1 Diss. ETH No A Combined Approach using Calorimetry and IR-ATR Spectroscopy for the Determination of Kinetic and Thermo...
Diss. ETH No. 15086
A Combined
Calorimetry
Approach using IR-ATR Spectroscopy
and
for the Determination of Kinetic and
Thermodynamic
Reaction Parameters
A dissertation submitted to the
SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH
for the
degree
of
Doctor of Technical Sciences
presented by Andreas
Zogg
Dipl. Chem. born November
ETH
26, 1974
citizen of Grabs SG
accepted
on
Prof. Dr. K.
the recommendation of
Hungerbühler,
Prof. Dr. M. Prof. Dr. F. Dr.
examiner
Morari, co-examiner
Stoessel,
co-examiner
U. Fischer, co-examiner
Zurich 2003
ISBN Nr. 3-906734-33-1
To my
parents
Preface This
thesis
is
based
Technology Group
research
on
Swiss Federal
of the
between
1999 and 2003
providing
a
performed
The ETH
Institute of
research fund
of the necessary
significant part
and
and kinetic
calorimetry
supported
my
evaluation,
as
Stoessel for their assistance Fischer for managing the whole research
phase
Sincere thanks
are
project during
the construction of the
and
thanks
introduced
kindly
thesis within this the
carry
on
I
also
am
project
project
in
TH-13
M
/99-3)
K
Hungerbühler
the
in
for
filed
of
for
reaction
Morari and Prof
Dr
F
I would like to thank Dr
U
and for his advice
during
the
from the mechanical and Max and inspiring
great
support during
to I
subject,
2001
and
Pastré,
J
finally
who started this
project
Zürcher who carried out her
to S
Gianoh and F
1997
in
Diploma
Visentin who will
future
to Dr
grateful
into the in
Schlapfer
Zurich
in
reaction calorimeter
presented
me
Dr
stage
for their
workshop
also addressed to Dr
are
Prof
its initial
extended to Hans-Peter
project
Especially
as co-examiners
Wohlwend from the electronic
Special
as
Environmental
gratefully acknowledged
is
Professor Dr
research well
and
Technology (ETH)
funding (Project
First of all I would like to thank my supervisor,
having accepted
Safety
the
at
Schildknecht of Roche Pharma, Dr
J
F
Mascarello, Dr A
Keller, J Jeisy and B Leuthe of Roche Vitamin and Dr C Heuberger of Novartis for their
inspiring
to Dr
calorimeter, for their
suggestions
and
support during
the
redesign
developed
I would also like to thank Dr the
epoxidation
mathematical
part
members of the
during
E
reaction,
of the
of the
presented
reaction
calorimeter into
a
commercial
Zass for
supporting
Dr
Stahel
W
reaction calorimeter and for
for
me
product reference data
gathering
in
inspiring
discussions
of this work and all members of the institute and
Safety
and Environmental
Technology Group
who
on
especially supported
the all me
the doctoral studies
My greatest appreciation Martin
construction
Linder, Dr B Schenker, and all other people of Mettler Toledo
M
their efforts to turn the
for
the
support during
Zogg
is
reserved for my
Without their unique also
like
support
Especially
I
would
assistance
in
the field of control engineering
to
thank
family
and my
parents
Bianca and Dr
this work would not have been
my
brother
Dr
David
Zogg
for
possible his
great
Content
CONTENT VII
Abstract
Zusammenfassung
IX
Symbols, Operators,
XI
and Abbrevations
Overview 1
1
Introduction 1.1
2
XIX
Context and Motivation
1
1.1.1
The Chemical reaction at the
1.1.2
Bottleneck: Parameters for
1.2
Goal of the Thesis
1.3
Suitable
2.1
Reaction
of
empirical
Integrated
Process
Development
reaction models
2
for kinetic and
thermodynamic screening....
8
calorimetry
Overview
2.1.2
Isothermal,
operation
on
the basic reaction calorimeter
isoperibolic,
adiabatic
and
9
types temperature
programmed
mode
11
2.1.3
Steady-state
2.1.4
Dynamics
2.1.5
Assessment of the three basic reaction calorimetric
of
heat-flow balance of the different calorimeter an
5
8
Background
2.1.1
1
4
analytical setups
Theoretical
core
types
isothermal reaction calorimeter
24
principles
Spectroscopy
2.2
IR-ATR
2.3
Evaluation of calorimetric and
12
27 30
spectroscopic
data
32
2.3.1
Overview and
2.3.2
Evaluation methods for isothermal calorimetric reaction data
33
2.3.3
Evaluation methods for isothermal
42
2.3.4
Combined evaluation of
2.3.5
Model selection
32
goal spectroscopic
spectroscopic
reaction data
and calorimetric data
47 48
I
Content
3
The
new
Calorimeter
3.1
Historical
3.2
Requirements
49 49
development for the
new
reaction calorimeter
3.2.1
Accuracy
3.2.2
Time constants of the calorimetric
3.3
Concept
50
of the calorimeter
53 56
signals
for the realization
3.3.1
Selection of
3.3.2
Split
57
appropriate
construction materials
fast and slow heat-flow
57
changes by introducing
intermediate
an
thermostat 3.3.3
57
Steady-state temperature profiles
of the
operating
conditions
3.3.4
Hot
on
3.3.5
Calculation concept for the inner
3.3.6
Calculation concept for the intermediate
3.4
Design
spots
of the
3.4.1
Complete
3.4.2
Copper
3.4.3
Cover,
3.4.4
Cooler,
3.4.5
Compensation
67
(reactor)
thermostat
69
(jacket)
thermostat
70
Jacket
72
connections and
75
magnetic coupling
Peltier elements and TPeit
78
sensors
heater
3.6
Software and controller
3.7
From measured
peripheral
Calculation
80
devices of the whole
signals of qtot
81
apparatus
82 to calorimetric data
by
combination
of the
89 inner and
outer
balance
heat-flow 89
3.7.2
Calculation of the total heat
3.7.3
Calculation of qstirr and qLoss
3.7.4
Final
calculation
measurement
69 70
reactor and overview
Setup
3.7.1
heater
compensation
calorimeter.
3.5
and
calorimeter at different 64
the surface of the
new
new
formula
pumped by
the Peltier elements qcooimg--- 91 96
for
qtot
and
filtering
of
the
required 99
signals
II
Content
Evaluation of the Calorimetric and
Combined
Spectroscopic Data,
a new
Approach
100
4.1
Historical
4.2
Requirements
100
4.3
Concept
103
of the evaluation method
4.3.1
Combined evaluation
4.3.2
Model selection
4.3.3
Step by step
4.4
100
background
103
algorithm
106
evaluation
107
procedure
Mathematical formulation of the combined evaluation
algorithm
109
4.4.1
Pre-treatment of the infrared data
109
4.4.2
Pre-treatment of the calorimetric Data
110
4.4.3
Step by step explanation
110
4.5
Automatic calculation of the combined
Applications Overview
5.2
Neutralization of NaOH with
5.3
function AComb.... 114
122
and Results
5.1
5.2.1
objective
122
H2S04
123
Evaluation of the calorimetric data
Hydrolysis
of acetic
123 126
anhydride
5.3.1
Combined evaluation of the infrared and calorimetric data
5.3.2
Simultaneous evaluation of all measurements at all temperatures.... 133
5.3.3
Summary
5.4
of all results
of
Epoxidation
134 135
2,5-di-tert-butyl-1,4-benzoquinone
5.4.1
Combined evaluation of the infrared and calorimetric data
5.4.2
Testing
5.4.3
Simultaneous evaluation of all
5.4.4
Analysis
different reaction models
of the automatic
126
ill
146
experiments
scaling
136
method
at all
temperatures
153 157
Content
6
Final Discussion and Conclusions 6.1
160
New reaction calorimeter
160
6.1.1
Accuracy
and time constants of the
6.1.2
Comparison
6.1.3
Calibration of the Peltier elements
166
6.1.4
Time correction of the baseline
167
6.1.5
Influence of the ambient
new
calorimeter
162
mathematical- measured baseline
165
signal (qcooimg )
168
temperature
6.2
Evaluation of the calorimetric data
169
6.3
Combined evaluation of calorimetric and infrared data
170
6.3.1
Feasibility study
6.3.2
Increased
with
a
information
simple
reaction
content
172
example
by measuring
two
different
analytical 172
signals 6.3.3
A
6.3.4
Comparison
more
complex
separate
7
of
the
three
evaluation
types:
173
Separate Calorimetric,
infrared and combined evaluation
174
6.3.5
Determination of pure
6.3.6
Limits of the IR-ATR
(infrared) signal
176
6.3.7
Limits of the model-based evaluation
177
component spectra
Outlook 7.1
Reaction calorimeter Reactor
7.1.2
Ideas for future
7.1.3
Ideas for the
Evaluation
175
178
7.1.1
7.2
8
reaction with different feasible reaction models
178 178
redesign developments
improvement
of the heat-flow balance calculations
181 182 183
algorithm
References
185
IV
Content
A 1
Appendix A
Reaction A. 1
Calorimetry
Combinations and further calorimetric
B
A 1
Infrared
developments
of the three basic reaction A 1
principles (isothermal)
Spectroscopy
A 3
B.1
Applicability
of Lambert Beer's Law in ATR
B.2
Evaluation methods that do not
B.3
Comparison
require
a
spectroscopy
reaction model
D
A 13
Construction details of the
reaction calorimeter
new
A 15
C.1
IR-ATR Probe and Teflon inliner
A 15
C.2
Stirrer.
A 16
C.3
Thermal insulation
A 16
C.4
Stirrer
A 16
C.5
Baffles
C.6
Position of the
temperature
C.7
Cooler, pettier
elements and
C.8
Periphery
Engine
A 16
devices
sensors
according
Calculation details
inside the copper jacket.
to
Figure
required for
ofS,
A 17 A 18
cooling liquid 3-14
A 22
the heat-flow balance of the
new
A 25
reaction calorimeter
E
A 7
and combination of model-based and model-free
evaluation methods
C
A 3
D.1
Determination
R and
A 25
D.2
Determination of kLoss
A 31
D.3
Mathematical baseline for the calculation of qtot
A 33
k
Applications: Experimental procedures
and additional
Calculations
A 34
E.1
Neutralization of NaOH with H2S04
E.2
Hydrolysis
E.3
Epoxidation
E.4
Industrial reaction
E.5
Heterogeneous
of Acetic of
Anhydride
2,5-di-tert-butyl-1,4-benzoquinone
A 35 A 50 A 68
examples
Reaction
A 34
Example
v
A 73
Abstract
ABSTRACT To
the
meet
need
calorimeter
chemical and substance
wall
device is of
a
copper block
(typically glass)
online measured
an
through
the reactor wall
Peltier elements is time
where
with
for
required
a
the
implemented
reaction
the
using
baseline
during
experiment
was
an
new
ideally
calorimeter has
suited
conditions.
to
fast
measure
The
and and
performance
demonstrated based
+
1
patented.
the
fine-
new
reaction double
a
accuracy
is
temperature
of the
To
heat transfer
using
This combination shortens the
same
steps
of
are
required,
not
cryostat (parallelisation).
exothermal
highly
was
s
and is therefore
reactions
the
new
isothermal
at
device
will
be
examples: reaction
(measured
enthalpy
at 25
kJ/mol, literature reference: -139.1 kJ/mol).
The
hydrolysis
60
5
+
for
additional heat-flow balance
The neutralization of NaOH with H2SO4
°C: -134
probe
Power-Compensation principle.
because calibration
several reaction
on
reaction
very small time constant of about 4
a
small
a
prototype
new
The
and
small amounts of test
typically only
and enables the connection of several devices to the The
IR-ATR
(compensate changes
reaction) and
design
particular importance
circulation fluid.
a
kinetic
intermediate thermostat instead of
as an
controlled at isothermal conditions allow
of process
integrated
an
of
gathering
available and time-to-market is crucial. The
uses a
vessel
quick
early phases
with
ml)
pharmaceutical products,
are
calorimeter
45
to
this work. Such
developed during
in
parameters
(25
and
systematic
a
reaction
thermodynamic reaction
for
of acetic
kJ/mol, measured first order
literature references:
reaction
anhydride (measured
-63
+
2
rate constant: 2.9
and 2.76
kJ/mol,
+
enthalpy
at 25 °C:
-
10"3 s"1, EA 56 kJ/mol, 10"3 s"1, EA 0.06 57 =
=
kJ/mol. Two
highly
of
2.5
«
exothermal In
kW/l).
both
calorimetric baseline is Furthermore
presented rate
a
new
industrial
examples
clearly
evaluation
reactions
the
(maximal
advantage
of
an
reaction online
power
measured
demonstrated.
principle
for the measured reaction data will be
that allows the identification of the unknown reaction
parameters
such
as
constants, activation energies, reaction orders and reaction enthalpies. The
evaluation is based evaluation
on
procedures
evaluated. Therefore
a
Neither pure infrared calibrations
empirical
reaction model. In contrast to conventional
the infrared and calorimetric data new
evaluation
algorithm
are
demonstrated
spectra
required.
by analyzing
The two
step
The the
performance
following
consecutive
hydrolysis
of acetic
parameters
of the involved chemical of the
reaction
epoxidation
anhydride.
VII
are
simultaneously
developed, using
was
in order to estimate all unknown reaction
optimization,
The
an
new
in
a
single step.
components
evaluation
nonlinear
nor
algorithm
any
will be
examples:
of
2,5-di-tert-butyl-1,4-benzoquinone
Zusammenfassung
ZUSAMMENFASSUNG Im Rahmen dieser Arbeit wurde ein 45
mit
ml)
einer
soll
Prozessentwicklung kinetischen und
Speziell von
dem
in der Feinchemikalien und
vorhanden
sind
zirkulierender
und
die
des
üblichen
einer
gewöhnlich
schnellen
im
der Basislinie
Die
eingesetzt.
isotherm
Prinzips
zu
Glas)
mit
Reaktionskalorimeter
ein
des
ermöglichen, ein
benötigte
Kalibrationsschritte mehr
Geräte
notwendig sind,
den
an
Zeit für
selben
und
ermöglicht
isothermen des
neuen
geeignet
Bedingungen
um zu
schnelle
messen.
Das
Kalorimeters werden anhand
Die Neutralisation 25 °C: -134
+
1
Die
Hydrolyse
-60
+
5
und
stark
von
exotherme
Leistungsvermögen
von
mehreren
NaOH mit H2SO4
£4
=
=
Zwei stark
an
patentiert. weil
Diese keine
den Anschluss mehrerer Das
ca.
4
auf und ist
s
Reaktionen
und die
neue
unter
Genauigkeit
Beispielreaktionen gezeigt:
(gemessene Reaktionsenthalpie
bei
kJ/mol, Literaturreferenz: -139.1 kJ/mol). von
Acetanhydrid (gemessene Reaktionsenthalpie
kJ/mol, gemessene Geschwindigkeitskonstante
10"3 s"1, EA
10"3s"1,
von
und
online
Wärmedurchgangs
(Parallelisierung).
Reaktionskalorimeter weist eine sehr kleine Zeitkonstante bestens
eine
Reaktionsexperiment
Kryostaten
wird
wurde eine zusätzliche
Kombination
die
(z.B.
Um
geregelt.
implementiert
verkürzt
werden
Reaktionstemperatur
(kompensiert Veränderungen Reaktion)
von
werden.
gehalten
Reaktormantels
entwickelten
neu
der
Erfassung
kurz
Wärmeflussbilanz mittels Peltierelementen
folglich
Phasen
geringe Testsubstanzmengen
nur
doppelwandigen
Zwischenthermostat
der Reaktorwand während einer
solcher
frühen
bis
(25
Industrie ist ein solches Gerät
pharmazeutischen
wird
Power-Compensation
Messung
Bedarf
In
Produkteinführungszeit möglichst
Kühlflüssigkeit, als
Kupferblock
weil
Bedeutung
Stelle
An
mittels
damit
entwickelt.
thermodynamischen Reaktionsparametern entsprochen
besonderer
muss.
IR-ATR Sonde
integrierten
Reaktionskalorimeter
kleinvolumiges
56
kJ/mol, Literaturreferenz:
-63
+
2
erster
kJ/mol,
bei 25 °C:
Ordnung:
und 2.76
+
2.9 0.06
57kJ/mol. exotherme
Rektionsleistung
«
2.5
Reaktionsbeispiele kW/1).
Bei
beiden
der
Industrie
Reaktionsbeispielen
Vorteil einer online gemessenen Basislinie klar
IX
aus
gezeigt
werden.
(maximale konnte
der
Zusammenfassung
Des
weiteren
wird
Reaktionsdaten
ein
Reaktionsenthalpien)
Reaktionsmodell.
empirischen
Auswertungsverfahren
werden
Dazu wurde ein
auf nichtlinearer
Optimierung,
einzigen Schritt
zu
Komponenten
erforderlich.
Die
um
von
zu
basiert auf
konventionellen
Auswertungsalgorithmus entwickelt,
basierend
alle unbekannten Weder
noch
Epoxidierung
Auswertung
simultan
Reaktionsparameter
Reininfrarotspektren
Kalibrationen des
neuen
Analyse folgender Reaktionsbeispiele
Hydrolyse
und
unbekannter
Aktivierungsenergien,
erlaubt. Die
Infrarot-
gemessenen
Identifikation
Gegensatz
Im
die
Kalorimetriedaten
Leistungsfähigkeit
Die Zweischritt Die
die
neuer
bestimmen.
chemischen
anhand der
die
für
(Geschwindigkeitskonstanten, und
Reaktionsordnungen
ausgewertet.
welches
vorgestellt,
Reaktionsparameter einem
Auswertungsprinzip
neues
von
Acetanhydrid.
X
of
irgend
der einer
in einem
involvierten Art
Auswertungsalgorithmus
demonstriert:
2,5-di-tert-butyl-1,4-benzochinon.
sind wird
and Abbrevations
Symbols, Operators,
SYMBOLS, OPERATORS, AND ABBREVATIONS Symbol #Hits
Unit -
Description Number of
same
solutions found for the non-linear
optimal
identification of the reaction model parameters 0, a
-
W/K
K
AATpeit
K
factor used for
Weighting Device
specific parameter
Up ~nri ana ipeit
or
-
M(di Np)
Pareto
diagram.
to
compensate the
sensor
offset of
down
rp
iPeit
Remaining
of squares of the linear least squares fit of
sum
Aoata in order to estimate the pure component spectra. Equals the infrared
objective function in the combined evaluation of
calorimetric and infrared data. It is model parameters 0, AA'
Np.
Heat conduction coefficient of the Peltier elements.
rp
AA
a
-
AAk
AA
a
function of the reaction
Np.
AAmln
-
Remaining
of squares of the linear least squares fit of
sum
Aoata in order to estimate the pure component spectra at the k'th AA
-
Minimum of the function model fit
possible AComb
number.
wave
Combined
error
A4(0; Np).
It is
to the minimal
equal
of the infrared data.
objective function used for the simultaneous
evaluation of calorimetric and infrared data.
Requires the
knowledge of AQmm, AAmm SQ, and Sm. AComb AH
AQ J/mol
-
AQmm
+
A4
Total measured
and the heat of transfer
ArH
J/mol
(ArHh ArH2)
AQor AQßj Np)
AAmm
enthalpy, including mixing Qmtx and
an
the reaction
enthalpy (first
Remaining
eventual heat of
and second reaction
calorimetric
objective
parameters 6t
a
function of the reaction
Np.
AQ
Aq0
W
Difference of qComp,w) The
7}).
An additional heat
jacket
wall
(T
=
Tw \
is shown.
2-6 shows the the
through
increases
operating
assuming e.g. hr
(Equation (2-1))
=
h}
=
aw
The
temperature profiles
The
the ambient
21
as
Figure
well
as
as
line
/L, constant reaction heat
temperature profiles
shown in
black
straight
and therefore constant heat flow
Chapter 2.1.3.1).
Chapter 2.1.3.2). Additionally
conditions.
the reactor wall
2-4
the
through
shown in
(Heat-Flow
jacket
wall
Figure
the 2-6
calorimeter
temperatures
2 Theoretical
Background
considered. Therefore the comments to
were
Balance calorimeter. The heat flow caused the
and the TAmb is
cooling liquid TJ
shown in. The amount of this insulation around the
According are
the main
temperature
hom*ogeneous
the whole
inlet
and
TjJN
outlet
Therefore the should
be
of the
jacket
of the
corrected
the
on
their
they change
as
on
the
of the thermal
quality
well
measure a
of the
out
of
cooling liquid a
reaction
cannot be assumed to be
has to be
cooling liquid
temperature
difference between
cooling liquid (see Figure 2-1). used in the
and
TjM
the
as
temperatures during
the flow rate of the
cooling liquid TJ,
basis
as
cooling liquid TJ
as
temperature TJ,
temperature
for the three different situations
wall, the jacket wall
in order to be able to
enough
difference between
wall.
jacket
measurement. The
chosen low
also valid for the Heat-
are
temperature
change depends strongly
dynamic elements, over
the
by
slightly changing
2-6 the reactor
Figure
to
2-4
Figure
TJ;
following calculations,
(e.g. [Landau 96], [RC1
out
Handbook]). For the Heat-Flow
as
heat-flow balance in
(qcomp
=
well
as
2-2
Figure
Power-Compensation
the
was
considered.
only
balance, have
to be taken into
account. It should be noted that the outer heat-flow balance indicated in
also contains the reactor can
differ from this ideal will
cover
picture
be
assessed
ideal
behavior
not
simplification
cover.
isothermal heat-flow balance IfIow
+
tflid
+
aFluid,IN
=
tfloss
and
Equation (2-12)
+
Depending and thus
by is
can
the
outer
the calorimetric
system
of the heat losses
part
assumed be
on
heat-flow and
expressed
as
therefore follows
the
(qComp
-
the reactor
However outer
can
2-2
the situation
through
balance.
Figure
for
the
steady-state
W): (2" 1 6)
aFluid,OUT
(2-16)
the inner
For the Heat-Balance calorimeter
the inner and the outer heat-flow
W) both,
calorimeter
be combined to the final heat-flow balance of
a
Heat-
Balance calorimeter: Qstirr
+
Ç/dos
Where qtot
+
'ïtot
[W]
~
Qloss
+
tfFluid,OUT
~
is the total heat release
The heat flows qDos and qSt,rr
(2-1)).
(2" 1 )
aFluid,IN
'
uptake
or
were
of the reaction mixture
already explained
in
(Equation
Equations (2-4)
and
(2-3). It is
important
to note that the
of the
Power-Compensation
(2-12))
could be eliminated
heat transfer
through
clearly dynamic. to
get
problematic
present
in the heat-flow balances
and the Heat-Flow calorimeters
by
This could lead to
(see
(Equations (2-14)
the outer heat-flow balance. But
the reactor wall
kinetic informations
term qFiow
as
well
errors
as
the
temperature
if qtot, calculated
discussion in
22
as
shown
of the
above, the
jacket
by Equation (2-17),
Chapter 2.1.4).
and
wall
are
is used
2.1 Reaction
In
Equation (2-17)
a
new
heat loss term, qLoss,
is introduced.
It describes all heat
losses from the outer reactor wall to the environment. Similar to can
k-Loss
TAmb)
=
Where
'
kLoss
Vj
~
is
temperature [K].
a
(2-18) coefficient
empiric proportional
an
Equation (2-13)
be chosen to describe qLoss\
general equation 4Loss
calorimetry
In contrast to kLld, kLoss does not
and
[W/K]
depend
on
TAmb
the
ambient
the conditions inside the
reactor and should therefore be easier to calibrate.
The other two
liquid,
heat flows in
Equation (2-17)
are
the heat
pumped by
the
cooling
qFimdjN and qFimdouf-
tf Fluid,OUT
Where
new
~
m
aFluid,IN is the
~
m
'
mass
CP,Fluid
'
\J
~
j ,OUT
flow of the
[J/(kg-K)]. By Equation (2-19)
the
^
j ,IN
(2-1 9)
)
cooling liquid [kg/s] dynamics
23
of the
and cPiFiuld the heat
cooling liquid
capacity
is taken into account.
2 Theoretical
Dynamics of an
2.1.4 If
Background
is not
calorimetry
certain
[Karlsen [Vincent If qtot
et.
is
al.
b], [Cesari
al.
et.
by
a
information about the time flow of the heat should be considered
system
81], [Hemminger
al.
et.
84], [Nilsson
[Becker 68],
et.
82], and
al.
02].
still
calculated
might
based
on
steady
a
previous Chapters 2.1.3.2,
described in the sources
provide
of the measurement
dynamics al. 87,
et.
used to determine the total amount of heat released
only
but also to
process,
release the
isothermal reaction calorimeter
deviations
cause
from
isothermal
sate
heat-flow
2.1.3.3 and 2.1.3.4. The
ideal
behavior
and
balances
following
consequently
a
error
time
distortion of qtot:
Source A: Deviations from isothermal If the total time constant of the
no
is similar
apparatus
constants of the chemical reactions
will
controlling:
investigated
be able to control the reaction
more
Consequently
heat accumulation will take
or
the control circuit
temperature
place
than the time
larger
even
(see Figure 2-7)
at isothermal conditions.
in the reactor content and should be
considered in the heat-flow balances.
Source B:
Depending maintained elements
Dynamic the
on
by
Elements: calorimetric
different
dynamic
(see Appendix
A.
temperature they
reactor
1.2)
principle
elements
will have to
change
accumulation inside of these elements will flow
already
was
Temperature path
sensors
temperature
In order to maintain
their
temperature
The
occur.
introduced and discussed in
Source C: Time Constants of
constant
(reactor wall, compensation heater,
cooling liquid).
or
the
applied,
Chapter
concept
an
is
Peltier
isothermal
and therefore heat
of this
dynamic
heat
2.1.3.1.
Temperature Sensors:
have their
own
time constants.
from the site of the event to the
measuring
Additionally
sensor can
the heat conduction
increase the observed
time constant.
If qtot is still calculated based
given
in
Chapters 2.1.3.2,
on a
2.1.3.3 and
distortion of qtot. The size of
source
calorimetric device. Therefore the into the main elements in basic
The
setup
is shown in
reactor content
causes a
a
for the reactor
mixing
and the
2.1.3.4) is
all the three
given by
the overall
following paragraphs an
will
sources
shall
dynamic give
a
(such
cause a
as
time
behavior of the
short introduction
isothermal reaction calorimeter. The
2-7.
Figure
produces
a
time-dependent
heat flow
inside the reactor content. This
temperature.
properties
A)
sate isothermal heat-flow balance
control circuit of
temperature change
sensor
steady
The
of the reaction
speed liquid.
24
of the heat
qtot(t).
This
change
heat flow
will reach the
transport depends
on
the
2.1 Reaction
The
temperature
or a
resistance
change
into
output
sensor
performance
or
For
a
Heat-Balance
or
of the main
time constant of about 0.5s
a
2s, will
convert the
the
compensate
significant
temperature
is connected to the
of the
performance
controller, the
the heat-flow
deviations of the reaction
Bad
change.
temperature
set-point. Heat-Flow calorimeter the electrical
a
This
cooling liquid TJ.
with
temperature signal
on
fast in order to
controller has to be converted the
Depending
will lead to
from the desired isothermal
thermocouple
The electric
signal.
slowly
a
time constant of about
a
PID controller.
a
will be varied
controller
with
electronic
an
controller, e.g.
for Tr, e.g.
sensor
calorimetry
by
the thermostat into
temperature change
dynamic element,
in this
will
change
a
cause a
of the
output signal of the
of the
change
of
temperature
temperature
the reactor wall. All these three sources,
case
thermostat, heat transport by the cooling liquid and the main dynamic element have their individual time constants that will contribute to the total
apparatus.
For
Toledo], [Karlsen For
a
BSC 81 reaction calorimeter,
a
et.
al.
Power-Compensation
the controller will be the
84] reported
compensation
or
or
the Peltier
system
Heat-Flow
or
main
dynamic
Heat-Flow
mass.
(see Appendix
A.
and then fed to the main
However the
Generally
as
the
1.2)
as
well
equivalent system
of the
a
Peltier element
a
compensation system
temperature
of
output
dynamic element,
cooling liquid
as
of
a
does
changed.
of the control circuit shown in
Figure
2-7 is the heat
transport
from the
element to the reactor content. or
Heat-Balance Calorimeter El.
Signal
Tr- Sensor
Controller
El.
Reactor Wall
Power-Compensation
or
Peltier Calorimeter
(see Appendix A.1.2) El.
Signal
Controller
El.
Peltier
Element
El. or
Compensation Heater
2-7: Control circuit of
an
isothermal reaction calorimeter.
25
Signal
Thermostat
Cooling Liq.
Tr- Sensor
Figure
the
the time constant of
have much smaller time constants than the
Heat-Balance calorimeter
not have to be
step
Peltier calorimeter
the Peltier elements.
because of its smaller thermal
[Mettler
time constant for the thermostat of about 50s.
electrically amplified
heater
precursor of the RC1 from
heater will be smaller than the time constant of
compensation
The last
a
a
behavior of the
dynamic
Signal
Signal Amplifier
2 Theoretical
Background
Correction of a time-distorted calorimetric
Depending
the calorimetric
on
signal
a
signal
correction of the measured
signals
should be
considered if the time constant of the measured chemical reaction is in the range of the time constant of the calorimeter.
Correction of source If the heat
capacity
baffles,
sensors)
or
measured reaction
A) of the reaction mixture is
as
well
known, e.g. by calibration, is
temperature change
as
the reactor inserts
correction
a
easily possible (see
according
(stirrer, to
the
Chapters 3.2.1,
also
6.1.1, and 7.1.3). Correction of sources
B) and C)
Various black box methods measured
signals
any other
physical
ignored. By same
using
model
[Cesari
and
the
time
an
off-line time correction of the
heat-flow balance for the calorimeter
81], and [Hemminger
al.
et.
for
where
systems
of the
these black box models the two
a
correct
measurement sources
et.
al.
physical
84]. They model is
B and C
are
are
quite
cannot
apparatus
or
be
corrected at the
time.
[Karlsen
et.
considered
al.
87,
the
Equation (2-9)
is
b].
on a
The
dynamic
approach
was
replaced by
a
was
flow
a new
a
applied
to
the
transient heat flux
dynamic
dynamic
model of the calorimeter
through element
found for Heat-Balance
82] described
In this work
physical
model
heat
the reactor wall is the main
al.
dynamic
constants
A correction method based
et.
a
developed
for micro calorimetric
mostly applied complicated
without
were
or
a
Heat-Flow
reactor
through
wall.
was
calorimeter The
Power-Compensation a
and
steady-state
the reactor wall because
(see Chapters 2.1.3.1).
heat-flow balance for
proposed by
No
analogous
calorimeters.
[Nilsson
Peltier calorimeter.
black box time correction method will be described to correct the
time distortion of the measured baseline
signal (see Chapter 3.7.2).
26
2.1 Reaction
2.1.5 Assessment of the three basic reaction calorimetric The
section tries to
following
the three different
give
an
overview
the most
on
calorimetry
principles related to
important topics
principles.
Heat Balance The
main
of
independent reaction
of
advantage In
technique
of the
changes
experiment.
this
is
that
heat transfer all
contrast to
other
the
determined the
through
techniques
reactor wall
are
also
for later scale
required, e.g.
meet two
that
requirements
hand, the flow
rate of the
transfer into the
up. The flow rate of the
difficult to
are
circulating
On the other hand, it should be low, to establish
jacket large enough temperature
the
on
finally
Therefore
principles.
be
to
good
measured
a
determined
qtot
cooling liquid
temperature The
signal
isolation of the reactor
is
at
a
influence
is
must
the
one
fast heat
constant level.
of the
large compared
jacket
a
difference
temperature
accurately.
a
the reactor wall
on
to realize
high enough
in order to control the reaction
jacket
during
accomplish simultaneously: On
fluid must be
is
qtot
additional calibration
an
heater must be introduced if informations about the heat transfer -
signal
over
ambient all
to
the
other
required.
Heat Flow As in
Heat-Flow calorimeter the measured
a
between reactor content and reactor chosen to be transfer
high
through
Power
al.
et.
a
reaction
constant.
point
Another
of view the
of the
quality
handled
cooling liquid
calibration heater and
a
in
correctly
be
can
However the heat
signal.
this
standard
advantage
required
of this
of this
temperature
technique
to maintain the
the noise of the measured drawbacks
Power-Compensation technique
because the
implement
to
electrical power
setup.
technique
are
the
heat-transfer surface of the
the constant heat flow
system
al.
through
changing
a
Heat-Flow calorimeter et.
possible
and that the
remains
at
constant level
a
hot
spots
et.
on
Al
the
84]).
