Determination of reaction parameters using a small calorimeter with an integrated FT-IR probe and parameter fitting

Article abstract of DOI:10.1021/op000072a

To identify optimal operating conditions of a chemical process, knowledge on kinetic and thermodynamic parameters of the main reactions is needed. In particular in the fine chemical industry during the early phases of process development this knowledge is usually low. One reason is that only small amounts of substrate are available to perform the required calorimetric and analytical experiments. Therefore, we present in this paper a new prototype reaction calorimeter with a volume of 50 mL. Despite its small volume, the reaction calorimeter is combined with an IR-ATR probe to obtain augmented information from semibatch experiments under isothermal conditions. Furthermore, we present a new method to analyze the calorimetric measurements. The novelty of the approach is that all heat flows in the calorimeter are modeled together with the chemical reaction. For general reaction kinetics this reactor model cannot be solved analytically, and thus, numerical methods are applied for fitting the model parameters to the measurement data. In contrast to the traditional method of thermal conversion the rate constants and the heats of reaction are computed at the same time. The new reaction calorimeter and the new evaluation principle of the thermal signal were both tested using a single-step second-order model reaction. Also the FT-IR data were evaluated by fitting the parameters in the reactor model numerically. The reaction parameters obtained with both measurement techniques are in good agreement with values published in the literature demonstrating the feasibility of the approach.

Full text of DOI:10.1021/op000072a

Organic Process Research & Development 2001, 5, 158−166
Determination of Reaction Parameters Using a Small Calorimeter with an
Integrated FT-IR Probe and Parameter Fitting
J o¨ rg Pastr e´ , Andreas Zogg, Ulrich Fischer,* and Konrad Hungerb u¨ hler
Swiss Federal Institute of Technology ETH, Laboratory of Technical Chemistry, Safety and EnVironmental Technology
Group, CH 8092 Zurich, Switzerland
Abstract:
analytical techniques such as FT-IR (Fourier transform
infrared) spectroscopy. Combinations of FT-IR with standard
reaction calorimeters were already presented in the literature.1
The calorimetric signal reflects the sum of all physicochem-
ical changes of the reaction system that have an impact on
the heat balance of the system, such as, for example, thermal
conductivity or a change of viscosity, which result in a
change of the heat transfer coefficient and influence the
calorimetric signal in addition to the heat produced by the
different chemical reactions. The FT-IR measurements on
the other hand reflect the sum of all chemical changes of
the system, even when the heat production is rather small.
The vast amount of chemical information is displayed in the
about 2000 wavenumbers recorded.
Unfortunately the reaction calorimeters that can be
equipped with an IR probe require a large volume on the
order of 200-2000 mL, meaning a considerable consumption
of test substance. However, in early stages of process
development the available amount of reactants is often small,
and thus the use of commercially available reaction calo-
rimeters is impeded. Therefore, we developed a small
reaction calorimeter with power compensation, which allows
stirring, different dosing profiles, and the combination with
an IR dipper.
To identify optimal operating conditions of a chemical process,
knowledge on kinetic and thermodynamic parameters of the
main reactions is needed. In particular in the fine chemical
industry during the early phases of process development this
knowledge is usually low. One reason is that only small amounts
of substrate are available to perform the required calorimetric
and analytical experiments. Therefore, we present in this paper
a new prototype reaction calorimeter with a volume of 50 mL.
Despite its small volume, the reaction calorimeter is combined
with an IR-ATR probe to obtain augmented information from
semibatch experiments under isothermal conditions. Further-
more, we present a new method to analyze the calorimetric
measurements. The novelty of the approach is that all heat flows
in the calorimeter are modeled together with the chemical
reaction. For general reaction kinetics this reactor model cannot
be solved analytically, and thus, numerical methods are applied
for fitting the model parameters to the measurement data. In
contrast to the traditional method of thermal conversion the
rate constants and the heats of reaction are computed at the
same time. The new reaction calorimeter and the new evaluation
principle of the thermal signal were both tested using a single-
step second-order model reaction. Also the FT-IR data were
evaluated by fitting the parameters in the reactor model
numerically. The reaction parameters obtained with both
measurement techniques are in good agreement with values
published in the literature demonstrating the feasibility of the
approach.
