Runaway and thermally safe operation
of a nitric acid oxidation in a
semi-batch reactor
B.A.A. van Woezik
RUNAWAY AND THERMALLY SAFE OPERATION
OF A NITRIC ACID OXIDATION IN A
SEMI-BATCH REACTOR
PROEFSCHRIFT
ter verkrijging van
de graad van doctor aan de Universiteit Twente,
op gezag van de rector magnificus,
prof. dr. F.A. van Vught,
volgens besluit van het College voor Promoties
in het openbaar te verdedigen
op vrijdag 22 september 2000 te 13.15 uur.
door
Bob Arnold August van Woezik
geboren op 6 januari 1969
te Nijmegen
Dit proefschrift is goedgekeurd door de promotor
Prof.dr.ir. K.R. Westerterp
This research was supported by the Technology Foundation STW, applied
science division of NWO and the technology program of the Ministry of
Economic Affairs.
Copyright © 2000 B.A.A. van Woezik, Eindhoven, The Netherlands
No part of this book may be reproduced in any form by any means, nor
transmitted, nor translated into a machine language without written permission
from the author.
CIP-GEGEVENS KONINKLIJKE BIBLIOTHEEK, DEN HAAG
Woezik, Bob Arnold August van
Runaway and thermally safe operation of a nitric acid oxidation in a semi-batch
reactor / Bob Arnold August van Woezik.
Thesis University of Twente, Enschede. – With ref. – With summary in Dutch.
ISBN 90 - 365 14878
Subject headings: runaway, liquid-liquid reactions, nitric acid oxidation.
Summary and Conclusions
A number of serious accidents has occurred due to a runaway reaction of a
heterogeneous liquid-liquid reaction whereby a secondary side reaction was
triggered. A basic lack of proper knowledge of all the phenomena, occurring in
such a system, is one of the prime causes that may lead to overheating and
eventually a thermal runaway. Therefore, a better understanding of these kinds
of processes is of great importance for the safe and economic design as well as
safe operation of those reactions. This thesis deals with the safe operation of a
multiple liquid-liquid reaction in a semi-batch reactor in the example of the
nitric acid oxidation of 2-octanol. A general introduction about runaways in
(semi) batch reactors is given in Chapter 1.
In Chapter 2 the oxidation of 2-octanol with nitric acid is studied. The oxidation
of 2-octanol with nitric acid has been selected as a model reaction for a
heterogeneous liquid-liquid reaction with an undesired side reaction. 2-Octanol
is first oxidized to 2-octanone, which can be further oxidized to carboxylic
acids. The oxidation of 2-octanol and 2-octanone with nitric acid exhibits the
typical features of nitric acid oxidations, like a long induction time without
initiator; autocatalytic reaction; strong dependence of mineral acid concentration
and high energy of activation. However, there is a limited knowledge of the
exact chemical structure of the compounds in the aqueous reaction phase and of
a number of unknown, unstable compounds in the organic phase. Next to this
the exact mechanism is still not elucidated. As a consequence of this, a
considerable model reduction was necessary to describe the overall reaction
rates.
An extensive experimental program has been followed using heat flow
calorimetry supported by chemical analysis. The oxidation reactions have been
carried out in a reaction calorimeter RC1 of Mettler Toledo, which contains a
jacketed 1-liter glass vessel. The reactions have been studied in the range 0 to 40
ºC, with initial nitric acid concentrations of 50 to 65 wt% and a stirring rate of
700 rpm. The kinetic constants have been determined for both reactions. The
observed conversion rates of the complex reactions of 2-octanol and 2-octanone
with nitric acids can be correlated using only two kinetic equations, in which the
effect on temperature is described through the Arrhenius equation and the effect
on acid strength through Hammett’s acidity function.
1
Summary and Conclusions
The nitric acid and the organic solution are immiscible, so chemical reaction and
mass transfer phenomena occur simultaneously. The results indicate the
oxidation of 2-octanol is operated in the non-enhanced regime when nitric acid
is below 60 wt% or when the temperature is below 25 ºC at 60 wt% HNO3,
while the oxidation of 2-octanone is operated in the non-enhanced regime for the
whole range of experimental conditions considered. Under these conditions the
mass transfer resistance does not influence the overall conversion rate, so the
governing parameters are the reaction rate constant and the solubility of the
organic compounds in the nitric acid solution. This has also been experimentally
confirmed by determining the influence on stirring rate.
