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Mathematical analysis of the meso-scale flow field in spiral-wound membrane modules / Margaritis Kostoglou in Industrial & engineering chemistry research, Vol. 50 N° 8 (Avril 2011) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 50 N° 8 (Avril 2011) . - pp. 4653–4666 Titre : Mathematical analysis of the meso-scale flow field in spiral-wound membrane modules Type de document : texte imprimé Auteurs : Margaritis Kostoglou, Auteur ; Anastasios J. Karabelas, Auteur Année de publication : 2011 Article en page(s) : pp. 4653–4666 Note générale : Chimie industrielle Langues : Anglais (eng) Mots-clés : Mathematical  analysis  Mesoscale  hydrodynamic  equations Résumé : The use of flat-sheet, spiral-wound, membrane modules for reverse osmosis and nanofiltration applications is very extensive. Design and performance optimization of these modules requires sound mathematical modeling. This study focuses on the mathematical analysis of the mesoscale hydrodynamic equations for the narrow channels with spacers, of the entire membrane sheet, previously derived from the microscale momentum conservation laws14. The mathematical problem is enhanced by considering a spatial dependence of the retentate channel and membrane permeabilities to account for fouling/scaling, aiming at future use of the proposed techniques to simulate long time fouling dynamic behavior of the process. The formal mathematical treatment of the original problem leads to several levels of approximation (depending on the problem parameter values) which admit either analytical or numerical solutions with reduced dimensionality, or numerical solutions with reduced convergence difficulties. To confirm the validity of conclusions obtained by following these procedures, several results from simplified cases are compared with numerical solutions of the original problem. Furthermore, all possible simplifications and analytical solutions of the particular problem have been obtained, as well as the conditions under which they hold, thus forming the basis for more comprehensive modeling, including mass transfer and scaling/fouling phenomena. Specific criteria are also provided for selecting appropriate simplified solutions to specific cases, helpful in the development of flow and membrane fouling simulators. DEWEY : 660 ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie102083j [article] Mathematical analysis of the meso-scale flow field in spiral-wound membrane modules [texte imprimé] / Margaritis Kostoglou, Auteur ; Anastasios J. Karabelas, Auteur . - 2011 . - pp. 4653–4666. Chimie industrielle Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 50 N° 8 (Avril 2011) . - pp. 4653–4666 Mots-clés : Mathematical  analysis  Mesoscale  hydrodynamic  equations Résumé : The use of flat-sheet, spiral-wound, membrane modules for reverse osmosis and nanofiltration applications is very extensive. Design and performance optimization of these modules requires sound mathematical modeling. This study focuses on the mathematical analysis of the mesoscale hydrodynamic equations for the narrow channels with spacers, of the entire membrane sheet, previously derived from the microscale momentum conservation laws14. The mathematical problem is enhanced by considering a spatial dependence of the retentate channel and membrane permeabilities to account for fouling/scaling, aiming at future use of the proposed techniques to simulate long time fouling dynamic behavior of the process. The formal mathematical treatment of the original problem leads to several levels of approximation (depending on the problem parameter values) which admit either analytical or numerical solutions with reduced dimensionality, or numerical solutions with reduced convergence difficulties. To confirm the validity of conclusions obtained by following these procedures, several results from simplified cases are compared with numerical solutions of the original problem. Furthermore, all possible simplifications and analytical solutions of the particular problem have been obtained, as well as the conditions under which they hold, thus forming the basis for more comprehensive modeling, including mass transfer and scaling/fouling phenomena. Specific criteria are also provided for selecting appropriate simplified solutions to specific cases, helpful in the development of flow and membrane fouling simulators. DEWEY : 660 ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie102083j

On the fluid mechanics of spiral-wound membrane modules / M. Kostoglou in Industrial & engineering chemistry research, Vol. 48 N° 22 (Novembre 2009) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 48 N° 22 (Novembre 2009) . - pp. 10025–10036 Titre : On the fluid mechanics of spiral-wound membrane modules Type de document : texte imprimé Auteurs : M. Kostoglou, Auteur ; Anastasios J. Karabelas, Auteur Année de publication : 2010 Article en page(s) : pp. 10025–10036 Note générale : Chemical engineering Langues : Anglais (eng) Mots-clés : Spiral-wound  membrane  modules  Fluid  mechanics Résumé : Spiral-wound membrane (SWM) modules are comprised of several large-size membrane sheets with a net-type spacer at the retentate flow channel and a porous cloth/filler at the low-pressure permeate side; thus, two strongly interacting flow fields exist with spatially variable properties. Mathematical models of the SWM operation, based on an accurate description of transport phenomena taking place in those narrow flow passages, are necessary tools for optimizing both module design parameters and the entire membrane-based plant. Such integrated SWM models are not available at present. In this problem, the coexistence of several flow length scales, from the pores of the permeate side filler to the macroscopic dimensions of the module, renders the modeling task quite complicated. Typical modeling efforts vary between the extremes of detailed description of transport phenomena at small scale to macroscopic phenomenological-type simulation of the entire separation process in a module. The scope of this work is to describe the hydrodynamics of spiral-wound membranes, starting from first principles, to suggest and analyze some realistic approximations and their origin and to present an integrated model where linking phenomena at different length scales is an essential feature. This effort has resulted in an efficient numerical algorithm, allowing predictions of the spatial distribution of pressure, permeation, and cross-flow velocities throughout the membrane leaves. In this work, all possible analytical solutions have been derived which facilitate the development of the simulation algorithm. Typical examples of predicted flow and pressure distributions are presented. En ligne : http://pubs.acs.org/doi/abs/10.1021/ie901129j [article] On the fluid mechanics of spiral-wound membrane modules [texte imprimé] / M. Kostoglou, Auteur ; Anastasios J. Karabelas, Auteur . - 2010 . - pp. 10025–10036. Chemical engineering Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 48 N° 22 (Novembre 2009) . - pp. 10025–10036 Mots-clés : Spiral-wound  membrane  modules  Fluid  mechanics Résumé : Spiral-wound membrane (SWM) modules are comprised of several large-size membrane sheets with a net-type spacer at the retentate flow channel and a porous cloth/filler at the low-pressure permeate side; thus, two strongly interacting flow fields exist with spatially variable properties. Mathematical models of the SWM operation, based on an accurate description of transport phenomena taking place in those narrow flow passages, are necessary tools for optimizing both module design parameters and the entire membrane-based plant. Such integrated SWM models are not available at present. In this problem, the coexistence of several flow length scales, from the pores of the permeate side filler to the macroscopic dimensions of the module, renders the modeling task quite complicated. Typical modeling efforts vary between the extremes of detailed description of transport phenomena at small scale to macroscopic phenomenological-type simulation of the entire separation process in a module. The scope of this work is to describe the hydrodynamics of spiral-wound membranes, starting from first principles, to suggest and analyze some realistic approximations and their origin and to present an integrated model where linking phenomena at different length scales is an essential feature. This effort has resulted in an efficient numerical algorithm, allowing predictions of the spatial distribution of pressure, permeation, and cross-flow velocities throughout the membrane leaves. In this work, all possible analytical solutions have been derived which facilitate the development of the simulation algorithm. Typical examples of predicted flow and pressure distributions are presented. En ligne : http://pubs.acs.org/doi/abs/10.1021/ie901129j