The traditional way of evaluating the thermal signal is to
2
apply the principle of thermal conversion. In this approach,
during the dosing period of a semibatch experiment, the
dosing temperature and the heat capacity of the feed have
to be known. If heats of mixing appear during the dosing
period they have to be determined in a separate experiment.
Furthermore, if the reaction is not run until completion, which
can take a long time for second-order reactions, the extent
of conversion at the end of the experiments has to be
determined by another analytical technique such as gas
chromatography.
We present a new method to analyze the calorimetric
measurements. The novelty of the approach is that all heat
flows in the calorimeter are modeled together with the
chemical reaction. The reaction model is expressed in terms
Introduction
To identify the optimal operating conditions of a chemical
process (e.g., by modeling using flow-sheeting programs)
knowledge on kinetic and thermodynamic parameters, in the
following referred to as “reaction parameters”, for the most
important main and side reactions is needed. In early stages
of chemical process development the focus lies on determin-
ing scale-up factors and macro-kinetic parameters rather than
on gathering in-depth mechanistic insight.
However, a conventional method for investigating a
reaction during process development is reaction calorimetry.
Reaction calorimeters are used mainly for safety assessments
and for understanding most necessary scale-up factors such
as heat of reaction and conversion time curves at working
temperature.
(1) (a) Landau, R. N.; McKenzie, P. F.; Forman, A. L.; Dauer, R. R.; Futran,
M. Process Control Qual. 1995, 7, 133. (b) LeBlond, C.; Wang, J.; Larsen,
R. D.; Orella, C. J.; Forman, A. L.; Landau, R. N.; Laquidara, J.; Sowa, J.
R.; Blackmond, D. G.; Sun, Y.-K. Thermochim. Acta 1996, 289, 189. (c)
LeBlond, C.; Wang, J.; Larsen, R.; Orella, C.; Sunn, Y.-K. Top. Catal. 1998,
5, 149. (d) am Ende, D. J.; Clifford, P. J.; DeAntonis, D. M.; SantaMaria
C.; Brenek, S. J. Org. Process Res. DeV. 1999, 3, 319. (e) Ubrich, O.;
Srinivasan, B.; Lerena, P.; Bonvin, D.; Stoessel, F. J. Loss PreV. Process
Ind. 1999, 12, 485.
To gather additional information on a reaction, the
reaction calorimeters are often combined with in situ
(2) am Ende, D. J..; Clifford, P. J.; Northrup, D. L. Thermochim. Acta 1996,
289, 143.
1
58
•
Vol. 5, No. 2, 2001 / Organic Process Research & Development
10.1021/op000072a CCC: $20.00 © 2001 American Chemical Society and The Royal Society of Chemistry
Published on Web 01/31/2001

Figure 1. Principle of power compensation calorimetry and experimental setup. The compensation heating is controlled by a
PID-controller. See text and Table 1 for notation.
of differential equations and comprises the change in volume
during dosing. For general reaction kinetics this reactor
model cannot be solved analytically, and thus, numerical
methods are applied for fitting the model parameters to the
measurement data. In contrast to the traditional method of
thermal conversion the rate constants and the heats of
reaction are computed at the same time.
The compensation heating controls the reactor temperature
so that it is always 4 K above the jacket temperature. When
a reaction proceeds, the power of the compensation heater
is reduced by the PID-controller, in dependence of the heat
of reaction. Such, a constant heat flow out of the vessel into
the jacket is generated as long as the reactor-sided heat
transfer coefficient does not change. The power of the
R
The new reaction calorimeter and the new evaluation
principle of the thermal signal were both tested using a
single-step second-order model reaction, for which reference
compensation heating qcomp, the reactor temperature T , the
J
jacket temperature T , the temperature difference between
jacket in- and outlet (∆TJE), and the difference between
reactor and jacket temperatures (∆TRJ) are recorded by a
LabVIEW program every 0.6 s.
3
parameters are available in the literature. Also the FT-IR
data were evaluated by fitting the parameters in the reactor
model numerically. Advantages of the new device and the
evaluation approaches are: less substance is needed for the
experiments; the temperature and the heat capacity of the
feed as well as mixing enthalpies have not to be determined;
the duration of the experiments can be shortened; and no
calibration of the FT-IR spectrometer was required.
