Development of a modeling-based strategy for the safe and effective scale-up of highly energetic hydrogenation reactions

Article abstract of DOI:10.1021/op500207r

A modeling-based strategy is disclosed for identifying reaction conditions for the safe and effective scale-up of highly energetic hydrogenation reactions. The model was developed within Scale-up Systemss DynoChem 2011 and takes under consideration the kinetics of the reaction, the reactor heat transfer capabilities, and the degree of mass transfer. Fourier transform infrared spectroscopy (FT-IR), heat flow, and H₂ uptake data were used to determine the reaction kinetics that were found to be most accurately described by a Langmuir-Hinshelwood type model. The scale-up model was validated within our kilo-laboratory using a 5 L reactor.

Full text of DOI:10.1021/op500207r

Article
pubs.acs.org/OPRD
Development of a Modeling-Based Strategy for the Safe and
Effective Scale-up of Highly Energetic Hydrogenation Reactions
Christopher W. Mitchell, Josiah D. Strawser, Alex Gottlieb, Michael H. Millonig, Frederick A. Hicks,
and Charles D. Papageorgiou*
Takeda Pharmaceuticals International Co., Chemical Development Laboratories-Boston, 40 Landsdowne St, Cambridge,
Massachusetts 02139, United States
S
* Supporting Information
ABSTRACT: A modeling-based strategy is disclosed for identifying reaction conditions for the safe and effective scale-up of
highly energetic hydrogenation reactions. The model was developed within Scale-up Systems’s DynoChem 2011 and takes under
consideration the kinetics of the reaction, the reactor heat transfer capabilities, and the degree of mass transfer. Fourier transform
infrared spectroscopy (FT-IR), heat flow, and H2 uptake data were used to determine the reaction kinetics that were found to be
most accurately described by a Langmuir−Hinshelwood type model. The scale-up model was validated within our kilo-laboratory
using a 5 L reactor.
the reaction and result in changes to the impurity profile,
meaning this approach should optimally be considered early in
development to ensure that a product of acceptable quality is
manufactured.6,7
INTRODUCTION
■
The batchwise reduction of aromatic nitro groups to their
corresponding anilines in the presence of H2 and a suitable
catalyst is a key step in the manufacture of numerous
pharmaceutical intermediates. These reactions are usually
highly exothermic, and their successful scale-up necessitates
understanding the mixing performance of both the develop-
ment-scale and proposed plant-scale reactors.1−4 The rate of
gas uptake in any gas−liquid−solid reaction, in this case a
hydrogenation, is dependent on the interplay of two factors:
supplynamely mass transfer, both of gas into the liquid and
then from the liquid to the solid phaseand demandthe rate
of gas consumption by the reaction.5 The driving force behind
the dissolution of a gas into a liquid is the magnitude of the
difference between the current gas concentration in the liquid
and the maximum possible concentration of gas in that liquid at
the saturation point. The saturation point is affected by the
temperature, the pressure, and the solvent and is defined by
Henry’s Law. The gas−liquid mass-transfer coefficient, or kLa, is
the rate constant for the dissolution of a gas into a liquid and is
dependent on the surface area of the gas−liquid interface which
is itself highly dependent on the degree of mixing. In the case of
a hydrogenation, if the kLa is much larger than the rate of the
reaction, the concentration of H2 in solution is maintained near
the saturation concentration and the reaction is said to be
kinetically controlled. However, if the kLa is much smaller than
the rate of the reaction, then the solution hydrogen
concentration is close to zero, the catalyst is starved, and the
reaction rate is retardedthis is described as mass-transfer
control. Assuming other mass-transfer processes (namely
liquid−solid mass-transfer) are not rate-limiting, then it is
possible to modulate the reaction rate and consequently the
rate of heat evolution by varying the kLa and hence the rate of
hydrogen uptake. A cautionary note is that catalyst starvation
resulting from operating under mass-transfer control could
potentially lead to catalyst denaturation and subsequent loss of
catalytic activity. This has the potential to alter the selectivity of
Recently, the heterogeneous hydrogenation of nitropyrimi-
dine 1 was scaled-up to an 11 kg scale in a 200 L hydrogenator
(Scheme 1). This reaction proved to be highly exothermic (a
20 °C exotherm was recorded within the first 20 min of the
reaction in spite of maximum cooling power being applied) and
the hydrogen dosing system was found to be unable to keep up
with demand. As a result the operator was required to
periodically adjust the agitation speed in order to control the
exotherm and maintain the batch temperature within the
desired range. A subsequent investigation showed that during
process development the reaction had always been performed
under mass-transfer control and in a system capable of very
efficient heat removal, whereas in the pilot plant, due to the
reduced surface area to volume ratio available for heat
exchange, the heat removal capabilities were significantly
lower, and the system was incapable of controlling the
exotherm. As a result, a project was initiated to better
understand the dependence of the reaction profile on the
degree of gas−liquid mass-transfer and to develop a strategy to
predict the reaction conditions required for optimum perform-
ance on scale, minimizing plant time while ensuring safety and
desired product quality.