(however The main
surface
[Singh 97]
jacket.
originates
from
an
big
compensation
heater is
drawback of this
of the
and
(change
of U
[Pollard 01].
or
A in
This is
optimally
signal
Equation (2-9))
actually
is that
technique
the reactor wall makes the measured
heat transfer
72] introduced
of the reactor
cooling liquid TJ
large [Hemminger
in the flow field of the stirrer. Another
sensitive to
simplest
is the direct measurement of the
temperature Tr
is rather
signal
of the
is the
heater. It is therefore crucial to check the ratio of reactor volume to
compensation
that
the flow rate of the
difference
Compensation
technique
[Köhler
be
cannot
temperature
82].
From the technical
placed
the
decreasing
is the
the reactor wall has to be calibrated with
changes during [Nilsson
without
jacket,
signal
the
air gap between the reactor wall and the
more
than
reason
a
why
cooling liquid
This increases the fraction of the total heat-transfer resistance the
external
resistance.
27
Other solutions to this
problem
are
2 Theoretical
Background
in literature.
reported a
2.1.4)
changing
discussed
general aspects
of the three different
principles
of
A
feature for the Heat-Flow and
fairly
temperature
slow control of the
element
is
the
calorimeters
reactor wall
are run
of the
temperature
especially
and
in isothermal
the
et.
al.
cooling liquid
Chapters 2.1.3.2,
As shown in
one or
several
dynamic
temperatures
Chapter
introduced
in
effort,
accurate
Therefore
dynamic As
the
the
for fast and
units
some
used to vary the
calorimeters however
can
be tuned
strongly exothermal reactions.
are
2.1.3.3 and 2.1.3.4 isothermal calorimeters elements in order to control the reactor
changing,
heat accumulation takes
are
done
errors
the
2.1.3.1.
of the
the basis of the
be
can
found.
temperature.
that will lead to
dynamic
It became clear that without
physical description on
concept
place
always
heat flow
enormous
Therefore
steady-state approximations.
was
calculation of
most
This
can
the lead
if the calorimetric data is used to determine kinetic informations.
three
different
shall
principles
be
compared
on
the
basis
of the
elements.
shown
dynamic
though
even
powerful [Riesen et. al. 85]. As
have to be fast and
time distortion of the calculated qtot. The
significant
dynamic
Elements
B) Dynamic
to
Therefore
The thermostatic
87, a].
even
calculations
because the main
still varies in the range of
temperature
to control Tr very
precisely
Chapter
to
mode, heat accumulation in the reaction liquid has
Power-Compensation
no
will be incorrect.
Heat-Balance calorimeters is the
cooling liquid.
will be shown in this work
a
the reactor wall
significantly:
jacket temperature [Regenass 83]
degrees Celsius [Karlsen
Whenever
no
control
to be considered because the reaction
require
uptake (qtot)
through
However if
above, the dynamics (according
differ
A) Quality common
heat transfer
or
A.1.
Appendix
of the three calorimeters
from the
Apart
a
reaction, the determined heat release
Dynamics
in the
presented
taken into account for
measures are
during
will be
They
above
Heat-Flow and
elements: The reactor wall
cooling liquid
are
as
generally higher
Balance calorimeter the
dynamic element,
Heat-Balance calorimeters
will be
well for
as
a
the
and
thus the
for the Heat-Balance calorimeter.
28
common
As the flow rates of
Heat-Flow calorimeter than for
temperature changes,
larger
cooling liquid.
have two
disturbance
a
Heat-
by
the
2.2 Reaction
In
Power-Compensation
calorimeters the reactor wall is
a
to the Heat-Flow and Heat-Balance calorimeters. However
temperature changes during
compared
the
to
Compensation
other
reaction measurement
a
principles
calorimeter the heat flow
reactor-side heat-transfer coefficient hr measurement. These
e.g.
by
changes
chemical reaction.
a
constant whereas
The main
generally
A.
mainly
two
1.2)
even
of
capacity
the heat
capacity
There is
no
heat
Heat-Flow
a
in order
principle
will
generally vary
of the reactor wall.
calorimeter is therefore the
inside
the
heater
element
to the heat accumulated in the wall of
Heat-Balance calorimeter.
or
types
Further it should
large.
h}
is
jacket
a
is
Peltier
There
are
of
area
heat transfer" a
(hj)
in
a
compensation
to
heater.
generally
bigger temperature changes temperature changes
on a
This
compensation
again
would
heater is
likely
smaller
cause
smaller than the
of the
compensation
of the reactor wall in
to be much
higher
than hr
temperature changes
a
on
on
the
heater.
the
different
control
principles
(see
Chapter 2.1.4)
it becomes clear that qtot determined based
(2-17)
much smaller than
compensation
heater is
compensation
expected compared
reactor wall.
calorimeter
generally
Heat-Balance calorimeter. On the other hand the reactor-side heat-
or
Considering
heater is
compensation
of the reactor wall.
"jacket-side
transfer coefficient hr
elements,
accumulation
Heat-Flow
of the reactor wall. Therefore
heater would be
and
Power-Compensation
a
the
be very
can
the
caused
changes
will vary for the latter calorimeter
h}
if the
changes during
of the reactor
larger temperature changes
compared
or
The total heat-transfer
the
A
Heat-Balance calorimeter
or
Power-
a
reasons:
The heat
area
even
But
much smaller
(see Appendix
to
element in
heater.
compensation
area
temperature
of the reactor wall
Heat-Flow
a
TJ leading
dynamic
Thus
In
only changes
much smaller than the
Furthermore the
temperature change
function of
the heat-transfer
generally
temperature Tr.
be considered that in as a
or
much smaller
Figure 2-6).
the reactor wall
through
2-5 its
Figure
generally
are
and
element similar
shown in
as
is varied for the Heat-Flow and Heat-Balance
TJ
to control the reactor
and the
are
2-4
(Figure
dynamic
calorimetry
will
be
less time distorted
compared
to
a
Compensation technique
Heat-Flow is
for
a
or even
therefore the
well
on
designed Power-Compensation
Heat-Balance calorimeter. The Power-
method
(see Chapter
29
dynamic
Equations (2-12), (2-14),
of choice
if fast
exothermal reactions have to be measured under isothermal conditions.
This will also be shown in this work
and
5.2 and
Appendix EA)
and
strongly
2 Theoretical
Background
Spectroscopy
2.2 IR-ATR
Spectroscopy
Infrared
Vibrations and rotations of molecules to
In
4000cm"1)
long
as
the
as
dipole
interactions. Therefore rotational
will
spectroscopy
spectrum
of
reaction mixture
a
reaction
experiment,
Conventionally where the
as
Therefore
changes
of the
Either
2.
Some solvents,
wise
absorption in the
give important
profiles.
technique
like water,
spectrum.
thicknesses
are
reflectance
(ATR)
Spectroscopy [Harrick 67]
cell with
or a
based
=e
spectrum.
experiments,
defined thickness. There
flow-through
two
are
analysis:
cell has to be constructed. on
wide range of the
a
thickness should be very small other
sample
will be very inaccurate. However in
small
practice
is the
problems
infrared
application
spectroscopy.
Books and Articles
of attenuated total
The
theory
[Fringeli
et.
of ATR al.
02],
on
the
2.3.3 all evaluation methods of the measured reaction
law of Lambert
profile
It will
of the
be used
in order to
get
It
was
absorbing components.
spectroscopic experiments:
-K c
=e
Beer.
d
i
r\-A
=10
i
r\-a d
=10
-t r\-£ =10
c
d
,Ä
Where T is the transmission at
a
decadic absorbance
a
[-],
a
and
d the thickness of the
coefficient
certain the
sample [m],
[l/mol/m]
and
c
wavelength [-],
Napierian k
and
B and A the
and decadic e
the
Napierian
absorption
Napierian
the concentration of the
30
ÄÄ.
(2-20)
T)
absorption
a
difficult to achieve.
Chapter
in
-ad
-B
e
a
of
spectra
[Mirabella 93].
derived for transmission
=
infrared
varying
strongly absorbing
are
informations about the concentration time
—
time
for the purpose of reaction
in combination with
explained
are
reaction
is well described in several
and
a
is carried out with transmission
Therefore the
quantitative analysis
a
as
sample
a
solution to both of these
general
spectra
the measurement of
have to be taken
samples
sample
[m"1],
infrared
changes origin
and therefore will
compounds
spectroscopy
of this
1.
=
but will lead to
more
molecules.
function of time. These
a
in future referred to
infrared
disadvantages
As will be
on
light passes through
infrared
r
molecular
Spectroscopy
The focus of this work lies
A
of the
be used to record relative
only
informations about their concentration-time
main
by
(400
rotation.
However the vibrations remain
spectrum.
groups
chemical modification of the reaction
ATR
influenced
or
is often used for the purpose of substance characterization. In this work
spectroscopy infrared
functional
specific
strongly
are
the vibration
cannot be resolved any
bands in the infrared
absorption
characteristic for
stages
in the infrared range
light
changes during
moment
the rotations of the molecules
liquid phase
broader
absorb
generally
and
coefficient
and decadic molar
absorbing component
in the as
well
the
as
path length
measured reaction
verified
coefficients
during
sampling
of IR-ATR
Equation (2-20)
can
be used to evaluate the
applicability
not transmission
are
of the Lambert Beer's law has to be
technique
are some
aspects
evaluated
(see
The
approach
jjm
on
be
always
spectra
et.
al. 98,
ATR
and
a]
are
as
carried out at constant
depends
on
in
Appendix
the
Consequently
medium,
only
the
liquid phase
on
the
as
is
fail to
technique might disappears
crystal
physical properties
mixture.
As
during
the Lambert Beer's law
changing
can
be
bands
strong absorption
identify components
in the measurement noise
also absorbs
cm"1,
this
In order to reduce the
measured
that may
IR-ATR measurements should be
reaction
light.
The ATR
made of diamond. As diamonds show 1800 to 2400
be
temperature [Furusjö
with
part
strong
of the infrared
signal
to noise ratio for
low concentrations
et.
used
can
no more
al. 00,
during
be
a]. this work is
region
of
will not be available.
measured
sampling
time is thus restricted.
31
averaged.
duration
of
several
measurement is therefore in the range of 10 to 60 seconds. The
typically
The
spectrum
standard
are
and
not be
a
spectra
recorded
a
might
absorbance in the
spectrum
reaction
a
evaluated.
are
[Furusjö
crystal
"sample"
neglected [Fringeli 03]
because their contribution to the total measured absorbance
The ATR
can
the effective thickness of the
on
these disturbances
should be taken when
or
the
the effective thickness of the ATR
of the
absorption
more.
is in the range of
the reaction in the bulk
03]. Additionally
B.1
Generally
detected
is
temperature.
fulfilled any
The
spectrum
that the
liquid phase depend
well.
absorption
care
infrared
assumption,
measured
are
al.
et.
measurement this
but
layer equals
the
generally temperature dependent,
[Furusjö
temperature
explained
ATR reaction
an
no
However there
examples.
(see Appendix B.1)
"sample" (see Appendix B.1) depends
vary with
As
in mind if
are
as
a].
vibrations of the molecules in al. 98,
analysis
organic compounds
crystal. Consequently
If slurries
analyzed [Furusjö
et.
kept
of the IR beam
of the ATR
top
be verified.
Infrared
As most
in reaction
Chapter 6.3.6):
reaction observed in this surface must
apply
should be useful for many reaction
penetration depth
some
required.
are
that should
also
is easy to
spectroscopy
cells
flow-through
or
active the
250
o 3
200
2500
+
150
a c
calorimeter
o
100
o
50
Heat
-*-
a-
O
1000
Capacity
500
0 i
(0
2000 1500
Conductivity
Thermal
-—
>
ö
re 0)
^ «f
qCoolmg.SS
Systems tested: A(q)y(t) B(q)u(t
Linear ARX:
Estimation of the model
=
-
nk)
+
e(t)
parameters (matrix A, B, C, D and F)
OE:
BJ:
System
y(t)
y{t)
=
^\u(t-nk) F(q)
=
+
e(t)
^M)-u(t-nk)+(^:e(t) F(q)
D(q)
inversion
Linear
System
identified
input
output y 'ft) ~
Figure on
the
qCoolmg.corr
3-21: Schematic
representation
~
a
time shift
'ft)
qCoolmg.SS
of the calculation of the time corrected qCooUng,corr based
steady-state approximation qCooUng,ss
represents
u
and
operator.
95
the
expected
ideal
qcooimg.exp- The
symbol
q
3 The
new
Calorimeter
3.7.3 Calculation The are
ofqStirr andqLoss
unknown heat flows that remain in the combined heat-flow balance
only
(3-12)
qsurr and qpOSs-
The heat flow qSt,rr carried out
during
measured
as
applications
a
qSt,rr
be calculated
can
according
this work the current function was
of time.
consumption
As
no
In all
Equation (2-3).
to
of the stirrer could
changes
be
assumed to be constant for all reaction
experiments
engine (Istirr)
measured
in
was
most
of this
experiments
work.
The heat flow qLoss
surroundings, qLoss is
[W] represents
similar to
independent
a
This
is feasible
change significantly. balance
as
temperature
it
is
was
(qLld)-
(see Chapter 2.1.3.4).
As the reactor is insulated
Because
as
long
However it is
as
more
measured
anyway
the ambient
sensors
the
during
»
during
a
the
reaction. does not
temperature (TAmb)
accurate to include TAmb into the heat-flow
measured at three different
3-22: Position of the
(see Figure 3-6)
could be assumed to be constant
^Amb,2
Figure
the thermal insulation into the
of the reactor content it is much easier to describe than qFhw and
surroundings
assumption
through
Heat-Balance calorimeter
the heat flow into the reactor lid heat loss to the
the heat loss
whole
positions
as
experiment. shown in
T
T
*
*
Amb.l
for the ambient
The
Figure
ambient
3-22.
Amb,3
temperature.
Sensor TAmbJ is located inside the thermal insulation, TAmbi2 close to the whole reactor and
far away
TAmbJ
following
correction
temperature
due to
of the ambient
TAmb,3
was
on
the back wall of the fume hood.
as
it is
opening
temperature
strongly
filtered
Both terms qStlrr and qLoss
(derivation
see
TAmbi3
less sensitive to short time
closing
or
is
a
(see are
of the
slow process
Table
cover
calculated in
below):
96
best suited for the
changes
of the ambient
of the fume hood. As the
(normally
3-5) prior
was
change
in the range of 2-5 °C
a
day)
to the evaluation shown below.
one
step using
the
following equation
3.7 From measured
Aq
=
q Loss
'
ÎComp.O
l Sùrr
tf Cooling,0
All terms with the index calculation
a
jacket temperature (TJ) the ambient
over
the
temperature.
Tn
reactor and
was
in
used is
does not
-T 1
(3-21)
Amb.O
(Figure C-2) device
a
depend
as
was
used.
it is most
specific
to
that
(used
to
the conditions inside the
parameters S,
R
experiment.
Equation (3-21) (qcomp.o
-
tfcootmgo)
eliminates the offset between
qcooimg and qComp before the start of the reaction. This offset will be called derived from
For the
[W/K]
In contrast to kLld on
For the
exposed
constant
therefore be estimated once, similar to the Peltier
and k, and then be used for any reaction
The first term
iß
(see Appendix D.2).
Equation (2-13)) kLoss
can
Amb
parameter kLoss
has to be determined in advance describe qLld in
T 1
T
range of minimum 4 minutes
a
sensor
The
w,
^Loss
to calorimetric data
determined before the reaction is started.
are
value
mean
~"~
signals
qtot and qDos to
Equation (3-12) by setting
zero
(no
Aq0.
reaction and
It is no
dosing): ^tfo
Àq0
~
tfcompß
was
-
tfcoolmgß
~
tfLossß
determined for the
5.3, 5.4).
Tho
~
Figure
3-23
~
(3"22)
tfstirrß
hydrolysis
shows
a
and
epoxidation
experiments (see Chapters
Aq0
the
of
plot
versus
temperature
difference
TAmbß.
0 -0.5
-1 -1.5
%.
Hydrolysis of Acetic Anhydride Epoxidation Polynomial Fit 3rd order
-2 2.5
-3 -3.5
-4.5 -30
-20
-10
j,0~ Figure
3-23:
experiments
Aq0 plotted
versus
described in
TjM
Chapters
-
Amb.O'-
10
20
30
J
TAl„,,„ (data is taken from the epoxidation and hydrolysis
5.3 and 5.4.
97
3 The
new
From
Calorimeter
3-23 the
Figure is
1) Aq0
obviously
(2
to
the
4°C)
and thus
proportional
not
studied. However the
change
difference
is not
when
zero
Equation (3-22) value
can
sources
be
that
Th0
Tji0
-
to
during
a
TAmb,o
-
in the whole
lead to
a
temperature range
reaction measurement is much smaller
could still be used but kLoss must be
a
function of
TAmbfi.
-
and
TAmb,o
explained by considering
can
7),0
be made:
can
consequently
qStlrr,o would thus be in the range of 1
shift of qcooimg
Shift of qcooimg due to
settings
experiments
the filter
for the
Calculated based
on
summarized in Table 3-5. The
shown in this work.
settings
required
are
Finally
of the inner thermostat
measurement
signals
of the
the calculated qtot
signals.
new
reaction calorimeter
the overall heat-flow balance.
Order
Cut off
of the filter
of the filter
4
0.001
Appendix C.8.4
4
0.001
Appendix C.7.4
4
0.001
Appendix C.7.4
TiUQ
4
0.001
Appendix C.6 (Equation (C-1))
TAmb [K]
2
0.0001
Chapter
3.7.3
Tßos [K]
2
0.02
Chapter
3.4.3.2
Tr[K\
2
0.02
3.4.3.2
Ucomp \Y\
2
0.02
C.8.4
1Comp L"J
2
0.02
C.8.4
fc*[W]1)
2
0.02
Equation (3-23)
I
Pelt
[A]
TpdT [K] T>
down
IPelt
rixi
LN
frequency
99
Description
same
of the
signal
4 Evaluation of the Calorimetric and
Spectroscopic Data,
a new
Combined Approach
4 EVALUATION OF THE CALORIMETRIC AND
SPECTROSCOPIC
DATA, A NEW COMBINED
APPROACH 4.1 Historical
background
A first version of
combined evaluation
the
a
thesis
diploma
of
I.
Zürcher
presented
4.2
[Zürcher 01].
successfully applied during
was
The
final
used
version,
for
work, will be explained in details in this Chapter. It
calculations shown in this at the AICHE
algorithm
Meeting
2002
[Zogg
et.
al.
all
was
02].
Requirements
Model-based identification of kinetic and based From
single
Chapter 3,
reaction
parameters
combined data set
on a a
thermodynamic
reaction
the
experiment,
new
reaction
calorimeter,
infrared data. Both contain information about the individual reaction
components
involved in the
Calorimetric Data:
experiment.
steps
This is shown in
Infrared Data:
qtot(t) [W]
A(t,
v
in
Calorimetric and
will deliver two different sets of measurement data:
the chemical
described
as
Figure
well
as
4-1.
) [-]
3 Measured q
f *
2
1
loi
k
-
n
20
40 Time
Thermodynamic
Reaction
Parameters:
Enthalpies
of
reaction,
mixing, phase changes
60
...
o
Wavenurnber fern
[min]
Kinetic Reaction
Spectroscopic
Parameters
Parameters:
Rate constants, reaction
Pure
orders, activation
components
Time
[mm]
Reaction
spectra of the individual
energies, phase-transfer /diffusion coefficients
Figure
...
4-1: Information content of the different data measured
(t=time [min],
v
=
wave
number
[cm"1], ,4
=
reaction
100
by
the
new
reaction calorimeter
spectrum in absorbance units [-]).
4.2
As
explained
Chapters
in
evaluation methods indicated
in
evaluation
2.3.2 and
4-1
However the
developed.
were
Figure
2.3.3, for both data
and
Table
(see Chapter 2.3.4).
In
a
1-1
has
stets many different
overlapping
not
been
yet
the evaluation of the calorimetric data in order to
reaction
parameters
in
4-1.
Figure
reaction
parameters
sets at the
versa.
it
Additionally will be
used
According
to the
be able to
identify
This is
robust
more
shown
schematically
of the thesis
goal
new
evaluation
the
(see Chapters 1.2),
reaction
following
reaction
parameters,
reaction
phase change
orders,
or
The determination of pure
algorithm
they
an
the
simultaneous
already
were
such
reaction
as
enthalpies.
constants, activation energies,
rate
as
/ diffusion coefficients.
side
a
presented
not the
product of the combined evaluation
based
empirical
on an
in
Chapters
evaluation
of
stays
in contrast to
2.3.2.2 and 2.3.2.3 that
to the kinetic evaluation. The
enthalpy prior
discussed in these
parameters
thermodynamic
and
kinetic
reaction
Chapters.
that have to be identified
are
kinetic model of the reaction
to be defined in advance
(see Chapter 1.2).
application
The whole evaluation
1.2).
data.
the evaluation method should
evaluation of the calorimetric data
determination of the reaction
The reaction
Fast
such
will be
the evaluation methods I.A and II.A
parameters
spectroscopic
a
primarily assumed to be unknown.
It should be noted that such
of
is to allow
spectra (spectroscopic reaction parameters) is
focus of this work. However
benefits
the dotted lines
parameters simultaneously
parameters,
a
by
have to suit the two individual data
they
as
for the
Kinetic reaction
require
combined
a
be assumed that the identification of the kinetic
can
requirement
Thermodynamic
are
in
identify thermodynamic
combined and simultaneous evaluation of calorimetric and
they
information content
time.
same
Therefore the main
as
separate
combined evaluation the infrared data would also
support
and vice
Requirements
Therefore
procedure
any calibrations of the
additional information from
Additionally that the
the
user
should be fast in
parameter
application (according
infrared
data
are
chromatographic experiments
identification should
should not have to
function, weighting functions
or
spend other
run
not
allowed
should not be
Chapter and
any
required.
completely automatic, meaning
time for the
adjustment
optimization parameters.
101
to
of the
objective
4 Evaluation of the Calorimetric and
Spectroscopic Data,
a new
Combined Approach
Inclusion of external information
Chapter
As mentioned in
adequately Therefore
educated
the
1.2 the
should
algorithm
information about the
Chemical
and not for
people
about
other
(e.g. gathered by
be
(see Appendix B.2))
reaction
model.
differential
equations.
include
to
reaction
possible
applied by background. and
knowledge
model
integration
the evaluation of the data. Thus the
model free evaluation
has
to
be
described
has to be carried out
complexity
an
empirical
in
terms
of
numerically during
of the model is not restricted.
If pure
infrared
possible
to include them into the evaluation. However the evaluation should
also work if If
no
enthalpies
al. 03,
spectra spectra
pure
of reaction
from heats of
of
by
or
products
mean
should be included in the form of
reaction The
external
mechanisms,
analytical techniques
methods
The
without any chemical
people
able
to be
designed
reaction:
investigated
knowledge
should be
algorithm
are
or
substances
some
available
other
available, it should be
are
(compare
to discussion in
thermodynamic parameters
are
6.3.5).
known
(e.g.
formation, quantum mechanical calculations (see also [Zogg
submitted])
or
group contribution
methods) they
et.
should be included into
the evaluation. If
physical
some
constraints for the reaction
negativity, temperature independency,
parameters,
such
as
non-
available, they should be included
are
into the evaluation. If certain time
regions
the reaction model
by
Chapter 2.3), Augmentation
(e.g.
it should be
one
of the data sets cannot be
if the
assumption
qtot
=
correctly
qReact is not
described
fulfilled,
see
also
to exclude it from the evaluation.
possible
of the measured data
The evaluation different
of
algorithm
should be able to treat the measured data sets from
experiments (e.g.
with different concentration conditions
or
at different
temperatures) simultaneously. Model selection As mentioned above the evaluation is based in advance. However in most
suggested
feasible
equally support the
for
the final
following
step
two main
1.
How well
2.
How
can
robust
corresponding Once the chosen
by
the
answer
the
investigated
on
cases
reaction.
a
reaction model that has to be
several reaction models will The
algorithm
of model selection. Therefore the
should
algorithm
seem
therefore
has to
answer
questions:
the reaction model be fitted into the measured data? is
the
identification
of
the
unknown
parameters
of
the
reaction model?
to these two
questions
is known the
user.
102
optimal
model
can
be
easily
4.3
Concept of
4.3
calorimetric
Chapter
in
explained
well
as
of the evaluation method
the evaluation method
4.3.1 Combined evaluation As
Concept
as
2.3
algorithm
there
infrared
basically
are
data
in
order
two
different ways to
identify
to
the
evaluate
desired
reaction
parameters: 1.
Model-free evaluation followed
by
as
initial
an
subsequent fitting
a
conversion and concentration 2.
step (Chapter
and
Appendix B.2)
of the reaction model into the determined
profiles.
Direct model-based evaluation of both data sets 2.3.3.2 and
2.3.2.1
(Chapters 2.3.2.2, 2.3.2.3,
2.3.3.3).
For the combined evaluation of calorimetric and infrared data the second was
chosen
1.
mainly
because of the
to show better
spectroscopic 2.
is was
performance
separate
Figure 4-1)
difficult to achieve
probably
therefore decided to
Chapter
in
are
supposed
evaluation of calorimetric and
data sets.
2.3.4 and
Equation (2-44) min
2.3.4 the model-based evaluations for the
approach
reasons:
A model-based combined evaluation of both data sets is
Chapter It
Chapter
As discussed in
following
two
use
whereas
or even
a
model-free combined evaluation
impossible.
model-based evaluation
a
straightforward (see
approach, according
to
2.3.4:
{f{errQ,err1R)\ rNt err0
(
,
\
(4-1)
z ^(O-E^CO-l-A^kft.e,Np)
mm
=
2\
NR
1=1
V 2
~
err,
=
min Ê
{
A-C^Q^JxE
Equation (4-1) represents calorimetric and function is done linear
a
spectroscopic objective using
a
combination
least-squares problems
reaction
nonlinear
are
of
least-squares optimization
combined
a
function. The combination of the
function/
Inside the nonlinear
objective
optimization,
two
to be solved in order to determine estimates for the
ArH1 NR (thermodynamic reaction parameters) and pure component spectra Ê (spectroscopic reaction parameters). The kinetic reaction enthalpies
parameters discussed in
defined
Chapter
As mentioned in However
by
the
2.3 it is assumed that qtot
Chapter
crucial
combination function
algorithm.
the chosen reaction model =
are
/ Of
most course
But then the benefits of
difficult
point
Equation (4-1) is
the
is
user
combined evaluation would be
103
As
already
straightforward.
appropriate
this could be left to the a
by 6L.Np.
qReact-
2.3.4 the formulation of
and
indicated
selection
the
of the evaluation
compensated by
4 Evaluation of the Calorimetric and
a
complicated
and
and time
automatic determination of will be described
models will
as
Chapter
in
be
automatically
appropriate weighting Equation (2-44)).
factors
Therefore
function/was developed
combination
an
and
4.5.
the basis for the
as
Combined Approach
and WIR in
WQ appropriate
an
separately
Using Equation (4-1)
(such
a new
determination of
consuming
combination functions
a
Spectroscopic Data,
included
evaluation, the following three physical
in the
calculation
4-2 for
(see Figure
an
example): Reaction
model, containing the kinetic model equations. By integration of the
reaction model the reaction rates
well
as
as
the concentration
can
be
(Equation ((2-2))
on
profiles
calculated.
Sensor model for the calorimetric data to calculate qReact the bases of the reaction rates
(qtot
=
qReact is
assumed).
Sensor model for the infrared data to calculate the reaction spectra A bases of the concentration
Total Reaction Model for the Reaction
example
Kinetic model
r(t,k):
r(t,k)
the
profiles.
reaction: A
+
B -> C
Concentration
Reaction model:
rate:
on
equations:
dCA
dc„
dcr
dt
dt
dt
profiles:
CA,\
CB,\
CC,\
CA,Nt
CB,Nt
CC,Nt
IS
V
t-calcik)
=
k-cA(t,k)-cB(t,k)
Sensor Model for Calorimetric Data:
Sensor Model for Infrared Data:
(Equation (2-2))
(Lambert Beer's Law (2-33): A(E,k) Ccalc(k)*E =
qtot*qReact(KH,k)
=
-ArH-r(t,k)-Vr
p
E
the two
4-2: Schematic sensor
representation
models. The model
rate constant k is the kinetic
spectroscopic
reaction
=
A'NX
p CB,1
p
p CC,1
p
Spectroscopic
Calorimetric Data
Figure
p
CA,\
of the total reaction model
equations
{&,), Afl
the
are
given
for the
thermodynamic,
parameter.
104
consisting
example
and E
(the
B-NX C-Nx
Data
of the kinetic and
reaction A
+
matrix of pure
B -> C. The
spectra)
the
4.3
By using
the
formulated in
approach expressed by Equation (4-1)
Chapter
The nonlinear
included
ArHl by generating
Ê. Analogous ArHl If several
NR
a
an
at different conditions
be
carried
can
can
constraints for
be included.
using
out
spectra
can
boundary
therefore be
corresponding
be introduced for
an
row
in
element of
a
are
single
carried out, the measured data is
vector qData
(calorimetric data)
and
a
J
(4-2)
'-''Data
the calorimetric and
If
reactions
are
infrared data from the
experiments
combined
that
were
i'th
reaction
will then be carried out measured
at
different
the Arrhenius law for the calculation of the kinetic rate constants will
certain reference
must
are
Consequently
a
rate constant will be described
temperature
the pure
Additionally
in
(infrared data):
single step.
temperatures,
be
Eventual known pure
The evaluation of all concatenated
experiment.
be used.
also
6L.Np
upper and lower bound for the
the time axis into
Where qReact.i and A,
one
will
using boundary
the values of
on
upper and lower bounds
tfüeactN
in
Ê.
remaining requirements
value is known in advance.
along
matrix AData
and
NR
experiments
concatenated
single
if
will be carried out
optimizations
constraints for
the
of the evaluation method
fulfilled:
easily
constraints
physical
linear
two
be
can
optimization
In this way
6L.Np. The
4.2
Concept
assumed
spectra that
the
by
rate constant at
a
and the Arrhenius activation energy matrix E will be identified for each
pure
component
temperature.
105
spectra
are
a
(Equation (4-5).
temperature
depending
on
as
it
the
4 Evaluation of the Calorimetric and
Spectroscopic Data,
Combined Approach
a new
4.3.2 Model selection The task of model selection
1)
How well
optimization
squares will be used
How
robust
nonlinear
is
task of
the
is
Equation (4-1)
indicator for the fit
as an
this
answer
identification
question
is
techniques
reported
are
solved, the remaining
minimize the time and
of
the
unknown
found time
objective
to note that the mathematical
to
calculate
the
in literature such
unknown
be
roughly Thus
practical applications
solution found initial values Based
on
model
for
the
it
function
From
are
the
the
are
can
parameters 0} reaction
corresponding optimum. objective
optimum, computing
more
time, the probability
to find the
However
algorithms.
will
generally depend
the
on
parameters 0i..Np.
10
use
best way to calculate the
10 random start values for the
solutions Np
obtained
(within
5
%)
the
by
nonlinear
and minimal value
be concluded that the identification is robust and
reliable.
If all
ten
solutions
are
different
robust, actually resulting in
a
it
must
be
random solution
Np.
approach, widely applied
determined
the
some
of these
performance
of the mentioned
parameters 0}
concluded that the identification is not
Another
after
stop
that
Np
counted. This number will be called "number of hits". If
identical it
are
The
concluded that the
was
with identical
parameters
for the reaction
some
identification is to
0L.Np.
ones
will all
global optimum,
indefinite calculation
one
Search.
Tabu
follows: The closer the local
is to the
for the model
parameter
parameters
objective
as
optimization
the calculation time is restricted to minutes. Therefore any
suggested
all ten solutions the
allowing
these reflections
optimization, of the
summarized
parameters by
Carlo,
Monte
solution.
locally optimal
a
of
step
global optimal parameters 0}
by any optimization algorithm
robustness of the model
only
will be close to
global optimum in
the
Gauss-Newton, Simplex, Levenberg-
as
given by Equation (4-1). They
optimization algorithm,
required.
was
function
model
different nonlinear
Many
to find the
guarantee
can
deliver
can
the
by
of
parameters
important
difficult to solve.
generally
of them
might
algorithms
of
sum
quality.
Marquardt, Simulated Annealing, Genetic Algorithm, none
parts:
it is
optimization, required
Equation (4-1),
However
into two
splitted
reaction model?
corresponding In order to
is
4.2)
the reaction model be fitted into the measured data?
can
After the nonlinear
2)
in
(see requirements
in
literature, is based
parameters
to calculate
on
However this method will
function and not the whole
problem
a
a
standard deviation for
sensitivity analysis
only
characterize the
of nonlinear
around
shape
the
of the
parameter optimization.
It
is therefore not used in this work. If several models model
are
parameters,
objective
evaluated 10
the
times, using random
best model
functions errq and errA in
will have
a
Equation (4-1)
hits".