The calorimetric device was combined via an ATR-Dipper
with an Equinox 55 FT-IR spectrometer from Bruker. The
dipper system was obtained from Axiom. The ATR crystal
is made of diamond, which combines the advantage of
chemical inertness with the disadvantage of a diamond
-1
vibrational band in the area of 2700-1700 cm . This means
a reduced amount of data because a lot of typical absorbance
bands are not visible. On the other hand, the complete
fingerprint area can be used even with high concentrations
because the pathway of the IR beam in the reaction system
is extremely short, only some µm.
Material and Methods
Experimental Setup. In Figure 1 the calorimetric device
is shown schematically. It consists of a small reaction vessel
made of glass with a cooling jacket and a lid, the latter being
equipped with an electric motor for stirring the reaction mass.
The device has a volume of 50 mL and uses the power
Determination of Device-Specific Heat Flow Param-
eters. As with most commercial calorimeters, the one
presented here also measures only one heat flow during an
experiment. For an isothermal experiment this would have
no further consequences if the heat produced by the chemical
reaction would be the only heat flow that varies over time.
All of the other heat flows could then be taken into account
by subtracting the baseline. However, in many cases the heat
transfer coefficients will change during the chemical reaction
because, for example, the viscosity of the reaction mixture
varies. Therefore, the single heat flow measured is influenced
by two processes varying over time: (i) the heat of reaction
and (ii) the changing heat flow out of the reactor into the
4
compensation approach. The vessel is not pressure-proof;
therefore, the experiments were done at ambient pressure.
The whole calorimeter is placed in an insulated box, which
is heated to the temperature of the cooling liquid (silicon
oil) in the jacket.
(
(
(
(
3) Leonhardt, J. Thermokinetische MessVerfahren im Vergleich; Wissenschaft
und Technik Verlag: Berlin, 1997.
4) (a) K o¨ hler, W.; Riedel, O.; Scherer, H. Chem. Ing. Tech. 1972, 44, 1216.
(b) Schildknecht, J. Thermochim. Acta 1981, 49, 87.
5) VDI. VDI-W a¨ rmeatlas, V. W a¨ rme u¨ bergang in R u¨ hrkesseln, 4th ed.; VDI-
Verlag: D u¨ sseldorf, 1984.
6) Zogg, M. Einf u¨ hrung in die Mechanische Verfahrenstechnik, 3rd ed.;
Teubner: Stuttgart, 1987.
Vol. 5, No. 2, 2001 / Organic Process Research & Development
•
159

Table 1. Calibration Model Describing the Heat Flows Occurring in the Experimental Device in the Absence of a Chemical
Reaction
0
) qcomp - qflow - qloss + qstir
(1)
heat flow balance
qcomp: compensation heating [W]
qflow: heat flow into the jacket [W]
qloss: heat loss through the IR dipper [W]
qstir: heat flow due to stirring [W]
1
heat loss through the IR dipper
Tdipper: temperature of the dipper [K]
qloss
)
)
(T - Tdipper) (2)
R
1
RrA
+
Pl
2
Adipper: dipper cross section [m ]
: reactor-sided heat transfer coefficient [W/K/m ]
dipper
2
R
r
2
P
l
: parameter to be fitted [m K/W]
heat flow into the jacket
: reactor temperature [K]
TJ: jacket temperature [K]
1
qflow
A (T - T ) (3)
w
R
J
1
Rr
T
R
+
PJ
2
R
A
P
r
: reactor-sided heat transfer coefficient [W/K/m ]
2
W
: wetted wall area [m ]
2
J
: function of T
J
[m K/W]
ηfl 0.14 dR -0.3
0.45
hR 0.2
equation to determine the reactor-sided
heat transfer coefficient; for notation see ref 5
-
1
2/3
1/3
h
R ) λ‚d ‚1.4‚Re ‚Pr ‚
‚
‚
‚
‚
r
B
( ) ( ) ( ) ( )
η
d
d
h
F
w
B
B
-
0.6
h
F
0.5 0.2
sin(γ) Z
(4)
(d
)
B
(
Pj•1‚TJ)
PJ is a function of the jacket temperature TJ
PJ ) e
P • + P •
(5)
j
2
j
3
P
j
•
1
- P
j
3
• : parameters to be fitted.
