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Numerical methods for simulation and optimization of chemically reacting flows in catalytic monoliths [Elektronische Ressource] / vorgelegt von Hoang Duc Minh

241 pages
INAUGURAL-DISSERTATIONzurErlangung der DoktorwurdederNaturwissenschaftlich-Mathematischen Gesamtfakult atderRuprecht-Karls-Universit at Heidelbergvorgelegt vonIngenieur-Informatiker Hoang Duc Minhaus Hue, VietnamTag der mundlic hen Prufung: 22. Dezember 2005Numerical Methods forSimulation and Optimization ofChemically Reacting Flows inCatalytic MonolithsGutachter: Prof. Dr. Dr. h. c. Hans Georg Bockhter: Prof. Dr. Olaf DeutschmannAbstractThe aim of this work is to develop numerical methods and software forsimulation and optimization of complex processes in catalytic monoliths toachieve better understanding of the physic-chemical processes in catalyticreactors.The uid dynamics are modelled by the boundary layer equations (BLEs),which are a large system of parabolic partial di eren tial (PDEs)with highly nonlinear boundary conditions arising from the coupling of sur-face processes with the o w eld inside the channel. The BLEs are obtainedby simplifying the comprehensive model described by the Navier-Stokes equa-tions and applying the boundary approximation theory. The surface andgas-phase chemical reactions are described by detailed models.The PDEs are semi-discretized using the method of lines leading to astructured system of di eren tial-algebraic equations (DAEs). The DAEs areintegrated by an implicit method, based on backward di eren tiation formu-las (BDF).
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INAUGURAL-DISSERTATION
zur
Erlangung der Doktorwurde
der
Naturwissenschaftlich-Mathematischen Gesamtfakult at
der
Ruprecht-Karls-Universit at Heidelberg
vorgelegt von
Ingenieur-Informatiker Hoang Duc Minh
aus Hue, Vietnam
Tag der mundlic hen Prufung: 22. Dezember 2005Numerical Methods for
Simulation and Optimization of
Chemically Reacting Flows in
Catalytic Monoliths
Gutachter: Prof. Dr. Dr. h. c. Hans Georg Bockhter: Prof. Dr. Olaf DeutschmannAbstract
The aim of this work is to develop numerical methods and software for
simulation and optimization of complex processes in catalytic monoliths to
achieve better understanding of the physic-chemical processes in catalytic
reactors.
The uid dynamics are modelled by the boundary layer equations (BLEs),
which are a large system of parabolic partial di eren tial (PDEs)
with highly nonlinear boundary conditions arising from the coupling of sur-
face processes with the o w eld inside the channel. The BLEs are obtained
by simplifying the comprehensive model described by the Navier-Stokes equa-
tions and applying the boundary approximation theory. The surface and
gas-phase chemical reactions are described by detailed models.
The PDEs are semi-discretized using the method of lines leading to a
structured system of di eren tial-algebraic equations (DAEs). The DAEs are
integrated by an implicit method, based on backward di eren tiation formu-
las (BDF). We develop a new BDF code with tailored e cien t and robust
numerical methods by exploiting the structure, and by an appropriate scal-
ing for ill-conditioned iteration matrices, and by computing consistent initial
values. E cien t methods for computation of partial derivatives in the frame-
work of automatic di eren tiation and of nite di erences are introduced and
compared. Our newly developed simulation tool is more stable than the ex-
isting simulation tool, and faster than by a factor of ten to more than 60,
depending on the applications.
To improve the performance of catalytic reactors (e.g., maximizing gas
conversion or selectivity) we can control certain process conditions, such as
temperature at the catalyst wall or the ratio of catalytic active surface area
to the geometric surface area or the gas composition, the temperature, or
the velocity at the inlet of the catalyst. It is the rst time that this problem
is generally formulated as an optimal control problem constrained by a sys-
tem of PDEs describing the chemical uid dynamics process and additional
constraints. The direct shooting approach in combination with sequential
quadratic programming (SQP) method is used for solving the resulting opti-
mal control problem. An e cien t numerical method for computation of the
derivatives required by the SQP method is introduced.