In this paper a scale-up strategy for highly exothermic
hydrogenation reactions is reported based on the creation of a
suitable computational model that considers the kinetics of the
reaction, the reactor heat transfer capabilities as well as the
degree of gas−liquid mass-transfer. The model is able to predict
both the kinetic and temperature profiles of the hydrogenation
Special Issue: Safety of Chemical Processes 14
Received: June 26, 2014
© XXXX American Chemical Society
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Scheme 1. Hydrogenation of substituted nitropyrimidine 1
of nitropyrimidine 1 with varying temperature, pressure,
substrate loading, catalyst loading, and agitation rate and has
been used to predict performance upon scale-up. Fourier
transform infrared spectroscopy (FT-IR), heat flow, and H2
uptake data were used to construct a suitable kinetic model
within Scale-up Systems’s DynoChem 2011 which was then
employed to simulate various scenarios and select appropriate
process parameters.8 These parameters were then validated
experimentally.
occur concurrently with the reduction step, for the purposes of
measuring conversion both aniline 4 and amide 5 were
combined into a single product species. In order to minimize
the error and increase the sensitivity of the model, the second
derivative of the raw data was used, and additional baseline
correction and scaling were found to be necessary in order to
normalize the data to accurately reflect both the initial charges
of nitropyrimidine 1 and the actual conversion to aniline 4 and
amide 5, as measured by HPLC. The FT-IR model was
validated by leave-one-out cross-validation (LOOCV) and
shown to be robust with R-squared values of 0.993 when
compared against the training points and 0.979 when compared
against the test points. This approach was able to extract trends
from the FT-IR data that matched the reaction profile as
measured by HPLC and enabled molar reaction data to be
obtained without requiring off-line analysis, although samples
were taken periodically to confirm the continued accuracy of
the FT-IR model. Separate FT-IR models were generated for
each temperature investigated to account for the temperature-
dependent intensity changes of the IR spectra.
Heat-flow calorimetry was used to determine the heat flow
into or out of the reaction system. The reaction temperature
was controlled isothermally via the modulation of the jacket
temperature. The heat flow is directly proportional to the
difference of the reaction and jacket temperatures defined by
the equation: Q = UA(Tr − Tj) [Q = heat flow (W); U =
overall heat transfer coefficient (W/(m2/K)); A = heat transfer
area (m2); Tr = reaction temperature (K); Tj = jacket
temperature (K)].9 The UA of the vessel was determined by
applying a known amount of power via a calibration heater
probe immersed in the reaction mixture and measuring the
resultant change in both reaction and jacket temperatures. The
reaction heat flow Qr was then calculated from the total heat
flow, Q, after accounting for any other heat flows present
including heat loss to the surroundings and the heat capacity of
the reaction mixture.
EXPERIMENTAL SECTION
■
Experimental Set-up. The hydrogenation of nitropyrimi-
dine 1 was performed in a Mettler Toledo RC1 reactor system
equipped with a 1 L glass pressure vessel rated to 90 psia, a
gassing impeller (Rushton turbine with a gassing shaft), a single
beavertail baffle, temperature probe, calibration heater probe,
an in-line FT-IR probe and a double-valve dip-tube sampling
system (see the Supporting Information for a PI&D of the
experimental setup). All reactions were conducted at a constant
H pressure which was delivered using a Buchiglasuster BPC
̈
2
controller through a PKP thermal mass-flow meter calibrated
for H2. The number of moles of H2 consumed during the
reaction was calculated by integrating flow rate over time and
subsequent conversion of the cumulative H2 volume into moles
using the ideal gas law.