106
start values for the
minimal value and
a
of the
final
maximal "number of
4.3
4.3.3
Step by step
In order to extract
(infrared
sets
be
one
part
procedure
and
of
that
an
evaluation
of the evaluation method
procedure
maximum amount of information from the two measured data
a
calorimetry)
the combined evaluation described above should
overall evaluation
was
Concept
elaborated and
procedure. applied
Reaction
The
complete step by step
in this work is shown in
Figure
evaluation 4-3.
Experiment Modify
•
Measurement Data
*
•
r
Reaction Model
i
Figure
only
"
"
Calorimetric Data
Infrared Data
Physical Constraints
:
4-3: Flow sheet of the overall evaluation
procedure
107
of the measured data.
Spectroscopic Data,
4 Evaluation of the Calorimetric and
The evaluation 1
procedure
following steps:
The measured calorimetric and infrared data
are
first evaluated
separately.
This is achieved
by only considering errq (evaluation of the calorimetric data) (evaluation of the infrared data) in Equation (4-1). This corresponds
or
errA
to
and
Equations (2-31) 2
consists in the
Combined Approach
a new
The focus
of the
calorimetric)
one
a
residuals
do
by
show
not
of the data sets
heat of
not
of the model fit. If both
measured than described
reaction shows will
quality
model-fit
concluded that in were
first, separate evaluation is
but the
parameters,
(2-34).
a
the
(spectroscopic
similar
physical
more
the reaction model.
mixing (the assumption
determined
qtot
as
can
be
chemical processes
or
it could be that the
E.g.
fulfilled).
This
affect the calorimetric measurement whereas the infrared data will be
only
unaffected. If the chosen reaction model does not model the heat of
quality
well
as
behavior, it
qReact is not
=
reaction
of the calorimetric model fit will be
worse
than the
quality
the
mixing,
of the infrared
model fit. 2.1
If the
qualities
exclude
of the
some
model fits
separate
data
of
points
the
are
different, it might be reasonable
linear
in the calorimetric data set all data
the
could
dosing period
be
excluded
if
a
in
least-squares optimizations
Equation (4-1). E.g.
heat
of
points
measured
mixing
is
to
during The
present.
calculation is then restarted with the modified data set. If the exclusion of data
improved 3
As
in order to
the reaction model
soon as
can
variance
remaining course
be
equally
in
in
the
data
be carried out.
except
practical applications
on
the
measurement
this will
was
can
case.
present,
distribution,
reaction model is not able to
However if
successful.
repeated.
At
identified
end
parameters
of
the
evaluation
physical
plausibility
must be verified based
If unreasonable reaction the
the
constraints
parameters can
be
on
were
changed
Otherwise the evaluation is finished.
108
significant underlying
the measured data sets. Thus
the reaction model must be modified and the calculation the
no
the combined
it must be concluded that the
accurately explain
the
distributed. Of
the other hand the residuals of the combined evaluation show
deviations from the normal
explain
(white noise),
normally
be the
never
parameters
parameters
noise
deviation from the normal distribution is
identification of the reaction If
to be
well fitted to the two data sets,
residuals of the combined evaluation will be
significant
5
can
If the reaction model chosen and the identified reaction all
4.1
unreasonable, the reaction model has
the observed difference to the measured data.
explain
the combined evaluation 4
is
points
of the
chemical and
reaction
physical knowledge.
identified either the reaction model and the evaluation must be
or
repeated.
4.4 Mathematical formulation of the combined evaluation
algorithm
4.4 Mathematical formulation of the combined evaluation
algorithm 4.4.1 Pre-treatment of the infrared data Baseline Correction
4.4.1.1 The
systematic
varying
variance in the data
baseline is
disturb the results
parameters might The
prior
following
All
the
using be
(see
baseline correction
expected,
where
or
then
compared
then
averaged
(caused by
the
therefore
The
to
reaction
baseline
changing
are
baseline
A at each
wave
spectral
In
calculation
spectrum
were
absorption changes All
spectral regions
Chapter 2.2) 4.4.1.3
were
is
calorimetric
drift)
a
it will
to
locally the
E.3.2): minimal
reaction
is
wave
profile
is
number.
evaluation time
not
during
the reaction
a wave
numbers
profiles
were were
number is chosen
reaction, the corresponding
profiles
and is therefore not
profile.
then
subtracted
from
the
reaction
It is assumed that the baseline drift wave
numbers.
region all
wave
Only
were
numbers
those
of the
measured
spectral regions,
where
selected for the evaluation.
where deviations from the Lambert Beer's law
are
expected (see
excluded from the calculation.
time ranges of the
spectrum
If
due to the
used for the evaluation.
occur
Resampling
points
due
at these
A)
profile.
and exclusion of data
points
In order to reduce calculation time and memory
data
Thus, if
E.2.2 and
with
A
change
of
with time but is constant for all
reduce the
Appendix
spectrum
deviates from the other
4.4.1.2 Selection of the order to
that
to all measured infrared data
in
given
are
profiles (columns
unique
a
profile
calculated
changes
assumes
instrument
to each other. All similar absorbance time
absorptions
spectrum
an
and
Chapter 2.3.3.3).
applied
absorbance
no
model
evaluation method and the estimated reaction
included in the calculation of the baseline
reaction
best
determined.
were
absorbance
3.
the
the reaction model.
explained by
also discussions in
was
in
The absorbance time
where
be
(application examples
numbers
wave
can
proposed
erroneous
absorption,
2.
determines
algorithm
in the infrared data
present
to the evaluation
1.
evaluation
values to describe all variance in the measurement data. It
parameter all
combined
proposed
consumption
experiment (see Chapter 4.3.3)
that will be used for the evaluation. The
available, do
not have to be
equal
signal.
109
the
user can
points
to the
or
in
to exclude certain
freely
time, where
points
choose the an
infrared
in time with available
4 Evaluation of the Calorimetric and
Spectroscopic Data,
Combined Approach
a new
4.4.2 Pre-treatment of the calorimetric Data 4.4.2.1 In
Resampling
and exclusion of data
points
order to reduce the calculation time and
experiment (see Chapter 4.3.3)
certain time ranges of the the data
that will be used for the evaluation.
points
calorimetric
is
signal
available infrared
available, do
not have to be
the
The
equal
or
user can
in
points
to the
to exclude
freely
choose
time, where
a
in time with
points
spectrum.
In contrast to the infrared measurement the
power release
consumption
memory
qtot is very fast
uptake
or
sampling frequency of the measured
(10 Hz). Therefore data reduction is crucial
in
order to enable reasonable calculation times.
4.4.3 The
Step by step explanation
reaction A
+
of the
functionality
algorithm
is
explained
on
the basis of the
example:
reaction model for
corresponding
Additionally
it is
now
batch
a
assumed that the
operation
constant. It
more
dnA
=
dt
dnc =
dt
can
r(t,k)
Where nA, nB and nc
(kinetic
unknown
parameter
well
the pure
as
unknown.
mm
k
x
Nv,
nA(t) nB(t) K(t)
dosing
r are
of
(4-3) dos
dt
Vr(t)
corresponding components [mol],
concentration of B
component spectra can
of the three
be rewritten
now
profiles
length Nt,Q,
see
[mol/l].
as
pre-treated
and therefore the
both vectors of
of the three
(dimension N,q
x
length Nt,Q.
components
the
only
enthalpy (ArH [J/mol]) are
assumed to be
follows:
infrared
(4-4)
pre-treated
spectrum.
calorimetric
the number of calorimetric time
spectra [-] (matrix
the number of infrared time
numbers in the reaction
vdos
k is the unknown rate
components
Chapter 4.4.1), N,q
Chapter 4.4.2), iV^
wave
no
equations:
dVr
parameter, compare Figure 4-1))
the measured and
see
number of
time
differential
any combination function, qData the measured and
samples, AData
and
the reaction.
f\rnmi\\qData -Vr •(-ArH)-r(k)^ mm(\\AData -Ccalc(k)x£||) [W] (vector
4-2.
the reaction volume Vr is
of the reaction model. Further the reaction
Equation (4-1)
Where/is data
following
the moles of the
are
reaction
constant
k
=
and cdos the
[l/s]
the
as
during
Figure
---r(t,k)-Vr(t) + vdos-cdos
dt
r(t,k)-V,(t)
rate
expressed by
dnB
-r(t,k)-Vr(t)
dosing
be
is shown in
B is dosed
component
Therefore the reaction model has to be extended
Nt,m
chemical
B^C
The
as
following
of dimension
samples
In contrast to
and
Nv
the
Equation (4-1) Vr
The matrix Ccaic contains the concentration
calculated
by integration
of the reaction model
Nc, Nc the number of chemical components in the reaction model).
110
4.4 Mathematical formulation of the combined evaluation
Matrix E contains the unknown pure several
experiments
carried out
are
the measured data
concatenating
component spectra (dimension Nc
they
according
vector and AData matrix. If several
A
unique
If
experiments
experiments
reaction
enthalpy ArH
to
augmented
an
If
single step by
one
evaluated at the
are
at different
is used for all
temperatures
matrices will be identified. Thus E
If
Equation (4-2)
to
iV^).
x
qData
time the
same
additions have to be considered:
following
2
mathematical
1
Baseline
0 0.8
£
0.7
50.6 0.5 3
4
time
Figure
5-2:
experiment lines. The
Comparison
of the
of NaOH with
H2S04
changing
baseline is
mathematical at 25 °C. The
mainly
[min]
and
measured
dosing period
caused
by
the volume increase.
125
the
of
change
baseline for the
neutralization
H2S04 is indicated with dashed of the heat-transfer
area
due to
5
and Results
Applications
Hydrolysis of
5.3 o
o
1
1
acetic
anhydride o
H2°
+
II
2
*-
AcOAc
AcOH
5-3:
Figure
of acetic
Hydrolysis
anhydride
with acetic acid in order to increase the
The in
the
required
Appendix
calorimetric
was
fed
together
in water.
anhydride
E.2.1. The evaluations described data.
measurement
well
as
anhydride
the
as
infrared
This
data
data
is
pre
given
in
for the evaluations is described in
algorithm required
4.
evaluation
separate
evaluation methods is this
in
of acetic
pre treated
use
E.2.2 and E.2.3. The
Appendix
Chapter
for the
solubility
given
are
following subchapters
treatment
A
conditions
experimental
with water. The acetic
of the
calorimetric and
given Chapter
infrared
data
based
E.2.4. All literature references
classical
on
also
are
given
in
Appendix.
5.3.1 Combined evaluation of the infrared and calorimetric data In the
the total power release
following
mainly
contains two different heat flows:
mixing (qmix) during
the
dosing period.
uptake
or
measured
by
the reaction power
1)
qtot is calculated based
the calorimeter
(qReact) on
(qtot)
and the heat of
the measured data
using Equation (3-23). Pretreated infrared and calorimetric data for all the calculations
Chapter
described in were
concatenated
(according
to
temperature
temperature (25,
A
Figure E-4).
only
a
one wave
However
evaluated and that allowed
visual
was
following
differential
single step.
vector
of all
be
of the
noted
of different
of the evaluation
formulated
applied
matrix
measured
The evaluation is then
measured and
that
the
components
algorithm
according
(compare
and
used is
data
(AData) at
one
repeated
for
°C).
40 and 55
should
were
temperature,
same
(qData)
the
number of A will be shown
It is the basis for all evaluations the
a
evaluation
comparison
overlapping
(see description
The reaction model
it
carried out at the
measurement
The
is thus carried out in
order to allow
spectrum
single
Equation (4-2)).
each measured In
4. All measurements, a
E.2.3)
in this section. The evaluation method
performed
into
E.2.2 and
(see Appendix
to
equations:
126
in
calculated
throughout whole at the
reaction
this section
reaction
(see
spectrum
same wave
is
number is
Chapter 4.4.3).
to the discussion in
Figure 4-2)
and
Appendix
implemented
E.2.4.1.
in form of
5.3
dn,
---r(k,t)-Vr(t)
dt
+
Hydrolysis
of acetic
anhydride
vdos-cdosAcOAc
dn^
-r(k,t)-Vr(t)
dt
dnAcO
2-r(t,k)-Vr(t)
dt
+
C5"3)
>
vdos-cdo^AcOH
dV. dos
dt
r(t,k)
nAcQAM)
k
=
K(t)
Where Vr is the reaction volume
component [mol],
anhydride
in the
kinetic reaction
components are
measured pure to be identified
model
anhydride
by
parameter
spectra
[l/s],
rate
were
used
as
acetic
(water,
All three chemical
anhydride
and acetic
in the calculation of the reaction constraints. The reaction
together
acid)
spectrum.
parameters
No
that have
with their bounds.
parameters (and their bounds) required for the evaluation of the acetic
Spectrum
[s1] (at each temperature).
coefficients
Absorption
at
each
new
Heat of reaction
absorption
number of the
wave
A and for all three chemical
temperature
coefficients
were
Chapter
first
measurement data
(calorimetric
set II Table E-4 and Table
plot
of
Therefore in
Figure
E-6).
and
a
infrared)
Upper
bound
bound
1e-4
0.1
5
-1000
each
ArH [kJ/mol] (at each temperature).
(Figure 4-3).
Lower
calculated.)
according
4.3.3
reaction
components [-]. (For
The whole evaluation will be carried out
the
step was
to the flow sheet
complete
evaluated
The result is shown in
Figure
points
and the simulated calorimetric
for the evaluation
signal (thin
black
It is obvious that the reaction model
time range of the measurement data.
127
presented
separately (evaluation 5-4.
(triangles,
see
(fat gray line),
Appendix E.2.3)
line, best fit according
(5-3)
in
time range of both
5-4 shows the total measured calorimetric data
the selected measurement
(4-12)).
[s~1].
only
measurements and their bounds.
Rate constant k
The left
corresponding
cdosAc0AC the concentration of acetic
rate constant k
the reaction model
listed in Table 5-1
are
the number of moles of the
is the
absorbing species
as
Table 5-1: Reaction
dosing
n
cdos,AcOH the concentration of acetic acid in the feed. The
feed,
defined
considered
is the
vdos
[I],
to
Equation
could not be fitted into the whole
5
and Results
Applications
However the
in the lower left
plot
(points, compare the
illustration)
according
reaction model could be fitted into the infrared data. This is shown
same
of
5-4: The measured absorbance time
Figure
Figure E-4, only
to
fits well into the simulated absorbance
mixing occurring during the
Figure
5-5
signal.
sows
quite The
as
the
black
profile (thin
cm"1
simplify
line, best fit
the
possible
as
anhydride. They
do
to exclude the calorimetric
only
affect the
data, measured
from the evaluation.
analogous plots
well
evaluations is due to the heat of
separate
of acetic
dosing
Therefore it is
dosing phase,
dosing phase separate
number is chosen in order to
one wave
It is assumed that the difference of the two
during
at 1139
Equation (4-13)).
to
calorimetric
curve
to
Figure
5-4
(left)
1 minute after and 0.5 minutes
calorimetric evaluation
(evaluation
but
the
now
before,
points during
excluded from the
are
I, Table E-5). The model agrees
set
the
now
well.
hypothesis made,
the calorimetric
that the heat of
signal during
the
mixing
are
dosing phase,
for the disturbance of
responsible
can
finally
be tested
by carrying
out
a
combined evaluation of the infrared and calorimetric data.
Evaluation of Calorimetric Data
Evaluation of Infrared Data
(25°C)
(25°C)
0.22 Measured q
Simulated Absorbance
(all)
tot
Simulated q
«
0.2
Measured Absorbance
tot
Measured q
(Eval) 0.18
s
0.16
0.14
0.12
0.1 20 Time
Figure
5-4:
Hydrolysis
infrared
(right)
reaction
experiments
of the reaction
anhydride
10
30
20 Time
[min]
of acetic
anhydride. Separate
data of the full time range at 25 °C is
(evaluation
displayed. Only
(only
24
s).
128
40
set
II).
one wave
In both
number
plots
(1139
50
[min]
evaluation of the calorimetric
spectrum is shown in the right plot. The reaction
/ acetic acid mixture
30
a
mean
cm"1,
starts with the
see
(left)
and
value of all
Figure E-4)
dosing
of acetic
5.3
Evaluation of Calorimetric Data
of acetic
anhydride
(25°C)
Measured 1 3
Hydrolysis
tot
(all)
Simulatec 1
tot
Measured 1
A
2.5
tot
(Eval)
2
1
0.5
0 10
20
30
Time
Figure
5-5:
points
measurement
(evaluation
of acetic
Hydrolysis
I).
set
starts with the
A
mean
dosing
shortly
before
value of all reaction
of acetic
anhydride
shown in
Figure
5-6
the measured data
(25,
40 and 55
(calorimetric
concluded that the reaction
as
model
/
evaluation of the calorimetric data. The after
the
dosing
at 25 °C
experiments
/ acetic acid mixture
The results of the combined evaluation
50
[min]
anhydride. Separate
and
during
40
(only
24
(see Equation (4-16)
°C).
period
excluded
are
displayed.
The reaction
s).
and
Figure 4-5)
are
As the differences between the model and
well
as
(5-3)
is
infrared) now
are
not
significant
it
can
be
able to describe both data sets
simultaneously. The are
determined rate constants k at the three different
independently plotted
separate
as
in
an
well
Arrhenius
as
plot (upper right plot
(calorimetry
Figure 5-6).
First of
the combined evaluation resulted in similar values for k. It
concluded that the reaction model data
in
temperatures
and
determined k at each fact further indicates
infrared)
is
now
all
lay
on a
be
straight
independently
line in the Arrhenius
proper choice of the reaction model.
129
can
able to describe both measurement
well. Further it should be noted that the
temperature
a
(5-3)
all, the
plot.
This
5
Applications
and Results
Combined Evaluation
(25°C) -3.5
3
Meas. q
tot
ü
Sim. q
2
(all)
Infrared Data
tot
Meas. q
(Eval)
20
30
40
-4.5
-
-5
-
-5.5
-
only
only
Combined Evaluation
o
ol 10
Calorimetric Data
»
50
Sim. Absorb. Meas. Absorb.
20
50
Time
3.1
3.2
[min]
3.3 1/T
3.4
3.5 -3
[1/K]
x
r
Combined Evaluation
Combined Evaluation
(40°C)
(55°C)
Meas. q
tot
Sim. q
15 Time
Figure
5-6:
results
are
Hydrolysis
of acetic
shown for all
Figure 4-5)
are
values at each
experiments (mean
by
the
separate
(Appendix E.2.4,
flow-sheet
and infrared data
proved
mixing, occurring during
E-7)
chemical
the
at all
temperatures.
the combined evaluation
to the
corresponding
well
basically
the
same
(see Figure 4-3)
for the evaluation of calorimetric
dosing phase
simple application,
of the acetic
(see
anhydride,
also discussion in
4.2 the determination of the pure
evaluation
and
reaction are
parameters (see Figure 4-2)
therefore
a
values
k and EA.
was
the heat of
successfully
Appendix E.2.4).
spectra of the involved
component is not the focus of the developed evaluation method.
spectroscopic
(see
results of the
the literature references.
as
results in
to be useful. Even for this
the
Chapter
temperature)
as
as
applied,
identified and excluded from the calculation
As mentioned in
well
compared
parameters ArH,
generally suggested
as
Table
any kind of evaluation method
for the desired reaction
[min]
Results of the combined evaluation. The model-fit
anhydride.
listed in Table 5-3 and
classical evaluation
Obviously
10 Time
[min]
All the results obtained
these
(Eval)
-
10
The
(all)
tot
Meas. q
S 0.15
10
side
130
product
However
have to be identified
of the
whole
during
calculation.
The
5.3
calculated pure
pure
spectra
spectra. Although
bounds of the pure
spectra spectra
at different
intensities
peak
similar.
matrix in Table No
well
as
the
be
can
5-1),
seen.
spectral position
of acetic
to measured
compared
are
spectra
anhydride
used
was
(see
the calculated and measured pure
difference
significant
temperatures
as
5-7 and
Figure
information about the pure
prior
no
spectra
quite
are
shown in
are
Hydrolysis
between
the
calculated
pure
However the deviations of the relative of the
peaks
is
significant.
0.4 Calculated 25°C CD
Calculated 40°C
O c
0.2
cc _Q
AcOAc
Calculated 55°C measured 25°C
O CO
<
0 0.015
CD
0.01
O C
CC _Q O
Water
0.005
CO
<
0 0.2
CD O
AcOH
C
0.1
CC _Q O CO
<
0 900
1000
1100
1200
1300
1400
Wavenumber
Figure (data
In
5-7:
set
Hydrolysis
I). They
Figure
and
5-8
(4-6))
are
of acetic
compared
(first
for
mentioned, the experiments Therefore the values lowest
infrared
infrared
model-fit
each
the
error
given error
AA
was
step (compare
temperatures
for each
1800
spectra by the combined evaluation
functions AA and
evaluation
at different
1700
spectra.
temperature.
found
behavior is found for the model-fit
all measurement
temperatures
As all evaluations
were
of the identification solutions found
of hits"
plot)
1600
the
by
were
AQ (Equations (4-8) Figure 4-5).
to
evaluated
As would be
separately.
expected
evaluation
separate
As
the
of the
data, the highest by the separate evaluation of the calorimetric data. The
analogous
Figure
are
Calculated pure
to measured pure
and second
shown
are
anhydride.
1500
[cm"1]
5-8. It are
are
carried out
can
using
is
be measured
by counting
sums
of
AQ
and AA
over
values, the quality
the number of
equal
and best
This "number of hits" is shown in the third
be concluded that all identifications
given
The
ten different random start
close to the maximum of 10. The
temperatures
AQ.
shown in Table 5-3.
(see Chapter 4.3.2).
can
error
in Table 5-3.
131
were
mean
very robust
value
over
as
plot
of
all "number
all measurement
5
Applications
The
and Results
automatically
(4-16)
to
(4-20)
calculated
and
scaling
Figure 4-5)
are
factors SIR and
SQ (see Chapter 4.5, Equations
shown in the last two
plots
of
Figure
5-8.
M Cal-Eval IR-Eval
il
1 ^B Comb-Eval 2 Comb-Eval 1
<
IH
1111
111
25
1 0.5 <
H 40
1
55
DLiiDi
Temperafiure [°C]
Figure
5-8:
Hydrolysis
of acetic
anhydride.
First and second
AQ. Third plot: Number of hits (maximum 10). Last
132
two
plot:
plots: SIR
an
Final
error
functions A4 and
Se (see Equation (4-16).
5.3
of acetic
Hydrolysis
anhydride
5.3.2 Simultaneous evaluation of all measurements at all
temperatures As
explained
different set I
in
Chapter
4.4.3 it is also
in
temperatures
single step.
one
E-4 and Table
(Table
E-5, all
for all
temperatures
components (matrix E) three sets of E
were
Equation (4-5).
The
evaluation
algorithm
Table 5-2: All reaction
anhydride
are
new
Heat of reaction
parameters
agreement
well
spectra
was
were
combined
temperatures.
Ea [kJ/mol] at
each
number
wave
coefficients
absorption
of
the
reaction
components [-]. (For were
it
are
shown in Table 5-3
the combined evaluation gave the
spectra
differences between the pure robustness of the evaluation 10 for each evaluation
E
was
spectra
was
(compare
high to
also
separate
same
results.
possible (similar
at different as
temperatures
the "number of hits"
Figure 5-8).
133
bound
1e-4
0.1
10
100
5
-1000
in
(shaded
with the results of the individual evaluations at each
identification of the pure
Upper
bound
calculated.)
be concluded that the
can
Lower
each
ArH [kJ/mol]
as
the
by
and thus
the Arrhenius
replaced by
identified
reaction
of the three
temperature dependent
[s1]
to the discussion in 5.3.1 as
that
one
parameters (and their bounds) required for the evaluation of the acetic
The results of this overall evaluation
infrared
In contrast to
temperatures).
had to be identified. The pure
A and for all three chemical
temperature
the evaluation data
using
summarized in Table 5-2.
coefficients
Absorption
done
measurements at all
still assumed to be
reaction
measurements at all
Activation energy
was
identified. The rate constant k
Rate constant k at 25 °C
Spectrum
were
This
to evaluate several measurements at
temperature (see Chapter 5.3.1) only
the individual evaluation at each
enthalpy ArH
possible
to
calorimetric and
They
are
in
good
temperature.
The
Figure 5-7).
The
negligible.
The
were
was
gray). Similar
at the maximum of
5
and Results
Applications
Summary
5.3.3 Table
5-3:
evaluation
SQ
=
the
0 in
of acetic
Hydrolysis
evaluations
Average
of all results
the
using well
as
as
the
literature
reference
but still both data sets
were
3>
data.
Each
activation energy EA
temperatures identified
were
maximum 10
given
a
energy EA and the
8)
and
(mean
Calorimetric
(4-6)). value
Chapter E.2.4.1, Comb
Sum over
and
over
all
all
the
separate and
The main
listed
3'4>
was
rate 7)
can
see
Table
carried out
E-7).
by setting
also be identified from
separately (see Chapter 5.3.1).
Arrhenius
plot.
(see Chapter 5.3.2). constant at
6)
25°C.
4>
5)
error
temperatures.
temperatures).
10>
function 9>
at
The
All measurements at all
Calculated based
Classic evaluation
on
the
determined
Number of hits
the
of the
Classic evaluation of the calorimetric data
infrared
1>
I, with excluded dosing period in the
Data set
evaluated
time
combined
results from the classic details
(for
separate evaluation
succeeding
same
of
evaluated. Therefore \H
was
(see Appendix E.2.4.1).
Appendix E.2.4.3). (Equations (4-8)
calculated in
evaluated at the
activation
calorimetric data
in
was
temperature
also
are
The
separate evaluation of the infrared data.
calorimetric
results
algorithm (see 4).
temperatures.2>
value of the three
(4-16)
evaluation
new
Final
anhydride.
(see
optimum
(see Chapter 4.3.2),
A detailed list of literature references is
Table E-7.
Cal
IR
Comb
Cal
IR
Classic Cal
IR Eval
Ref.
Eval6)
7)
10)
Eval
Eval
Eval
Eval
Eval
Eval
3)
3)
3)
4)
4)
4)
-57
-57
-58 2)
-57 ±1
-60
-60
-60 2)
-62 ±2
[kJ/mol]
-59
-60
-58 2)
-60 ±1
ArH av.1)
-59
-59
-58
[kJ/mol]
±1
±2
±1
56
56
Classic
ArH25°C [kJ/mol]
-57
ArH 40°C [kJ/mol] ArH55°C
-59
-59
-58 2>
-60 ±3
56
57
54
57
EA
[kJ/mol]
55
57
/f25°C
2.8
[1(r3s-1]
2.9
3
2.8
2.8
2.8
2.8
/f40°C
[1(r3s-1]
7.8
8
7.6
8.2
5)
8.4
5>
7.9
5>
8.5
7.8
23.5
[1(r3s-1]
5)
23.2
5)
20.6
5)
22.5
23.5
21.5
21.9
5.4
4.9
6.9
6.5
5.6
9.1
1.425
1.431
1.423
1.425
1.429
1.424
9.3
9.7
10
10
10
10
AQ* [w2] A48» [-]
[-]
0.2
9)
134
±
0.6
/f55°C
# Hits
3 ±0.2
0.8
57 ±
2.76 ±
0.3 ±
22.2 0.5
±
5.4
of
Epoxidation
2,5-di-tert-butyl-1,4-benzoquinone
Epoxidation of 2,5-di-tert-buty 1-1,4-benzoquinone
5.4
Hydroperoxide 0
V
O
OwH
'
„
^
.
,
^
'
,
.
Mono
Educt
Figure
5-9:
Consecutive
hydroperoxide.
The
Triton R
S\
][
\
O
Epoxide
dosed
was
>r I
Alcohol
Epoxide
Di
of
^OH
..
>\ ^
^
B
Alcohol
epoxidation
catalyst
.„
.
-^— Triton
o
\
X
^
!
/\/"^
O
X>'
„.
>r0H I
Triton B
°
^^M
AA
~°-
x
Hydroperoxide
\,
2,5-di-tert-buty 1-1,4-benzoquinone into
the
reaction
mixture
in
with
order to
tert-butylinitiate
the
reaction.
The in
experimental
the
are
following subchapters for the
required
treatment
given
use
in
E.3.1. The evaluations described
Appendix
pre treated
calorimetric
as
measurement
well
the
as
data.
infrared
A
separate
is
given Chapter
evaluation of the calorimetric data based
Chapter.
discussed in
E.3.4. Literature data
Literature
Special
E.3.6.
Appendix
on
on
the reaction
are
The reaction
experiments
observations made
following subchapters
during
are
were
evaluated based of additional
was
same
for each
performance
Then
using
different
different
the
in
given
reaction
measurement data but also
at all
temperatures
reaction
these
Appendix
Appendix
E.3.5.
In
a
first
combined evaluation for
each
models
were
enthalpies
reaction
using
measurement data
(see Chapter 5.4.2).
In third
carried out
the
was
are
experiments
temperatures.
new
possible
at different concentrations
experiments
enthalpies
the
the
experiments
the evaluation all
which
on
evaluated
Chapter 4) using
in
temperature (see Chapter 5.4.1).
Finally
pre
also discussed in
summarized in
carried out at four different
were
measurement data
algorithm (described
reaction
is
kinetics of the
E.3.5. The behavior of the measured baseline qCooimg is also shown
the
data
data
classical evaluation methods
enthalpy
references that describe the
that will not be mentioned in the
step
This
E.3.2 and E.3.3.
Appendix
this
conditions
using
step
same
temperature (see Chapter 5.4.3).
of the automatic
used for all the three
steps
scaling
method described in
mentioned
above,
was
(Chapter 4.5), a
Pareto
ArH2)
will be
analyzed
in
plot (Chapter 5.4.4). One
more
presented
different way to evaluate the measured data in
[Zogg
et.
al.
(setting Afli
-
03, submitted] and the results will be compared to semi
empirical quantum mechanical calculations.
135
5
Applications
and Results
5.4.1 Combined evaluation of the infrared and calorimetric data In the
the total power release
following contains
mainly based
on
measured
uptake
flow, the reaction power (qReact)-
heat
one
or
the measured data
qtot is
E.3.2 and
(see Appendix
the calculations shown in this section. The evaluation method 4.
All
carried
measurements,
concatenated into
single
a
The evaluation of all
carried out in
single step.
In
order to allow
spectrum
A
only
a
evaluated and that
Two
it
main
expressed
reaction as
and matrix
is then
used
were
is described in
temperature,
same
repeated
to
is thus
temperature
one
were
(AData) (according
for each measured
of the
measured and
calculated
throughout
should
whole
be
noted
of different
of the evaluation
steps
follows
applied
number of A will be shown
overlapping
(see description
(qData)
E.3.3)
°C).
comparison
one wave
However
Figure E-12). allowed
visual
the
at
measurements at
The evaluation
30 and 36
temperature (17, 24,
out
measurement vector
Equation (4-2)). a
calculated
always
using Equation (3-23).
Pretreated infrared and calorimetric data
Chapter
(qtot)
the calorimeter
by
(according
to
at the
components
this section
reaction
in
Chapter 4.4.3).
during
the
epoxidation.
(see
spectrum
same wave
algorithm
involved
are
that the
reaction
is
number is
These
be
can
Figure 5-9):
h
Educt
+
Hydroperoxide
Mono
—»
Epoxide
+
Alcohol
(5-4) Mono
Epoxide
+
Hydroperoxide
The reaction is initiated
by rapid
people [Hairfield
applied
a
large
excess
al.
et.
of the
tert-butyl-1,4-benzoquinone). pseudo
Epoxide +
addition
(24s)
was
Alcohol
of the
catalyst
measured data
by [Moore 67] According
as
and
was
batch
catalyst
investigated
85], [Bijlsma
et.
al.
98],
steps
dosed
during
experiments.
a
and
(Triton
B in
[Mayes
et.
al.
to the educt
92].
by All
(2,5-di-
where therefore assumed to be
(mono Epoxid).
As
only
a
small
very short time, all authors evaluated the
The reaction mechanism is further discussed
[House 72].
to these literature references the reaction model
following
solution
under similar conditions
tert-butyl hydroperoxide compared The two reaction
first order in the concentration of the educt
amount of
of the
Di
The kinetics of the reaction
Methanol). several
—»
differential
equations.
was
implemented
It is the basis for all evaluations
Figure 4-2):
136
in form
(compare
5.4
dn
Educt
Hydroperoxt de
A
{-r&kJ-r&kjYv,«)
dt dn
2,5-di-tert-butyl-1,4-benzoquinone
r,(t,k,)-K(t)
dt dn
of
Epoxidation
Mono Epoxide
dt dn Dl
Epoxide
r2(t,k2)-V,(t)
=
dt dn
y
{r^k^ + r^k^-V^t)
Alcohol
dt dn Solvent
dnMethanol
dt
V
dt
•
dos
c
dn TntonB dos JsÄethnol
V
dt
•
dos
c
(5-5)
dosJntonB
dV„ dos
dt
rl(t,kl)
n
kl
=
Educt
'
vr(t) n
r2
(A k2 )
k2
=
(0 "mtonpit)
Vr(t)
Mono Epoxide
(0
Hydroperoxide, 0
,(0
«T
'
K(t)
vr(t)
where Vr is the reaction volume vdos is the
component [mol], in the
feed,
reaction
model
short
[I],
dosing
J
the number of moles of the
n
rate
[l/s],
parameters
addition
catalyst
catalyst (Triton B).
the two rate constants kj
are
phase (24 s)
remains
kinetic
only
[l/(mol-s)].
