population balance equation) by increasing the number of primary particles (sections). The one-group reduced population balance provides the possibility of a one-equation model for the solution of the PBM in CFD based on the mathematically consistent d30 instead of the classical d32 mean droplet diameter. Droplet breakage and coalescence are considered in the PBM, which is coupled to the fluid dynamics in order to describe real droplet behavior in a stirred liquid−liquid extraction column. As a case study, a full pilot-plant extraction column of a rotating disk contactor (RDC) type consisting of 50 compartments was simulated with the new model. The predicted results for the mean droplet diameter and the dispersed-phase volume fraction (holdup) agree well with literature data. The results show that the new CFD−PBM model is very efficient from a computational point of view (a factor of 2 less than the QMOM and a factor of 5 less than the method of classes). This is because the one-group reduced population balance requires the solution of only one equation (the total number concentration) when coupled to the CFD solver. It is therefore suitable for fast and efficient simulations of small-scale devices and even large-scale industrial processes. ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie901411e