High-pressure liquid chromatography (HPLC) calibration
curves were generated for nitropyrimidine 1 and amide 5 using
an Agilent 1100. Aniline was used during the reactions as an
internal standard to ensure reproducible sampling and
normalize peak area. Off-line HPLC analysis was conducted
by removing samples (3−5 mL) through a double-valve dip-
tube, which avoided the need to depressurize the system−
multiple blank samples were removed between samplings to
prevent cross contamination. The fleeting intermediates nitroso
2 and hydroxylamine 3 (Scheme 1) were never observed in
sufficient amounts, nor were standards available to allow for
quantification so they were not tracked.
The FT-IR measurements were conducted using a ReactIR
45m system with a DST 9.5 mm × 1.5 m × 305 mm DiComp
probe through the icIR software, both developed by Mettler
Toledo. Differences in the spectra between 1125 and 1800
cm−1 were correlated to off-line quantitative HPLC data and
molar hydrogen uptake data using a partial least-squares (PLS)
model. As the objective was to study the hydrogenation and not
the secondary cyclization, and since the latter was found to
Determination of Mass-Transfer Coefficients. The
mass-transfer coefficients were determined according to the
batch absorption method.10−13 Each experiment was conducted
in triplicate and the average kLa value determined for each
condition investigated. In order to avoid introducing error, the
system leak rate was measured prior to each run and was always
found to be insignificant with respect to the rate of mass-
transfer induced pressure drop (typically <1 mbar/min). A
statistical model was developed within JMP 9.0.0 (SAS Institute
Inc.) that was then used to predict mass-transfer coefficients for
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Chart 1. Data collected during the laboratory-scale evaluation of the plant conditions (agitation started at the 4 min time-point)
our laboratory reactors with varying reactor fill-volume,
agitation speed, pressure, temperature, and solvent (see the
Supporting Information for the experimental procedure for the
determination of kLa, as well as further information on the
generation of the model).
RESULTS AND DISCUSSION
■
Evaluation of Plant Conditions. An experiment was
initially conducted in the RC1 calorimeter to evaluate the plant
conditions of 20 °C, 30 psia H2, THF (5 L/kg), acetic acid (2
equiv), NH4VO3 (5 wt %), and 3% Pt/C catalyst (20 wt %).
The agitation speed was set as high as possible (2000 rpm) in
order to ensure a high mass-transfer rate. Hydrogen uptake,
FT-IR, and heat flow data were all consistent with each other,
showing reaction completion within 30 min and demonstrating
that reaction conversion can be monitored in three different
ways (Chart 1).14 Moreover, the reaction was, as expected,
highly exothermic with a heat of reaction of 634 kJ/mol of
reactant corresponding to a theoretical adiabatic temperature
rise of 97.5 °C. Under these conditions the reaction was not
isothermal, and a temperature rise of 14 °C was observed as
shown in Chart 1.
Effect of Ammonium Metavanadate. Ammonium
metavanadate is a common additive that was included in the
original reaction conditions in order to reduce the amount of
hydroxylamine 3 present during the reaction, as accumulation
of such hydroxylamines is known to present a potential safety
hazard.15 An additional experiment was performed using the
plant conditions but omitting the ammonium metavanadate in
order to determine any effect that it might have on the reaction.
The HPLC profile over the course of the reaction was
monitored and did not show any appreciable differences
compared to that of the plant conditions. Furthermore, the data
shown in Chart 2 clearly showed that ammonium metavanadate
did not exert a significant effect on either the rate or heat
evolution of the reaction and suggested that it could be omitted
from all subsequent experiments in order to simplify the
reaction system and subsequent modeling activities.
General Experimental Procedure. All reactions, unless
otherwise stated, were run on a 50 g scale (nitropyrimidine 1 as
the limiting reagent). The solvent, THF, was charged to a clean,
dry, nitrogen flushed 1 L jacketed pressure reactor followed by
all the solids (nitropyrimidine 1, ammonium metavanadate and
Johnson Matthey 3% Pt/C catalyst, type B502032-3, 50% wet
-not corrected for water content) and finally acetic acid. The
reactor was sealed and inerted by performing three N2 pressure-
vacuum cycles (pressurized to 30 psia N2) while agitating above
the impeller gassing speed (in this case at 500 rpm) with all
solids being visually well-suspended. The reaction mixture was
then heated to the desired temperature, and a calibration was
performed using the calibration heater probe in order to obtain
the initial UA and heat capacity values. The reactor was inerted
again by performing three N2 pressure-vacuum cycles
(pressurized to 30 psia N2) before suspending the agitation
and exchanging the headspace atmosphere for H2 by perform-
ing three pressure-vacuum cycles (pressurized to 30 psia H2).