The
only varying during
during
constant
The
and k2
is included in r7 and r2. However it is and
corresponding
cdosMethanoi the concentration of methanol
cdos,TntonB the concentration of the
concentration of the the
Hydroperoxide, 0
the
of
rest
the
experiment. All
eight
chemical
defined
components
the reaction model
by
(educt (2,5-di-tert-butyI-
1,4-benzoquinone), hydroperoxide (tert-butyl hydroperoxide), (tert-Butanol), considered measured
(including
as
di
solvent
(ethanol
absorbing species
pure their
Epoxid, spectra
bounds)
Table 5-4: All reaction
were
and
Dioxan),
mono
methanol and Triton
in the calculation of the reaction
used
as
constraints.
that have to be identified
are
alcohol
Epoxid,
All
the
B)
are
spectrum.
No
reaction
parameters
listed in Table 5-4.
parameters (with bounds) required for the evaluation of the epoxidation
measurements.
Rate constant kt and k2
Absorption
Spectrum
[l/(mols)] (at
coefficients
A and for all
temperature
new
at
each
eight
absorption
each
coefficients
Heat of reaction 4A and ArH2
number
wave
chemical
temperature). of
the
reaction
components [-]. (For were
[kJ/mol] (at
Upper
bound
bound
1
5
-1000
each
calculated.)
each
137
Lower
temperature).
5
Applications
and Results
The whole evaluation will be carried out
according
Chapter
first
4.3.3
Therefore in
(Figure 4-3).
measurement data
data set I Table E-9 and Table are
shown in
The left
Figure
plots
and
(calorimetric 5-10 and
E-10). Figure
a
infrared)
step
to the flow sheet
the
The results of the
points
for the
simulated calorimetric
black
is obvious that the reaction model
Only slight
the measurement data.
at 30 and 17 °C
5-11.
evaluation
signal (thin
separately (evaluation
experiments
show the total measured calorimetric data
measurement
time range of both
complete
evaluated
was
in
presented
(triangles,
(fat gray line),
and
Appendix E.3.3)
see
line, best fit according
(5-5)
the selected the
Equation (4-12)).
to
It
could be fitted into the whole time range of
deviations
be
can
seen
for the data measured at
17°C.
The
reaction model
same
also fitted into the infrared data. This is shown in the
was
right plots of Figure 5-10 and Figure 5-11: The measured absorbance time curves at 1687 cm"1 (points, compare to Figure E-12, only one wave number is chosen in order to
the
simplify
line, best fit according calorimetric
It
evaluation,
The
significantly. was
Equation (4-13)).
to are
a
using
slight deviations,
quality
of two
or
the
observed at the
evaluations does not differ
separate
deviations of the calorimetric data at 17 °C
slight
different model
carried out
The
black
profiles (thin
not visible in the infrared data.
concluded that the fit
was
argue
fit well into the simulated absorbance
illustration)
exclude data
same
Evaluation of Calorimetric Data
are
too weak to
Therefore the combined evaluation
points.
data set I and the
same
reaction model.
Evaluation of Infrared Data
(30°C)
(30°C)
0.11 Simulated Absorbance Measured Absorbance
0.09
0.08
0.07
0.06 20
40 Time
Figure
5-10:
calorimetric
(1687
cm"1,
initiated
by
of
and infrared
value of all reaction
80
20
40 Time
[min]
Epoxidation (left)
60
experiments
see
Figure E-12)
the
dosing
data of the full time range
at 30 °C is shown in the two
of the reaction
of the
catalyst
spectrum is shown
Triton B
(only
138
24
s).
(evaluation plots. Only
on
the
right
80
[min]
2,5-di-tert-butyl-1,4-benzoquinone. Separate (right)
60
evaluation data set
I).
one wave
of A
the
mean
number
side. The reaction is
5.4
Evaluation of Calorimetric Data
Epoxidation
of
2,5-di-tert-butyl-1,4-benzoquinone
Evaluation of Infrared Data
(17°C)
(17°C)
0.09 Measured q
Simulated Absorbance
(ail)
tot
Simulated q
Measured Absorbance
tot
Measured q
0.08
(Eval)
0.07 3
0.06
0.05
*»«#******«»#*«#«*
0.04 40
60
80
Time
Figure
5-11:
calorimetric is initiated
by
the
of
and infrared
dosing
14C
5-12. The
of the
corresponding quality
of the
mean
model fit
separate
40
60 Time
80
(right)
data at 17 °C.
catalyst
Triton B
Explanations
(only
24
see
Figure
(Equation (4-16)
are
Generally
evaluation.
139
120
14C
evaluation
of
the
5-10. The reaction
s).
and
Figure 4-5)
values of all measurements at each shown.
100
[min]
2,5-di-tert-butyl-1,4-benzoquinone. Separate
The results of the combined evaluation
Figure
20
[min]
Epoxidation (left)
100
the model-fit
are
temperature
quality
shown in and the
is similar to the
5
Applications
and Results
Combined Evaluation
20
40
60
80
Combined Evaluation
(17°C)
100
120
(24°C)
14C
10C
0 1 Simulated Absorbance
Simulated Absorbance
Measured Absorbance
Measured Absorbance
g
IQ 08
5
0 06
0 08
0 06
-
***mw****w^w**¥W¥*
0 04
0 04 20
40
60
80
Time
100
40
60
Time
[mm]
Combined Evaluation
(30°C)
10C
(36°C)
-
Simulated q i
10
14C
[mm]
Combined Evaluation
15
120
Simulated q
tc
Measured^
to
Measured^
-
._.i 20
40
60
60
80
0 12
S
01
^
0 08
Simulated Absorbance
Simulated Absorbance
Measured Absorbance
Measured Absorbance
-
-
0 06
0 06 20
40 Time
Figure
5-12:
Epoxidation
20
of
calorimetric and infrared data
40 Time
[mm]
2,5-di-tert-butyl-1,4-benzoquinone. (evaluation
at each
temperature is shown. Only
reaction
spectrum is shown.
data set
one
wave
140
I).
A
mean
number
60
Combined
evaluation
value of all reaction
(1687
cm"1,
see
80
[mm]
of the
experiments
Figure E-12)
of the
5.4
The
combined
well
as
30 and 36
temperature (17, 24,
and k2 at the four different 5-13.
First
evaluation
of all did
it
infrared
in
evaluation. for the
significantly higher
proper reaction model
the
independently
lay
values
However the
carried
were
for
out
each
determined rate constants k} an
separate for k}
Arrhenius
as
well
and
as
deviations
plot
in
the
combined
Figure
k2. The independently
line for the combined
straight
on a
2,5-di-tert-butyl-1,4-benzoquinone
in
plotted
are
same
separate
was
The
clear that the
determined k} and k2 values all
separate
°C).
of
evaluations
separate
temperatures
becomes result
not
the
as
Epoxidation
from
the
as
well
line
straight
the
as
are
calorimetric evaluation. This fact indicates that
chosen but that the
separate
calorimetric evaluation
a
was
difficult.
-0.5 -£2 "ö E
-1 -1.5 -2
-v
¥ -2.5 3
3.25
3.3
3.35
3.4
3.45
3.5 x10"'
-tf)
Calorimetric Data
"Ö E
Infrared Data
only
only
Combined Evaluation -v
""if -4 3.2
3.25
3.3
3.35
5-13:
Figure
constants
of
Epoxidation
3.5 x10"'
2,5-di-tert-butyl-1,4-benzoquinone.
by
the
separate
(compare
three
to the
and
columns)
evaluation
(7th
compared
column,
for details
well
as
calorimetric and infrared data
to
see
Chapter 5.4.3).
thermodynamic
as
well
as
as
Arrhenius
plot
of the two rate
corresponding
see
Appendix
In the last column kinetic reaction
the combined evaluation of the
Figure 4-5)
overall evaluation of all measurements at all
details
3.45
k, and k2 determined by the separate and combined evaluations.
The results obtained
an
3.4
[1/K]
l/T
141
listed in Table 5-5
results of the
(first
classical, separate
E.3.4 and Table
E-12) as well as to temperatures (4th to 6th column, for
only
links to literature references for the
parameters
reference data is bad.
are
are
listed
as
the
quality
of the
5
Applications
Table 5-5:
and Results
Epoxidation
combined evaluations classic evaluation
kj I k2
are
are
listed in the
of
2,5-di-tert-butyl-1,4-benzoquinone.
(data
also listed same
data
sets
evaluated evaluated
evaluated.
were
separately
on
was
carried out
ArH
or
directly
identified
at 30°C and the activation
determined
mean
Comb.
5)
values.6)
value overall
Cal.
and
-150 2)
[kJ/mol]
-270
-290
-190
-370 1)
-360 1)
-340 1)
ArH 25 °C
-140
-180
-150 2)
[kJ/mol]
-210
ArH2.2)
All
1)
on
-260
-200
[kJ/mol]
-180
-140
-150
Sum
over
all
but still both
temperatures
are
temperatures.
8)
function at the Number of hits
maximum 10.
Eval.
4)
Cal. Eval.
-
Cal.
IR 4)
Eval.
-
4)
-
Ref.
Classic -
-
-440±50 -
-
-
-
-
400 1)
-440±20
2)
-
-
-
-350 1)
-
-
-480±30
-190
-290
-2002)
[kJ/mol]
-170
-130
-150
-360 1)
-410 1)
-350 1)
ArH5)
-150 ±40
-200±100
-170±30
-160
-240
-180
[kJ/mol]
-210 ±50
-190±70
-170±20
-200
-150
-170
-360 ± 10
-390±20
-350 ± 4
-360
-390
-350
EA
34
6
50
60
61
53
[kJ/mol]
72
17
72
70
76
73
k17°C
0.21
0.28
0.13
0.13 6)
0.09 6)
0.136)
[l/mol/s]
0.030
0.032
0.035
0.033
0.015
0.035
k24°C
0.27
0.21
0.24
0.24 6)
0.16 6)
0.22 6)
[l/mol/s]
0.062
0.045
0.068
0.065
0.031
0.071
K30°C
0.37
0.25
0.33
0.38
0.25
0.34
[l/mol/s]
0.121
0.051
0.139
0.155
-
-
-
-
-
-440±10
8)
0.057 8)
0.51 6)
0.49
0.33
0.47
0.61
[l/mol/s]
0.179
0.049
0.210
0.196
0.103
0.222
AQ7)[W>]
125
86
168
201
173
294
2.541
2.637
2.527
2.529
2.685
2.528
4.25
7
3.25
8
10
6
142
0.41
-
-450±10 -
-
-
-
-
E.3.4 E.3.6
E.3.6
-
E.3.6
0.127
k36°C
8)[-]
separate
are
error
ArH 36 °C
#Hits
as
the rate constants determined
-340 1)
-180
7)[-]
The
well
measurements
all
at
as
-190
-200
ArH 30 °C
AA
EA>11 EA>2
values of the evaluations at the different
Comb. 3)
-70
-
identified.
3>
Calorimetric and infrared
IR
-100
I ArH2
Equation (4-16)
measurements
temperatures),
ArH 17 °C
-360 1)
7)
(4-6)).
Eval.
-370
be
0 in
=
separate and
The main results from the
Sum of ArH] and
Calculated based
Eval.3)
-350
All
Average
Eval.3)
1)
still
4>
energies EA1/EA>2.
optimum (Equations (4-8)
(see Chapter4.3.2,
1)
by setting SQ
can
temperature.
(5-5).
Appendix E.3.4). ArH,
see
top of each other.
simultaneously (Chapter 5.4.3).
temperatures
reaction model
on
details
Therefore
each
at
(for
field
evaluation of the infrared data
based
I)
set
Final results of the
-
-
-
-
-
-
-
-
5.4
Table 5-5 first of all shows that the reaction and the
separate
all
evaluations
disagree.
The
plot Figure
5-13. The
only
the
are
of ArHj
sums
2,5-di-tert-butyl-1,4-benzoquinone
identified
parameters
evaluations
from the Arrhenius
of
Epoxidation
conclusion
same
the combined
by
values in Table 5-5 that
and ArH2.
and
EAJ
EA,2
drawn
already
was
similar for
are
similar for the
are
combined and the infrared evaluation but differ to the calorimetric evaluation. The activation
energies
physically
unreasonable.
Also
calculated
based
to all evaluations
common
is
increasing ArH2 (less exothermal) reaction The
enthalpies
are
show the
in the range of 100% for be
can
a
physical
chemical
or
Another doubtful result is the
explanation
the
at
epoxidation
In the second
EA,2.
the
From
a
of the
As mentioned the
a
energies
comparison
of view this is
be
cannot be
bigger.
about
quite surprising.
In the
has to be broken.
has to be
broken, but
However such
a
large
expected.
to literature data turned out to
not observed.
was
and
only
difficult. The
quite
hard fact that could be extracted from the literature data is that the
EA,i and EA,2
energies EA,i
benzoquinone system
probably
No
for this behavior.
conjugated system
will
19 K.
only
temperatures
calorimetric evaluation is
as
point
smaller
epoxidation
difference of the activation
well
of the whole
epoxidation only
hindering
as
mechanistic
conjugation
given
of the
calorimetric evaluation.
difference of the two activation
large
EA,2- Ea,i obtained by the combined half of the size of
be
all
an
calorimetric
separate over
are
and
changes
increase of
temperature
separate
can
The
temperature.
observed
standard deviations for the
highest
the steric
function of
Therefore the average values of ArHj and ArH2
reasonable
first
calorimetric evaluation
separate
decreasing ArH} (more exothermal)
a
as a
largest temperature change
evaluation.
the
on
large
For details and literature references
only
difference of
see
Appendix
E.3.6.
The
large temperature change
energies EA,i
and
Figure 5-13,
deviations from the
EA,2
as
well
of ArH}
as
calorimetric evaluation
separate
and ArH2,
the bad
quality
straight line) are
less
the
unrealistic small activation
of the Arrhenius
hints that the results from the
are
reliable
regression (see
compared
to
the
infrared
and
combined evaluation.
In
5-14
Figure
(first
and
(4-6))
the
experiments
values
model-fit
highest
at different
for each
given
error
for the
AA
the
separate
are
given
error
temperature.
functions AA and
step (compare
temperatures
found for the
was
were
evaluated
As would be
separate
to
error
AQ.
The
sums
in Table 5-5.
143
AQ (Equations (4-8)
Figure 4-5).
As mentioned
separately,
therefore the
expected
the lowest infrared
evaluation of the infrared
evaluation of the calorimetric data. The
is found for the model-fit
temperatures
plot)
shown for each evaluation
are
are
and second
of
AQ
and AA
analogous
over
data, the behavior
all measurement
5
Applications
and Results
As all evaluations
were
of the identification solutions found E-15. It
can
followed
by
carried out
can
be measured
(see 4.3.2).
each
The
be concluded that the
automatically and
is
given
are
separate
point
calorimetric evaluation
separate
of view. The
scaling
plot
and best of
most
was
Figure robust,
evaluation of the infrared data
mean
value
over
the evaluations at
factors Sm and
shown in the last two
100
SQ (see 4.5, Equations (4-16) plots of Figure E-15.
to
Cal-Eval
ill
IR-Eval
CN~~'
Ë
equal
in Table 5-5.
calculated
Figure 4-5)
values, the quality
the number of
by counting
the combined evaluation. The
temperature
(4-20)
ten different random start
This "number of hits" is shown in the third
most difficult from that
was
using
Comb-Eval 1
50
Comb-Eval 2
17
24
30
36
24
30
36
JIOL
^
17 10
5
X
i^
!
'4
17
É.
ni
hfcnn
3D
36
0.5
I
Ol
to
I 17
I 24
,__
X
30
36
400
E
200
to ^m
17
'
LH
24
i
MB
MB
30
36
Temperature [°C]
Figure error
5-14:
Epoxidation
functions AA and
of
2,5-di-tert-butyl-1,4-benzoquinone.
First and
AQ. Third plot: Number of hits (maximum 10). Last
(see Equation (4-16).
144
second two
plot:
plots: SIR
Final an
Se
5.4
The
discussion
of
the
different
Epoxidation
evaluations
is
of
summarized
combined evaluation is the most reliable but still leads to Table 5-6:
Epoxidation
of
2,5-di-tert-butyl-1,4-benzoquinone
some
2,5-di-tert-butyl-1,4-benzoquinone. Summary
in
Table
5-6.
The
unreasonable results. of the discussion of the
different evaluations.
Combined
Calorimetric
Infrared
Evaluation
Evaluation
Evaluation
Robustness
Medium
Best
Worst
(see Figure 5-14) Arrhenius
plot kt
Best
Worst
Medium
Arrhenius
plot k2
Best
Worst
Best
medium
largest
smallest
Temperature change of ArHj and ArH2 Activation
EAil
and
energies
chemical
Chapter
spectroscopic
4.2 the determination of the pure
is not the focus the
component
reaction
therefore
are
prior
information about the pure
spectra pure
concentration
is
B.2).
as
in
spectra.
matrix
Equation (4-1), identified
matrix
Ccaic
equal
spectra
Table
It
this
(calculated
is
to five. Therefore
a
(5-3))
these linear
It is
reaction
parameters (klt k2, ArHj chemical and
Chapter
flow sheet shown in
1.
Testing
2.
Applying
a
they
and
surprising the
to
bounds of
extract
physically
the
as
reaction
are
were
linear
model
be
of
(5-3),
spectra
the see
could be
dependent (see Appendix
assumed
can
rank
(all components
seen
in the
in the calculated pure
do not influence the estimation of the other
ArH2)
as
they
have
no
effect
on
the size of A4.
Figure
plausible reaction parameters. According to the
4-3 two modifications of the evaluation
following Chapters:
different reaction model. See
more
possible
E-15. No
(see
maximum of five pure
profiles
during
physical knowledge it must be concluded that the evaluation
did not reveal
will be discussed in the
on
dependencies
to note that
important
not
not
based
However,
Appendix Figure
used for all evaluations was
of the involved
have to be identified
shown in the
was
5-4).
However
spectra.
shown in this
are
spectra
of the calculation. The calculated
product
eight absorbing components
reaction model
on
only)
all the other concentration
Because
Based
side
a
evaluation
spectra (combined
meaningful
most reasonable
evaluation method.
presented
parameters (see Figure 4-2)
pure
pure
difference and
very small values
the evaluation and
the
large
EA>2
As mentioned in
these
difference
large
Chapter 5.4.2.
physical constraints. See Chapter 5.4.3.
145
are
possible and
5
Applications
5.4.2
and Results
Testing different
As discussed in
Chapter
reaction
(5-5),
model
reaction models
5.4.1 the evaluation of the measured
did
of ArH} and ArH2
dependency
lead
not
well
as
reasonable
to
large
as
results
difference of
data, based
on
the
(large temperature
EAJ and EA:2). A possible
reason
could be that the reaction model is not correct. Therefore different reaction
models
were
Chapter
tested, using the
same
evaluation method and
5.4.1. The aim is to show that it is
reaction models but also to
see
possible
to
settings
distinguish
as
described in
between different
whether another reaction model suits better into the
measured data.
The
reaction
formulation
models
of the
corresponding pure
spectra
parameters
basically equal
are
two
reaction
reaction model
matrix E
given
are
rates
purpose
as
a
concentration of
The models
E-9 and Table
strange
In order to
tert-butyl hydroperoxide decreased concentration were
thus evaluated
E-9
and
Table
different
that have to be identified
models
the
and
the
additionally
applied
tert-butyl hydroperoxide
concentration
evaluated based
E-10).
The
in
to the
for the reaction
in Table 5-7. It should be noted that for the reaction model 9
tert-butyl hydroperoxide
were
r2.
differ
(5-5) they only
shown in Table 5-8. The bounds
are
the lower bound of the reaction order of on
and
r}
parameters
model
to
a
three
on
get
more
dependency
(see
that
discussion
measurements at 30 °C
includes
rates to the
below).
(see Appendix
Table
informations about the reaction order of
more
tert-butyl hydroperoxide (see
on
set to -3. This is
of the reaction
the evaluation data set I
second time based
E-10)
observed
was
was
on
were
Table
carried out with
E-9).
the evaluation data set II
these
three
measurements
The models
(see at
Table
different
concentrations.
Table 5-7: All reaction
equal
parameters defined in Table 5-8 and their bounds. The bounds
were
for the evaluation data set I and II.
Rate constant k Reaction orders Reaction order
Absorption
Spectrum
A
temperature
or
kj and k2 [...] (at each temperature).
ordc, ordcl, ordC2 [-] (at
each
temperature)
ordP [-] (at each temperature)
coefficients and for all new
Heat of reaction
at
eight
absorption
ArH
or
each
wave
chemical
coefficients
number
of
the
reaction
components [-]. (For were
Upper
bound
bound
1
3
-3
3
5
-1000
each
calculated.)
ArHi and ArH2 [kJ/mol] (at each temperature).
146
Lower
5.4
Table 5-8:
Different reaction models that
that have to be identified
listed
are
for the calculations shown in
'
"
'
CEd
(7)a) 2
CEd
(8)a)
^
'
^
'
'
(5)a) 4
K
'
(6)a) 5
the
right
a>
side.
CCat
'
CEd
'
CEd
'
CCat
CCat
CPeroxide
'
n
•
n
•
C
C
'
mEpoxide
'
mEpoxide
C
(1)a)
'
""I
'
6
(2)a) 7
(3)a) 8
(4)a) 9
(11)a)
j
""I
'
7
"1
'
CEd
'
CEd
'
CEd
'
CEd
'
CCat
'
CPeroxide
'
CEd
'
n
ordç
C
CCat
C
•
^2
ordc CCat
CmEpoxide
'
2
j
CCat
'
Cat
'
C
'
mEpoxide
CmEpoxide
'
'
K
ordp CPeroxide
'
C
'
2
'
mEpoxide
C
C
'
2
'
mEpoxide
(9)a)
ordC,\
"Î
'
CEd
'
C
11
ordC,\
i
(10)a)
""I
'
CEd
'
'
CCat
•
'
k
CPeroxide
c
•
^mEpoxide
C
ordn '
2
c
•
mEpoxide
Reaction
Const.
Enthalpies
Orders
k
ArH
k
ArH
k
ArHj, ArH2
-
k
ArH], ArH2
-
ki, k2
ArHj, ArH2
-
ki, k2
ArH], ArH2
-
ki, k2
ArHj, ArH2
ordc
ki, k2
ArH], ArH2
ordc
ki, k2
ArH], ArH2
ordc
-
Peroxide
c
Peroxide
ord p
ordn '
Cat
c
Peroxide
ordp ki, k2
9
ArHj, ArH2
ordc.x
c
^
Cat
ordc.i ki, k2
ordr •
C
Cat
ordr
k n2
CCat
'
Cat
ord^,
10 7
Reaction
CCat
-,
K
Rate
Peroxide
CCat
j
CPeroxide
'
ord„
,
"1
^2
CCat
parameters Model used
Cat
b)
"1
b>
5.4.1 and 5.4.3.
CPeroxide
'
identical to
are
Internal model number.
CCat
'
2,5-di-tert-butyl-1,4-benzoquinone
tested. The reaction models
were
r2
"
K
on
Chapters
ri
1
of
for the definition of the reaction rates /•/ and r2. The reaction
Equation (5-5) except
3
Epoxidation
c
ArH], ArH2
ordc.i
-,
•
Cat
p
ordc,2
Peroxide
In order to be able to discriminate between different reaction models the described in
indicators). objective
Chapter
function AComb
model
parameters has to be
was
However it is not
Equations (4-18) reaction
4.3.2
are
judged
(Equations (4-6)
and
applied (quality
possible
to compare the models based
(Equation (4-16))
(4-17)) depend
parameters (0i..Np).
on
As
as
the
shown
the
and
on
in
Table
5-8
the
quality
147
as
the combined
of the
sensitivity analysis
the unsealed calorimetric and infrared fit
(4-8)).
on
factors Sm and
scaling
different for different models. Therefore the based
concept
and robustness of the model fit
SQ (see unknown
reaction
model
of the model fit
errors
AQ
and AA
5
Applications
The
and Results
results
of the
combined
evaluation data sets I and II between 0...
(only
1). Only
evaluation
are
shown in
the results at 30 °C
evaluation data set
I)
are
(infrared Figure
are
and
5-15
calorimetric
(AQ
and AA
shown. The results at
of the
data)
normalized
are
17, 24 and 36 °C
similar.
10u < CD
lu"1
111
N
"ÖJ E
lu"2
i_
o c
lu"3
A 1
il
±
H
n
1{1} 2{1} 3{1} 4{1} 5{2} 6{2} 7{3} 8{3} 9{4} 10{4}11{4}
10° <
Data Set 1
lu"1
Data Set 2
CD N
"ÖJ E i_
o
io-2
Willi
10"3
c
IO"4
1{1} 2{1} 3{1} 4{1} 5{2} 6{2} 7{3} 8{3} 9{4} 10{4}11{4} 10
tn
-
%
ifl
0L
n,
n.
n
nl
1{1} 2{1} 3{1} 4{1} 5{2} 6{2} 7{3} 8{3} 9{4} 10{4}11{4} Model Number
Figure
5-15:
Epoxidation
evaluation of the and AA
are
Based
on
Parameters}
2,5-di-tert-butyl-1,4-benzoquinone.
Results
data set I and
II)
of
the
combined
at 30 °C. The minimal
plot.
only
a
few model errors
identify (number
AQ
parameters (0j Np) and AA
of hits
<
2)
are
high.
is
generally
robust
Models with four
but show small
AQ
(number
of hits
parameters
identification
was
Although
robust
(number
the reaction
of hits
order, that
influence the reaction measurement constant after
dosing)
was
during
it influences the
5)
>
148
additionally
the
quality
and the
>
were
and AA.
The best model for evaluation data set I would therefore be model number 7
small.
AQ
the results of evaluation data set I it becomes clear that the identification of
but the model-fit
difficult to
of Model
epoxidation experiments (evaluation
not visible in the
models with
5)
of
{Number
errors
AQ
and AA
fitted in model
dosing phase (catalyst
of the model fit.
as
are
the
both
7, does only concentration
5.4
It should be noted that model 7 is not the number
5)
model 7
are
«T
IL
-0.5
Chapters
and used in
shown in the
Figure
Epoxidation
of
2,5-di-tert-butyl-1,4-benzoquinone
suggested by
one
the literature
(model
5.4.1 and 5.4.3. Further results of the evaluation of 5-16 and Table 5-9.
o
I
-1
.£
-1.5 -2
^
^
-2.5 3
3.25
3.3
3.35
3.4
3.45
3.5 x10
3
«T
^
-1
O
E
i:
a
Calorimetric Data
Infrared Data
•
Combined Evaluation
only
only
-2
-^
""if
-4 3
3.25
3.3
3.35
5-16:
Epoxidation
constants determined measurements
by
of
the
(evaluation
combined)
Arrhenius
plot
of
the
rate
calorimetric, infrared and combined evaluation of the epoxidation
data set
I, reaction model 7). one
and does not show
Similar to the results shown in same
3.5 x10"'
2,5-di-tert-butyl-1,4-benzoquinone.
The reaction order identified is close to infrared and
3.45
[1/K]
l/T
Figure
3.4
a
(calorimetric,
significant temperature dependency.
Chapter 5.4.1,
values for all the other reaction
for all three evaluations
the three evaluations do not
parameters.
The
give
the
temperature dependency
of
ArHj and ArH2 remains and is largest for the separate calorimetric evaluation. The difference
of the
activation
energy
EAJ
and
EAi2
is
decreased
but
is
still
in
an
unreasonable range. It should be noted that the
separate
the "number of hits" is close to calorimetric evaluation
It
was
was
one
evaluation of the infrared data
(see
Table
5-9). Similar
was
to 5.4.1
unstable
the
as
separate
the most robust.
concluded that the combined evaluation of reaction model 7 is the most
reliable but still leads to shown in
Figure
constraints
some
unreasonable results.
4-3 the calculation should be
(see Chapter 5.4.3)
149
According to the flow sheet
repeated applying
more
physical
5
Applications
Table 5-9:
and Results
Epoxidation
combined evaluations well
as
kj I k2
evaluated.
infrared data.
3>
(evaluation
was
data set field
same
carried out
Therefore ArH
can
All measurements
I)
on
based
also
be
=
temperatures.6)
optimum (Equations (4-8)
(see Chapter4.3.2,
mean
0 in
and
value overall
1)
7)
(4-6)).
ArH2, EA>11 EA>2
the
at each
temperature. on
5)
Average
Calorimetric and infrared
error
function at
temperatures.8) Number of maximum 10.9) [(l/mol)ord-c/s]
Sum of
over
all
Calorimetric
Infrared
Evaluation3)
Evaluation3)
Evaluation3)
-110
-370
-80
-370
-150 2)
[kJ/mol]
-140
V
-280
V
-190
ArH25°C
-140
-350
-170
-370
-160 2)
[kJ/mol]
-210
V
-200
V
-180
ArH30°C
-170
-360
-240
-380
-200 2)
[kJ/mol]
-180
V
-140
V
-150
ArH36°C
-180
-360
-260
-400
-210 2)
[kJ/mol]
-180
V
-130
V
-140
ArH5)
-150 ±30
-360
-190±80
-380
-180±30
-350
[kJ/mol]
-210 ±30
±10
-190±70
±10
-160±20
±3
75
38
44
100
56
66
0.12
0.2
0.24
0.021
0.025
0.065
0.31
0.25
0.44
0.070
0.051
0.123
0.48
0.33
0.39
0.151
0.079
0.161
0.83
0.53
0.89
0.265
0.103
0.386
ordc17°C[-J
0.88
0.93
1.21
ordc24°C[-]
1.04
1.03
1.20
ordc30°C[-J
1.08
1.06
1.05
ordc36°C[-J
1.14
1.12
1.20
k17°C
[...]9) k24°C
[:.]9) k30°C
[:.]9) k36°C
[:.]9)
ordc5)H AQ7>[W*] AA 7)[-J # Hits
8)[-J
1.0
+
0.1
1.0
+
0.1
1.2
+
0.1
89
61
183
2.53
2.60
2.53
7
9.5
1.5
150
The
the rate constant
ArH 17°C
[kJ/mol]
as
separate evaluation of the
Combined
EA
2)
but still both data sets
Calculated based
temperatures),
separate and
Sum of ArHj and ArH2.
Equation (4-16)
separately
determined at 30°C and the activation energy EA.
hits
reaction model 7. ArH, I
identified from
evaluated
are
on
top of each other.
by setting SQ
values of the evaluations at the different
the determined
Final results of the
2,5-di-tert-butyl-1,4-benzoquinone.
listed in the
are
separate evaluation were
of
-340 1>
-340 1)
-350 1)
-350 1)
5.4
The
results
of
the
evaluation
measurements with
set
lower concentration
II
(only
of tert
This is reasonable
(see Figure 5-15).
order to estimate the reaction
Comparing of
data
of
the model-fit
°C,
30
at
including
compared
show that
to evaluation data
information is
more
three
now
present
AQ
and AA of the models
not included in the reaction
1, 3, 5, 7, 10 (concentration
model)
to the models
2, 4, 6,
8, 11 (concentration of tert-butyl hydroperoxide included in the reaction model
first-order)
it is obvious that the latter group shows
explained
by
the
concentration of
fact
that
Model 9 is very robust
AQ (therefore are
the
actually
tert-butyl hydroperoxide
The model selection based
shown in Table 5-10.
tert-butyl hydroperoxide
reaction
of hits
Figure 5-15).
According
carried out
reaction
from
sense
for
5-17:
In
fast
a
Assuming
that at
concluded
that
a
reaction
catalyst
model, that also
was
respect
to the total on
the
a
active
TntonB
__*?-
is
concentration. Such
of the
new
Figure
evaluation
© +TntonB-H
o
151
o
epoxidation
be
agent
reaction.
a
negative reaction
algorithm,
[Moore 67], [House 72].