In addition, error analysis for the numerical Newton method is investi-
gated in detail. We introduce a new error model. Based on our error model
and analysis, the limiting accuracy of the solution of nonlinear equations by
the numerical Newton method can be obtained.
Our newly developed software package for simulation and optimization
can be applied to di eren t reaction mechanisms and channel settings with dif-
5ferent initial/boundary conditions. This software is applied to two practical
applications: catalytic combustion of methane and conversion of ethane to
ethylene. The numerical results are presented. The simulation software pro-
vides a useful tool for the validation of reactions mechanisms. The software
package allows, e.g., for a better design and operation of the conversion of
natural gas to higher hydrocarbons or the improvement of exhaust treatment
in cars.
6Kurzfassung
Ziel dieser Arbeit ist die Entwicklung numerischer Methoden und Pro-
gramme zur Simulation und Optimierung komplexer Prozesse in katalyti-
schen Monolithen, um die physikalisch-chemischen Prozesse in katalytischen
Reaktoren besser verstehen zu k onnen.
Die Str omungen werden mittels der Grenzschichtgleichungen modelliert.
Sie bilden ein gro es System von partiellen Di eren tialgleichungen (PDEs)
mit hochgradig nichtlinearen Randbedingungen, die sich aus der Kopplung
der Ober achenprozesse mit dem Str omungsfeld innerhalb des Kanals ergeben.
Die Grenzschichtgleichungen werden abgeleitet, indem das Navier-Stokes-
Modell vereinfacht und die Grenzschichtn aherung angewendet wird. Die
Beschreibung der Gasphasen- und Ober achenreaktionen erfolgt durch de-
taillierte Modelle.
Die PDEs werden mit der Hilfe der Linienmethode semi-diskretisiert. Da-
raus ergibt sich ein di erential-algebraisc hes Gleichungssystem. Das di eren-
tial-algebraische Gleichungssystem wird durch eine implizite Methode in-
tegriert, die auf den "Backward-Di eren tiation-Formulae" (BDF) beruht.
Es wird ein neuer BDF-Code mit speziell zugeschnittenen, e zien ten und
robusten numerischen Methoden entwickelt, der insbesondere alle Struk-
turen ausnutzt, schlecht-konditionierte Iterationsmatrizen geeignet skaliert
und konsistente Anfangswerte berechnet. E zien te Methoden zur Berech-
nung der partiellen Ableitungen im Rahmen der automatischen Di eren-
zierung und der niten Di erenzen werden eingefuhrt und miteinander gekop-
pelt. Das neu entwickelte Simulationswerkzeug ist stabiler als das existierende
und in Abh angigkeit der Anwendung 10 bis 60-mal schneller.
Durch Variation bestimmter Prozessparameter l asst sich das Verhalten
katalytischer Reaktoren verbessern (z.B. durch Maximierung von Umsatz
oder Selektivit at). Dazu z ahlen die Temperatur an der Katalysatorwand, das
Verh altnis von katalytisch aktiver und Gesamtober ache sowie die Gaszusam-
mensetzung, die Temperatur und die Geschwindigkeit am Eingang des Kataly-
sators. Dieses Problem wird zum ersten Mal als Optimierungsproblem all-
gemein formuliert, das durch ein System von PDEs dargestellt wird. Dabei
beschreiben die PDEs die reaktive Str omung sowie zus atzliche Bedingungen.
Zur L osung des sich ergebenden Optimierungsproblems wird ein "direktes
Schie v erfahren" in Verbindung mit der Methode der sequentiellen quadratis-
chen Programmierung (SQP) benutzt. Eine e zien te Vorgehensweise zur
Berechnung der fur die SQP-Methode erforderlichen Ableitungen wird dar-
gestellt.
Ein neues Modell zur Fehleranalyse der Newton-Methode wird eingefuhrt.