The desired pressure of H2 was then set, and the reaction was
initiated by switching on the agitator at the desired set point.
The temperature (both reaction and jacket), pressure, hydro-
gen flow, and FT-IR data were recorded, and samples for off-
line HPLC analysis were removed through the double-valve dip
tube as required (the sampling lines were rinsed between
samples with enough THF such that the waste solvent was
visibly free of particulates). Finally, after the reaction had
reached completion, the calibration was repeated using the
calibration heater to obtain the final UA and heat capacity
values.
Determination of Kinetic Control Conditions. In order
to determine the true kinetics of the reaction, plant conditions
operating under kinetic control needed to be identified.
Therefore, the agitation speed was varied from 800 to 2000
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different pressures was found to be 1.67 which demonstrates
that the reaction does not follow first order kinetics with
respect to H2 concentration. This is typical of heterogeneous
hydrogenation reactors and is indicative of a more complex
reaction mechanism possibly involving the adsorption of one or
more of the species involved in the reaction onto the surface of
the catalyst.
Chart 2. Effect of ammonium metavanadate on the
temperature and reaction profiles
Effect of Liquid−Solid Mass-Transfer. In order to
determine the impact of liquid−solid mass-transfer on the
rate of reaction, two otherwise identical experiments (using the
plant conditions) were run under conditions of gas-liquid mass-
transfer control (at a kLa of 0.4 s−1), one with the typical 20 wt
% catalyst loading and the other doubled to 40 wt % catalyst
loading. The rates of these two reactions were identical and
resulted in superimposable reaction profiles (Chart 4). It is
therefore valid to assume that liquid−solid mass-transfer is not
rate-limiting allowing us to neglect its contribution to the
observed rate in all subsequent experiments.
Chart 4. Effect of increased catalyst loading on the reaction
rate when under gas-liquid mass transfer limited conditions
(kLa 0.4 s−1)
rpm (corresponding to estimated kLa values of 0.4−1.5 s−1
using the model described in the Supporting Information). It
was expected that the observed rate of reaction would increase
as the kLa increased until it reached a plateau at which point the
reactor would be maintained near the H2 saturation
concentration. Indeed, as shown in Chart 3, above 1600 rpm
Chart 3. Effect of agitation speed on the reaction rate
Development of the Kinetic Model. In order to
determine the kinetics of the reduction of nitropyrimidine 1,
it was important to first identify isothermal conditions under
which to operate, as changes in the temperature during the
course of the reaction would affect the observed kinetics. This
was achieved by fixing the kLa at 1.5 s−1 and reducing the
catalyst loading from the initial 20 wt % to 4 wt % resulting in a
reduction of the reaction exotherm from 12.7 to 0.9 °C (Chart
5).
A kinetic model for the hydrogenation of nitropyrimidine 1
based on first-order kinetics was initially developed within
Scale-up Systems’s DynoChem 2011. The rate constants of the
three chemical transformations (that is nitropyrimidine 1 →
nitroso 2 → hydroxylamine 3 → aniline 4 + amide 5, Scheme
1) were fitted to the available molar data obtained from a
reaction performed at 20 °C, 30 psia, and 4 wt % catalyst. While
good fits were obtainable for any single data set, the model was
unable to be extrapolated and failed to predict the outcome of
test reactions performed under varying conditions, as shown in
Chart 6a. This is not surprising as it was shown earlier that the
reaction does not follow first-order kinetics.
there was no significant change in the reaction rate and
therefore all subsequent experimentation using the RC1 1 L
pressure vessel was performed at an agitation speed of 2000
rpm.