5-17: Guess fora modified reaction model for the
can
is decreased due to
Y O-o© o
it
the observed and identified
application
more
deprotonated.
epoxidation
hydroperoxide
hydroperoxide
^V-°-0ß
A
situation, is given in
Hydroperoxide_dep
+
empirical
reaction.
hydroperoxide
the
explain
mechanistic considerations
Hydroperoxide
>v-0~CrH
of
the
reaction order does
nearly completely protonated
increases if the amount of
found based
supported by
is
concentration
the total volume decrease. This would reaction order with
the
negative
(ordP) represent
epoxidation
to describe such
preliminary equilibrium
the
the
hydroperoxide proceeded
negative
a
The
of view and indicates that the
model, able
the
less
using
describe the
accurately
equilibrium
(Hydroperoxidejdep)
point
negative.
concentration
However
experiments.
mechanistic
model 9 does not
appropriate guess Figure
experiments a
when
above, the reaction order of the
identified to be
was
fact that the reaction
not make
increasing
be
only
Further results of the evaluation of model 9
to the discussion
concentration
to the other
can
and shows the lowest AA and the lowest
10)
=
hydroperoxide
compared
is
rate
This
quality.
is decreased.
reaction orders determined for the
faster
fit
worse
as
evaluation data set II is trivial: The identification of
on
(number
not visible in
in
parameters.
error
tert-butyl hydroperoxide
as
2,5-di-tert-butyl-1,4-benzoquinone
butyl hydroperoxide)
-
the robustness of the identification increases
generally set I
of
Epoxidation
is
5
and Results
Applications
it should
Again
unstable
be
noted
the "number of hits"
as
concentration
determined
reaction model 7. The
mechanistic
is
evaluation of the
separate
is
close
only
to
and
one
evaluation
(see
infrared
data
The reaction order of the
one.
thus
similar to the
difference of the reaction
large
calorimetric
separate
that the
Table
enthalpies is
5-10)
was
catalyst
evaluation
identified
unreasonable
of
by
the
based
on
considerations, whereas the combined evaluation results in the
most
reasonable values.
Finally it tool to
can
be concluded that the
proposed evaluation algorithm is also
much
more
For
comprehensive analysis,
be
II
clearly showed that the reaction mechanism is
complex than suggested by any of the chosen empirical reaction models.
required. However it
was
measurements at different concentrations would
more
possible to establish
the evaluation results that resembles the
Care should be taken if any kinetic
conditions,
Table 5-10:
The sets
as
Epoxidation
well
as
separate were
infrared
estimated
kj I k2
of
(data
are
evaluation
5)
set
parameters, determined at different concentration
II, only 30°C) based
listed in the was
Average
value.
7)
and
(Equations (4-8)
same
carried out
Final results of the
can
field
on
reaction model 9
on
1)
top of each other.
by setting SQ
=
0 in
Calorimetric
(4-6)).8)
and
infrared
Number of hits
function
error
(see
(see Chapter 4.3.2),
at
separate and
Table
temperatures
the
maximum 10.
Evaluation
Evaluation
Evaluation
Artii, Arti2, 2jArHi
-180
-240
-200 2)
[kJ/mol]
-180
-140
-140
k
-340 1)
0.61
0.42
0.66
[(l/mol)(ord-c ord-P)/s]
0.185
0.097
0.260
ordc [-]
1.13
1.12
1.20
ordp [-]
-0.16
-0.15
-0.18
AQ7)\W2]
58
45
104
AA^l-]
0.284
0.326
0.282
10
10
1
+
8)[-]
or
determined
Infrared
380 1)
ArH2.2)
separate evaluation of the
Calorimetric
-
I
but still both data
Combined
-360 1)
5-8). ArH,
Sum of ArHj and
Equation (4-16)
also be identified from the
values of the evaluations at the different
30 °C
# Hits
on
reported mechanism of the reaction.
2,5-di-tert-butyl-1,4-benzoquinone.
evaluated. Therefore ArH
data.
reaction model, based
a new
compared to each other (compare to Appendix E.3.6).
are
combined evaluations
ArH2
valuable
distinguish between different reaction models. However for this reaction
example the evaluation of data set a
a
directly
optimum
5.4
5.4.3 Simultaneous evaluation of all
Chapter
As discussed in reaction model
5.4.2), ArH2
well
as
on
well
as
as
in
different
EAi2). According
in such
Figure 4-3,
Chapter
4.4.3 it is
in
temperatures
Chapter
situation
a
data, based
to the
the
(see Chapter of ArH} and evaluation
general
constraints
physical
more
on
is therefore to check weather it is still the additional
using
possible
single step.
one
Table E-9 and Table
(Appendix
physical
constraint that
to evaluate several measurements at
This
E-10, all
set of reaction
one
done
was
the evaluation data
using
measurements at all
temperatures).
temperature (see Chapters
contrast to the individual evaluation at each
5.4.2) only
temperatures
ArH2 should be constant in the temperature range of 17 to 36 °C.
in
explained
at all
(large temperature dependency
and
EAJ
The aim of this
applied.
experiments
any other tested reaction modes
to model the measured data
possible
set I
as
difference of
large
as
presented
should be
As
well
as
2,5-di-tert-butyl-1,4-benzoquinone
5.4.1 the evaluation of the measured
did not lead to reasonable results
flow sheet
ArHi
(5-5)
of
Epoxidation
and
enthalpies (ArH}
ArH2)
for all
5.4.1
temperatures
In
and
has to
be identified.
The pure
assumed to be to
attempt an
use
eight
the
model
temperatures
was
chosen
replaced by
the
Arrhenius
identified
as
of the chemical
was
Table 5-11: All reaction
used
still
were
identified. An
temperatures
failed. This is
components
This
for
(Equation (5-5), 5.4.1).
the
the
not
was
involved case
in this for
algorithm
are
individual
evaluation
the
of
The rate constants kj and k2
The
Equation (4-5).
the combined evaluation
by
E for all
were
anhydride (see Figure 5-7).
reaction
same
spectra
temperature depending.
are
of acetic
spectra
components (matrix E)
and thus four sets of E
matrix of pure
same
example
hydrolysis
involved chemical
temperature depending
indication that the pure
reaction
The
of the
spectra
reaction
parameters
that
all
were were
summarized in Table 5-11.
parameters (with bounds) required for the evaluation of the epoxidation
measurements.
Rate constant
kj
and
Activation energy
EA,i
at 30 °C
and
coefficients
Absorption
Spectrum
k2
[l/(mols)]
EA,2 [kJ/mol] at
each
wave
A and for all three chemical
temperature
new
Heat of reaction
absorption
ArHi
and
coefficients
5-18.
They
evaluation of each
are
of
the
reaction
components [-]. (For were
compared
are
shown in Table 5-5
to the results obtained
temperature (Chapter
5.4.1
153
Upper
bound
bound
1
10
150
5
-1000
each
calculated.)
ArH2 [kJ/mol]
The results of the overall evaluation
Figure
number
Lower
).
by
(shaded
in
gray)
and in
the individual combined
5
Applications
Generally quality
it
and Results
can
of the
functions
AA
evaluation for
be concluded that the overall evaluation model
and
fit
is
still
but
especially AQ
are
single temperatures (see
the
differences
evaluations of the
are
However the
both
increased
Table
5-5). infrared and
(calorimetric,
much
smaller
compared
compared
as
to
the
individual
combined) to
error
the
are
still
individual
temperatures.
In contrast to the results obtained in
EAJ and EAi2 determined to
successful and that the
satisfying (see Figure 5-19).
The results of the three evaluations different
was
are
Chapters
5.4.1 and 5.4.2 the activation
all reasonable and in
a
energies
relatively small range (compare
Figure 5-18). ——
0 w
^
-0-5
[-
Calorimetric Data
only (all Temperatures) only (all Temperatures) Combined Evaluation (all Temperatures) Combined Evaluaiton (for each Temperature) Infrared Data
,
r^^--«^
•
c -^
-1.5 -2
-2.5L 3.2
3.45
3.5 x10"'
CO
"Ö E
-v
^g 3.2
3.25
3.3
3.35 1/T
Figure
5-18:
constants
Epoxidation
and
activation
of
3.45
[1/K]
energies
determined
by
the
by
plot
of
the
set
rate
I, reaction model 5, Equation
the combined evaluation of each
temperature is shown (reaction model 5, Chapter 5.4.1).
154
Arrhenius
3
calorimetric, infrared and combined
temperatures (data
the rate constants determined
3.5 x10
2,5-di-tert-butyl-1,4-benzoquinone.
evaluation of the measurements at all
(5-5)). Additionally
3.4
single
5.4
Combined Evaluation
*
Epoxidation
of
2,5-di-tert-butyl-1,4-benzoquinone
Combined Evaluation
(17°C)
(24°C)
2
40
20
60
80
100
120
14C
10C
0 1 Simulated Absorbance
Simulated Absorbance
Measured Absorbance
Measured Absorbance
8
0 08
»
0 08
0 06
0 04 20
40
60 Time
80
100
120
14C
40
[mm]
60
Time
Combined Evaluation
(30°C)
10C
[mm]
Combined Evaluation
(36°C)
15 Simulated q A
10
20
Simulated q
tc
Measured q
A
15
to
Measured q
S 10 *
5
-
5
0 60
80
ArftfftTÉ%fa**faMAMfcA
0 12
20
40
Simulated Absorbance
Measured Absorbance
Measured Absorbance
g
0 1
^0 08
0 1
^0 08
-
0 06
0 06 20 Time
Figure
5-19:
calorimetric
Epoxidation and
of
2,5-di-tert-butyl-1,4-benzoquinone. data.
set
All
experiments
I, reaction model 7). A
temperature is shown. Only
the reaction
40 Time
[mm]
infrared
simultaneously (evaluation each
80
0 12 Simulated Absorbance
g
60
one wave
number
spectrum is shown.
155
at mean
(1687
all
60
[mm]
Combined
temperatures
evaluation were
value of all reaction
cm"1,
see
of the
evaluated
experiments
at
Appendix Figure E-12)
of
5
Applications
and Results
The reaction
evaluations. The
largest
calorimetric evaluation and
(40 kJ/mol) on
and ArH2 still differ
enthalpies ArHi
a
difference of ArHj and ArH2
(90 kJ/mol),
mechanistic considerations such
formation
of the
different
large
mechanical calculations involved
Hamiltonians
compounds. Cache
(AM1,
PM3,
The
large
difference
Based
(10 kJ/mol).
argued. Semi-
be
cannot
HyperChem
out to be
slightly
well
In
most
of
also
of
EA>1
and
EA>2 (20 kJ/mol) suggested by
evaluation is unreasonable
The robustness of all three evaluations The calorimetric evaluation is
5).
reliable
can
contain any
*>
Table
is
5-5)
(number
of hits
=
in
given
Appendix
quite high (number
(number
of hits
physically
or
was
robust
[Zogg
=
large
infrared
separate
10)
E.3.6.
of hits
>
and the
6).
be concluded that the results of the combined evaluation
the identification
as
(see
the most robust
again
infrared evaluation the less robust
Finally it
the literature data
considering
the
the
calorimetric
separate
evaluation of ArH1 and ArH2 is thus unreasonable. On the other hand the difference
four
as
exothermal than
more
significant (see the
suggested by
as
used.
were
However the estimated difference is not
submitted]).
al 03,
et.
step.
and
MNDO)
PM5,
separate
carried out to estimate the heat of
were
calculations, the first epoxidation step turned the second
difference
the
by
the combined evaluation
by
the infrared evaluation
by
a
between the different
obtained
was
medium difference
a
very small difference
empirical quantum
significantly
(number of hits
=
8) and
as
are
most
they do not
chemically unreasonable information:
Difference of ArH} and ArH2 is
only
25 %
EAJ ~EAi2 (17 % difference). The obtained
thermodynamic and kinetic reaction parameters
reference values
reported
in literature
Thus the introduction of the
(Chapters
It
5.4.1
unreasonable unreasonable
This
can
to
in
large difference ofEAJ and EAi2
on
chemical and
et.
a
al. 03,
of
ArHj
were
critical
were
and
temperature,
was
too
high and therefore
ArH2
as
well
as
an
obtained.
analysis of the obtained reaction
physical knowledge
will
always be necessary.
might lead to misinterpretation of the final results.
analysis is also indicated
4-3. A third evaluation
[Zogg
function of the reaction
dependencies
Otherwise mathematical artifacts
Figure
as a
5.4.2) the degrees of freedom
example further shows that
This critical
E.3.6).
be concluded that in both evaluations without this constraint
temperature
parameters based
E.3.4 and
quite close to
additionally physical constraint, that the heats of reaction
(ArHj and ArH2) should be constant successful.
(see Appendix
are
in the
general evaluation flow sheet shown
introducing the constraint ArH}
submitted].
156
=
in
ArH2 will be presented
5.4
5.4.4
Analysis of the
Epoxidation
scaling
automatic
of
2,5-di-tert-butyl-1,4-benzoquinone
method
previous Chapters (5.3.1
The basis for all combined evaluation results shown in the and 5.3.2
well
as
this work. It
5.4.1 to
as
explained
was
5.4.3)
is the automatic
in details in
Chapter
method
scaling
4.5. The
analysis
experiments (see previous Chapters) clearly
showed that the
the
not
infrared
reaction
and the calorimetric data did
parameters.
between the two
(4-6) The
and
to
example
objective
error
of the two
error
is therefore
functions
separate
result in the
interesting
epoxidation
evaluation of
values for the
same
the
analyze
to
and
AQ(6L.Np)
of the
relationship
AA(6L.Np) (see Equations
(4-8))).
dependency
optimization was
This
developed during
done
functions is best shown
of the infrared and calorimetric data the
using
using
varying scaling
a
definition for the combined
following
the combined
by repeating objective
factor. This
function
(compare
Equation (4-16):
AComba(6lNp) a-(^4(0, Np)- AAmm)+ [AQ^ Np)-Aßmm j =
The
optimization,
based
on
the combined
for the overall evaluation of all to
Chapter
1e6
[W2].
Pareto
logarithm
of the
according
to
plots
separate
of
a-
the results of the
4-5 and
Sm/Sq (see
(a
=
lower
plot
0, AQ
using
to the upper
of
plot
reaction
energies
in this
(Equation (4-6).
model
of
=
AQmin)
are
become
and
of
AA)
are
shown in
a
5-20 shows the
Figure
oo, AA
=
AAm„)
=
as
well
as
the
indicated. Also the results of
are
scaling procedure (see Chapter 4.5,
shown. The
parameter alpha
5-20 the infrared
curve
long
as
was
calculated
as
as
error
AQ
(see Equations (4-8)
and
parameters 0}..Np (two
scaling procedure, lies
only
shows
is smaller than
(4-7)),
significant 220 W2. This
rate
is less sensitive to
constants
to the linear least squares
The solution
A4
indicates that the internal linear least squares,
A reasonable combined
W2.
(a
evaluation
the automatic
Figure
case) compared
range of 173 to 220 automatic
plot
varied from 0 to
a was
Figure 5-20).
of the Pareto
to calculate AA
infrared
separate
Equation (4-16))
asymmetric shape of the
temperatures (compare
used to carry out the combined evaluation
was
deviations form its minimal value AAmin
required
(AQ
error
carried out
was
Equation (5-6).
calorimetric
According
that
a
at all
parameter
The lower
Figure 5-20).
parameter
the combined evaluation
Figure
The
5-5).
calorimetric and infrared
remaining
plot (upper plot
In both
epoxidation experiments
5.4.3 and the results in Table
The
function AComba,
objective
and
required
two
changes
activation
to calculate
optimum should therefore show
a
AQ
AQ
in the
proposed by the combined evaluation, using the
in this
region where the changes of
significant. Form the Pareto plot it
can
scaling performs well.
157
AA start to
thus be concluded that the automatic
5
and Results
Applications
2.7 Pareto Curve
Separate Separate
2.65
t
Calorimetric Evaluation Infrared Evaluation
Combined Evlautaion 1
+
Z6
Combined Evaluation 2
2.55
160
180
200
220
240
260
280
300
10°
ö10°
160
180
200
a
Separate
+
Combined Evlautaion 1
•
Combined Evaluation 2
220
240
5-20:
curve)
calculated based
Upper plot:
Infrared on
curve
be noted that the
remaining
model-fit
A4
enthalpies, plotted
as
see a
combined evaluation
Figure
5-21
dependency
shows on
that
defined
the
the chosen
parameters identified by
a
plotted
The
plot
in
parameter
as a
of the
5-20
combined
Therefore in
the results of the
5-5)
identified
are
a
Figure
a.
optimization
separate
parameters Further it can
also
by the separate calorimetric and infrared evaluation.
158
on
AQ (Pareto
is that
AQ.
only
shows the
evaluation
5-21 an
used
was
all
is to
error as
it
identified
two reaction
Equation (5-6)
are
and the automatic
indicated.
reaction
scaling parameter
combined
error
function of
Figure
identified based
were
to Table
300
and not to minimize the model-fit
errors.
that
AQ. Again
(compare
a.
constants, two activation energies
rate
Chapter 5.4.3)
function of
curve
parameters
contains all kinds of measurement
parameters (two
increasing
However the focus
errors.
280
function of the calorimetric
a
is shown in the lower
Pareto
determine the reaction model
reaction
as
with
Equation (5-6)
for the calculation of the Pareto
It should
error
260
[W2]
AQ Figure
Calorimetric Evaluation
show
a
nonlinear
clearly shows that the
lay outside of the range
5.4
Epoxidation
of
2,5-di-tert-butyl-1,4-benzoquinone
0.4 -to
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-v
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260
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"Ag[\r Figure
5-21: Identified reaction
(Equation (5-6)),
as a
parameters,
on
function of the calorimetric
the basis of the combined error
159
AQ. Compare
to
Figure
objective 5-20.
function
6 Final Discussion and Conclusions
6 FINAL DISCUSSION AND CONCLUSIONS 6.1 New reaction calorimeter this
During
work
combined with online.
The
Chapter
small-scale
new,
standard
a
development
IR-ATR
consuming
carried
was
to
calorimeter
was
additional
measure
according
out
the
to
First of all it
Chapter
infrared
spectra
formulated
goals
is
in
3. The
applicability
be concluded that the
can
widely
are
as
well
of the calorimeter
calorimeter
is
basically
combination
of
Compensation principle,
for the
requirements
fulfilled. The calorimeter has
ml, is pressure resistant up
The
principle
as
was
little time
as
the construction is verified
by carrying
reactions, described in Chapter 5.
(see Chapter 3.2)
to 10
a
and
Power-Compensation
volume of 25 to to 200 °C.
(see Chapter
calorimeter
volume, the fast responding Power-
reactor
algorithm (see Chapter 3.6)
control
sophisticated
a
sample
bar, and temperature resistant up
small
a
a
reaction calorimeter
new
makes this reaction calorimeter well suited for measurements of fast and
Several of such reaction
exothermal reactions.
Chapter
It
developed.
should be
application
The measurement
possible.
out several test
2.1.1).
probe
of test substance and the
as
described in
The
reaction
1.2: The calorimeter should be small in volume in order to decrease the
consumption
45
a
5.2 and
Appendix E.4)
2.5 kW/l the reaction
of
the
despite
°C),
deviation of 4
measured
data
calorimeter
is
high
thermodynamic constants of the
and
reaction
new
far
by
point.
sufficient
screening.
jacket
with
basis of most conventional reaction
a
elements.
advantages
medium
By are
the
and
Peltier
introduction
of
carried out
(see
reaction powers of up to
This allows when
case
The accuracy of the for
the
in
given
on
purpose
calorimeters,
Subchapter
basically
elements this
achieved:
160
was
as
of
easy
the
reaction
new
reaction
kinetic
and
6.1.1.
that
replaced by
consists of
a
represents
an
thermostat
the
intermediate
copper block
dynamic cooling
intermediate
an
the accuracy and the time
circulating cooling liquid,
thermostat. This intermediate thermostat heat-transfer
the
to
An overview
reaction calorimeter is
The double wall reactor
high
far unrivaled.
so
compared
would deviate from the set
temperature
the
were
could be controlled at isothermal conditions
temperature Tr
(maximum temperature evaluation
and
examples
highly
and the
as
heating following
6.1 New reaction calorimeter
S
It is
to control the
possible
from the
independent
jacket T}
of the
temperature suited for
S
No
The
S
A or
(for
each
heat flow of
changes
separately
topics
the
capacity
is therefore
through
physical
Subchapter
in
development
turned out to be
also be relevant for
x
clearly
of
properties
important
new
thermostat,
3.7.2 and
a
The time
parameters
(e.g.
the
due to volume
reaction
mixture)
developed
following
cannot
be
are
outlook
and
Subchapter
They
will
precalibrated
calibration method
practicable
accuracy the
on
as
method for well
determined
as
a
the
reaction
6.1.3.
of the
ambient
Therefore
precalibration presented
as
However other to the
compared
well
as
the
chosen
influence of the
the determined reaction
a
on
the
corresponding
parameters
a
precalibration
measured
correction
Appendix D.2) during
is
baseline
method
this work and
of the reaction
was
applied
calorimeter,
of the Peltier elements. A better solution of this in
outlook 7.1.1.
influence of the correction method further discussed in
on
be
temperature
requires
It
should
is useful.
6.1.4.
to all measurements.
be
method
The accuracy
3.7.3 and
will
The
Subchapter
developed (see Chapter
problem
developed
a more
7.1.2).
calibration
possible
7.1.2).
neglected.
similar of the
three main
turned out to be useful for the purpose
replaced by
time-correction method
influence
The
developed (see Chapter 3.7.2)
outlook
further discussed in
The
be
can
of the intermediate thermostat has to be corrected. The
methods
(see
changes
application.
Appendix D.1)
developed
correction method correction
to
measured baseline will be discussed
experiment).
is further discussed in
dynamics
required
reduced.
reaction calorimeter the
commercial
application (see
influence of the
method
see
coefficient,
for the accuracy of the measured baseline.
and not for each
once
commercial
x
required.
are
the reactor wall
of this work but would have to be
The
of the
6.1.2.
of this
potential
a
(see Chapter
x
the outside
The Peltier elements of the intermediate thermostat have to be
(only
shown that
changes
to
of the heat-transfer
experiment)
the heat
area or
single experiment
a
changing
the
was
reaction calorimeter is therefore well
new
measured online. The benefit of such
During
temperature Tr
parallelisation.
the heat-transfer
carry out
independent
cooling liquid (provided by
calibrations
more
qtot is
signal
Appendix D.1, Figure D-3).
the reactor
as
of the outside thermostat. It
temperature
the determined calorimetric
well
as
Subchapter
on
6.1.5.
161
The accuracy
as
the determined reaction
well
as
the
parameters
is
6 Final Discussion and Conclusions
The mechanical
design
of the
industrial and standard reaction needs further as
the
applied principle
commercial version.
A
proved
still showed
completely
and would not be
leakage
some
only component
solution will therefore be
new
that
probe (see Appendix C.1)
of the IR-ATR
sealing
be well suited to all
to
The
examples investigated.
is the
improvements
calorimeter
new
applicable
presented
in
a
in the
outlook 7.1.1.
6.1.1
and time constants of the
Accuracy
The accuracy
requirements
were
commercial available reaction
Chapter
in
specified
new
calorimeter 3.2.1
also related to
(and
The actual accuracy of the
calorimeters).
presented
reaction calorimeter is described below.
Relative This
of the measured total heat
error
specification
accuracy
reactions and Total
a
of reaction of the
integration
relative
of
enthalpy
determined
5.2.1):
-134
direct
by +
reaction
1
of
the
integration
(see Appendix E.2.4.1):
error:
kJ/mol; reference: -136
+
hydrolysis experiments
errors
made
compared The
requirement
Relative
Only
error
for the
measured qtot
to the total
of the measured baseline
neutralization
reaction deviates
requirement
by 2%
baseline from the
is met. The
compared decrease
5.2 to 5.4 and
precision
to
a
~
H2SO4 it
of the
error
conventional device
(for
determined
during The
in the range of 4%
cases.
was
possible
to
The determined
guess
an
enthalpy
of
is therefore met.
E.4.1 to be
presented
1 %.
determined with the measured baseline.
determined based
Appendix
«
2%
(see Chapter 5.2.1).
was
were
is therefore met in all
with
enthalpy
was
error:
qtot.
power-compensation signal
The detection limit of the qComp
Chapters
of NaOH
of maximum 10 %
Detection limit of the
in
error
H2S04,
with
anhydride (see Appendix E.2.4.2).
integrated signal
of maximum 10 %
-10%.
signal (see Chapter
5 kJ/mol -» relative
the correction of this heat flow
by
accurate mathematical
The
of acetic
was
NaOH
of
The accuracy of the measurement of the heat flow qDos the
-60 ± 5
~5 %.
neutralization
of the
determined
anhydride,
reproducibility of the acetic anhydride measurements
Total
reference
special dosing experiment:
enthalpy
direct
by
~
«
~
2 W/l
on
the
2 W/l. The
experiments
requirement
calorimeter is thus about details
see
162
twenty
Chapter 3.2.1).
corresponds to the decrease of the sample volume.
described of 3 W/l
times smaller
This accuracy
6.1 New reaction calorimeter
Detection limit of the baseline The
highest
change
detection limit of qCooimg
described in
example is
signal
and the total
quite strong
the maximum. This resulted in
determined based
was
E.4.1
Appendix
However for standard
case.
of the Peltier elements is close to
cooling power
of the measured baseline in the range
error
of 20 W/l at the end of the reaction. The this
of 3 W/l is therefore not met in
requirement
applications,
as
described in
5.4, the detection limit of the baseline signal is
Maximum absolute was
determined
deviation
temperature
by
linear
a
regression
the maximum reaction power measured
Chapters
5.2 to 5.4 of
requirement
as
well
clearly
of the reaction
Chapters to the
temperature
example
is
capacity
<
were
Appendix
of water
quite high (in
measured power
kqaCcu,rei
zero as
requirement
/
maximum
80%)
values
the reaction
AQaccu,rei
error
E.4.1
and E.4.2 a
The
(slow dosing rate).
standard reaction E.4.2
Appendix
example
is
(fast dosing rate)
Aqaccu,rei
~
20
%, AQaccu,rei ~1 % assumed to be
was
equal
The instantaneous heat accumulation
at the start
point
qtot is close to
smaller
dosing
zero.
During
The
because the the
dosing
requirement
of
the instantaneous heat accumulation
dosing is
of the
20%.
of up to about
temperature
was
capacity
in
always
than
well controlled. The
1%
for
all
integrated
experiments.
The
is thus met.
the maximum
the
accuracy
reaction calorimeter
(see
In the actual
of the
setup
can
of
possible cooling power,
baseline correction. This
be
problem
outlook new
handled.
deviations
investigated,
outlook
described in
production
reaction power. The closer the
to be
applications
(4.2kJ/kg/K).
increasing
temperature
the reaction
E.4.1. The heat
especially
kW/l
deviation to
error:
However
2
temperature
described in
10 % is therefore not met. After the
accumulation
of the maximum
determined for the measurements described
the range of
consumption
reaches
is close to
to the
about 4 K and thus outside of the desired range.
was
AQaccUirei
as
5.2 to 5.4 and
heat
AqaCcu.rei
close
demonstrates the limits of the actual device: The maximum deviation
well
as
and
5.2 to
°K/(kW/l)
maximal deviation of 0.5 K for
a
Maximum relative heat accumulation
AqaCcu.rei
0.5
~
during
Appendix
as
therefore met. The reaction however
5 W/l
Chapters
of 3 W/l.
requirement
It
the industrial reaction
on
to be about 20 W/l. As shown the baseline
offset
an
5 W/l
~
>
the
measured
baseline
larger
will
with
of the Peltier elements is to
cooling power
the
decreases
be the offset
is addressed in the
redesign
error
of the
of the
presented
7.1.1). calorimeter
Reactions
a
maximum reaction power of about
with
1 Kfrom the set
point.
higher If
reaction
even more
powers
powerful
will
cause
reactions have
the number of Peltier elements would have to be increased
7.1.1).
163
(see
6 Final Discussion and Conclusions
Time constants The
requirements
3.2.2
(and
and the definition for the time constants
also related to commercial available reaction
time constants of the
Time constant of the
Chapter 5.2). constant the
power
controlling
more
see
and
was
determine
based
is
on
the
already
wise
change
3.2.1
The actual
of the stirrer
experiments
is about 1s. The time constant of the
speed
of NaOH
(see
compared
to
a
sensor
presented
and the
calorimeter
conventional device
(for
). signal:
This time constant of the qcooimg
signal
speed (see Chapter 3.7.2).
time correction of the qCooimg
applied
step
Chapter
below.
given
included. The time constant of the
Time constant of the baseline
stirrer
a
calorimeters).
in
r~4s
neutralization
than ten times smaller
Chapter
by
specified
of 10s is met. It should be noted that in this time
requirement
supply system
is thus details
The
are
power-compensation signal:
This time constant of qComp
(see Chapter 3.7.2)
reaction calorimeter
presented
were
The
r
~
was
40
s
determined
requirement
signal
was
for all evaluations.
164
of
<
by
a
step
wise
change
of the
30s is not met. Therefore
developed (see Chapter 3.7.2)
a
and
6.1 New reaction calorimeter
6.1.2 The
Comparison
following
table
mathematical
gives
reaction calorimeter. It be
possible
guessed Table
6-1:
Baseline 1>
reaction
specifies a
the
on
weather
mathematical baseline.
of
changes
all
the
2>
mixture.
using
Difference
If
either the mathematical
or
Described in
Experiment
of the Stirrer
total
Figure
Neutralization of NaOH
carried
with
out
proportional reaction
the
to the volume
enthalpy
reaction
new
of
change
AH determined
Baseline
Math.
Change
Correction
the
Occurred
reasonable
qtot
yes
no
by
Difference of
integrated
signals2) -
3-19
5.2,
yes
yes
1)
2%
1)
6%
1)
7%
5-2
Figure of Acetic
be
can
the measured baseline.
3.7.2,
Speed
Hydrolysis
the
mathematical baseline
given.
is
change
new
occurred and if it would
change
a
experiments
between
carried out with the
experiments
baseline
a
It is assumed that the baseline
of qtot
integration
Change
overview
the difference to the measured baseline is
calorimeter. the
to guess
an
measured baseline
-
5.3
yes
(small)
yes
5.4,
yes
(small)
yes
Anhydride Epoxidation
Figure Industrial
Example
A
E.4.1,
Figure Industrial
Example
B
of the heat flow
industrial
as
baseline
applications
no
-
yes
no
-
E-19
Power-Compensation principle
As mentioned in 2.1.5 the
Table 6-1
yes
E-18
E.4.2
Figure
changes
E-14
through
changes showed
the reactor
occurred in all reaction
strong
baseline
changes
the baseline is not measured online. But also the
during
the
and
hydrolysis
the calculated reaction baseline. The reaction
production signal the
measured
epoxidation
qtot
enthalpy enthalpy
calculated
(Equations (3-23)
baseline.
Of
the
and neutralization
three
experiments)
It
an
therefore be concluded that
the accuracy
sensitive to visible in
clearly
are
small baseline
significant
by integration
changes
deviations in
the measured
of the measured heat
either the mathematical baselines
or
(hydrolysis,
used to calculate Table 6-1 is
the
difficult to handle if
replaced by
mathematical
experiment
significantly improves
caused
(2-21)) using
and
This is
that
if the mathematical is
was
quite
experiments. Especially
relatively
epoxidation experiments
the baseline for the neutralization
can
jacket.
is
acceptable (deviation
~
only
2%).
online measured baseline is crucial and as
well
measured calorimetric data.
165
as
the information content of the
6 Final Discussion and Conclusions
6.1.3 Calibration of the Peltier elements First of all it
be concluded that
can
Chapter 3.7.2)
it
function of the
temperature.
two Parameter sets
No
significant
were
the
to determine the Peltier
As the Peltier elements
were
constant Peltier
experiments
parameters
k.)
this
at the
parameters
as a
work,
shown.
experiments
beginning
Thus for standard
be assumed
can
and
replaced during
could be measured.
experiment
procedure (see
parameters (S, R,
used for the evaluation of all reaction
reaction
a
calibration
developed
difference between the calibrated Peltier
and at the end of reaction
possible
was
using
during
a
reaction
measurement.
In order to
get
estimation for the
an
parameters (see Chapter 3.7.2) neutralization and
E.2.4.1)
parameters S, in
Chapter
Table
6-2:
R and
k.
Sensitivity
manufacturer values
of determined to the
5.2.1
and
are
of
NaOH)
Peltier
[Melcor]
5.2.1 and
for the
corresponding
Appendix
three results
Peltier
given
summarized in Table 6-2.
are
parameters. Relative changes
(neutralization
Chapter
to
The relative deviations from the
5.2.1 and Table E-7
of the
the classical evaluation of the calorimetric data of the
hydrolysis experiments (compare
repeated using
was
of the calibration
importance
reaction
enthalpies
corresponding
Chapter
E.2.4.1
and
reaction
rate
constants
the
on
Peltier
parameters reported in Chapters
(hydrolysis
of acetic
Table
anhydride,
E-7)
listed.