3
heat flow due to stirring
equation from ref 6
qstir ) P Fn
(6)
s
n: speed of the stirrer [1/s]
q
P
stir: heat flow due to stirring [W]
: parameter to be fitted
s
cooling jacket. To be able to take the changing heat transfer
coefficients into account, the device-specific heat flow
parameters have to be determined. Such a calibration has
only to be done once and can then be applied to all following
reaction measurements.
The measurements for the calibration were carried out at
steady-state conditions. The power signal of the heater (qcomp
)
was determined at different settings of jacket temperature
J
(T ) and difference between jacket and reactor temperature
(∆TRJ). The stirrer speed was kept constant at 750 rpm during
the calibration and the later reaction measurements. Toluene
and water were used as calibration fluids. The calibration
surface (qcomp vs T vs ∆TRJ) obtained for toluene is shown
J
in Figure 2.
The equations given in Table 1 describe the different heat
flows shown in Figure 1 (ignoring qreact) and considered in
the calibration model:
Equation 1 describes the heat flow balance in the
calorimeter.
Figure 2. Thermal calibration of device using toluene: Surface
of compensation power (qcomp) measured for different jacket
temperatures (T ) and temperature differences between reactor
J
and jacket (∆TRJ).
Equation 2 describes the heat loss through the IR-Dipper.
This correction is necessary because the dipper tube is made
of hastelloy steel, which is a good heat conductor. To
establish constant conditions, the outside temperature of the
dipper was controlled and kept constant at 313 K () TDipper).
Equation 3 describes the heat flow through the reactor
wall into the cooling fluid of the jacket. The overall heat
transfer coefficient can be divided into several parts. One
part, depending on the content of the reactor, is described
second part, accounting for the thermal conductivity and
thickness of the wall as well as for the jacket-sided heat
transfer coefficient, is described by the function P
J
(T
) given in eq 5, in which the parameters P
, and P have to be fitted. The parameter P
J
, P
j
•
•
1
,
,
P
P
j
•
2
2
, P
j
•
3
j
1
j
•
j
•
3
J
depends
on the temperature in the jacket, due to for example the
temperature dependence of the viscosity of the cooling fluid.
Equation 6 describes the heat flow due to stirring.
Other terms such as the heat of vaporization were
neglected in the heat balance because for the applied
temperature ranges and duration of the experiments solvent
by R
r
, the reactor-sided heat transfer coefficient. For the
was calculated according to eq 4. The
calibration liquids, R
r
160
•
Vol. 5, No. 2, 2001 / Organic Process Research & Development

dosing was omitted for the parameter fitting. Nevertheless,
the simulation of the reactor included this period because it
is important for the correct determination of the reaction
parameters. Contrary, for the evaluation of the spectra,
measurements recorded during the dosing period were
considered.
Model Reaction. We used the reaction of butan-2-ol (1)
with isocyanatobenzene (2) to phenyl-carbamic acid sec-
butylester (3) conducted in toluene to test the new calorimeter
and evaluation procedure:
Figure 3. Thermal calibration of device using toluene: Dif-
ference between measured (see Figure 2) and simulated (see
eqs 1-6 in Table 1) compensation power (∆qcomp) measured
3
The reaction is described well in the literature and the
reaction parameters are known.
J
for different jacket temperatures (T ) and temperature differ-
The molar ratio 1 to 2 was varied between 0.5 and 3.5.
The concentrations 1 and 2 were varied in the ranges from
1.5 to 5.5 mol/L and 1 to 4 mol/L, respectively. The reaction
kinetics have been described using the Arrhenius approach:3
ences between reactor and jacket (∆TRJ).
vaporization and condensation at the lid were negligible.
l j 1 j 2 j 3 s
The parameters P , P • , P • , P • , and P of the model
given in Table 1 were fitted using the measured values shown
in Figure 2. The fitting procedure was performed using the
Optimization Toolbox in MATLAB. The finally resulting
deviations between the fitted model and the calibration
measurements were in the range of 2-4% (Figure 3). The
two calibrations obtained with toluene and water agreed well.