Effect of Pressure. The effect of pressure on the rate of
reaction was investigated by performing two otherwise identical
experiments (under the plant conditions) with a kLa of 1.5 s−1
at both 30 psia and 60 psia. The initial rate of nitropyrimidine 1
consumption was determined by measuring the gradient of the
initial linear portion of the curve during the first few minutes of
the reaction. The ratio of the two rates measured at the two
This behavior is indicative of the adsorption of one or more
species onto the surface of the catalyst as described by the
Langmuir−Hinshelwood model.16−18 This model accounts for
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Chart 5. Effect of catalyst loading on the observed reaction exotherm (agitation started at the 3 min time point)
Chart 6. Comparison of first-order kinetic model vs Langmuir−Hinshelwood model: kLa 1.5 s−1, [nitropyrimidine 1] 0.528 M,
60 psia H2, 20 °C
species adsorbing onto active sites present on the surface of a
catalyst at a rate proportional to both the partial pressure (or
concentration) of the species and the number of uncovered
active sites on the catalyst. Once adsorbed onto the catalyst
surface, the species react to form adsorbed products at a rate
proportional to their respective concentrations on the catalyst
surface. The adsorbed products finally desorb into the gas (or
liquid) phase at a rate proportional to the concentration of the
covered fraction of the catalyst surface.
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In applying the Langmuir−Hinshelwood model to this
reaction system, the individual equilibrium constants for both
the adsorption and desorption of each of the species present in
the reaction need to be considered as well as the fundamental
reaction steps, described in Scheme 1. These processes are
shown in Figure 1 which also describes each phase present in
Table 1. Kinetic parameters obtained from DynoChem 2011
using the Langmuir−Hinshelwood model
rate
constant
(L/mol·s)
equilibrium
constant
(L/mol)
activation
energy
(kJ/mol)
a
step
H2 + cat = H2cat
b
50000
166
8
b
Nitro + cat = Nitrocat
50000
b
Nitroso + cat = Nitrosocat
Hydroxyl + cat = Hydroxylcat
Product + cat = Productcat
50000
7652
4
b
50000
b
50000
14
Nitrocat + H2cat > Nitrosocat +
H2O + cat
3013
4148
4901
27
5
Nitrosocat + H2cat > Hydroxylcat
c
+ cat
Hydroxylcat + H2cat > Productcat
67
c
+ H2O + cat
a
The symbol “=” is used to denote a reversible reaction, while “>”
b
denotes an irreversible reaction in the forward direction. Parameter
values were manually defined and not obtained through fitting to
c
experimental data. Steps are not rate-limiting therefore, kinetic
parameter values are arbitrary and not statistically significant.
(Table 1). These activation energies were then successfully
used to predict reaction outcomes at other temperatures (e.g.,
30 °C) demonstrating the ability to accurately model the
temperature dependency of the system.
In order to model the heat flow of the reaction, once all of
the kinetic parameters had been fitted, the heats of reaction
(ΔH) of the three chemical transformations were fitted to
experimentally obtained heat flow data. This attempt yielded no
advantage, in terms of statistical significance, over simply using
standard literature values for the heats of these transformations.
As such it was decided to use the literature values moving
forward.
Figure 1. A graphical representation of the Langmuir-Hinshelwood
type kinetic model within DynoChem 2011. The symbol “=” is used to
denote a reversible reaction while “>” denotes an irreversible reaction
in the forward direction. Both aniline 4 and amide 5 have been
combined into a single species, product.
the system, the constituents comprising those phases along
with any reactions taking place. All heat- and mass-transfer
statements between the phases are also shown.
Development of the Physical Model. The kinetic model
was then expanded to include the physical aspects of the
system, including the equipment used, namely the hydrogen
dosing system and the heat exchanger. In addition, the
relationship between agitation rate and the mass-transfer
coefficient kLa was defined. Using kLa values obtained from
the developed statistical model, a simple regression of agitation
speed vs mass-transfer was plotted, and the slope and intercept
of this straight line were included in the model enabling the
selection of the appropriate kLa for any defined agitation speed
within the regressed range. The maximum rate of hydrogen
dosing was obtained from the equipment specifications sheet. A
simple regression defining the relationship between the heat
transfer coefficient (UA) and the agitation speed was created
from experimentally obtained data and used to define the
reactor’s varying heat removal capability with changing
agitation speeds. The response of the heat exchanger was
defined by proportional and integral (PI) gain constants. Initial
attempts to fit the PI constants to experimental data failed.
Therefore, they were obtained by manually varying them until
the resultant model was visually able to describe the reaction
temperature profile of a test reaction performed within the
equipment. In order to model jacket temperature the heat
exchanger would need to be fully characterized, for example the
relationship between the master and slave controller, the flow
characteristics of the heat transfer fluid, and the type and
response time of individual valves within the system would all
need to be defined. As the goal of the project was to model the
reaction temperature and predict the maximum exotherm, such
characterization was not performed.