Reaction
parameter
AH
Neutralization of
Hydrolysis
NaOH
Anhydride
5%
9 %
25 °C
16%
40°C
25 %
55 °C
3 %
25 °C
0 %
40 °C
1 %
55 °C
4 %
25 °C
7 %
40 °C
3 %
55 °C
(model free, integrated)
ArH
(model first k
Table
based,
order)
(pseudo
6-2
pseudo
clearly
first
order)
shows
significantly depend
on
that the final
elements) [Huang
et.
of qCooimg-
00, a].
improved by using one
To
parameters
improve
should be calibrated in al.
of the
chosen
the chosen values for the Peltier
determination of these three calculation
results
Especially
several
in order to determine
a
a
the
the
correct
the
mean
on
cooler
TPenp
(including and
the
Peltier
reported by
TPeitdow"
could
each side of the cooler instead of
temperature (see
166
parameters.
examples
An accurate
device similar to the method
measurement of
thermocouples
reaction
is thus crucial for the accuracy of the
accuracy,
separate
of Acetic
also outlook
7.1)
be
just
6.1 New reaction calorimeter
Further
Table
determined This
is
6-2
is much
by integration hint that the
a
shows
clearly
reaction model acts like
that
the
model-based evaluation a
"filter"
In order to the
signal
reaction
get
classical
results
evaluation
Table
in
6-3:
Chapter
Sensitivity
Table
E-7)
5.2.1 are
of
determined
changes
(neutralization
of
following Chapter 6.2).
The
5.2.1
relative
reaction to the
(model first
Appendix E.2.4.1)
enthalpies
and
rate
parameter
based,
reactor
(pseudo
reaction
E.2.4.1
improve
jacket
first
Hydrolysis
of Acetic
NaOH
Anhydride
6%
3 %
25 °C
3 %
40°C
6 %
55 °C
1 %
25 °C
1 %
40 °C
3 %
55 °C
2 %
25 °C
3 %
40 °C
4 %
55 °C
order)
However
the
sensitivity
would have to be
on
a
on
the Peltier
important
developed (see
higher compared
sensitivity
time-
anhydride,
(compare
examples depend
time
correction
to the
parameters (see Chapter
also outlook
of the reaction
more
or a
more
dynamic
7.1). enthalpy
determined an
by
additional
reliable because the reaction model
following Chapter 6.2).
167
is
for the accuracy of the calculation of
to the model-based evaluation. This is
hint that the model-based evaluation is "filter"
sensitivity
the
the accuracy other time-correction methods
Further Table 6-3 shows that the
acts like
was
parameters reported in
Neutralization of
An accurate time correction is
integration
the
on
of acetic
pseudo
smaller than the
is
and
corresponding
(hydrolysis
Chapter
order)
time-correction.
qcooimg- To
the
constants
Table 6-3 shows that the final results of the chosen reaction
6.1.3).
neutralization
summarized in Table 6-3.
are
corresponding
and
of the
and
ArH
generally
successful for the
was
deviations from
(model free, integrated)
on
of the Peltier
of the time correction of the qcooimg
calorimetric data
Chapter
to
NaOH)
AH
the
the
listed.
Reaction
k
reliable because
signal (total cooling power
5.2.1 and Table E-7
correction method. Relative
Chapters
enthalpy
signal (qCooimg)
importance
of the
without time-correction.
given
reaction
examples.
hydrolysis experiments (compare repeated
the
more
(see Chapter 3.7.2)
this work
estimation of the
an
is
to compare to the
(compare
The time-correction method for the qCooimg
elements) developed during
of
to the model-based evaluation.
higher compared
6.1.4 Time correction of the baseline
investigated
sensitivity
6 Final Discussion and Conclusions
6.1.5 Influence of the ambient The
reaction
the
values for
examples. Unique
In order to
get
qcooimg
estimation of the
an
signal,
neutralization and
E.2.4.1)
the
and
kLoss,a
importance
classical
kLoss,b
without
deviations from the
of
results
given
in
investigated
ambient-temperature the
calorimetric
Chapter
to
Chapter
correction
data
5.2.1 and
correction.
ambient-temperature
corresponding
of the ambient
obtained.
were
of the
evaluation
changes
successful for the
was
hydrolysis experiments (compare
repeated
was
this work to take
during
(see Chapter 3.7.3)
into account
temperature
of
correction method
developed
temperature
of
the
Appendix
The
relative
5.2.1 and Table E-7
are
summarized in Table 6-4. Table 6-4:
of determined reaction
Sensitivity
temperature correction. Relative changes
Chapters Table
5.2.1
E-7)
of
(neutralization
NaOH)
enthalpies
to the
and
and rate constants
parameters reported in
(hydrolysis
of acetic
Neutralization of
Hydrolysis
of Acetic
NaOH
Anhydride
0%
6 %
25 °C
2 %
40°C
11 %
55 °C
1 %
25 °C
0 %
40 °C
0 %
55 °C
3 %
25 °C
1 %
40 °C
1 %
55 °C
Chapter
E.2.4.1
Reaction
parameter
AH
(model free, integrated) Aß
based,
(model first
pseudo
order)
(pseudo
first
order)
Table 6-4 shows that the final results of the chosen reaction on
the
ambient-temperature
temperature
correction is
correction. However the
generally
parameters (see Chapter 6.1.3).
important
also outlook
Table
determined This is
a
An
smaller than the accurate
isolated, the total
decreased and the infrared
Further
anhydride,
probe
area
examples depend
sensitivity
on
sensitivity
of
improve
passive jacket
should be made of
a
the ambient-
on
ambient-temperature
for the accuracy of the calculation of qcooimg- To
reactor should be better
(see
the ambient-
listed.
are
k
reaction
corresponding
on
the Peltier
correction
is
the accuracy the
surface should be
less heat conductive material
7.1.1).
6-4
clearly
by integration
shows
is much
that
the
sensitivity
higher compared
a
"filter"
(compare
to the
168
the
reaction
enthalpy
to the model-based evaluation.
third hint that the model-based evaluation is
reaction model acts like
of
more
reliable because the
following Chapter 6.2).
6.3 Evaluation of the calorimetric data
6.2 Evaluation of the calorimetric data In order to
get thermodynamical
reaction
parameters (such
the evaluation of the measured calorimetric of
reaction model
a
the
(see Chapters
signal
2.3.2.2 and
classical, model-free evaluation based
(see Chapter >
2.3.2.1
All thermal
)
due to the
following
effects that
processes described
by
are
reaction
the classical
integrated using
measurement data is
is
the basis
of the measured
to the
model of
(heat
approach.
only possible
as
long
to
signal
Of
heat of
the
phase change) exclusion
course
the
chemical
be excluded from
can
mixing,
as
and
physical
remaining
time still allows the identification of the desired reaction to
enthalpies),
on
clearly advantageous
integration
related
evaluation. Whereas all these effects will be
(Equation (3-23))
2.3.2.3)
on
reaction
reasons:
not
the
qtot
as
of
measurement
parameters (compare
Chapter 5.3.1).
The influence of any measurement
errors
(e.g.
specific parameters (see Chapters
device
determined reaction
enthalpy
base line
6.1.3
to
drifts)
6.1.5)
or errors
the
to
in
finally
is smaller because the reaction model acts like
a
filter.
The difference of the two shown for the
approaches
in
of acetic
hydrolysis experiments
epoxidation experiments (Chapter 5.4). Table 6-5: Difference of the reaction
(ArH )
and
by integration (AH).
1)
ArH determined
determined
by
the
evaluation of all
by
the
qtot
the reaction
are
determined
enthalpy
3)
on
the basis of of qtot
Average
(Chapter E.2.4.1).
of the values at 17
separate calorimetric evaluation (Chapter 5.4.1). at all
and the
reaction model
a
separate calorimetric evaluation (Chapter 5.3.1).
experiments
also be
can
summarized in Table 6-5.
by integration
(Chapter E.3.4).
enthalpy
anhydride (see Chapter 5.3)
The results
AH determined
AH2 determined by integration of 4)
calculating
6)
5)
...
ArHj
Acetic Acetic
Anhydride Anhydride Anhydride
Epoxidation Epoxidation
17 °C 24 °C
ArH [kJ/mol]
model free
model based
25 °C
-60 1)
-57 4)
5%
40 °C
-59
1)
-60
4)
2%
-57
1)
-60
4)
5%
-440
2)
-440
2) 2)
Difference
-360
5)
20%
-370
5)
20%
-400
5)
20%
Epoxidation
30 °C
-480
Epoxidation
36 °C
-440 2)
-410 5)
7%
-450 3)
-390 6)
15%
Epoxidation
+
36 °C. +
ArH2
temperatures (separate calorimetric evaluation, Chapter
AH[kJ/mol]
55 °C
AH!
Result of the overall
5.4.3).
Acetic
2)
169
6 Final Discussion and Conclusions
6.3 Combined evaluation of calorimetric and infrared data In
a
second
algorithm
of this work
part
was
is
during
feasible
identify
to
One
following input or
several
differential
Initial
is
reaction the
stochiometry,
reaction
an
evaluation
models with
energies
or
their
reaction
parameters (such To
enthalpies).
as
perform
required: models that describe the
feeds
or
other
any
empirical kinetics,
processes
in
of
terms
the
ordinary
equations.
conditions
of
the
Calorimetric
and
infrared
temperatures
reaction
specified
concentrations of the involved chemical
different
Chapter 4)
in
chemical reaction. The task of the evaluation
a
reaction rate constants, activation this task the
description
that allows the model-based evaluation of the calorimetric
developed
and infrared data measured
algorithm
detailed
(see
as
initial
components.
measurement
and concentrations
If measurements at different
such
model,
can
temperatures
data.
Several
experiments
be evaluated at the
are
evaluated
same
at
time.
simultaneously
the
Arrhenius law will be used to model the rate constants of the reaction model.
Bounds for the reaction
pure
No
enthalpies.
parameters within the
unknown
are
required
specified
spectra
simultaneously. included but
of
initial as
parameters
guesses
for
the
such
rate
as
unknown
constants,
kinetic
ten different random start values
are
reaction
generated
bounds. In order to evaluate the infrared data the unknown the
involved
If bounds
they
reaction
are
not
chemical
for the pure
components
spectra
are
required (see also discussion
170
are
known, in
determined
they
can
Chapter 6.3.5).
be
6.3 Combined evaluation of calorimetric and infrared data
Based
this
on
evaluations
1.
(for
detailed
a
Separate The
data
input
description
measured
Separate The
...)
constants
reaction
were
well
as
are
identified in
one
single step
profiles. Similar
power
methods
are
based
on
described
in
discussed in 2.3.2.3.
...)
constants
the measured reaction
same
methods
as
the reaction model based
single step
one
numbers
wave
of the
overlapping absorption peaks
is allowed.
components
Combined evaluation of calorimetric and infrared data:
3.
the
Typically
separate
not lead to the
6.3.3). Several the
cases
However reaction
the
evaluations of the calorimetric and infrared data will
same
reasons
reasons
only
one
reaction
for this deviation
are
will be measurement
reaction
optimization
parameters (see e.g. Chapters
as
parameter
set
can
But in the
majority
all
reaction
parameters in
component spectra)
(reaction power profiles function
has to
model-fit
errors
be into
(reaction
one
be used for the purpose of
1.1. In such
combined
cases a
reaction
enthalpies,
single step using
and infrared reaction
single
identify
and
rates
pure
both measured data sets Therefore
spectra).
calculated that combines the one
of
and unmodeled processes.
errors
Chapter
described in
possible.
5.4.4 and
evaluation of the measured data is therefore essential. The aim is to
an
objective
calorimetric and
infrared
value.
The combination of the calorimetric and infrared third
on
described in literature and
are
to note that several
important
time and
well
as
identified in
are
spectra. Similar
discussed in 2.3.3.3. It is
evaluated at the
pure
the reaction model
infrared evaluation:
parameters (rate
are
as
spectroscopic (pure component spectra)
were
three
following
Chapter 4.4, Figure 4-5):
see
thermodynamic (reaction enthalpies ...)
literature and
2.
the
developed algorithm performs
calorimetric evaluation:
parameters (rate the
the
objective function, required
for the
evaluation, represents the main challenge within all the three evaluations. As
shown in
signals
Chapter
4.5 and
is not useful.
combined
evaluation.
optimization however
Appendix E.3.8,
This
crucial
task
impedes
is
a
combination of the two different
detailed
description
see
generally
their and
completely automatically
interaction. For
simple
It is necessary to scale the two
tools and therefore
runs
a
left
application. requires
Chapter
171
error
4.5.
functions to
The
no
the
prior
user
developed
time
to the
of
such
method
consuming
user
6 Final Discussion and Conclusions
As all the three evaluations shown above values
it
is
then
identification.
parameters,
possible
characterize
to
carried out the
the identification
indicator is useful to
robust whereas
was
If several reaction models
distinguish
then
was
the
parameter
few identical best solutions
a
evaluated this robustness
are
(see Chapter 4.3.2).
between different models
developed evaluation algorithm
of
solution for the reaction
same
only
ten different start
using
robustness
If all ten start values resulted in the
indicates low robustness.
The
are
applied to two example reactions, the
hydrolysis of acetic anhydride (first-order one-step reaction,
Chapter 5.3)
see
and the
epoxidation of 2,4 di tert-butyl benzoquinone (two-step consecutive reaction,
Chapter 5.4).
Based
these two
on
studies the
case
following conclusions
see
be
can
drawn.
6.3.1
Feasibility study
The evaluation acetic
with
simple
a
accurate and
performs
anhydride (see Chapter 5.3).
robust for the
The combined
of the calorimetric and infrared data gave the with classical evaluation results
(reaction enthalpy
reported
and rate
literature references
evaluation
is
algorithm
that
principles (see
example
reaction
can
as
same
be
well
as
5-3).
can
example
well and
were
verified The
systems.
are
of
evaluation
separate
for such easy
applied
It
the
results. The results
constant) agree very
Table
reaction
simple
close to the
therefore be concluded that the
correctly implemented.
6.3.2 Increased information content
by measuring
two different
analytical signals As
an
additional information the evaluation of calorimetric and infrared data of the
hydrolysis
reaction revealed that
the acetic
anhydride. This in
analytical signals
clearly
parallel. Especially
the
related
spectrum also
is
mixing only
could be identified
to
the
1.2 and Table
allow
(see Chapter
an
during
E.2.4 and
several different
signal
of the
involved
as
well
the infrared
6.1.1 for the calorimetric
Therefore many identification
of
cases
reaction
might
this work.
172
no
as
signal
and
exist where
parameters
evaluation will lead to reasonable results. However
encountered
and
are
chemical
1-1).
own
will
(see Appendix
measuring
concentrations
have their
signals
signal
of
the reaction power is related to reaction rates whereas
Chapter
signal).
dosing phase
the calorimetric and the infrared
it should be considered that the calorimetric
for the infrared
the
visible in the calorimetric
Generally
limits
during
occurs
demonstrates the benefit of
as
components (see
are
spectrum, they
well suited for combination reaction
heat of
As these effects
do not affect the reaction
Chapter 5.3.1).
a
or
Chapter
only
only
such reaction
signal
a
one
6.3.6
of the
combined
example
was
6.3 Combined evaluation of calorimetric and infrared data
6.3.3 A
complex
more
reaction with different feasible reaction
models The evaluation of the consecutive to the
complex, compared feasible and the
are
give
the
applied By
for the
(see
(see 5.4)
show
that
Pareto
evaluation
Chapter 5.4.4).
in
analysis
with
algorithm
reaction
kinetics
is
(see Chapter 5.4.2). Only
conditions was
the
more
evaluations of the infrared and calorimetric data do not
several
The classical evaluation
is not
reaction
strongly depending of the eleven
one
possible any models
measurements at different initial concentrations of the educts it to
much
was
different reaction kinetic models
as
hydrolysis experiments (see Appendix E.2.4)
the
running
hydrolysis example,
separate
results
same
reaction
epoxidation
was
based
further
the
on
more.
on
possible
concentration
reaction models
proposed
able do describe the reaction at different concentration conditions. The reaction
orders of this model constants
(results
evaluation
algorithm
the identification
also
were
see
Chapter
identified
5.4.2 and Table
is able to deal with
("number
of
at the
hits",
complex
as
the reaction
rate
This demonstrates that the
5-10).
reaction models. The robustness of
Chapter 4.3.2) proved
above and
see
time
same
to be
a
useful indicator to select between different reaction models.
Several
experiments
were
carried out at different
initial concentrations of the educts. unreasonable reaction
activation
enthalpies
Consequently enthalpies
two additional
are
not allowed
these
Using
temperatures described in However
was
well
as
physical to
constraints
change
as
repeated
constraints
(see Chapters
5.4.1
introduced:
were
function
and
the
reliable
5.4.3 and Table 5-5.
should
a
be
taken
for
this
obviously of
temperature dependencies
as
of
evaluation
results
They
were
are
1)
of all
by
and
5.4.2).
and
2)
The
the Arrhenius
experiments
obtained.
the
The reaction
temperature
of the reaction rate constants is described
additional
Chapter
care
The evaluation however resulted in
for any chosen reaction model
temperature dependency law.
energies
but with constant
temperatures
The
at
results
all are
similar to literature references.
comparison
as
the
literature
data
are
problematic (see Appendix E.3.6). This reaction reaction
example thus demonstrates that
parameters based
necessary.
on
chemical and
Otherwise mathematical artifacts
final results.
173
a
critical
analysis of the obtained
physical knowledge
will
always be
might lead to misinterpretation of the
6 Final Discussion and Conclusions
6.3.4
Comparison
of the three evaluation
types: Separate
Calorimetric, separate infrared and combined evaluation Based
on
the
different evaluations carried out for the
Chapters 5.4.1,
comments in
5.4.2 and 5.4.3 and the
corresponding
5-5, Table 5-9 and Table 5-10) the following observations The
calorimetric
separate
estimation
("number
chemically The
of hits"
infrared evaluation
of hits"
minimal)
reasonable reaction
more
The combined evaluation the
identification
between
the
determined
calorimetric
or
even
evaluation a
further
of the automatic
(see Chapter 5.4.4) combined
objective
physically
or
less robust estimation
physically
chemically
or
and It
is
(see by
the
different solution for was
reaction
important
Appendix the
5-16 and
to
always
parameters that
note
The
E.3.8).
the
reaction
optimum that sometimes
separate
evaluation
Figure 5-18).
method
scaling
a
identification
real combined
plots Figure 5-13, Figure
analysis
in
solution that is either similar to the
a
lies outside of the range defined
Arrhenius
the
able to find
evaluations
parameters identified represent
robust
most
than the calorimetric evaluation.
always
combined evaluation did not result in infrared
the
resulted
resulted in
reasonable.
physically
were
always
was
parameters
separate
results in Table
parameters.
mostly
was
(see
made:
always
The robustness of the
problem.
two
but
was
were
but often
maximal)
unreasonable reaction
separate
("number
evaluation
reaction
epoxidation
on
(see e.g.
This fact and the
the basis of
a
Pareto
plot
allow the conclusion that the automatic calculation of the function
performs
evaluation of the measured data
problems might
be the
well and that
might
be
performing only
a
separate
misleading.
for the difficulties encountered
two
separate
evaluation of the calorimetric data and the deviation of its results to the
reason
during
the
Basically
other evaluations:
1.
The calorimetric data contain qtot
=
qReact is not
fulfilled)
physical
that
were
significantly
integration
(e.g.
not modeled
models and do not influence the reaction fact that the
effects
spectrum.
when the
by any
This is
of the reaction
supported by
of the total reaction power measured
different total reaction
enthalpies
Further observations described in
Appendix
that
effects and eventual side reactions
occur.
174
(qtot)
the
leads to
than the model-based evaluation
(see Chapter 6.2). phase change
assumption
E.3.5 indicate
6.3 Combined evaluation of calorimetric and infrared data
2.
The evaluation in
is
step,
one
task,
two reaction rates and two reaction
identify
to
robust but leads to
mathematically
physically
enthalpies
unreasonable
results.
The
for the low robustness of the infrared identification
reason
of freedom of the internal linear
degrees
and
Equations (4-8)
the calorimetric evaluation
pure
but
spectra
Due to the
only
enthalpies
combined with evaluation of the infrared data.
reasonable results.
where the
separate
simple
example,
the
the identification of the pure
5-7),
since
matrix is also
equal
measured pure
However the
Chapter 5.4) five,
are
three to
components
component spectra
But it is
parameters
is still
In contrast to the
failed when
to
the
parameters.
successful
(rank
(see Figure
of the concentration
three). The estimated pure spectra differ significantly from the
because
possible
important
physically
anhydride (see Chapter
was
had to be identified
identification of the pure
discussion in
with
clearly superior
of acetic
hydrolysis
Chapter to
significant temperature dependency.
spectra
of the
different
epoxidation
spectra
of the concentration
B.2 and the identified pure that
note
a
eight
mathematically possible (rank
see
robust identification
evaluations, and essential for examples
spectra and do not show
is not
be
can
component spectra
5.3),
five
different
shown that both data sets
was
evaluations result in different reaction
reaction
only
It
for
have to be identified.
The combined evaluation is thus
6.3.5 Determination of pure For the
medium
a
calorimetric and infrared
separate
example eight
developed algorithm the evaluation of the calorimetric data
support each other and lead to
larger
optimization problem
In this reaction
(Equation (4-6)).
two different reaction
be the
optimization problem (see Chapter 4.4.3,
to the internal linear
(4-7)) compared
might
the
identification
are
identified and matrix is
profile
spectra
of the
reaction
in
(see only
equal
to
Figure E-15).
desired reaction
possible. reaction the identification of the reaction
hydrolysis
the pure
component spectra
were
assumed to
parameters
be constant in the
investigated temperature range. It
can
with
therefore be concluded that
(see
temperature
measured
pure
component spectra
are
Chapter 2.2)
also
spectra.
component spectra may vary
Care
should
and
thus
may be
taken
used in order to evaluate reaction
175
differ
in
a
reaction mixture
significantly
when
spectra.
measured
from
pure
6 Final Discussion and Conclusions
6.3.6 Limits of the IR-ATR Based
on
the
reactions
(infrared) signal
investigated during
this
work
the
limits
following
were
observed:
In
of solid and
suspensions
observed. In the solid
example in the
component
infrared
During
liquid components only
studied
(see Appendix B.2)
liquid phase
was
even
the
liquid phase
be
the concentration of the
too low to be visible in the
signal. the
epoxidation experiments (see Chapter 5.4)
industrial reaction
example
isomers)
are
reaction
spectrum
Additionally
B
(see Appendix E.4.2)
However
produced.
their
as
intermediate
an
industrial reaction
would
be
is not
spectrum
before, the reaction spectrum does mostly
information to
identify
concentration B.2 and
profiles
are
linear
in
the
for
the
might
be
suggested reason
regio
similar.
quite
are
been
As mentioned
spectra
and
the
to the other concentrations and
therefore the contribution to the overall reaction
all pure
during
(stereo
but could not be identified. The
compared
as
distinguished
spectra
have
well
as
isomers
not
component
product
example B,
could
they
pure
that the concentration is too low
dependent (see
significant.
not contain
of all involved chemical
species
discussion in
enough as
their
Appendix
Chapter 5.4.1).
Care must be taken when strong
absorption
relation between
component
Law) might
absorption
be violated
The maximal lower
can
(see Chapter 2.2
and
to the calorimetric
the
spectral region
because diamond is used
as
are
evaluated
concentrations
as
the linear
(Lambert-Beer's
Appendix B.1).
sampling frequency (6 S/min)
compared
Unfortunately
and
bands
of the infrared
signal
is much
signal (600 S/min). from
ATR-crystal.
176
1800 to 2400
cm"1
is not available
6.3 Combined evaluation of calorimetric and infrared data
6.3.7 Limits of the model-based evaluation As shown
both data sets,
evaluated based
on an
of the model-based and
6.2).
As
soon
were
should
that the
assume
the reaction.
it
as
as
well
reaction model. The
empirical
approach
Additionally
approaches
the calorimetric
already
be
infrared
advantages
discussed earlier
mentioned
that
changes
occur
they
should
data,
can
be
disadvantages
(see Chapters of
most
and
the
of the reaction mixture is not
density
such
the
as
2.3.4
model-based
changing during
be considered
in the
reaction model.
However the often mentioned drawback of model-based difficult to find
*>
appropriate reaction models, is not reasonable: with
Any person
adequate
the
represent
mentioned in to be used
mechanistics
Chapter
they
quite
lot of other
background
the
reaction
proposed
who have little
would like to
will
information
data
isolated
can
be
but
evaluation
or no
investigate.
analytical
(chromatographic samples, All this
of
1.2 the
by people
reaction a
chemical
always
be able to
suggest
reaction models. The reaction model does not have to
appropriate empirical
...).
approaches, it would be
In
the
procedure
chemical
practical
used to
is not
As
designed about the
situations there
products, suggest
kinetics.
background
available for the mean
overall
might
be
investigated
reaction
identified side
products
an
appropriate empirical
reaction model.
Model selection based model fit
was
on
the two
shown to be easy and
indicators, quality and robustness of the
specific (see Chapters
177
4.3.2 and
5.4.2)
7 Outlook
7 OUTLOOK 7.1 Reaction calorimeter 7.1.1 Reactor the thesis
During 3)
was
made.
properties
bar.
is
The
main focus
calorimeter new
has
design
7-1: Left side: New can
of the
of the
reaction calorimeter
presented
redesign
Power-Compensation part
available. The
reactor
complete redesign
completely redesigned.
The
Figure
a
was
to
improve
of the intermediate thermostat but also to introduce
Sensor. The
jacket
redesign
be
replaced
are
already
been
of the copper
and is made of
shown.
new
Right (CAD
built
but
no
of ATR-
but the copper
made
178
performance
data
6 Peltier elements from
jacket using
Hastelloy.
Drawings
changed
type
are
yet
following figures:
The IR-ATR
side: The covered reactor -
new
calorimetric
device will be pressure resistant up to 20
is described in the
design
the bottom of the reactor. Peltier elements
The
is therefore not
a
the
(Chapter
by
H. P.
as
probe well
is
as
directly
a
side. The
mounted into
the six coolers of the
Schläpfer, Workshop ETH).
7.1 Reaction calorimeter
Stirrer
Engine
Cover
Reactor
and Connections
Covering
Plate
Cooler
Thermal Insulation Reactor
Peltier Elements ATR
Figure
7-2: Final
setup of the
(CAD
Drawings
made
The
-
main
problems
mentioned
in
addressed
by
The
by H.
Chapter this
a new
Toledo
reactor with the
Sensor
insulation and the stirrer
jacket
engine.
Schläpfer, Workshop ETH).
the
6.1.
reaction
calorimeter
Most of them
but also
more
Chapter
3
were
practical problems
were
presented
in
redesign:
problem
using
of
P.
new
-
and
of the
type AS I.
sealing
of the infrared
of ATR-Sensor The
new
dipper
kindly provided
ATR-Sensor
was
completely
from the
should
solved
companies
even
show
by
Mettler
increased
sensitivity. The reactor is not any to
remove
insert
a
more
made of Teflon but of
the reactor from the copper
dummy
reactor that includes
179
a
jacket.
Hastelloy.
It is
now
Thus it should be
separate
possible
possible
heater. With such
a
to
dummy
7 Outlook
reactor it will be
The
and not at the
night
over
jacket
beginning
and at the end of
more
be useful if In
to the actual
compared
thermocouples
element
The total
introduced to
are
operating
The increased the
improve
further reduced. Six for
Tj (compare
The total
to
insulation of the of the reactor The
temperature gradients
of the reactor
area
is
jacket
improved
discussion in
Chapter 3.4.4).
two
springs
the
same
elements and
5
The
temperature.
they
in
an
6.1.4 and
jacket
will be
average value
reduced
heavily
temperature
6.1.5 and
3.7.3).
can
be carried out
contact
mounting
compared
to
should therefore Also the thermal
from the insulation
separated
is
screws
The
as
2, 4,
to the
(see Chapter 3.4.4)
(not
shown in the
screws
is not
performance
in two
are
figures).
present any
of the cooler is
separate cooling
turns in
the six Peltier elements should all work at
In order to further minimize the
Element
for each
individually
guaranteed (compare
mounting
cooling liquid
connected in the and 6
potential
following way:
in series.
drift of the six Element
The two blocks
are
1, 3, then
parallel. thermal insulation of the reactor
the whole box e.g. with N2 in order to insulation.
This is crucial for
should also increase the elements
is
now
Chapter 3.4.4).
electronically
are
in series.
separate
thermal
inside the copper
should
mass
(see Chapters 6.1.1,
it is
due to the
circulation of the
by
connected in
3.7.2).
around all cooler elements
leakage
discussion
The
direction. This is crucial
opposite
as
thermal
optimal
Therefore the heat
(see
jacket
of the Peltier elements
thus
increased
larger.
cooling power qCooimg
will be used to calculate
thermocouples
element and
more
).
cover.
mounting
replaced by
6.1.1 and
significantly (see Chapters
be decreased
Peltier elements
and D. 1
the calculation of the
The influence of the ambient
setup.
the
Appendix C.6).
passive
the actual
by
TPenp and TPeitdow" for each
measure
behavior of the reactor
the
3.7.2). Additionally
caused
of the reactor and reduced copper
symmetry
dynamic
6.1.4).
temperatures.
of the
Appendix C.7.4
(see Chapters
accurate
more
and
reactor wall. This will
as
studied at low
quality
of the
conditions should be further away from the maximum
cooling capacity. Consequently should be
6.1.1
of the Peltier elements is three times
cooling performance
Therefore their
are
calibration
to the discussion in
(compare
with Teflon
setup
experiment.
dynamics
temperature gradients
exothermal reactions
strongly
order to further increase the
twelve
reaction
a
systematically (see Chapters 3.7.2,
Another benefit will be the much lower reactor wall
systematically e.g.
reactor could also be used to calibrate the
dummy
same
reactor
to calibrate the Peltier elements
possible
(see
performance
discussion in
remove
humidity
applications as
well
Appendix C.7.2).
180
jacket
as
allows the
purging
of
of the air inside the
at low
temperatures
and
the life time of the Peltier
7.1 Reaction calorimeter
7.1.2 Ideas for future The
developments
following
ideas could be
The
of
problem
solved
an
by introducing
a
a
heat-flow
distance.
specified
measurements is
improve
sensor measures
The
proportional
heat
to the
flow
of the material between the
The
temperature
difference
be
baseline correction
introduced
However in the
new
Peltier elements
Hastelloy
two
difference
temperature
long
as
the
as
is constant.
sensors
baseline function for the A
heat-flow
and the
it should also be
design
difference between the
temperature
the
(see Appendix D.3).
between the reactor
temperature
difference
as
Chemisens
the
to
temperature
could be used
signal
the
between
temperature
conductivity
could
analogous
sensor
heat
mathematical
the reaction calorimeter:
accurate calibration of the Peltier elements could also be
reaction calorimeter. A heat-flow over
to further
investigated
sensor
jacket.
copper
possible
to
the
use
reactor and the surface of the
Peltier elements.
Another solution to the Peltier calibration Peltier elements
by
method will be the increased
limits
of the
measure
TJ
noise of the
whole
and
device.
al.
73]. However
Such
big
a
for the
principle
a
drawback of this
cryostat.
for slower
Pt100
elements In
applications.
could
be
parallel
used
the
wall thickness of the copper
jacket
switching
automated. qcooimg
or
qcomp
of the
dynamic
of the controller
E.g.
the
signals
to
sensor
was
calculated. A finite element calculation could be carried out in order to
The
was
measurement would be decreased.
optimal
possible improvement
the
support
measurement is crucial for the detection
Therefore
eventually Tr
As mentioned the
et.
cooling requirements
temperature
temperature
would be to
additional heater element.
an
already implemented by [Christensen
The accuracy of the
problem
switching
became small.
181
verify
a
behavior.
settings could
never
at
occur
point as
© in
soon
Figure
as
the
3-15 could be
changes
of the
7 Outlook
7.1.3 Ideas for the
improvement of the heat-flow balance
calculations The the
ideas
following
recommended to be
are
investigated
So far the
cooling power
of the Peltier elements qCooimg
in the heat-flow balance. However
accuracy of the qcooimg This
correction
signal
use
it
as
satisfying
not
replaced by
be
reactor
experiment
no
parameters errors
used
as
the basis to calculate qcooimg could
possibilities
to
that
were
a
measure
of the
change quick
the initial
inserts)
determination of the heat
qComp is
capacity
For the reaction
and end of the
be achieved. However the
So far it
during
a
was
dosing)
over
correction
of
reaction
the
Peltier
already
water.
when
on
a
instant
tests for this
carried out and gave
Only during
improvement
according
182
of the reactor content
shown in this work qaccu
of the
the results
by
(see Chapter 3.7.3).
engine.
this heat flow
applied. Feasibility
examples
an
by including
temperature Tr
were
all influence
reaction measurement
of the stirrer
a
of the reactor content would
assumed that the heat flow caused
case, qsurr could be corrected
02].
should be observed in
capacity
capacity
calculated, assuming the heat capacity of
phase (start
are
would have to be determined. A fast
of the reaction
compensation power
promising results.
al.
correction
in the heat-flow balance.