In parallel a model has been developed to describe the conversion rates, that
successfully can predict the behavior of the semi-batch reactor, i.e. concentration
and temperature time profiles. The experimental results and simulations are in
good agreement and it has been found possible to describe the thermal behavior
of the semi-batch reactor for the nitric acids oxidation reactions with the film
model for slow liquid-liquid reactions and a simplified reaction scheme.
In Chapter 3 the thermal behavior of this consecutive heterogeneous liquidliquid reaction system is studied in more detail by experiments and model
calculations. An experimental installation has been built, containing a 1-liter
glass reactor, followed by a thermal characterization of the equipment. Two
separate cooling circuits have been installed to study different cooling
capacities: a cooling jacket and a cooling coil. The reactor has been operated in
the semi-batch mode under isoperibolic conditions, i.e. with a constant cooling
temperature. A series of oxidation experiments has been carried out to study the
influence of different initial and operating conditions. The thermal behavior has
been studied with a coolant temperature of -5 to 60 ºC, a dosing time of 0.5 to 4
hours, an initial nitric acid concentration of 60 wt% and a stirring rate of 1000
rpm.
The reaction is executed in a cooled SBR in which the aqueous nitric acid is
present right from the start and the organic component 2-octanol is added at a
constant feed rate. The 2-octanol reacts to 2-octanone, which can be further
oxidized to unwanted carboxylic acids. A dangerous situation may arise when
the transition of the reaction towards acids takes place in such a fast way that the
reaction heat is liberated in a very short time and it results in a temperature
runaway. The use of a longer dosing time or a larger cooling capacity effectively
moderates the temperature effects and it will eventually even avoid such an
undesired temperature overshoot. In the later, the process is regarded as
invariably safe and no runaway will take place for any coolant temperature and
2
Summary and Conclusions
the reactor temperature will always be maintained between well-known limits.
The conditions leading to an invariably safe process are determined
experimentally and by model calculations.
Because of the plant economics one must achieve a high yield in a short time
and under safe conditions. The reaction conditions should rapidly lead to the
maximum yield of intermediate product 2-octanone and after that the reaction
should be stopped at the optimum reaction time. The appropriate moment in
time to stop the reaction can be determined by model calculations. The influence
of operation conditions, e.g. dosing time and coolant temperature, on the
maximum yield are studied and will be discussed.
In the oxidation of 2-octanol one focuses on the first reaction because high
yields of ketone are required, while the danger of a runaway reaction must be
attributed to the ignition of the secondary reaction. The reaction system can be
considered as two single reactions and, therefore, also the boundary diagram
− developed by Steensma and Westerterp [1990] − for single reactions has been
used to estimate critical conditions for the multiple reaction system. The
boundary diagram can be used to determine the dosing time and coolant
temperature required for safe execution of the desired reaction. However, for
suppression of the undesired reaction it leads to too optimistic coolant
temperatures.
Studying the dynamic behavior of heterogeneous liquid-liquid reactions involves
a number of difficulties, because chemical reaction and mass transfer
phenomena occur simultaneously. The interfacial area is essential for an
accurate prediction of the mass transfer and chemical reaction rates in liquidliquid reactions. The interfacial area for a liquid-liquid system in a mechanically
agitated reactor is determined in Chapter 4. This has been done by means of the
chemical reaction method. This method deals with absorption accompanied by a
fast pseudo-first order reaction. The saponification of butyl formate ester with 8
M sodium hydroxide solution has been used. The extraction rate is determined
in a stirred cell with a well-defined interfacial area equal to 33.4 cm2 and a
correlation has been derived to describe the mole flux of ester through the
interface. The kinetic rate constants have been calculated and are compared to
data from literature. The reaction is affected by the amount of ions in the
solution. The reaction rate constant is described by an extra term in the usual
Arrhenius equation to account for this effect of the ionic strength.