Dadurch l asst sich die maximal erzielbare Genauigkeit der L osung von nicht-
7linearen Gleichungen besser absch atzen.
Das neu entwickelte Softwarepaket zur Simulation und Optimierung eignet
sich fur verschiedene Reaktionsmechanismen und Kan ale mit verschiedenen
Anfangs- und/oder Randbedingungen. Die Software wird exemplarisch fur
zwei Anwendungen eingesetzt: katalytische Verbrennung von Methan und
Umsetzung von Ethan zu Ethylen. Die numerischen Ergebnisse werden
dargestellt. Diese Simulationssoftware ist geeignet zur Validierung von Reak-
tionsmechanismen. Sie erm oglicht die Optimierung chemischer Prozesse, wie
zum Beispiel die Umsetzung von Erdgas in wertvolle Kohlenwassersto e oder
die Abgasnachbehandlung in Kraftfahrzeugen.
8Acknowledgments
I would be extremely grateful to my advisors Prof. Dr. Dr. h.c. Hans Georg
Bock, Prof. Dr. Dr. h.c. Jurgen Warnatz, Interdisciplinary Center for Scien-
ti c Computing (IWR), University of Heidelberg, and Prof. Dr. Hoang Xuan
Phu, Institute of Mathematics, Vietnamese Academy of Science and Technol-
ogy, for supervising this interdisciplinary project, for continuous support and
encouragement, and for many inspiring discussions. I am greatly indebted to
Dr. Johannes Schl oder for many fruitful discussions and numerous valueable
advices. His patience and availability for any help whenever needed with his
heavy workload is appreciated.
I wish to thank Prof. Dr. Olaf Deutschman and Dr. Ste en Tischer, In-
stitute for Chemical Technology and Polymer Chemistry, University of Karl-
sruhe, for many stimulating conversations and suggestions, for giving me the
DETCHEM source code, which is partly used in this work, and for introduc-
ing me to many interesting practical applications.
I would like to thank my colleague and former roommate Dr. Stefan
K orkel, for always having an open ear for my questions and for his friendly
help with many problems in my social and study life in Germany. I would
like to thank my colleagues in the group of Prof. Dr. Dr. h.c. Hans Georg
Bock and Dr. Johannes Schl oder for their friendship and their assistance.
In particular, I would like to mention Dr. Tran Van Hoai and Dr. Tran
Hong Thai for many useful helps and for sharing the study life with me in
Germany, and Dr. Moritz Diehl, Dr. Andreas Sch afer for their friendly helps
on the software MUSCOD-II. Special thanks to Margret Rothfu for helping
me dealing with many documents.
I gratefully acknowledge the many helpful suggestions and comments of
Prof. Dr. Robert J. Kee, Division of Engineering Colorado School of Mines,
USA, especially during the time he visited the IWR. I also would like to
thank Prof. Dr. Claudia Bruno, Department of Mechanics and Aeronautics,
University of Rome, Italy and Prof. Dr. William E. Schiesser, Lehigh Uni-
versity, USA for useful conversations. I wish to thank my former advisor Dr.
Nguyen Thanh Son, Department of Information Technology, HCMC Univer-
9sity of Technology, who always encourages and supports me to continue my
higher education.
I would like to thank Dr. Johannes Schl oder, Dr. Ste en Tischer, Dr. Moritz
Diehl, Dr. Ekaterina Kostina, Kaspar Sakmann, and Nikolay Mladenov for
proof-reading the thesis.
I am very much appreciate the nanical support from the German Science
Foundation (DFG|Deutsche Forschungsgemeinschaft) within the Graduier-
tenkolleg program: \Complex Processes: Modeling, Simulation and Opti-
mization", and SFB (Sonderforschungsbereich) 359 "Reactive Flows, Di u-
sion and Transport".
Most of all, I wish to thank my parents and my brothers and sisters
for their love and support, and for always being there. They also always
encourages me to continue my higher education, in which this research work
could be carried out.
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