However the heat
slope
et.
changes
dependent
and easy way to determine the heat be to
time
a
The
2.1.4).
parameters during
could be eliminated
mixture and reactor
out
and
the heat flow qaccu in the isothermal heat-flow
by neglecting
into the heat-flow balance.
2.1.3.1
99] and [Vincent
implement
(see Chapter 6.1.1)
(reaction
al.
temperature
would be easy to
made
et.
carry
of the Peltier
changes
applications
heat flow
Chapters
observed. However if such
were
dynamic
3.7.2
to
[Velâzquez-Campoy
As mentioned
balance
occurred.
Chapter
described in
signal
based model of the
physical
jacket (compare More
replaced.
mentioned in
future
error
not
the baseline
a more
steady-state equations then
as
6.1 and 6.1.1 the
offset
an
used
(see D.3).
the
through
as
directly
using qcooimg directly in the heat-flow function bl(t) in the mathematical baseline
by
The black-box time correction of the qcooimg could be
was
Chapters
discussed in
as
was
could be solved
problem
balance but to
The
improve
of the heat-flow balance calculations:
quality
C as
measured
was
of the
profiles
they
Several
procedure.
99] the selection of NPC is
al.
et.
absorbing species.
with low concentration.
species
and B
must be
it will be difficult to decide whether
represents
+
[Valle
but often the selection is done
Generally
A
and
[Malinowski 02]
mathematical
proposed
3.
in
explained
components
chosen
a
(B-9) feasible number of
components (NPC )
in
PCA,
the next
step
in
SMCR methods will be the transformation of the abstract concentration and pure
spectra A*
=
matrix
and
(Cabs
Eabs)
[CabsxT]x[TlxEabs]
Where T is any
physical meaningful
matrixes
matrix of size NPC
[Hamilton
As mentioned before the SMCR
techniques
are
only
some
examples
Equation (B-10) clearly
will be
shows that
et.
proposed
matrixes
by any
these rotational
for Eabs and Cabs
al.
90] and [Jiang
et.
al.
02].
not the main focus of this work and
shortly explained.
during
the reconstruction of
Eabs and Cabs the problem of rotational ambiguities will matrixes
Ereai):
NPC. Many different approaches for
x
in literature
therefore
and
(B-10)
proposed
are
(Creai
=CRealxEReal
non-singular
this transformation
into
can
always
come
physical meaningful
up because any
be transformed into another
new
pair
of
transformation matrix T. The task of SMCR is therefore to break
ambiguities
physical meaningful
and to find
a
unique
matrices Creai and Ereaï.
A8
transformation of Cabs and Eabs into
ß Infrared
Iterative
Target Testing it is
By target testing of
matrix C of to
one
that
Equation (2-33)).
of the
guessed
Cabs
close
as
determined
or
that
assume
a
corresponds
x
concentration
method
by any
in Cabs
a
profile
corresponds
transformation vector t has to be found
a
possible
as
c
to
column in
(one
In order to test if this concentration vector
principal components
transforms
test vector
a
Let's
Equation (B-9).
could be
component
one
(ITTFA)
to test whether
possible
of A* in
principal component c
Factor Analysis
Spectroscopy
the
to
target
vector
(least-squares
c
solution):
minfc"Cabs xt]2 If
c
is
similar to
corresponds be
can
to
c
or
it
concluded
that the
component
in the reaction
successful
target
be
can
until
NPC
t
=
transformation vectors t, is constructed
Equation (B-10)
(CabsTCAsYlCabf
xt=c*c
real chemical
a
repeated
corresponding in
Cabs
found.
are
estimates of the desired Creai and Ereai and the
given by A
=
The
the
t real
~
of
principle
A
C real
=
C abs
X
1
X
the estimated
and
evaluated
again by Equation (B-11).
of the
final estimates of the concentration an
determined
=
X-^abs
implemented ct
profiles
and
c,
to
t,
reaction
a
matrix.
The
spectra À*
are
step
is
~
^ real
(B-12)
in the ITTFA method. ITTFA
according
concentration This
1
to
repeated
constraints, mostly These
profiles.
new
non
targets
are
until convergence and the
ct fulfill all the constraints. The start
profiles
Creal that contains the initial targets c. developed by Gemperline ([Gemperline 84]
was
[Vandeginste
et.
al.
unimodality
applied
for the
99], [Dyson
et.
non-negativity Alternating The ALS
point
constraints for the concentration elution of reaction
00], [Johnson
and
Least
[Gemperline 86])
85] for the analysis of HPLC elution profiles using
decomposition al.
and
unimodality
et.
al.
profiles.
spectra by [Bellet,
02], and [Zhu
constraints
were
et.
al.
al.
It
was
02]. In
and
negativity
successfully et.
al.
most of these works
applied.
Squares (ALS)
method starts with
initial guess for the matrix Creai.
chemical
components (columns)
in Creai has to be chosen either
chemical
knowledge
following
non
98], [Gemperline
an
the
procedure
initial guess for
ITTFA
and
c
the transformation matrix T
Finally
reproduced
EreaJ
targets
negativity
unimodality
C reaJ
is used and
target testing
iteratively changes
is
This
system.
profile
following equation:
^real
X
concentration
target
concentration
the
by adding
(B-11)
xc
or
by PCA analysis.
Then Ereaï
can
The number of on
be calculated
the basis of
according
linear least squares:
Ereal=(CjCreaiyCjxA
(B-13)
A9
to
Appendix
The unconstrained Ereaï new
estimate
^real
can
now
be constrained
to be
(e.g.
non-negative)
^
~^
Creai
a new
be calculated
can
unconstrained
unimodal)
to
t-real
~^
according
linear least squares:
following
to
get
Creai
a new
(B-15)
can
be
now
estimate
Creal
constrained
(e.g.
be
to
:
^ real
Cmal
new
(B"16)
can now
be inserted in
Equation (B-13).
The iteration is continued until
the difference the residuals R of the estimated and measured reaction not
change any C
R
It is also
xE
[Tauler
al.
et.
general shape The
to
replace
the measured reaction
the PCA reduced reaction
of ALS
discussed
was
The
93, a].
same
constraints
technique
was
also
[Tauler
al.
and further
93]
in several
applied
was
Equations (B-13),
(Equation (B-9)).
A*
developed by
reaction
non-negativity, unimodality, closure,
as
al.
et.
et.
A in
spectrum
spectrum
by [Casassas
method
different constraints such
applying
do
(B-17)
real
(B-17) by
technique
spectrum
more:
possible
and
(B-15) The
real
and
non-negative
constraints
The
a
(B"14)
real
Creal=AxÊJ(ÈrealÊabsTrl The
get
Êreal :
constraints
Then
to
94], [Saurina
applied by [Furusjö
et.
al.
et.
al. 98,
98], and [Tauler
a], [Bezemer
or more
al.
et.
al.
et.
studies
99].
02], and
[Miller 00].
Evolving In the
PCA.
Factor Analysis factor
evolving The
analysis approach,
procedure
proceeds, adding in the backward
starts
one
giving eigenvalues
(EFA) using only
from
a
The sets of
enters the
procedures
components appear
EFA
first also leaves
first,
one can
procedure
analysis
to
eigenvalues
similar to
86]. As the technique HPLC
can
was
target
first
was
Assuming simply
procedure
that the
combine the
A*.
profiles.
repeated
eigenvalues at which
decomposition used
compound
that
eigenvalues
from
In
step
a
second
For this second et.
by [Maeder 87]
procedures
A10
If the
is
picture showing
proposed by [Maeder
transformation
both
thus
decomposed,
be used to obtain initial estimates of
concentration
for the
sub-matrix and
is obtained.
is then fitted into
applied
measurements,
give
the
eigenvalues. a
decomposed by
are
are
same
plotted,
disappear
reaction.
alternating least-squares procedure
or
are
the
the matrix of combined
GC
sets of
profiles during
the forward and backward
iterative
and
eigenvalues produced by
system
more
in
spectrum
time, until all spectra
a
direction, yielding NT
the concentration
the first
total of NT sub-matrices. The
from the forward and backward times chemical
at
spectrum
A*
sub matrices of
al.
86] and
and
profiles
existence
an
a non-
[Gampp
of elution
the
step
of
et.
al.
from
pure
ß Infrared
concentration windows. The method
spectrum by [Bell second
of EFA. EFA is
step
ALS method
This
technique
decomposed Eabs
are
physical
of
a
reaction
used to
mostly
generate
initial guess of
an
for
Creal
an
analysis (RFA)
is similar to the ALS method. In
by PCA.
into Cabs and Eabs
transformed constraints of Creau
unimodality
decomposition
(see above).
factor
Resolving
for the
98] who applied non-negativity constraints and ALS in the
al.
et.
applied
was
Spectroscopy
by as
are
a
Then
transformation
applied then
in
ALS,
applied
to
a
first
the reaction
step
according
to
spectrum
A is
Equation (B-10) Cabs
and
matrix T into Creai and Ereai-
such
as
non-negativity
The
same
of Creai and Ereai
or
Creai and Ereai in order to calculate Creal and
p ^real
(-real
=
t abs
^ real
~^
X *
(B"18)
constraints
Ereal=T
X
^'abs
Ereal
"^
(B-19)
constraints
As
an
initial guess of the unknown transformation matrix T random numbers
chosen. The NPC
x
NPC unknown matrix elements of T
least-squares optimization, given by
the
identified
are
by
a
can
be
nonlinear
following equation:
2
mm T
Creal (T)XEreal (T)
The number of unknown -
Npc by normalizing
reaction
T.
(B-20)
parameters
in
This method
example by [Mason
et.
al.
01].
Equation (B-20) was
No
developed
applications
be reduced to NPC
can
and to
a
applied
real
to
a
example
x
NPC
simulated
were
found
in literature.
ConcIRT
[ConcIRT]
is
one
of the few commercial SMCR programs. An
reported by [Zilian 01]. Unfortunately
the calculation
A11
principle
application example
is not
public.
is
Appendix
Conclusions: Form the
of the literature about SMCR
study
have to be considered when
following problems Rotational
are
in
generally
not
constraints such will not be
unique as
unique.
due to rotational
In these cases,
physical
and chemical constraints of the
constraints
applied
problem. Systems
with
good
yield
a
problems
arise
especially
unique
shaped profiles (either
As
et.
al. 98,
al.
95], [Tauler 01], Even
or
closure
unique profiles,
a
range
data and
experimental
system
the resolution
applied,
are
though
band of
or
fulfilling
has to be considered. The
the
more
resolution in either the kinetic
solution
or a
in kinetic
et.
al.
possible
or
spectral
solutions.
direction However
evaluations, where lack of selectivity and similarly
concentration
b], [de Juan
band of
narrow
(time)
profiles
or
spectra)
by SMCR
are
often encountered. Thus
methods will often be
00], and [Diewok et.
al.
severe
03].
deficiency of the reaction spectrum:
mentioned
concentration the
well the
in the solution obtained
ambiguities
et.
the smaller will be the range of feasible solutions to the SMCR
will often
Rank
the
algorithms:
ambiguities (Equation (B-10)).
instead of
profiles (Creal) fitting equally
[Furusjö
experience
03] the results of SMCR algorithms
al.
et.
non-negativity, unimodality
feasible
the
these
[Gemperline 99], [Gemperline 98], [Tauler
01], [Miller 00], and [Diewok
al.
et.
using
own
ambiguity of the solutions:
As discussed
[Smilde
and
algorithms
analysis
before
profiles
all as
of reaction
concentration-time
SMCR will
well
as
pure
reveal
only
spectra
are
spectra rank-deficiency
profiles
are
linked
by
component
information
if their
linearly independent. Especially has to be
expected
the chemical reactions
for
because the
taking place (see
above). Initial guess of a
Creal
ALS,
iterative and therefore
et.
al.
ITTFA
are
:
depend
good
on a
initial guess of
Creal [Zhu
02].
Intensity ambiguities: Due to
intensity ambiguities
method will
only
the
resulting
contain relative values
matrices
[Tauler
et.
Cmal
al. 93,
b]
and and
Èreal
from any SMCR
[Smilde
et.
A**{k-Crea)x[^.Êrea^ Where k is more
an
external
applied.
knowledge,
01]: (B-21)
arbitrary scaling such
However in many real
al.
vector. In order to solve these as
closure,
applications
intensity ambiguities
has to be introduced into the constraints these
A12
ambiguities
will remain.
ß Infrared
Spectroscopy
Baseline drifts: If baseline drifts occur, all SMCR methods will treat them
[Furusjö
al.
et.
It
b].
98,
is
possible
not
as
them
distinguish
to
additional
components
from
a
chemical
deficiency,
rotational
component. Solutions to A
some
problems:
and easy
general
is
intensity ambiguities
or
to address the
approach
matrix
of rank
problems
augmentation,
several
e.g.
measured at different concentration conditions but with the therefore
same
pure
spectra)
will be concatenated to
spectra
components (and
same
single
a
reaction
reaction matrix
Aaug.
A, A
(B-22)
aug
AN where
exp
is the number of
Nexp
spectra
all
A
SMCR
described
instead of
experiments. Using Aaug techniques
still
can
be
carried
reaction
single
a
without
out
any
changes.
B.3
and combination of model-based and
Comparison
model-free evaluation methods Generally step
the model-free
to the model-based evaluation
essentially completely theoretically) a
(Appendix B.2)
evaluation methods
(Chapter 2.3.3.3).
The model-free
automatic and does not need any
and there is not much
not to
reason
applied
are
perform
as an
analysis
operator input (at
it. The results
of the reaction
underlying (see
also
based
spectra might already
reaction model and
Appendix
E.2.2 and
target testing,
on
to
an
SMCR
be sufficient in order to
E.2.2.1). [Amrhein
identify
will not reveal
analysis
the
et.
al.
stochiometrics
new
99] reported of the
is
least
can serve as
basis for the elaboration of the correct reaction model. However in many
shape
initial
the
cases
the
identify
information
a
technique,
chemical
reaction
investigated. However the most
important
role in the initial
the chemical intuition and
knowledge
essential
specific
to
use
more
chromatography [Dyson
et.
of reaction model
about the reaction. For this
offline
to
identify possible
it
step
such
analysis techniques
00] in order
al.
step
design
will be
might
also be
as
NMR
intermediate
or
or
side
products. The task that has to be solved and
much
usually
less constrained.
orders
of
by
the model-free
In model-free
magnitude
higher
analysis
analyses,
than
in
a
is of
course
much heavier
the number of unknowns is model-based
approach.
The
mathematical robustness of the evaluation is therefore much smaller. As discussed in
Appendix
B.2 the calculated concentration
profiles
A13
are
not
unique
and
depend
on
the
Appendix
initial guess. This The
shown
was
showed
comparison
a
clear
There are, of course, many In those
modeling. change The
as a
A
of the soft and hard
hard constraint
new
to fulfill
profiles
reaction
a
constraints
soft-modeling the
whose
instrumental
shifts. The method and
by
Maeder et. all
applied
was
is
to evaluate
The
consecutive
three-step
The
to evaluate
as
technique,
complex
of
a
rotational and
using
treated
was
they
reaction
al.
et.
method
system
both
by [de
did
compared
by
was
et.
Maeder
al.
the SMCR
not
conclude
all
the
to
or
a
chemical
absorption
approach reported
superior
where
example
was
similar
to the model-
01] in order
the
classical
presented by [Diewok
was
used
was
to
ALS et.
by [Bezemer
al. et.
system. additional constraint in
theoretical basis it
was
a
SMCR
shown that
of SMCR solutions
can
be
et.
al
as
in
for a
later
evaluated with
well
as
a
the
the hard
of
a
consecutive
publication by [Zilian 01]
the
same
ConcIRT,
another SMCR method. In
modeling
methods
profiles.
unique
evaluation
result
were
both able to
However the two different SMCR and
showed
worse
performance
to the model-based method.
the combined
explain
the et.
as an
01]. On
reaction. In
additionally
Despite [Dyson
due
Juan et. al.
example,
chemical reaction
reasonable concentration time
methods
some or
00] compared the model-free ITTFA method with the model-based
publications
predict
inclusion of
systems.
heterogeneous hydrogénation both
of the
using exclusively
consecutive reaction
intensity ambiguities (see Appendix B.2)
developed
reaction
Appendix
decreases the
baseline drifts
were
algorithm
kinetic model
by [Smilde
eliminated for certain reaction
[Dyson
by [de
cycle
of the combined method
used
was
of the
application
a more
concept,
same
in
iterative
obtained
03]. A similar ALS algorithm with hard modeling constraints 01]
02].
combined
drastically
optional
two-step
a
However
algorithm
same
evaluation failed. A third
al.
the
all the concentration
or
exclusively
not
performance
modeling approach.
free ALS method. The a
response
(see 2.3.3.3).
to the pure hard
al.
explained
to the classical model-free ALS and model-based
compared
evaluate
The
(see Appendix B.2).
et.
were
at each
profiles
involved in the kinetic process, such
components
some
model, which is refined
as
where the reaction orders
the ALS method
introduced to force
long
as
into the kinetic model allows the successful treatment of data
absorbing species
matrices
applicable
modeling approaches on
to be useful in
complex
presented by [Zhu
was
associated with the kinetic
ambiguity
reaction.
simple one-step
This modification of the ALS method
optimization process. rotational
is
will still be
example reaction,
00]. The evaluation is based
Juan et. al.
a
mechanism is too
techniques
constant. An
are
for
b]
of the model-based evaluation.
a
function of reaction progress,
advantages
B.2.
where
cases
al. 98,
et.
advantage
the SMCR
cases
component spectra
by [Furusjö
complete
al.
application
of Raman and IR
behavior of the reaction
00].
A14
as
techniques,
measured
by
it
was
not
possible
off line NMR
to
analysis
C Construction details of the
new
reaction calorimeter
C CONSTRUCTION DETAILS OF THE NEW
REACTION CALORIMETER C.1 IR-ATR Probe and Teflon inliner As ATR
probe
C276
tube material
as
of about 16
standard DMD-260 Probe from
a
further
(see
analogous
mm
[Axiom]
C.8.5).
in
specifications
used with
was
The tube has
Hastelloy
a
diameter
to ATR Probes from other manufactures such
as
ASI
[ReactIR]. The
purpose of the Teflon
substances.
For
Therefore Teflon
a
inliner
IR-ATR
caused
some
sensor
head
as
the sides of the
C-1
from Axiom has
). Together
there is sensor
no
head
just
with the company
applied.
Figure C-1
is not
only
the
The copper block is heated to about 200 °C
2.
The Teflon
small, thus leaving enough Teflon material
a
By doing cover
jacket (indicated pushed inside, The
(indicated
cone
was
on
in
sealing of the
top
therefore to seal
solved
side in
as
Figure
follows:
to be
pushed
prepared
back into the
pushed
back into the bore for
this the thickness of the Teflon material decreases.
the 0
ring
Figure 3-6).
onto the ATR
that
was
This 0
previously
inserted into the copper
will press the Teflon that
ring
was
probe.
is then removed and with
into the channel. The whole
a
system
will have the exact form of the
special was
tool the ATR
probe
was
inserted
then cooled down. Thus the Teflon
ATR-probe.
Using this technique the ATR-probe should be sealed pressure proof up to about bar. It
can
on
Figure 3-6).
cone, the still hot and thus soft Teflon is
The Teflon will
to seal
of the copper block. The hole for the ATR-Probe is
in
mm.
diameter, is then introduced into the
but too
Using
head the
sensor
was
opening
the ATR Probe.
4.
in
large
2
section.
begins (see right
reactor
bore for the ATR-Probe 3.
too
minimum
following
possible
problem
1.
be
chemical
The introduction of the Teflon
solution
before the tube
[Technova]
inliner, slightly
should
rather delicate
a
surface. The
plane
copper block from
described in the
shortly
troubles. As shown in
the
thickness
cannot be
coating techniques
probe
protect
the
good protection
inliner into the reactor is therefore
As the
is to
be removed and reinserted for
cleaning purposes using
A15
a
special tool.
10
Appendix
Figure
C-1
:
view
Top
(left side)
and side view
of the IR-ATR Probe from Axiom.
(right side)
C.2 Stirrer The stirrer is made of two
parts:
blades of the stirrer. The Teflon
A
Hastelloy
part
replaced
if another blade
geometry
only
stirrer
(see Figure
one
was
used
shaft and
a
Teflon
part
is screwed onto the shaft and
is
required.
For all
3-5 and Table
experiments
that forms the therefore be
can
done in this work
3-2).
C.3 Thermal insulation The insulation
was
made of
of about 0.03 W/mK. The different
together
to
get
reproducible
a
C.4 Stirrer
parts
the
speed
a
of the thermal insulation
heat can
conductivity
easily
be
put
insulation.
Engine
The stirrer revolutions per minute rate stirrer
to 180°C with
Rohacell, resistant up
is controlled
by
an
can
be
adjusted
between 0 and 600 rpm. The
external controller and
a
speed
meter mounted
on
engine.
C.5 Baffles The baffles
intensity
of
were
introduced in order to
mixing. They
are
prevent
made of Teflon and
needle that is inserted into the Teflon. The baffles and
can
be removed
easily
a
if desired.
A16
large are
are
vortex and to increase the
strengthened by
a
syringe
screwed into the reactor
cover
C Construction details of the
C.6 Position of the
temperature
new
reaction calorimeter
inside the copper
sensors
jacket View
Top
Figure
C-2: Position of the
temperature
sensors
inside the copper
jacket
of the intermediate
thermostat.
Figure C-2
shows all the available
They
used to
were
investigate
the
temperature
inside the copper
sensors
temperature gradients
and to control the
jacket. jacket
temperature. The
same
type
(see 3.4.3.2) 0.6
of
and
thermocouples
TPeUup
s) Inconel® Alloy
dynamics,
I
was
chosen
as
TPeitdown (see C.7.4): Type
600
thermal grease
as
jacket
was
put
used for the measurement of Tr K
(1
mm
material. In order to
into the
sensor
sensor.
A17
bore
diameter, time
improve
prior
constant
the measurement
to the introduction of the
Appendix
However for the control of the used.
different combinations of the
Many
definition showed the best
^
There
jacket temperature only
temperature tested
were
value
but the
can
be
following
performance:
i=2
three
mainly
are
reasons
for this selection:
1.
By using
the
2.
Possible
inhom*ogeneities
3.
The two different heat-flow
mean
compensated by
value of four sensors, the
inside the reactor
changes,
signal
jacket
shown in
the intermediate thermostat
of the copper
plate
C.7
sensors
one
are
to noise ratio is reduced.
are
leveled out.
that have to be
Figure 3-9, best
acquired
on
the bottom
jacket.
Cooler, peltier elements and cooling liquid
C.7.1 Different methods for thermal contact
A)
Thermal grease
This is the standard
only
little thermal grease
as
There
and
as
If
is taken
care
possible
is
during
the
mounting procedure
used, good performance
can
be
and
expected.
different classes of thermal greases, with different heat conductivities.
are
Several of these best
technique.
were
applicability.
tested. However the standard thermal grease
Thermal greases cannot be used in
vacuum
[Melcor]
[Huang
showed
al. 00,
et.
a]
[Marlow].
As thermal grease should not be
applied
in thick
must be taken when several Peltier elements
they were
do not
always
ordered and
cooler
as
same
mounted onto the
mm)
same
care
plate
as
thicknesses. Therefore several Peltier elements
that showed the
only pairs
are
about 0.02
same
thicknesses
were
fixed onto the
described in 3.4.4.
B) Soldering
and adhesive
All metal
parts
elements
with
technique. Of compared greater
show the
layers (only
used in this metalized course
coefficients
x
2
cm
of the
application
plates
are
the thermal
to the other two
than 2
bonding available
performance
techniques.
([Melcor]
connected
and
together. Special
could be soldered and
could
of such
a
also
be
system
used
Peltier
for this
is the best
as
However it should not be used for surfaces
[Ferrotec])
materials.
due to the different thermal
Temperature changes
will
expansion
thus
lead
to
problems. If
parts
cannot be
shows the
same
soldered, adhesive bonding would be another possibility however
drawback
as
the
soldering technique.
A18
C Construction details of the
C)
Gels
or
Graphite in the
reaction calorimeter
films
films
or
silicon
gels
tested with the actual
were
new
also be used
can
but the
setup
thickness of the films
huge
low thermal
conductivities
thermal interface. Both materials
performance
(as compared
was
bad. The
copper).
to
This
lie
might
reason
to thermal grease and the still
compared
useful if the contact surfaces show
as
relatively
mounting technique
is
large inhom*ogeneities.
C. 7.2 Peltier Elements As shown
in
Figure
(Chapter 3.4.4)
3-12
two
Peltier elements
were
used in the
cooler, electronically connected in series. Many different types of Peltier elements are
available
only
a
on
the market. However if the
few remain. For this calorimeter the HT series from Melcor
chosen. The
liquid (TCry) situation
cooling power
is shown in
(TPC
=
°C
10
Figure C-3.
well
is
calculated
as
the
temperature based
manufacturer values a
maximum
zero
(Tph
reaches
=
a
on
W/K).
TPC
The calculations
The
cooling power
temperature
are
of
(HT 6-12-40) of the
carried out for
one
=
4.5
-
°C).
for the
required
Peltier
of about 42 W if the
The
(TPH,
parameters.
temperature
cooling capacity drops
value of about 95 °K
(TPH
=
see
105
°C, TPC
concluded that two Peltier elements in series should be
application.
A19
10
was
cooling
standard
A, thermal
(qcooimg)
Figure 3-4) well
as
as
The element shows
difference TPH -TPC is
down to =
a
Peltier element
steady-state equations (see Chapter 3.7.2)
[Melcor]
10
function of the
of the hot side of the Peltier element
cooling capacity =
a
(see Figure 3-4, Chapter 3.3.3), lPeb
resistance of the cooler 0.2 as
as
qcooimg
is up to 200 °C
application temperature
°C).
0 W if TPH It
was
-
TPC
therefore
powerful enough
for this
Appendix
50
110 -
40
»
90
*
_
"
*
E
_
»
30
.
*
I
20
£
q_Cooling
A
m.
_
^
*
*
T_PH
#
w
10
30 *
-
" -
L 10
^ -5
10
25
40 1
Figure
C-3: Performance
the Peltier
plot
of
°C, the Peltier
70
85
^J
Y
cry
Peltier element
one
parameters [Melcor]). TPC is
varied from -5 to 90
55
(HT
6-12-40
series, manufacturer values for
°C, the temperature of the cooling liquid TCry is
set to 10
current is set to
-
4.5 A. The thermal resistance of the cooler
is assumed to be 0.2 W/K.
Peltier
elements
elements
3-6).
vacuum
there is
placed
are
Best
should
be
protected
inside the bottom
performance
plate
suitable
moisture.
Therefore
of the thermal insulation
of the Peltier elements is achieved if
[Ferrotec], [Melcor] and [Huang no
against
et.
mounting technique
al. 00,
they
a]. However,
for the actual
as
can
Peltier
(see Figure operated
discussed
that
setup
are
the
in
above,
be used in
vacuum.
Most of the manufactures
performance
guarantee
of the elements will
life time of their elements. However the
long
a
be constant
not
calibrations carried out should therefore be
over
repeated
long
a
time
period. Any
in the range of half
a
year
[Melcor]. C.7.3 Cooler and
cooling liquid
The task of the cooler is to
Therefore it should show smallest and
[Buistet.
al.
94].
the
remove
heat
pumped by
the
total heat resistance
possible
The total heat resistance is influenced
by
the
Peltier elements.
[Huang
et.
al. 00,
a]
following points:
Material of the cooler: The material should show
high
heat
conductivity,
thus copper is the
material of
choice.
Cooling liquid: Water is
one
temperatures
of the best
cooling liquids
lower than 0 °C. It is
benefit is their
available.
possible
high temperature range
of
to
use
Unfortunately special
application
performances.
A 20
but
oils
they
as
it cannot be used at
cooling liquids.
The
have bad heat-transfer
C Construction details of the
As mentioned in 3.3.2 the for the
Flow
(2:1 )
and
pattern
calorimeter reduces the
Therefore for all
cooling liquid.
water and EtOH
new
pure water
or
mass
was
flow of the
A cooler should maintain
applications
discussed in this work
elements
cooling liquid:
pattern
that tries to
However the
distribution
will decrease will
again
goal
of
and fine
the
lead to
cryostat
an
Therefore
a
The
flow
a
flow
will not be
increase of the
pattern
chosen
pattern
temperature
for
drop
this
were
C.7.4 Measuring
ofTPeUup and TPeUdown
3-12
as
Type K,
1
(Chapter 3.4.4)
shows the
As
up
a
local
temperature
quite complex
diameter, time
designed
and fine
the
bigger
will be the
cooling liquid
to maintain the flow rate. This
differences and
complex is
application
position
worse
of the
(see later).
used for the measurement of the mm
the two
the flow rate of the
and
also tested but showed
will be used for the calculation of qcooimg chosen
performance
consequently
flow
patterns
shown
in
had to be 3-12.
Figure
performance.
TPeUup and Tpeifow"
The
same
sensors
thermocouples
as
from the
close
top
as
of the
possible
cover
jacket temperatures (see Appendix C.6):
constant 0.6 s, Inconel®
Alloy
600
as
jacket
differ from TPC and TPH
conductivity
35
W/mK)
to the surfaces of the Peltier elements
plates).
as
However it is clear that
the alumina ceramics
cause
plates
significant temperature
A 21
that
were
material.
Tpei"p and Tpeitdown should be estimates of TPC and TPH (see Figure 3-6) they
placed
the
distribution will not be achieved.
Commercial coolers
Figure
is
strong enough
between pressure
compromise
therefore be
Consequently
hom*ogeneous temperature
a
found.
as
build
cooling
measurement drifts.
setup might
inside the channels.
drop
pressure
and
the
on
best thermal contact of the two different Peltier elements.
get
complex
more
diverge
can
can cause
for the actual
optimal design
flow
top
on
inside the cooler. This
gradients An
mounted
mixture of
a
used.
surface and maximum heat transfer. If the cooler will have bad Peltier
reaction calorimeter
temperature range required
hom*ogeneous temperature
a
new
(0.3
mm
are
shifted
TPeup and TPeitdown will always of the Peltier elements
differences
(heat
(see Figure 3-6).
Appendix
C.8
devices
Periphery
C.8.1
Rotary
according
The two feeds that
can
Chapter 3.4.3.2)
each connected to
connection controlled
with
be used with the current
Teflon
by RS232
clean the reactor and to
position rotary
valves
rotary
inputs
oxygen /
made
of the
rotary
1
Gastight
2.5,
Figure
3-12
Figure 3-3)
or
reach the desired
heater
to
syringes (series 1000)
remove
is
the heat
tempered by used
were
done with the
an
the
temperature Tr in
computer (Number I,
output signal,
rotary RS232
by
(volumes 25, 20, 5,
outside
F6
cryostat (Haake
As
-
cooling liquid pure
of the individual
(see
C25)
to
water
or
experiments).
compensation
as
well
V, has
amplifiers
the
jacket temperature T}
detailed
Figure 3-14,
in the range of -10 to 10
as
to be
description amplified
is smaller than the
in
is
Chapter
to the desired
update
rate of
computer signal (10 Hz).
compensation
to be
equal
to the
voltage drops
heater is controlled
The actual
amplifier [Kepco].
output
due to the
heater
(IComP),
cabling
is monitored
Figure 3-14).
to 10 V it
(indicated
can
in
be
directly
on
the
signal.
by
the
assumption
during
with
and
signal IComP
is
already
ATM-55-5M
heater is assumed
experiment the
required by
acquired by
an
is feasible because any
reaction
a
The actual current
amplifier
voltage
compensation (UComP)
constant
are
As the monitored
the
and thus
compensation
computer (indicated
scaled within the range of 0
feed to the AD converter without further
signal conditioning
Figure 3-14).
Peltier elements
amplifier [Kepco]. same as
voltage
the
by adjusting
of the controller. This
do not affect the calorimetric
the
of the
the Peltier elements
pumped by
(see description
power range. The time constant of both
The
order to
(in
(Upeit, Ipeu, fJcomp, Icomp)
As the control of the reactor
in
as
syringe pump)
position
used
are
C.8.3 Amplifiers for the Peltier elements and the
The
used
are
pump is done
syringe
temperature TCry (see Figure 3-4).
water / ethanol mixtures
the
are
Cryostat
cooling liquid required
3.6),
and
ml).
C.8.2 The
Hamilton
valves
Vacuum
4)
(see
(Omnifit, 11526),
of Teflon
connect to the
be connected to the open
can
cover
moisture).
vales in order to dose reactants. The control of the commands.
valve
are
oxygen from the reactor
remove
remove
of the reactor
setup
reaction) 2) Open (to
the
syringe pump (kdS 200)
The
four
a
commands. The four
be able to
3) Nitrogen (to
The
tubes).