The heat flow due to stirring was neglected for further
evaluations because for P in all cases very small values were
s
obtained. The stability of the results was checked by varying
the initial values of the parameters to be fitted.
Experimental Procedure for Determining Reaction
Parameters. Due to the sensitivity towards changes in
temperature, isothermal experiments are strictly preferred in
combination with FT-IR analysis. The experiments were
performed in the semibatch mode. The solvent and one of
the reactants were filled into the calorimeter, and the
experimental temperature as well as the temperature differ-
ence between reactor and jacket temperature were set by the
LabVIEW software. After allowing 30 min for thermal
equilibration, dosing was started using a syringe pump. To
keep the dosing time as short as possible, the feed rate was
set to a maximum value such that the PID-controller could
still maintain a constant temperature. In the work presented,
dosing was performed at a rate of 1 mL/min.
dc3
â1 â2
-(Ea/RTR) â1 â2
)
k(T )c c ) k e
c c
2
(7)
R
1
2
0
1
dt
, and c
where c
respectively, t is time, k
is the activation energy [J/mol], and â1 and â2 are the
1
, c
2
3
are the concentrations of 1, 2, and 3,
0
is the frequency factor [L/mol/s],
E
a
reaction orders of 1 and 2, respectively. The reaction has
been reported to be of second order, every reactant in the
kinetic law having an order of one. The reaction is definite
3
and homogeneous. In a wide range of temperatures the
reaction provides heat release rates that are sufficiently high
for the resolution used. In total 33 experiments with 10
different initial concentrations of the reactants have been
performed. The reactor temperature was varied from 272 to
42 K in intervals of 5 K. Reproducibility was checked by
conducting five experiments at 327 K and identical concen-
trations.
For the experiments we used Fluka and Merck KGaA pro
analysi quality chemicals, compound 2 was of g98% purity.
We did not work under strictly water free conditions.
Compound 2 was dosed to the mixture of 1 and toluene
because it is the more reactive chemical. It was checked by
NMR measurements that no unwanted side reactions pro-
ceeded like the reaction of water with 2.
Evaluation of the Thermal Signal Recorded in Reac-
tion Measurements. As data pretreatment for the thermal
signal (compensation power readings), we first applied a low
pass filtering using MATLAB and then re-sampled the
filtered data to reduce the number of measurement points.
Data pretreatment was applied to increase the performance
of the following fitting procedure.
3
First, an IR measurement was done to obtain a background
spectrum. Then, the time-resolved IR measurement was
started. The FT-IR spectra were taken every 50 s, and 40
scans each were sampled to generate one spectrum with a
resolution of 2 cm- using the Chrom software from Bruker.
The duration of the experiments from the beginning of dosing
until termination was about 150 to 250 min depending on
the experimental temperature.
1
When a reaction is proceeding, a corresponding term qreact
W] has to be added to the heat balance given in Table 1:
During early phases of process design, any additional
experiment means a significant burden. Thus, to avoid the
measurement of parameters required for an exact modeling
of the dosing period (i.e., the temperature and heat capacity
of the feed, mixing enthalpies), the power signal during
[
0
) qcomp - qflow - qloss + qstir - qreact (8)
where qreact can be described by the following equations in
Vol. 5, No. 2, 2001 / Organic Process Research & Development
•
161

which both â1 and â2 of eq 7 are set equal to one:
dn3
qreact
)
‚∆HR
(9)
(10)
(11)
dt
dn3
1
1
)
k(T )c c V
R 1 2 R
dt
n1
c1 )
VR
n2
c2 )
(12)
VR
V ) V + Vt during dosing
(13a)
(13b)
R
0
VR ) const after dosing
Figure 4. Evaluation of the calorimetric data: Measured signal
of one of the 33 experiments (317 K) after filtering (black dots)
as well as fitted model curve (black line). Data recorded during
dosing procedure (indicated by two vertical lines) are not used
for fitting.
dn1
dt
dn3
dt
)
-
(14)
dn2
dn3
vF2
)
-
+
during dosing
(15a)
dt
dt
M2
calibration is the Lambert Beer’s Law:
dn2
dt
dn3
dt
)
-
after dosing
(15b)
n3
A ) ꢀ(ν)l(ν)‚
(16)
VR
where n
respectively, ∆H
volume [L] of the reaction mass at time t, V
L] at time zero, V is the dosing rate [L/s], and F
are the density [g/L] and molar mass [g/mol] of 2, respec-
tively.