It was assumed that the rate of the adsorption processes is
rapid with respect to the rate of the chemical transformations
(as liquid−solid mass-transfer was previously shown not to be
rate-limiting), and therefore each of the five adsorption rate
constants was set to an arbitrarily high value and fixed (i.e., not
fitted to experimental data, Table 1). The adsorption
equilibrium constants and the rate constants of the three
chemical transformations were then fitted to experimentally
obtained molar data at a single temperature (20 °C). The rate
constants (Table 1) obtained using this approach were able to
successfully predict the outcome of a test reaction shown in
Chart 6b. As mentioned previously, data were not available to
describe all of the intermediate reactions, and consequently
where data were not available for fitting, the modeled rate
constants for those steps were not statistically significant. In this
system the rate-limiting step was found to be the initial
reduction of nitropyrimidine 1 to nitroso 2 (Nitrocat + H2cat >
Nitrosocat + cat + Water) for which data were available. As
only the rate-limiting step appears in the overall rate equation,
the fact that the rate constants for the other steps were not
significant does not have an effect on the overall prediction; in
fact these rate constants could, if desired, simply be arbitrarily
assigned a high value and then not fitted.
These fitted chemical rate and adsorption equilibrium
constants were then fixed and, in combination with data
obtained at a second temperature (40 °C), used to fit the
activation energies of the three chemical transformations
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However, the loss to the surroundings was accounted for by
creating a “surroundings phase” within the model. This
“surroundings phase” was assigned a mass several orders of
magnitude larger than that of the reaction system and was given
the initial temperature of 22 °C (i.e., ambient temperature).
Heat transfer statements were defined between each of the
reaction phases (headspace and bulk liquid) and the
“surroundings phase”. The UA values defining the extent of
this heat transfer were then fitted to supplied reaction
temperature data. This approach was found to be very effective
and permitted the generation of modeled reaction temperature
data that provided a good fit to experimentally obtained test
data across the investigated temperature range of 20−40 °C.
Validation of the Physical Model. The physical model
was then applied to the original plant conditions (described in
the first section) and used to predict the maximum reaction
temperature under different mass-transfer conditions in a
laboratory scale 5 L Hastelloy C-22 pressure reactor. Not
surprisingly these predictions (shown in Chart 7) show that the
maximum reaction temperature increases with increasing kLa
(or agitation speed) and that it should be possible to control
the maximum reaction temperature to within a defined limit,
simply by selecting the appropriate agitation speed. A number
of reactions were performed on a 320 g scale with respect to
nitropyrimidine 1, to test the validity of these predictions. The
results obtained from one of these experiments (700 rpm, kLa
0.5) are shown in Chart 8 and demonstrate good agreement to
the predicted temperature profiles, while the maximum
exotherm measured during each experiment is plotted against
the predicted curve in Chart 7.
CONCLUSIONS
■
It has been demonstrated that the highly exothermic hydro-
genation of a substituted nitropyrimidine can be successfully
modeled by performing a small number of reactions and taking
advantage of in-line process analytical tools (FT-IR and H2 gas
uptake) to collect detailed reaction profile data without
necessitating the tedious analysis of off-line samples. Utilizing
Scale-up Systems’s DynoChem 2011, it has been possible to use
this data to create both a comprehensive kinetic model and a
simplified physical model capable of predicting reaction
temperature profiles as well as the maximum expected
exotherm, as a function of agitation speed. This approach
could form the basis of the scale-up strategy for successfully and
safely scaling both this and other classes of highly exothermic
reactions.
Chart 7. Effect of kLa on maximum reaction temperature in a
5 L pressure reactor, experimental results (points) vs
predicted (line)
ASSOCIATED CONTENT
■
S
* Supporting Information
Further details on the equipment setup, a general experimental
procedure for the determination of kLa via the batch-absorption
method, and a more detailed discussion of the development of
the statistical model for the prediction of kLa. This material is
available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: charles.papageorgiou@takeda.com.
Chart 8. Comparison of the experimentally obtained temperature profile to that predicted by the physical model, kLa 0.5 s−1
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Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We would like to thank Wilfried Hoffmann of Scale-up Systems
for his invaluable help and advice throughout the course of this
work and Neil Faiber without whose support this project would
not have been possible.
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