The reactor, with a total volume of 0.5 liter, has been operated continuously to
study the interfacial area in a turbulently mixed dispersion. A correlation has
3
Summary and Conclusions
been derived for the Sauter mean diameter for both, reaction in the dispersed
phase as well as reaction in the continuous phase. A viscosity factor had to be
incorporated to obtain one single correlation. The Sauter mean diameter can be
described by correlations similar to those in literature, only the constants
deviate, because the specific properties of the system investigated and the
reactor configuration are different. These constants were found to depend also
on the phase that is dispersed. With the organic ester phase dispersed, droplet
diameters were found between 35 and 75 µm and between 65 and 135 µm in
case the aqueous phase is dispersed. The drop size seems to be influenced by the
density of the continuous phase as well as the ratio of the viscosities of the two
phases. It is not unambiguous which phase dispersed will give the smallest drop
size and, hence, the largest interfacial area. It is, therefore, recommended to
determine the drop size for both liquids as the dispersed phase.
The mass transfer with reaction is described using the film theory. This model
can usually be applied within the uncertainties of the estimated physicochemical parameters, even though it is the simplest approach. The validation for
the chemically enhanced reaction regime is presented. The necessary conditions
are all full-filled in all experiments except that of a large Hinterland ratio.
Therefore, the reaction between ester and sodium hydroxide in a single drop has
been described numerically. The effect of a small Hinterland ratio shows itself
by the inability of either the film theory or penetration theory to allow for
eventual depletion of the reactant within the droplet. For the used experimental
set-up and experimental conditions, the contact time is relatively short and
deviations due to depletion of NaOH in the droplet are not to be expected. For
the smallest experimentally determined droplet diameters, the assumption of a
flat interface is no longer valid and the influence of the curvature of the interface
has to be taken into account, otherwise the film theory can be used with
confidence.
References
Steensma, M. and Westerterp, K.R., Thermally safe operation of a semi-batch
reactor for liquid-liquid reactions. Slow reactions, Ind. Eng. Chem. Res. 29
(1990) 1259-1270.
4
Contents
Summary and Conclusions
1
Chapter 1: General Introduction
9
1.1 General
1.2 Present work
References
11
13
14
Chapter 2: The nitric acid oxidation of 2-octanol and 2-octanone
17
Abstract
2.1 Introduction
2.2 Oxidation reactions with nitric acid
Oxidation of 2-octanol
Oxidation of 2-octanone
2.3 Derivation of overall conversion rates
Kinetic expressions
Conversion rates in a semi-batch reactor
2.4 Experimental set-up and principle of measurements
Reaction calorimeter
Experimental set-up and experimental procedure
Chemical treatment and chemical analysis
2.5 Experimental results
Identification of reaction regime
Determination of kinetic parameters
2.6 Simulation of isothermal runs
2.7 Model validation and limitations
Model verification with isoperibolic experiments
2.8 Discussion and conclusions
Notation
References
18
19
19
22
27
34
45
49
55
56
59
5
Contents
Chapter 3: Runaway behavior and thermally safe operation of multiple
liquid-liquid reactions in the semi-batch reactor
63
Abstract
3.1 Introduction
3.2 Nitric acid oxidation in a semi-batch reactor
Reaction system
Mathematical model
3.3 Thermal behavior of the nitric acid oxidation of 2-octanol
Sudden reaction transition
Gradual reaction transition
3.4 Recognition of a dangerous state
3.5 Experimental set-up and procedure
Thermal characterization of equipment
Check on the validity of the model for slow reactions
3.6 Experimental results
Temperature profiles
Thermally safe operation of the nitric acid oxidation
Influence of dosing time
Influence of cooling capacity
Invariably safe operation
3.7 Prediction of safe operation based on the individual reactions
3.8 Discussion and conclusions
Notation
References
Chapter 4: Determination of interfacial areas with the chemical
method for a system with alternating dispersed phases
Abstract
4.1 Introduction
4.2 Measurement of interfacial area, the theory
Determination by the chemical method
4.3 Experimental set-up
Chemical treatment and chemical analysis
4.4 Measurements in the stirred cell
Experimental procedure
Determination of flux equation
Calculation of kinetics
6
64
65
66
75
86
88
95
105
108
109
112
113
114
115
116
120
123
Contents
4.5 Determination of interfacial area
Experimental procedure
Determination of drop size correlation
4.6 Validity of the assumed conditions
The effect of small Hinterland ratio
4.7 Discussion and conclusions
Notation
References
Appendix 4.A:
Physico-chemical parameters
Appendix 4.B:
Numerical model
130
137
145
146
148
151
154
Samenvatting en conclusies
155
Dankwoord
159
List of publications
162
Levensloop
163
7
Contents
8
1
General Introduction
Chapter 1
10
General Introduction
1.1 General
At Seveso on July 10th 1976 a runaway reaction took place that led to a
discharge of highly toxic dioxin contaminating the neighboring village. The
runaway reaction in the unstirred mixture took place seven hours after stirring
had been stopped and was triggered by a small heat input from the hot wall, see
Kletz [1988]. It turned out to be one of the best-known chemical plant accidents
and it became clear that the safety margins had not been recognized. The
accident induced the fine chemicals industry to review their safety systems and
to develop more refined methods for safeguarding their reactors.