1
, n
2
, and n
is the heat of reaction [J/mol], V
is the volume
and M
3
are the number of moles of 1, 2, and 3,
R
R
is the
where A is absorbance, ꢀ(ν) is the absorption coefficient,
and l(ν) is the thickness of the medium in which the
absorption is proceeding. Both ꢀ and l are dependent on the
wavenumber, but because they are constant for a given
wavenumber, they can be combined to one factor. Equations
10-15 complete the reactor model used for evaluating the
FT-IR measurements.
0
[
2
2
As calibration is already done, the unknown reaction
R R
parameters in the model are now ∆H and k(T ). The reactor-
sided heat transfer coefficient R , which is included in qloss
r
The absorbance-time curves at selected wavenumbers
were normalized using the maximum absorbance value
recorded for a given wavenumber. Using numerical algo-
rithms, concentration-time curves for the product were
calculated. These were normalized analogous to the measured
absorbance-time curves. In the evaluation procedure realized
in MATLAB, the calculated relative concentration-time
curves were fitted to the measured relative absorbance-time
and qflow (see eqs 2 and 3), is also unknown, because the
physical properties of the reaction mixture are of course not
equal to the properties of the calibration liquids. This
parameter was dissected into a constant value describing the
heat transfer before dosing is started, a value describing the
change during dosing, and a value depending on the
conversion of the reaction.
Using the already calibrated device parameters, the
R
curves by varying k(T ). Thus, four different values of k (one
reaction parameters ∆H
R
and k, as well as the three values
for each wavenumber) were obtained for each of the 33
experiments. Arrhenius fits were done for the four wave-
numbers separately as well as for all values of k together.
As for the calorimetric measurements, also in the evaluation
of the FT-IR measurements observation of a reaction until
100% conversion is not required because parameter fitting
is applied.
describing the reactor-sided heat transfer were fitted to the
measurements obtained for various initial concentrations and
temperatures. The fitting procedure was implemented using
ACSL, and seven different initial parameter sets were used
for fitting each experiment. The k(T
as average over the results obtained for the seven initial
values, while ∆H was determined as average over all 33
experiments (and seven initial values each). The resulting
k(T ) values were plotted in an Arrhenius plot to obtain the
and k by curve fitting.
Evaluation of FT-IR Measurements. Also the time-
R
) values were determined
R
Results and Discussion
R
Calorimetry. As an example, Figure 4 shows that the
reactor is in thermal equilibrium before dosing is started.
When dosing starts, the PID-controller reduces the power
E
a
0
resolved FT-IR signals were evaluated by parameter fitting
for determining kinetic rate constants assuming that Lambert
Beer’s law is strictly fulfilled. Four wavenumbers (1540,
R
of the compensation heating to keep T strictly constant (the
maximum temperature deviation recorded during all experi-
ments was 0.3 K). As explained above, the data points
recorded during dosing were omitted for the parameter fitting
(and therefore are not shown in Figure 4), while the
-
1
1443, 1224, and 1053 cm ) belonging to the spectra of the
product 3 were selected. The basis of the fitting without
162
•
Vol. 5, No. 2, 2001 / Organic Process Research & Development

Table 2. Reaction Parameters Obtained for the Model Reaction as well as Comparison to Literature Valuesa
3
f
power compensation calorimeter
FT-IR: fit to absorbance values
40 ( 1b
literature : several methods
E
a
[kJ/mol]
33 ( 1b
96 ( 1b
41
(
39-44)
1800
1400-2100)
5.1E-4
k
0
[L/mol/s]
1200 ( 230b
(
c
e
g
k (327 K) [L/mol/s]
∆H [kJ/mol]
5.0E-4 ( 1E-5
5.9E-4 ( 2E-5
-
-
R
93 ( 19d
85
(
82-90)
a
See text for further explanation on derivation of standard deviations. The term “initial values” refers to the different start values used in the fitting procedure.
b
Standard error obtained from least square fitting (Arrhenius plot). c Standard deviation obtained for results from five replicate experiments and seven different initial
values each. d Standard deviation obtained for results from all 33 experiments and seven different initial values each. Standard deviation obtained for results from five
e
-1 f
replicate experiments using the wavenumber 1540 cm
Calculated from mean values for k and E .
