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Gregory J. McRae. Obrigkeit, Darren Donald, 1974- Massachusetts Institute of Technology. Dept. of Chemical Engineering. Massachusetts Institute of Technology. Department of Chemical Engineering 2006-02-02T18:47:57Z 2006-02-02T18:47:57Z 2001 http://hdl.handle.net/1721.1/31099 49544532 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2001. "June 2001." Includes bibliographical references. Population balances describe a wide variety of processes in the chemical industry and environment ranging from crystallization to atmospheric aerosols, yet the dynamics of these processes are poorly understood. A number of different mechanisms, including growth, nucleation, coagulation, and fragmentation typically drive the dynamics of population balance systems. Measurement methods are not capable of collecting data at resolutions which can explain the interactions of these processes. In order to better understand particle formation mechanisms, numerical solutions could be employed, however current numerical solutions are generally restricted to a either a limited selection of growth laws or a limited solution range. This lack of modeling ability precludes the accurate and/or fast solution of the entire class of problems involving simultaneous nucleation and growth. Using insights into the numerical stability limits of the governing equations for growth, it is possible to develop new methods which reduce solution times while expanding the solution range to include many orders of magnitude in particle size. Rigorous derivation of the representations and governing equations is presented for both single and multi-component population balance systems involving growth, coagulation, fragmentation, and nucleation sources. A survey of the representations used in numerical implementations is followed by an analysis of model complexity as new components are added. The numerical implementation of a split composition distribution method for multicomponent systems is presented, and the solution is verified against analytical results. Numerical stability requirements under varying growth rate laws are used to develop new scaling methods which enable the description of particles over many orders of magnitude in size. Numerous examples are presented to illustrate the utility of these methods and to familiarize the reader with the development and manipulations of the representations, governing equations, and numerical implementations of population balance systems. by Darren Donald Obrigkeit. Ph.D. 396 p. 19237722 bytes 19291663 bytes application/pdf application/pdf eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Chemical Engineering. Numerical solution of multicomponent population balance systems with applications to particulate processes Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="7be780d0-5364-4c4c-9185-e7964b31a2e5"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Numerical solution of multicomponent population balance systems with applications to particulate processes</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2001</PublicationDate> <Authors> <Author> <DisplayName>Obrigkeit, Darren Donald, 1974-</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Chemical Engineering.</Keyword> <Abstract>Population balances describe a wide variety of processes in the chemical industry and environment ranging from crystallization to atmospheric aerosols, yet the dynamics of these processes are poorly understood. A number of different mechanisms, including growth, nucleation, coagulation, and fragmentation typically drive the dynamics of population balance systems. Measurement methods are not capable of collecting data at resolutions which can explain the interactions of these processes. In order to better understand particle formation mechanisms, numerical solutions could be employed, however current numerical solutions are generally restricted to a either a limited selection of growth laws or a limited solution range. This lack of modeling ability precludes the accurate and/or fast solution of the entire class of problems involving simultaneous nucleation and growth. Using insights into the numerical stability limits of the governing equations for growth, it is possible to develop new methods which reduce solution times while expanding the solution range to include many orders of magnitude in particle size. Rigorous derivation of the representations and governing equations is presented for both single and multi-component population balance systems involving growth, coagulation, fragmentation, and nucleation sources. A survey of the representations used in numerical implementations is followed by an analysis of model complexity as new components are added. The numerical implementation of a split composition distribution method for multicomponent systems is presented, and the solution is verified against analytical results. Numerical stability requirements under varying growth rate laws are used to develop new scaling methods which enable the description of particles over many orders of magnitude in size. Numerous examples are presented to illustrate the utility of these methods and to familiarize the reader with the development and manipulations of the representations, governing equations, and numerical implementations of population balance systems.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>