Modeling of suspension crystallization processes with complex particle characterization [Elektronische Ressource] = Modellierung der Suspensionskristallisation mit komplexer Partikelcharakterisierung / von Heiko Briesen

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2008
• Nombre de lectures: 4
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

CommunicatedbyProf. Dr. Ing. W.Marquardt
Modelingofsuspensioncrystallizationprocesseswith
complexparticlecharacterization
–DeutscherTitel–
ModellierungderSuspensionskristallisationmitkomplexer
Partikelcharakterisierung
VonderFakultat¨ fur¨ MaschinenwesenderRheinisch–Westfalischen¨
TechnischenHochschuleAachenzurErlangungdervenialegendifur¨
dasLehrgebiet
Modellgestutzte¨ Partikeltechnik
genehmigteHabilitationsschrift
von
Dr. Ing. HeikoBriesen
ausHeidelberg
Berichter:
ProfessorDr. Ing. WolfgangMarquardt
RWTHAachen
ProfessorMichaelJ.Hounslow
UniversityofSheffield
ProfessorDr. Ing. WolfgangPeukert
Friedrich AlexanderUniversit at¨ Erlangen N urnber¨ g
Aachen,den4.3.2008I
Preface
The work presented in this Habilitation has been done during my time as an Ober
ingenieurfromsummer2002untilfall2007attheChairforProcessSystemsEngineer-
ing(LPT)attheRWTHAachenUniversity. I’mgratefultoProfessorDr. Ing. Wolfgang
Marquardt for giving me the opportunity to pursue my interest. In this work you see
what this has led to. I tried to live up to the high standards of scientific originality and
rigor which I experienced all around me during my years at LPT. Additional thanks
I owe to Professor Mike J. Hounslow (University of Sheffield) and Professor Dr. Ing.
WolfgangPeukert(Friedrich AlexanderUniversit at¨ Erlangen N urnber¨ g)foragreeingto
reviewandevaluatethiswork.
All LPT members who I was lucky to meet during the last years deserve my grate
fulness. I think the atmosphere you all created is something very special. I’m glad to
have been around such a cumulation of intelligent, creative, and interesting people. I
will never forget this important time in my life. My very special thanks go to my group
membersRobertGrosch,ViatcheslavKulikov,andNorbertKail. Itwasagreatpleasure
to work with you guys and to explore together the amazingly difficult field of crystal
lizationprocesses.
I also would like to thank Professor J.R. Barber (University of Michigan, USA) for
providing the basic Maple files for the solution of the strain energy distribution pre
sentedinsection3.3.3. ThehelpofProfessorDr. Ing. JoachimUlrichandDipl. Chem.
Katrin Jager¨ (Martin Luther University Halle, Germany) in finding appropriate crystal
geometries(seefigure3.5)isgreatlyappreciated.
The thanks I owe my family cannot be expressed in words. Eva, Malin, and Kolja,
youaremylife.
HeikoBriesenIIContents III
Contents
Notation VII
KurzfassungindeutscherSprache XIII
1 Introduction 1
1.1 Habilitationoverview . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Particlecharacterization 6
2.1 Simpleparticlecharacterization . . . . . . . . . . . . . . . . . . . . . 6
2.2 Complexparticleforcrystals . . . . . . . . . . . . . . 10
2.2.1 Shape . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Non geometricalparticleproperties . . . . . . . . . . . . . . . 14
2.2.3 Particlepositioninspace . . . . . . . . . . . . . . . . . . . . . 15
2.3 Matchingcharacterizationformodelingandexperimentalcharacterization 16
3 Singlecrystalmodeling 18
3.1 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.1 Continuumtheoriesofcrystalgrowth . . . . . . . . . . . . . . 19
3.1.2 KineticMonte Carlosimulationsofcrystalgrowth . . . . . . . 20
3.1.3 Moleculardynamics(MD)simulationsofcrystalgrowth . . . . 20
3.1.4 Morphologyprediction . . . . . . . . . . . . . . . . . . . . . . 21
3.1.5 Lumpedgrowthkinetics . . . . . . . . . . . . . . . . . . . . . 23
3.2 Breakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Attrition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Previousworkonattritionmodeling . . . . . . . . . . . . . . . 29
3.3.2 AttritionmodelbyGahnandMersmann . . . . . . . . . . . . . 30
3.3.3 Extendedmodelingforcomplexcrystalandimpactgeometry . 34IV Contents
3.3.3.1 Model assumption relaxation and resulting strain en
ergydistribution . . . . . . . . . . . . . . . . . . . . 34
3.3.3.2 AttritionvolumeasafunctionofΩandΨ . . . . . . 35
3.3.3.3 Crystalgeometry(Ω) . . . . . . . . . . . . . . . . . 39
3.3.3.4 Impact(Ψ) . . . . . . . . . . . . . . . . . 42
3.3.4 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . 44
3.3.4.1 Generaleffectofcornergeometry . . . . . . . . . . . 44
3.3.4.2 Comparison to experimentally determined attrition