0 a
. Mean values as well as minimum and maximum values (in brackets) obtained from different methods.
g
Figure 5. Evaluation of the calorimetric data: Arrhenius plot of the fitted kinetic rate constants for the determination of k
0
and
a
E . The data points represent 33 experiments for which each 7 initial values were used in the fitting procedure. The numerical
values obtained are given in Table 2.
simulation of the reactor also included this period. Although
this procedure means that less data are available, it is feasible
because not the concept of thermal conversion was used for
determining the reaction parameters but instead parameter
fitting was applied.
in nonuniqueness of the optimization problem. When for the
determination of ∆H one set of initial parameters was used
for evaluating all experiments, a mean deviation over seven
sets of initial parameters of 20% was obtained. Similarly, a
three times higher average deviation was obtained for the
R
When the principle of thermal conversion is applied, the
area under the baseline of a calorimetric signal is integrated
to obtain the heat of reaction. For this procedure almost
complete conversion must be observed. Contrary, in the
present work from the 33 measurements used for determining
the heat of reaction only the measurements at temperatures
above 313 K were conducted until almost 100% conversion
was reached. All other experiments were stopped at a
conversion of about 90%.
evaluation of k(T
R
R
) and ∆H from five replicate experiments
conducted at 327 K and identical concentrations when the
experimental effects on the results were considered in
addition to the purely numerical ones. The overall variability
in determining these two parameters from replicate experi-
ments is 2% for k(T
reproducibility of the approach.
The value obtained for ∆H
reported in the literature (Table 2). It is important to mention
that the literature values referenced in Table 2 are average
values obtained from calorimetric measurements done in
isothermal, isoperibol, adiabatic, as well as temperature-
R R
) and 4% for ∆H , thus showing a high
R
agrees well with the one
As an example, Figure 4 shows that the fit of the reaction
model agrees well with the power compensation signal
recorded. The average deviation for determining k(T
R
) and
3
∆
H
R
from a single experiment using different initial values
programmed measurements.
of the parameters to be fitted is 7 and 6%, respectively. These
deviations result mainly from the fact that the three heat
transfer parameters have to be fitted as well, thus, resulting
The k(T
in an Arrhenius plot in Figure 5. The values of k
fitted to these data are somewhat different than those reported
R
) values fitted for the 33 experiments are shown
0
and E
a
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163

Figure 6. Comparison of Arrhenius plots obtained from the calorimetric as well as from the FT-IR data with results reported in
3
the literature. The numerical values obtained are given in Table 2.
Figure 7. Section of the time-resolved absorbance spectra
Figure 8. Plot of the relative absorbance recorded at 317 K
obtained at 317 K. Growing bands represent the increasing
-1
and 1540 cm versus time: Points represent the measured and
normalized absorbance, while the line represents the fitted
model curve. All data including those sampled during dosing
are used in the fitting procedure.
amount of product. The wavenumbers marked by black lines
were used for the fitting procedure.
in the literature (Table 2), but in the investigated temperature
range (272-342 K) the resulting k(T
of magnitude as can be seen from Figure 6. The general
R
) have the same order
agree well for the four wavenumbers and a given temperature
because they all represent the concentration of the same
product molecule. Consequently, also the values obtained
applicability of the Arrhenius model is demonstrated by a
2
value of r of 0.97.
for k
shown by the curves in Figure 9. Therefore, in a final step
and E were determined from fitting all k values obtained
for the four wavenumbers together (Table 2). The resulting
values of k and E result in k(T ) values that agree well
0 a
and E and the different wavenumbers agree well as
FT-IR Measurements. In Figure 7 a section of the time-
resolved FT-IR spectra is shown, in which the four wave-
numbers used for evaluation are marked by black lines. The
fit of the kinetic model to the absorbance at 317 K and 1540
k
0
a
0
a
R
-
1
cm is shown in Figure 8. A good agreement between
measurements and simulation was obtained in this as well
as in all other cases. Unlike the calorimetric evaluation, here
the fitting is done for the whole semibatch.
with the results reported in the literature (Figure 6). The value
for k (54 °C) agrees well with that obtained from calorimetry
2
and literature results (Table 2). A value for r of 0.98 again
supports the applicability of the Arrhenius law. As already
discussed, the FT-IR cannot give the reaction enthalpy like
the calorimetric measurement.