Heat rates
A considerable number of accidents has occurred, that can be attributed to this
so-called runaway reaction. The basic understanding of a runaway reaction
arises from the thermal explosion theory according to Semenov. This theory
deals with the competition between heat generation by an exothermic reaction
and heat removal from the reaction mass to, for instance, the cooling jacket. The
heat generation depends, according to Arrhenius, exponentially on temperature,
while the heat removal depends linearly on temperature, see Figure 1.
2
Heat removal rate
1
Heat production rate
Temperature
Figure 1:
Heat flow diagram. Heat production rate by chemical reaction and
heat removal rate by cooling.
11
Chapter 1
A steady state will be reached as soon as the heat production rate is equal to the
heat removal rate. This will be the case for both the temperatures of the
intersections in Figure 1. The degree of control of the heat production rate
directly follows from this plot. At intersection (1) the slope of the heat removal
line is greater than that of the heat production curve and consequently a small
deviation from this steady state automatically results in a return to its origin.
Therefore, intersection (1) represents a stable operation point and the exothermic
reaction is under control. On the other hand, intersection (2) represents an
unstable operation point. If, for some reason, a temperature deviation occurs, the
original operating conditions will never be reached again. In case of a
temperature decrease the steady state of intersection (1) will be attained. In case
of an increase, the rate of heat generation will always exceed that of the heat
removal. This will lead to an unhindered self-acceleration of the reaction rate
and thereby of the heat production rate, which is known as a runaway reaction.
When the reaction is carried out in the batch reactor the process will not reach a
steady state. The batch reactor has great flexibility and is therefore extensively
used in the production of fine and specialty chemicals and accordingly
contributes to a significant part of the world’s chemical production in number
and value. However, batch processes are usually very complex with strong nonlinear dynamics and time-varying parameters. The process requires a continuous
safeguarding and correction by the operator. Furthermore, due to the small
amounts produced and variety of processes, obtaining complete understanding
of the reactor dynamics is usually not economically feasible. This lack of
knowledge gave rise to a number of accidents. Barton and Nolan [1991] have
reported the prime causes of industrial incidents, which were mainly related to
the lack of knowledge of the process chemistry, to inadequate design and to
deviation from normal operating procedures. The study of accidents also shows
that batch units are usually more frequently involved in accidents than
continuous process plants.
An attractive way to reduce the potential hazard is to avoid the use of truly batch
reactions and instead switch to semi-batch. With this type of operation the
reactor is initially charged with one of the reactants and the other reactants are
added continuously to the vessel. This makes it possible to control the reaction
rate and hence the generation of heat. Therefore, semi-batch reactors are often
used for highly exothermic reactions.
For semi-batch reactors with homogeneous reaction systems Steinbach [1985]
and Hugo and Steinbach [1985] demonstrated that too low reaction temperatures
could cause runaways. If the initial temperature is too low, the added reactants
12
General Introduction
will not react immediately and will start to accumulate. Under certain
circumstances the combination of increasing concentration and a gradual
temperature rise may lead to a runaway. Criteria for safe operation of a semibatch reactor are based on the prevention of accumulation of unreacted
reactants. The semi-batch reactor should therefore be operated with a
temperature high enough to maintain the reaction rate approximately equal to
the feed rate.
A great number of industrial processes in semi-batch reactors involve systems in
which two immiscible phases coexist, generally an organic and an aqueous one.