constants . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.5 Concludingremarksontheproposedattritionmodel . . . . . . 49
3.4 Remarksonsingleparticlemodeling . . . . . . . . . . . . . . . . . . . 51
4 Deterministicpopulationbalancemodelingofcrystallizationprocesses 52
4.1 Generalperspectiveonpopulationbalancemodeling . . . . . . . . . . 53
4.2 Fundamentalconceptsofthepopulationbalanceequation . . . . . . . . 54
4.3 Specificationofrateprocessesforoneinnercoordinate . . . . . . . . . 56
4.3.1 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.3 Breakage(Disaggregation) . . . . . . . . . . . . . . . . . . . . 58
4.3.4 Aggregation/Agglomeration . . . . . . . . . . . . . . . . . . . 60
4.4 Numericalsolutionofthedeterministicpopulationbalanceequation . . 63
4.4.1 Approximationofthepopulationbalanceequation . . . . . . . 65
4.4.1.1 Finitedifferences(FD) . . . . . . . . . . . . . . . . 65
4.4.1.2 Finitevolume(FV)formulations . . . . . . . . . . . 65
4.4.1.3 Discretizedpopulationbalance . . . . . . . . . . . . 67
4.4.2 Approximationofthesolution(MWR) . . . 67
4.4.2.1 Localbasisfunctions(finiteelements,FE) . . . . . . 68
4.4.2.2 Globalbasis . . . . . . . . . . . . . . . . . 69
4.4.2.3 Hierarchicalbasisfunctions . . . . . . . . . . . . . . 70
4.4.2.4 Concludingremarksonthesolutionofpopulationbal
anceequations . . . . . . . . . . . . . . . . . . . . . 70
4.5 Multivariatepopulationbalancemodeling . . . . . . . . . . . . . . . . 71
4.5.1 Previousworkonmodelingandnumericalsolution . . . . . . . 71
4.5.2 Casestudy1: Two dimensionalgrowthmodel . . . . . . . . . . 73
4.5.2.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5.2.2 Modeltransformation . . . . . . . . . . . . . . . . . 78Contents V
4.5.2.3 Modelreduction . . . . . . . . . . . . . . . . . . . . 80
4.5.2.4 Discretizationoftheone dimensionalpopulationbal
ance . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5.2.5 Numericalresults . . . . . . . . . . . . . . . . . . . 83
4.5.2.6 Conclusionsonmodelreduction . . . . . . . . . . . 87
4.5.3 Casestudy2: Modelingtheattritionround offeffect . . . . . . 87
4.5.3.1 Intuitive two dimensional population balance formu
lation . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.3.2 Transformationofcoordinatesystem . . . . . . . . . 90
4.5.3.3 Modelingoftherateprocesses . . . . . . . . . . . . 92
4.5.3.4 Nondimensionalizedmodelformulation . . . . . . . 98
4.5.3.5 Selectionofthenumericalsolutiontechnique . . . . . 100
4.5.3.6 Modelspecification . . . . . . . . . . . . . . . . . . 103
4.5.3.7 Numericalresults . . . . . . . . . . . . . . . . . . . 112
4.5.3.8 Conclusionson2Dattritionmodel . . . . . . . . . . 119
4.6 Concludingremarksondeterministicpopulationbalancemodeling . . . 121
5 Stochasticmodelingofcrystallizationprocesses 123
5.1 Previouswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.1.1 Stochasticmethodsforsingleparticlegeometry . . . . . . . . . 124
5.1.2fordisperse phasesystems . . . . . . . . . 126
5.1.2.1 Methodicalclassification . . . . . . . . . . . . . . . 126
5.1.2.2 Contributionstonon crystallizationapplications . . . 127
5.1.2.3 Stochastic crystallization/precipitation process mod
eling . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.2 Hierarchicalparticlecharacterization . . . . . . . . . . . . . . . . . . . 129
5.2.1 Primaryparticles . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.2.2 Agglomerateparticles . . . . . . . . . . . . . . . . . . . . . . 130
5.2.3 Substitutionsystems . . . . . . . . . . . . . . . . . . . . . . . 133
5.3 Stochasticmodeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.3.1 Realizationofthegrowthprocess . . . . . . . . . . . . . . . . 137
5.3.2oftheaggregationprocess . . . . . . . . . . . . . . 139
5.3.3 MCscheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.4 Casestudy1: Agglomerationwithsimpleprimaryparticlegrowth . . . 141
5.5 Casestudy2:withcomplexprimaryparticlegrowth . . 144
5.6 Discussionandconclusionsonthehierarchicalparticlecharacterization 148VI Contents
5.7 Perspectiveonstochasticpopulationbalancesimulation . . . . . . . . . 151
6 Perspectiveonpredictivemodels 152
6.1 Modelingondifferentscales . . . . . . . . . . . . . . . . . . . . . . . 152
6.2 Integrationofscalesandmodelingmethodologies . . . . . . . . . . . . 154
7 Concludingremarks 157
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.2 Conclusionsandperspectives . . . . . . . . . . . . . . . . . . . . . . . 159
A Methodofmomentsforthedomainofψ 161
A.1 Recursionformulaforhigherordermoments . . . . . . . . . . . . . . 162
A.2 Matricesandvectorforthereducedsystem . . . . . . . . . . . . . . . 163
B Detailsontheproposedattritionmodel 164
B.1 Derivationofthemode