To ensure that only bands of the product were used, FT-
IR spectra of the pure components were taken (Figure 10).
The fitting results derived from the FT-IR measurements
are shown in Figure 9 as well as in Table 2. The Arrhenius
plot in Figure 9 shows the values for the kinetic rate constants
resulting from the mentioned fit procedure. These values
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Figure 9. Evaluation of the FT-IR data: Arrhenius plots of the fitted kinetic rate constants determined from the four wavenumbers
indicated in Figure 7. Symbols represent measurements, and lines, the corresponding Arrhenius fits. The values resulting from
fitting the k values obtained for all four wavenumbers together are given in Table 2.
Summary and Conclusions
In our work we were able to show that it is possible to
work with a small calorimetric device which can provide
augmented information by the use of an additional on-
line measurement technique (FT-IR in our case). Repro-
ducible measurements were obtained with both the calori-
metric and the FT-IR technique, and the resulting reaction
parameters are in good agreement with literature values.
Thus, the feasibility of the whole approach (small device,
parameter fitting instead of principle of thermal conversion,
combined measurements) was shown with a simple model
reaction.
Crucial constants during process development are the
amount of reactants and the time needed to perform experi-
ments. Considering that a standard reaction calorimeter with
Figure 10. Absorbance spectra of the pure components.
FT-IR is 10-40 times larger than the one presented, during
the development phase of a new process many more
experiments could be done with the same mass of reactants
if the smaller device is used. We used the same quantity of
chemicals for 33 measurements than one experiment in a
standard calorimeter with a volume of 1.5 l would have
needed.
By applying parameter fitting for the evaluation of the
thermal signal, the time needed to perform experiments can
be shortened significantly, because complete conversion of
the reactants is not required (most of the experiments were
stopped at about 90% conversion). With the conventional
calorimetric assessment (based on the principle of thermal
conversion) the experiments can only be shortened when the
conversion at the end of the experiment is determined by
another analytical technique such as gaschromatography.
Furthermore, for the new procedure the temperature and heat
capacity of the feed as well as mixing enthalpies have not
to be determined.
When discussing Figure 10, one has to be aware of the fact
that the relative absorbance between the various species is
altered as compared to the reaction mixture, where the
concentrations are different. The mixture might have slightly
shifted absorbance bands due to the presence of hydrogen
bonds.
In this work wavenumbers unique to a single compound
could be identified and were used for the evaluation of the
kinetic parameters. For each wavenumber a linear depend-
ency between absorbance and concentration of the product
was assumed (eq 10) so that the rate constants could be
obtained by direct fitting. We are aware of the fact that not
in all cases a sufficient number of unique wavenumbers can
be identified to make a direct fit. In these cases more
sophisticated chemometric and factor analytical techniques
have to be applied to obtain the reaction parameters from
the FT-IR measurements.
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In the approach presented additional information is
provided by online spectroscopic measurements. For the
simple reaction investigated in this work, reaction parameters
could be obtained from each measurement technique sepa-
rately. For more complex reactions the combined evaluation
of the two sources of information will be required.
Due to the fact that more experiments can be performed,
more possible working conditions of a reactor can be tested
in detail so that at the end of the development phase much
more knowledge would be available. In summary, the new
device presented in this paper is a valuable tool for
determining reaction parameters in early stages of process
development.
Acknowledgment
We thank Dr. P. Skrabal and Dr. O. Kut for comments
on the manuscript and F. Mayer, P. Steiner, H. P. Schl a¨ pfer,
and M. Wohlwend for technical support.
Received for review July 3, 2000.
OP000072A
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