1) Closed (during
follows:
3-14
Figure
syringe pump
valves and
are
to
the
are
controlled
The actual
voltage
voltage
monitored
by adjusting on
by
the
current with
the Peltier elements the
amplifier.
A 22
This
(UPeit)
a
BOP-36-6M
is assumed to be
assumption
is feasible
as
C Construction details of the
new
Upeit is only used for evaluation purposes when IPeit is equal to current of the Peltier elements IPeU
the
acquired by and Ipeit
are
(^ in
computer (indicated
already
point
set
of the
amplifier) they
signal conditioning (indicated
C.8.4 DA/AD converter, data
The actual
zero.
and UPeit
As the monitored
Figure 3-14).
scaled within the range of -10 to 10 V
the AD converter without further
reaction calorimeter
can
in
be
are
both
signals UPeit
directly
feed to
Figure 3-14).
acquisition, signal conditioning
and
signal generation The
I in
computer (Number
has
Figure 3-14)
two different tasks within this
mainly
application: 1.
Data
acquisition: Analog signals
converter. These
Signal generation:
2.
have to be
Both
tasks
the measured
are
signals
of the
In order to interact with the
generated
from
performed by
are
converted to
are
values
digital the
by
a
an
AD
system.
device, analog output signals
DA converter.
PCI-MIO
same
digital signals by
16XE10
card
from
[National
Instruments]. The frequency of signal acquisition and generation is 10 Hz and is
triggered by
a
The different show low
timer built in the PCI-MIO card.
signals acquired by
voltages
SCXI
1124
computer
is carried out with SCXI 1125
(SCXI
1325
Terminal
Instruments]. The conditioned signals
settings Table C-1
of the
signal conditioning
Description
Tr
Reaction
T,1-6,TT1
Jacket
Amb
reactor
Current
the desired
UPeh, IPelt
fed
to the AD
passed
of the measured
the stirrer
from
[National
converter.
input
data in the
new
the
PCI-MIO
The
calorimeter.
Amplified
Filter
yes
4 Hz
yes
4 Hz
yes
4 Hz
yes
4 Hz
engine
to maintain
yes
4 Hz
No
No
stirring speed (Figure 3-14).
Appendix C.8.3 to
modules
(see Chapter 3.4.3.2)
required by
that
Block, input)
(see Chapter 3.7.3)
istirr
See
then
output)
temperature, measured outside of the
Reactor pressure
ComP> +ComP>
Block,
1328 Terminal
Temperature (see Chapter 3.4.3.2)
Pr
*J
are
(SCXI
Temperatures (see Appendix C.6)
Ambient
signals
shown in Table C-1.
Signal-conditioning specification
Signal
'
are
listed in Table C-1. All
are
to the range of -10 to 10 V and filtered. The
pre-amplified
are
signal conditioning and
the
and
(Figure 3-14). Directly
card
without
conditioning.
A 23
SCXI
signal
Appendix
C.8.5 Infrared measurement The infrared measurements used in the
previous
work
as
ATR
done with the
same
DMD 260 /
crystal,
16
mm
up to 200°C and 30 bar, cutoff
FT-IR
OpusNT
Software:
that
was
already
270, 3 reflections, angle of incidence 45°, diameter, Hastelloy C-276,
outside
1800 to 2400
region
Detector: External MCT detector cooled with
Spectrometer:
equipment
[Pastré 00]. It consists of the following elements:
ATR-Probe: Axiom Diamond
were
spectrometer
from Bruker
liquid nitrogen.
from Bruker
running
resistant
cm"1.
on an
(Equinox 55). second
computer (number
II in
Figure 3-14) In contrast to the
spectra during
triggered by Figure 3-14).
a
previous
reaction
the
work and most
were
exact start of the
reaction. The two
not recorded at
LabVIEW program
In this way it is
applications
running
possible
to
fixed
a
on
adjust
described in
sampling
the main the
rate. The
are
connected
by
sampling
Ethernet
sampling
computer (number time
reaction, the dosing actions and, if desired,
computers
literature, the
(indicated
according
to the
in
I
is in
to the
rate of the
Figure 3-14).
C.8.6 Endoscope In order to be able to look inside the reactor into the reactor. The
endoscope
was
an
purchased
A 24
endoscope from Storz.
can
be
optionally
inserted
D Calculation details
required for
the heat-flow balance of the
new
reaction calorimeter
D CALCULATION DETAILS REQUIRED FOR
THE HEAT-FLOW BALANCE OF THE NEW
REACTION CALORIMETER D.1 Determination of S, R and Chapter
As described in based
the three
on
resistance
3.7.2 the calculation of qCooimg
and
[Q])
temperature. S,
k
(heat
conduction coefficient
R and
Tcare
device
(3-16).
to
coefficient
[W/K])
are
and
specific parameters
is
The calculation is
[V/K]),
known
are
qcooimg.corr)
to
(electrical
R
function of
as a
independent
possible to calibrate these parameters
from the
and then
once
them for any reaction measurement.
The
characterization but
experiments
of S,
combined to
two
the
at
in
and R
was
carried
not
and
beginning
Chapters
unique parameter
a
5.2 to 5.4.
set that
be
can
out
the
at
in
parameter
sets
were
end
of
each
The individual values
applied
on
the
were
then
for any reaction within the the
replaced during
in this work
carried out with
are
sets and not with the individual calibration results. The two
based
reaction
calculated.
All calculations and results shown
parameter
calibration
separate
studied. As the Peltier elements had to be
temperature range work,
k
always
measurement described
are
(Seebeck
S
parameters
reactor content. It is therefore use
(corresponding
steady-state Equations (3-14), (3-15)
if the three
only possible
k
one
of these
parameter
sets
following experiments:
Set A: Neutralization of NaOH
(see Chapter 5.2)
and
Hydrolysis
of Acetic
anhydride
(see 5.3). Set B:
Epoxidation
reaction
(see Chapter 5.4).
Parameter S For the determination of S the Peltier elements of the elements
voltage the cold
plate
according
to
[Huang
s=^PenVpelt K1 Pelt
Where
~
1
a
indicating evaluation
=
0)
and
temperature
TPeifown
see
Equations (3-14)
to
and the
difference between the hot and
Figure 3-12).
00, a] the following equation
is the measured
supply.
that the
of. The whole
(TPei"p
the
s
was
For the evaluation used
(steady-state
(3-16)):
)
of time.
was
al.
as
turned off for 25
»J
UPeit(IPeit
function
et.
follows from
Pelt
off the current
well
measured
was
approximation;
as
were
voltage
over
The value of S, determined
the Peltier elements after
according
After about 5 seconds the value did
steady-state approximation was
repeated
s
three times and
A 25
(D-1),
not
is sufficient. The
therefore taken in the range of 5 to 25
procedure
to
was
plotted
change any mean
as
more,
value of the
after the current
averaged.
turning
was
turned
This resulted in
Appendix
one
value for S at the
single
the accuracy of the
temperature
the offset of the two
Set A: AATpeit After
=
difference ATPeU
sensors was
0.05
subtracted
K, Set B: AATPeit
determined S at different
having
For the determination of S
corresponding temperature.
=
TPei"p
=
prior
-
TPeitdown
is crucial. Therefore
to the evaluation of
Equation (D-1 ):
0.085 K
temperatures
a
linear
regression
was
applied
to
these values: f
S
=
pup
,
"""
1Pelt
S,
p
down
1Pelt
\
+
sh
(D-2)
The result for both sets A and B
provided by
are
shown in
Figure
D-1 and
compared
to the values
the manufacturer.
0.104 0.102 0.1 *
0.098
co
0.096
Measurements Set A Measurements Set B
1
1
0.094
IL__^
A
J
0.092
I
0.09
ii
270
275
280 up
(T,Pelt Figure
D-1
:
w
| i
i
285
290
7i
do
")/2
ii
295
300
305
[K]
Results of the calibration of the Seebeck coefficient S of both calibration sets A and
B.
The deviation between the two sets A and B is
only
about 2 % whereas the deviation
from the manufacturer values is in the range of 10%
Chapter 6.1.3).
The difference of the calibrations at the
the reaction measurement
changes
will be
S
determined
=
S(T)
(see
neglected
was
also
sensitivity analysis
beginning
in
and at the end of
maximal 0.5 % in Set A and 0.8 % in Set B. These
in all evaluations done in this work and
by Equation (D-2)
at T
period.
A 26
=
a
single
value of
Tr will be used for the whole reaction
D Calculation details
required for
the heat-flow balance of the
new
reaction calorimeter
Parameter R After
determined S
having
the
by (D-2),
parameter
following equation (steady-state approximation;
R
follows
can
be determined
from
by
Equations (3-14)
the to
(3-16)): SNtYi o
o
However this
complex of
-88kJ,mo1
epoxidation enthalpy
was
not
calculation scheme. Therefore it
C=C
saturated
enthalpies Table E-11:
of
double
of
was
measured but is the result of to the
compared the
(calculated by
epoxidation
of saturated
standard heats of formation. The oxygen
epoxidation enthalpy
difference
of
the
source
is not
included.a) [Dowdet.
al
91]
based
on
[NIST]
[kJlmo\]
-104 a)
gas
-105 b)
o
^^
-115a)
gas
-^
-
^~~~~^o HCT
b)
AH
State
A
r
standard
C=C double bonds calculated
Epoxidation step —
a
The data is shown in Table E-11.
formation).
Enthalpies
bonds
directly
^
epoxidations
apparent
For the
should be closer to -153 kJ/mol.
enthalpy
order to compare these literature values to the measured total reaction has to be
by tert-butyl
was
signal.
that
no
observed
used for the
signals
were
stable.
Changes Figure second the
of the heat-transfer coefficient
during
the reaction measurements
3-20 shows the measured total calorimetric
plot
shows the measured baseline
corresponding
calculation
was
mathematical baseline
carried
out
analogous
signal
signal (shifted (proportional
to
A 58
the
qtot in the first
qcooimg
in
The
signal) compared
to the volume
description
plot.
change).
Chapter
5.2.1.
to
The This
E
second
plot clearly
temperature. deviates 24
shows
Applications: Experimental procedures
that
the
behavior of the
The measurement at 17 °C shows the
significantly
°C still shows
a
from the
supposed
similar behavior but the
of the qtot
and 4 %
Figure was
(36 °C)
curves.
no
if the measured baseline is
observed
during
all
are
by
12
baseline
replaced by
consumption
smaller.
can
(17 °C),
However the
deviation to the
6
(24 °C),
5
by
the
(30 °C)
engine.
No
change
17 °C 24 °C _
30 °C 36 °C
\\
Dosing
2(T
3CT
40
50
10
20
30
40
50
10
20
30
40
50
Comparison The
mainly
of the
dosing period caused
by
the
mathematical of the
Period
~
10
time
baseline is
and
experiments.
I
experiments.
change
be obtained
of the stirrer
,
E-14:
the
the mathematical baseline.
.
Figure
with
changes
significant
more
enthalpies
The results deviate
3-20 further shows the power
largest
changes
mathematical baseline. The reaction
integration
baseline
mathematical baseline. The measurement at
measured baselines at 30 and 36 °C show
supposed
and additional Calculations
catalyst
change
[min]
and
measured
baseline for the
epoxidation
is indicated with dashed lines. The
of the heat-transfer coefficient and is
temperature.
A 59
changing
changing
with
Appendix
Large The
standard deviation in the determined AH at 17 °C
large
(see
Table
E-12)
standard deviation of the determined AH values of the four
carried out at 17°C
(> 10%,
observations discussed above
see
Table
they
as
are
E-12) mainly
could be
explained
experiments
based
on
the
related to the measurements at 17
°C.
Change
of the color
Further it showed
was
observed that the color
increasing intensity
stored for
some
with
of the final reaction mixture
increasing temperature.
months at 4 °C and it
and thus the differences almost
(slight orange) was
disappeared.
A 60
The reaction mixtures
observed that
during
were
this time the color
E
E.3.6
Comparison the
Unfortunately rather
conditions
pseudo
are
to literature values
published
unreliable.
The
three
references
found
as
It is therefore
similar.
and
Based
concentration of
well
as
surprising the
on
the
reported
that the
the
the
published
were
not chosen
reaction
is
first
order
Table
E-13:
Epoxidation
problems of
were
were
encountered
(see
comments
parameters reported in the literature. Comments market with "?.."
Reported kj
1/min
Reported k2
1/min
Bijlsma
10 17
Hairfield
transformed
are
During
of
the
kinetic
listed below.
Mayes
This Work
0.1 0.3
0.24
?1
30
0.8
10
0.03
c
0.07
?1
17
the
below).
2,5-di-tert-butyl-1,4-benzoquinone. Comparison
T
in
and first order in the concentration of the
into third order rate constants. The calculation is summarized in Table E-13. this calculation several
as
first-order rate constants
first-order rate constants
reported pseudo
all
were
catalyst
reported pseudo that
assumption
experimental
However the concentrations of
the concentration of the
tert-butyl hydroperoxide
catalyst (Triton B),
[1/min].
turned out to be
example
summarized in Table E-13. The rate constants
tert-butyl hydroperoxide are
kinetic data for this reaction
first-order rate constants in units of
identically.
and additional Calculations
Applications: Experimental procedures
0.04
30
Reported
0.3 1.3
0.05
see
0.26
0.17
Table 5-5
68.6
82
(74)?2
Eaj [kJ/mol] Reported
73.4
69
50
36.5
EA,2 [kJ/mol] Tert-Butyl
Catalyst
HP
40%
mmol in
12
58.3
?3
ml
0.24
1
0.5
ml
31.1
50
22.5
0.8
Methanol
K
Tert-Butyl
HP
36 ?4
mol/l
0.39
1
1.62
1.62
mol/l
0.017
0.044
0.049
0.049
5.4
3.8
see
30
18.3
16.3
following
10
0.7
Concentration
Catalyst Concentration transformed
ki
[l2/mol2/min]
10
17
transformed
k2
[l2/mol2/min]
17
2.6
45.3
6
30
A 61
?5
Table E-14
1.6
0.6
5.8
2.1
Appendix
Comments to the 91
experiment reported by [Hairfield et. 10, 17 and 30 °C
The rate constants at and
energies
of
pair
one
rate
is
corresponding temperature question
was
not answered.
were
constants
al
85]
determined but
reported.
was
the activation
only
Unfortunately
the
given. Also after contacting the author the
not
Therefore the reference
temperature
was
suggested
tobe17°C.
Comments to the 92
experiment reported by [Mayes
In the article the activation energy of Ea
using
the two
was
et. al
92] to be 74 kJ/mol. However
reported
rate constants k} at 17 and 30 °C Ea
reported
was
calculated to be
82 kJ/mol. 93
Nowhere in the text it solution is
94
From the
really
40 % in Triton B. For the calculations this
to the
written that the
is
are
twenty
answer
controlled the
given by of
are
[Mayes
concentrations et.
isothermally.
reported
values
al.
given
in the
98]
out of the range
indeed
applied
the other two authors.
applied by
responded
chosen
compared
smaller than
According
were
to
to this fact with
92] because otherwise the temperature could
But the different concentrations
rate constants.
in
the
not be
not considered in
to the author the difference caused
by
the
significant.
the transformed rate constants in Table E-13 it becomes clear that the
reported by [Bijlsma
et.
al.
98] deviate significantly from the other references.
The other two references however agree E-14 and
of the
However in the text it is
et. al
completely
were
different concentrations should not be
Comparing
excess
questions.
the other references. The author
that the
answer
publication
to any of these
from the concentrations
Therefore the scaled rate constants
the
ten fold
a
fold. For the calculations the values
experiment reported by [Bijlsma
significantly
the values
calculated.
assumed.
to the calculations shown in Table E-13 the concentrations
According deviated
was
section
was
catalyst
used.
Unfortunately the author did not Comments to the
experimental
benzoquinone
excess
section
experimental
95
in the
quantities reported
hydroperoxide
stated that the concentration of the
clearly
was
compared
quite
well.
They
to the values calculated in this work.
A 62
are
summarized in Table
E
Table E-14:
Epoxidation
of
Applications: Experimental procedures
2,5-di-tert-butyl-1,4-benzoquinone. Summary
parameters reported in literature and comparison value
of the transformed
Hairfield
Separate given
are
used).
b>
rate
shown
constants
Calculated based
on
are
measurements at all
transformed
transformed
in
Table
(only
values
of
a>
Mean
Mayes
and
A, and k2 at 17 and 30 °C.c)
temperature (see Chapter 5.4.1). The values d>
to Table E-13
temperatures (see Chapter 5.4.3). The
according
E-13
the two average values of
according
of the kinetic reaction
to the calculated values of this work.
evaluation of the measurements at each
in Table 5-5
and additional Calculations
Simultaneous evaluation of all
rate constants
given
in Table 5-5
are
to Table E-13.
ki 17°C
ki 30°C
k2 17°C
k2 30 °C
Ea,1
[l2/mo 2/min] Literature
5±1a)
17±1a)
Combined
8
14
5
14
EA,2 [kJ/mol]
4±3a)
75b)
72 b)
1.1
4.5
34
72
1.2
4.2
60
70
1 ±
1a)
Evaluation c)
Combined Evaluation
Although
d)
the values shown in the first
be taken
when
using
these values for
straightforward (see problems assumption, required first
order
incorrect
in
row
comparison
discussed
to transform the
tert-butyl hydroperoxide
of Table E-14
and
rate
the
as
reasonable,
care
their calculation
should
was
not
It should also be noted that the
above).
reported
are
constants, that the reaction is
catalyst
concentration
might
be
(see Chapter 5.4.2).
However the combined evaluation of all
Chapter 5.4.3)
agrees
quite
combined evaluation of each
measurements at all
temperatures (see
well with the literature values whereas the
temperature
results in
energy £47.
A 63
a
significantly
separate
different activation
Appendix
E.3.7 Estimated pure
spectra
Estimated 17 °C Estimated 24 °C Estimated 30°C Estimated 36°C go
§1 o Educt
(Benzoquinone)
0.4
(n
0.2
.Q
<
tert-Butyl Hydrogenperoxide
co
.Q
0.5
<
0L 600
800
100
1200 tert Butanol
A 64
1400
1600
1800
E
Applications: Experimental procedures
and additional Calculations
Estimated 17 °C Estimated 24 °C
=
Estimated 30°C
2
Estimated 36°C
oo
§1 0 di
Epoxide
0.06
II0-04 00
< 0.02
Solvent 0.02
00
.Q
\K
0.01
<
»ZJLiL, I &i
MeOH 0.2
00
.Q
0.1
<
0L 600
[
i
800
1000
Hi 1200
Ln'-'k
111 1400
1600
1800
Wavenumber[cm"1], Catalyst
Figure
E-15:
Epoxidation
combined evaluation
of
(data
2,5-di-tert-butyl-1,4-benzoquinone.
set
I).
A 65
Calculated pure
spectra by the
Appendix
E.3.8
Importance of the
scaling
automatic
method for the combined
evaluation On the bases of this reaction
example
the
importance
of the
automatic
developed
scaling procedure
for the combined evaluation of calorimetric and infrared data
Chapter 4.5)
be demonstrated. Table E-15 shows the deviation of all reaction
parameters
can
determined
by
determined
individual
by
evaluation
corresponds
combined
a
evaluations the
to
temperatures (see Chapter
identification
of the
overall
the
to
reaction
calorimetric and
evaluation
5.4.3 and results in Table
of
all
(see
parameters
infrared
data.
experiments
The all
at
The combined evaluation
5-5).
is carried out two times:
Method 1: The
functions
error
AQ
and AA
(sum
simulated to the measured calorimetric and
(4-8)) AAmm
simply
are
AQmm
=
=
added
0 in
of this
with
by
automatic
respect
a
corresponds
method described in
scaling scaling
calorimetric and infrared data achieved
This
infrared
data, Equations (4-6)
setting SQ= *\, SIR=
to
to
*\ and
Equation (4-16).
Method 2: The automatic aim
together.
of squares of the deviation of the
method on
sensitivity analysis
to the reaction model
is
to
Chapter
achieve
4.5 is
of the
parameters.
This is
of the calorimetric and infrared
parameters (equal
The
influence
equal
the determined reaction
applied.
error
functions
to the evaluation shown in
Chapter 5.4.3).
Table E-15: and
Comparison
2) Developed
corresponds
of two different combination methods:
automatic
method of
scaling
to the evaluation overall
AQ and
AA
1) Simply adding AQ
(see Chapter 4.5).
and AA
The evaluation
temperatures described in Chapter 5.4.3 and Table 5-5.
Reaction
Deviation to
separate the
Parameter
Calorimetric Evaluation
[%]
Deviation to
separate the
Infrared Evaluation
[%]
Method I
Method II
Method I
Method II
kt 17°C
54
36
2
k, 24°C
52
30
6
k, 30 °C
51
25
13
kt 36 °C
49
20
19
£217°C
123
57
5
k2 24°C
110
56
7
k2 30 °C
99
54
10
k2 36 °C
90
53
12
Ea.i
2
17
14
Ea.2
8
5
4
Afli
33
33
11
ArH2
32
11
17
A 66
E
Table E-15
clearly
shows that
a
combined evaluation
functions does not lead to useful results: a
separate
evaluation
of
the
measurements of the infrared
However it should be
sign
for
a
kept
of the reaction
changes
But still the result
6.3.4).
calorimetric
spectrum
are
the two
by simply adding
error
identical to the results obtained
data
(deviations
are
all
would therefore be without any
%).
It
parameters compared
to AA
only
might
be influenced
by
function
is
AQ
(compare
use.
measurement
or
more
model
no
sensitive to
Chapters
to
by
The
in mind that the dominance of the calorimetric data is error
It is therefore essential to
get
They
tells that the
superior quality.
and additional Calculations
Applications: Experimental procedures
5.4.4 and
errors.
apply the developed automatic scaling method
in order to
real combined evaluation of the data sets. Table E-15 shows that the results
a
obtained to the
by this method
are
neither
equal to the separate calorimetric evaluation
separate infrared evaluation.
solution where the scaled reaction
AQ and
nor
They represent the best possible combined
AA have the
parameters.
A 67
same
influence
on
the determined
Appendix
E.4 Industrial reaction E.4.1
examples Reaction A:
Experimental section,
Acetylation
H+ R-OH
*~
'
E-16:
Figure
reaction. The
Acetylation
catalyst
was
OH
dosed into the reaction mixture in order to
initiate the reaction.
First the reactor and
with N2. After
purged
infrared measurement
anhydride
were
added
and the reaction were
to the
brought
was
jacket temperature T}
minutes
some
a
reference
-
background spectrum
sequently
to the reactor. The stirrer
was
10 °C
the
by
cleaned for the
mixture)
was
turned
to 550 rpm
on
set to 60°C. To start the reaction 0.4 ml of acid
dosed within 48 seconds into the closed reactor. The
liquid (water,
being
taken. Then 23.5 ml of the alcohol and 5.25ml of acetic
was
temperature Tr
alcohol
-5 °C after
temperature
of the
connected to the cooler of the calorimeter
was
cooling set to
-
cryostat.
Calorimeter
Settings:
Cooling liquid: Water,
alcohol mixture
(2:1).
Peltier Parameter Set Set A D.1 and fitted values.
AATPelt(seeDA): Filter
settings:
kLoss settings: Controller the
0.05 K
see
see
3.7.4
D.2
settings:
3.6, Point © in Figure 3-15
see
chosen 5 min after the end of
was
dosing.
E.4.2
Experimental section,
A second reaction calorimeter
example
(described
in the
25 ml of the educt solution set to
Tj
=
60
temperature within
1.5
°C,
to Tr
the =
was
Reaction B carried out
diploma was
temperature In
a
given of the
second
the
work of I. Zürcher
pre-version
cooling liquid was
initiated
experiment
seconds.
A 68
the
of the
presented
[Zürcher 01]).
into the reactor. The
100 °C. The reaction
minutes.
using
jacket temperature
was
TCry 20 °C and the reaction by dosing 0.4 ml of the catalyst
to
=
catalyst
was
dosed
within
25
E
Applications Experimental procedures
and additional Calculations
E.4.3 Measurement results These reactions
exothermal reactions
and
serious
A)
However
(example B) during
spectra
Chapter
satisfying
2 3 2 2
to the
according
all
in
the
a
point
during
Example
A:
shows the
example
the reactor content
85]
caused
(example
signals
then
were
of the reaction
The
according compared
agreement
was
carried out
of the
potential
strictly is
calorimeter to control fast and
new
isothermal conditions
reached within
only changing by
is
was
0 6 K
a
few
a
maximum
seconds, the temperature of
period
over a
Although
of about 1 minute
(see
However this reaction also showed the accuracy limits of the measured
Figure E-17)
Using is
the Peltier
parameter
about 0 7 W
5 2 to 5 4 this offset difference
might
compared
to all other
was
al.
et.
Acetylation
reaction power of about 1 3 kW/l
the reaction
the range of up to 30°C
these reactions and evaluated
profile
conversion
exothermic reactions at
base line
(RC1 [Riesen
experiments
E.4.3.1 Reaction
highly
in
The calorimetric and the infrared
predicted
Both reactions
of several minutes occurred
period
No further evaluation of the measured data
This reaction
calorimeter
strongly
isothermal-temperature controlling
time
also recorded
were
presented
conventional reaction calorimeter
Deviations from the set
problems
and 25 °C
Infrared to
a
[RC1 Handbook])
order to demonstrate that fast and
in
be handled with the
can
investigated using
were
carried out
only
were
close to the
For all the standard
error was
be caused
1
_L
and that the
Chapter
also
cooling
7 1
The
change
Chapter
reason is
for this
larger (6 W)
power of the Peltier elements
i
L
Dosing
y~
in
)
1
J
described
to 0 2 W
the fact that the baseline
by
(see
experiments
the range of 0 1
in
experiments
maximum
set A the offset of the baseline at the end of
Peroid
---^jw«(|4h^^-ä/^ ~~
¥
.
I
I
I
I
I
S
10
15
20
25
Time
Figure
E-17: Measured Tr of the reaction
kW/l has to be removed. It
only
Analogous
5-2
to
Figure
causes a
reaction power qtot
mathematical calculated
example
E-18
analogous
to
(first plot,
reaction
shows
(first plot, straight line)
baseline
A. A maximum reaction power of about 1.3
temperature deviation of about 0.6 °C.
(neutralization
(epoxidation reaction), Figure
30
[mm]
NaOH)
comparison
and
of the
E-14
Figure
total
measured
and the reaction power calculated using
dotted
Equation (5-2)
a
of
line)
and
A 69
is
The shown
mathematical in
the second
baseline
plot
of
a
was
Figure
Appendix
E-18
The measured baseline
(dotted lines).
set A. The Peltier
parameter
minimization of the qtot
parameters
was
were
not calculated based
on
obtained
least-squares
by
linear
a
the Peltier
at the end of the reaction.
signal
In contrast to the neutralization reaction of NaOH the measured baseline not caused constant
by
during
change might
the reaction
therefore be
transfer coefficient hr
viscosity
is
indicated
(Figure E-18, Such
an
third
on
linear
area
the reaction volume
as
The main
increasing viscosity, resulting
the reactor wall
by
A
(or slightly increases).
an
reason
in
a
is
remains
for the baseline
change
of the heat-
the reaction. The increase of the
during
increasing power consumption
an
of the
stirrer
engine
plot).
effect cannot be
assumes a
heat-transfer
changing
a
change
change
correctly
described
of the baseline
during
by
the mathematical
the
dosing
the mathematical and the measured baseline deviate
example.
The
baseline)
deviates
of
integration
measured baseline
by
15%.
as more
the
This
two
qtot
of the
catalyst.
significantly
(mathematical
curves
baseline, that
for this reaction and
measured
shows the benefit of
example clearly
Therefore
an
online
information about the process is available.
40 q
1tot a
1tot
-20
measured baseline mathematical baseline
Dosing
Period
12
14
16
18
20
12
14
16
18
20
0.8
S 0.7 10.6 0.5 8
10 time
Figure
E-18:
Acetylation
dosing period caused
by
the
of the
reaction at 60°C. The maximum reaction power
catalyst
change
[min]
is indicated with dashed lines. The
of the heat-transfer coefficient
viscosity.
A 70
on
equals
changing
1.3 kW/l. The
baseline is
the reactor wall due to the
mainly
increasing
E
E.4.3.2 Reaction As
this
reaction
calorimeter Both
only
maximum
period
slower
of about 1
are
potential
shown in
minute
and
kW/l
of the
new
an
reached
than the initial burst
during
within
a
reaction,
few
0.4 K
over a
with faster
experiment,
example
a
seconds.
maximum of about 2.8 kW/l
changes
of the Peltier elements. This
online measured baseline
In the first
slower
only changing by
significant
the reaction. These baseline
cooling power (qcooimg)
conditions.
In the second a
E-20.
Figure
resulting
demonstrates the
reaction calorimeter.
Furthermore both measurements also show
of
is
reaction
presented
calorimeter to control
consequently
of the reactor content is
(see Figure E-19).
new
isothermal
strictly
1.2
the
E-19 and
deviation of about 4°C. This reaction
dynamics
signal during
Figure
and the limits of the
addition
of about
power
of
pre-version
a
the reaction power reaches
temperature
limits of the
with
catalyst
temperature
catalyst addition, a
show the
reaction
However the
measured
exothermic reactions at
with
and additional Calculations
B
the measured data
highly
experiment,
in
was
experiments
fast and
Example
Applications: Experimental procedures
baseline
are
of the qComp
compensated by
example clearly
the observed baseline
as
changes
shows the benefit is much slower
change
the reaction and would be difficult to
the total
predict.
60 50 40
Cooling q
20
40
60
20
40
60
Comp
Dosing Time
80
160
20 10 0
»iw«»ii.i>j^i
)«M—'
80
>(t'«
120
140
iimi
160
100.5 ü
100
' im •*>*
,jiw*t*mi*'
i»h*i»
^
99.5 0
20
40
60
80 Time
Figure
E-19: Measured qComP and qcooung
measured reaction
100
120
140
160
[min]
(first plot),
the calculated qReact
(second plot)
and the
temperature Tr (third plot) of reaction example B (1.5 minutes dosing time).
A 71
Appendix
60
40 Cooling q
20
Comp
Dosing Time
0 0
20
40
60
80
100
120
60 40 * ^
20 0
f"
20
40
60
80
100
120
20
40
60
80
100
120
104
O102 ^
100
98 0
Time
Figure
E-20: Measured qComP and (/,„„/,„„
measured reaction A
maximum
[min]
(first plot),
the calculated qReact
(second plot)
and the
temperature Tr (third plot) of reaction example B (25 seconds dosing time).
reaction
power of 2.8
kW/l
has to
deviation of about 4°C.
A 72
be
removed. It
causes
only
a
temperature
E
E.5 The
Heterogeneous
Reaction
following heterogeneous
thesis of I. Zürcher
Applications: Experimental procedures
reaction
and additional Calculations
Example
example
was
investigated during
the
diploma
[Zürcher Ol]:
solid
Dissolution
N H
2.3-4.5 eq
MeOH, 40°C
Figure
E-21
Reaction scheme of the
work of I. Zürcher
The
applied
they
reaction
investigated during
the
diploma
[Zürcher Ol]
reaction calorimeter
versions of the
heterogeneous
presented
final
as
well
as
the evaluation
implementations. Though
cannot be evaluated for this thesis.
A 73
algorithm
the results
were were
both pre
promising
Curriculum Vitae Personal Data Name:
Andreas
Date of Birth:
November
Birth
Burgdorf, Switzerland
place:
Zogg 26, 1974
Education 1981-1987
Primary
and
1987-1994
Gymnasium
1994
Matura
1994-1996
Basic studies
secondary at
schools at
Oberburg
BE
BE
Burgdorf
certificate, type C in
chemistry, Swiss
Federal
Institute
of
Technology
(ETH Zürich) 1996-1998
Diploma
studies of technical
chemistry, Swiss
Federal
Institute
of
Technology (ETH Zürich) 1998-1999
Diploma
thesis at the Institute for Chemical and
Bioengineering,
ETH
Zürich, Safety and Environmental Technology Group (Prof. Dr. K.
Hungerbühler). "Bestimmung thermo-kinetischer Parameter mit Hilfe eines
kleinvolumigen Reaktionskalorimeters: Modellentwicklung und
Anwendung auf eine ausgewählte Reaktion." Dipl. Chem.
1999
Diploma
1999-2003
Doctoral student at the ETH K.
as
Institute for Chemical and
Bioengineering,
Zürich, Safety and Environmental Technology Group (Prof. Dr.
Hungerbühler).
ATR
ETH
"A Combined
Spectroscopy
for
the
Approach using Calorimetry and Determination
Thermodynamic Reaction Parameters
"
of
Kinetic
IR-
and
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