Like in the manufacturing of organic peroxides, sulphonates, nitrate esters and
other nitrocompounds. Steensma and Westerterp [1990, 1991] developed models
for liquid-liquid reactions to study thermal runaways taking place in such
heterogeneous systems. In case the reaction takes place in the dispersed phase,
the system was found to be more prone to accumulation than when the reaction
takes place in the continuous phase. In the latter case, the system exhibits a
better conversion rate at the start, which reduces the danger of runaway
reactions. Also a distinction could be made between slow reactions, where the
reaction takes place in the bulk of one of the liquid phases, and fast reactions i.e. chemical enhanced - with reaction in the boundary layer of one of the
phases. A runaway can occur in liquid-liquid reaction systems due to
accumulation of the added reactants in the reacting phase for slow reactions, and
in the non-reacting phase for fast reactions.
Although the contents of a reactor vessel may normally yield the desired
reaction products, deviations from normal operating conditions or upset
conditions such as loss of jacket cooling can lead to increased temperatures.
This may initialize unwanted decomposition reactions, elevate the system
pressure and lead to an emission as in the case of Seveso. The general approach
in preventing a runaway reaction is to avoid triggering off side and chain
reactions. It is a rather conservative approach, while in some cases it is
inevitable to allow an unwanted reaction partially to take place.
1.2 Present work
The thermal behavior is studied of a multiple liquid-liquid reaction in a semibatch reactor. The main goal is to understand and to ensure safe operation of this
kind of system by means of experiments and model calculations.
13
Chapter 1
Experimental studies of the thermal behavior of runaway reactions in a (semi)
batch reactor are scarce and no experimental systems have been described in
detail in which strongly exothermic side reactions can be triggered. The
oxidation reaction of 2-octanol has been chosen as a model reaction. Chapter 2
deals with the kinetic study of the nitric acid oxidation of 2-octanol to 2octanone and to the further oxidation products. The reactions have been studied
in a reaction calorimeter and a model, based on the film theory, has been
developed to describe the conversion rates.
In chapter 3 the nitric acid oxidation of 2-octanol is used to study experimentally
the thermal runaway behavior of an exothermic heterogeneous multiple reaction
system in a 1-liter glass reactor. The reactor is operated in a semi-batch manner
with a constant cooling temperature. Typical reaction regions can be
distinguished with increasing operation temperatures, which will be
demonstrated and explained. Parameters are studied to produce the required
intermediate product, 2-octanone, with a high yield and in a safe manner. The
results of the simulations are compared to the experimental observations.
One of the causes of accidents, see Barton [1991], is that the phenomena in, for
instance, liquid-liquid reactions are not understood. Essential for an accurate
prediction of the mass transfer and chemical reaction rates in liquid-liquid
reactions is the interfacial area. Chapter 4 deals with the interfacial area in a
mechanically agitated reactor. The interfacial area of a liquid-liquid system has
been determined by the chemical reaction method using the saponification of
butyl formate ester. Although drop sizes in dispersions have been studied
extensively, experimental data for the same system and alternating phases
dispersed are scarce. In this chapter the results are given for the two types of
dispersion. The mass transfer with reaction is described using the film theory
and the necessary conditions are verified. For the smallest droplets with hardly
any bulk, the film model is not realistic anymore. Induced deviations are studied
and discussed.
References
Barton, J.A. and Nolan, P.F., Incidents in the chemical industry due to thermalrunaway chemical reactions. In: Euro courses, Reliability and risk analysis,
Vol.1: Safety of Chemical Batch Reactors and Storage Tanks, A. Benuzzi and
J.M. Zaldivar (eds.), Kluwer Academic, Dordrecht 1991, pp. 1-17.
14
General Introduction
Hugo, P. and Steinbach J., Praxisorientierte Darstellung der thermischen
Sicherheitsgrenzen für den indirekt gekühlten Semibatch-Reaktor. Chem. Ing.
Tech. 57 (1985) 780-782.
Kletz, T., Learning from accidents in industry, Butterworths, London 1988, pp.
79-83.
Steensma, M. and Westerterp, K.R., Thermally safe operation of a semibatch
reactor for liquid-liquid reactions. Slow reactions, Ind. Eng. Chem. Res. 29
(1990) 1259-1270.
Steensma, M. and Westerterp, K.R., Thermally safe operation of a semibatch
reactor for liquid-liquid reactions - Fast reactions, Chem. Eng. Technol. 14
(1991) 367-375.
Steinbach, J., Untersuchung zur thermischen Sicherheit des indirekt gekühlten
Semibatch-Reaktors, PhD-thesis, Technical University of Berlin, Berlin, 1985.
15
Chapter 1
16
2
The Nitric Acid Oxidation of
2-Octanol and 2-Octanone
Chapter 2
Abstract
The oxidation of 2-octanol with nitric acid has been selected as a model reaction
for a heterogeneous liquid-liquid reaction with an undesired side reaction. 2Octanol is first oxidized to 2-octanone, which can be further oxidized to
carboxylic acids. An extensive experimental program has been followed using
heat flow calorimetry supported by chemical analysis. A series of oxidation
experiments has been carried out to study the influence of different initial and
operating conditions such as temperature, stirring speed and feed rate. In parallel
a semi-empirical model has been developed to describe the conversion rates.
18
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
2.1
Introduction
A number of incidents concerning runaway reactions involve systems in which
two immiscible phases coexist, generally an organic and an aqueous one.
Examples of such systems, in which simultaneously mass transfer and chemical
reaction are important, are nitrations, sulphonations, hydrolyses, esterifications
and oxidations. Experimental studies of the thermal behavior of runaway
reactions in a (semi) batch reactor are scarce. Only homogeneous reaction
systems are described in literature: the homogeneous, sulfuric acid catalyzed
hydrolysis of acetic anhydride, see e.g. Haldar and Rao [1992a,b] and the
homogeneous, acid catalyzed esterification of 2-butanol and propionic
anhydride, see Snee and Hare [1992]. No experimental systems have been
described in detail for a heterogeneous liquid-liquid reaction, in which strongly
exothermic side reactions can be triggered. However, in many nitrations it is
known that dangerous side reactions can play a role like undesired oxidation
reactions, see Camera et al. [1983]. They studied the oxidation of ethanol with
nitric acid, where decomposition reactions can give rise to explosions.
To study the thermal behavior of a liquid-liquid reaction the oxidation of a long
chain alcohol with nitric acid has been chosen. The ketones formed in the
oxidation of secondary alcohols are more stable than aldehydes, so the oxidation
of 2-octanol with nitric acid has been chosen as a model reaction. Secondary
alcohols are also oxidized in the commercial production of adipic acid, in which
cyclohexanol is oxidized. This reaction has been studied by van Asselt and van
Krevelen [1963a,b,c,d] and has been reviewed by Castellan et al. [1991].
This work presents experimental data for the oxidation of 2-octanol to 2octanone and further oxidation products. The main objective is to develop a
model to describe the conversion rates of 2-octanol and 2-octanone.
2.2
Oxidation reactions with nitric acid
Nitric acid is a commonly used oxidizer. Especially alcohols, ketones, and
aldehydes are oxidized to produce the corresponding carboxylic acids, for
instance adipic acid, see Davis [1985]. The oxidation of cyclohexanol with nitric
acid is very similar to the oxidation of 2-octanol, see Castellan et al. [1991]. The
mechanism of these nitric acid oxidations is still not elucidated. Oxidations with
nitric acid are in general very complex and usually several intermediates are
formed, see e.g. Ogata [1978]. The elucidation of the real pathways was beyond
19
Chapter 2
the scope of the project: therefore, it has been chosen to simplify the description
of the conversion rates of 2-octanol and 2-octanone.
The oxidation of 2-octanol occurs in a two-phase reaction system in which a
liquid organic phase, containing 2-octanol, is contacted with an aqueous, nitric
acid phase. The main organic components during the reactions can be
represented as follows:
2-octanol
2-octanone
carboxylic acids
These reactions are further described in more detail in the following paragraphs.
Experimental results of nitric acid oxidations from literature will also be used.
Oxidation of 2-octanol
Different reacting species have been proposed like N2O4 by Horvath et al.
[1988], NO+ by Strojny et al. [1971] and NO2 by Camera et al. [1983]. Castellan
et al. [1991] concluded that at ambient temperatures the oxidation proceeds
mainly via an ionic-molecular mechanism. This indicates that the (NO+)
nitrosonium ion mechanism is applicable for the conditions used in this work.
This ion can be formed from nitrous acid and nitric acid through reaction (1):
HNO2 + HNO3 ↔ NO+ + NO3− + H2O
(1)
The oxidations with pure nitric acid exhibit in general a long induction period,
see e.g. van Asselt and van Krevelen [1963a] and Ogata et al [1966]. This
induction time can be shortened or even eliminated by adding an initiator like
NaNO2, which forms nitrous acid:
NaNO2 + H3O+ → HNO2 + Na + + H2O
(2)
The reaction is completely suppressed by addition of urea, which reacts with
nitrous acid, see e.g. Camera et al. [1979], according to:
2 HNO2 + CO( NH2 )2 → 2 N2 + CO2 + 3H2 O
(3)
This is in agreement with the above-mentioned formation of a nitrosonium ion
or its equivalent.
20
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
OH
RCH2C-CH3
H
+ HNO2
+ HNO3
- H2O
- HNO3
ONO
RCH2C-CH3
O
+ HNO3
-2HNO2
RCH2C-CH3
H
Figure 1: Reaction pathway for the oxidation of 2-octanol with nitric acid.
R = CH3(CH2)4—
The oxidation of 2-octanol to 2-octanone proceeds via the formation of an
intermediate, which has been identified, as 2-octyl nitrite, using GC-MS. The
reaction pathway of the first steps of the oxidation of 2-octanol can be
schematically represented as in Figure 1. After addition of the initiator, HNO2 is
formed, the oxidation starts and proceeds autocatalytically. One molecule of
HNO2 - or NO+ according to Equation (1) - is consumed in the first step, while
two are formed in the second step. This net formation of an equimolar amount of
HNO2 also has been found for the oxidation of cyclohexanol to cyclohexanone,
see van Asselt and van Krevelen [1963a, d].
Oxidation of 2-octanone
2-Octanone can be further oxidized to carboxylic acids. During this reaction an
equimolar amount of nitrous acid is consumed, the same as in the oxidation of
cyclohexanone, see van Asselt and van Krevelen [1963a].
O
O
RCH2C-CH3
+ HNO2
+ HNO3
- H2O
- N2O
RCH2C-OH + HCOOH
O
RC-OH + CH3COOH
Figure 2: Reaction pathways for the oxidation of 2-octanone with nitric acid.
R = CH3(CH2)4—
21
Chapter 2
The nitric acid oxidation of 2-octanone is studied simultaneously with the
oxidation of 2-octanol. Van Asselt and van Krevelen [1963a] found different
products when oxidizing cyclohexanone with nitric acid and nitrite, compared to
the oxidation of cyclohexanol. This probably has been caused by side reactions
with the NO2 formed, when a large amount of nitrite is added. The oxidation of
2-octanone is accompanied by the formation of small amounts of unidentified
and unstable compounds. These compounds were too unstable to be isolated and
identified. The simplified reaction pathways can be represented as in Figure 2.
Depending on the carbon bond broken, hexanoic acid and acetic acid or
heptanoic acid and formic acid are formed. The amount of hexanoic acid as
found experimentally is approximately two times the amount of heptanoic acid.
The formic acid may further react to CO2, see Longstaff and Singer [1954].
During the reaction nitrous acid and nitric acid are consumed.
In the description of the oxidation reactions it is assumed that the reaction
proceeds only via the nitrosonium ion NO+. However, at high temperatures
above 60 ºC, the oxidation is known to proceed via a radical mechanism, see
Castellan et al. [1991]. This is outside the operating conditions that will be
applied.
2.3
Derivation of overall conversion rates
The determination of unambiguous stoichiometry and kinetic parameters for
oxidation reactions is impossible due to the lacking knowledge of the exact
composition of the inorganic compounds in the aqueous reaction phase and the
unidentified and unstable intermediates in the organic phase. Hugo and Mauser
[1983] confirmed this for the nitric acid oxidation of acetaldehyde. Therefore, it
has been chosen to derive semi-empirical equations for the conversion rates and
heat production rates.
The oxidation of 2-octanol (A) to 2-octanone (P) and further oxidation products
(X) is simplified to the following two reactions:
A + B→ P + 2B
rnol
(4)
P + B→ X
rnone
(5)
where B represents the nitrosonium ion which accounts for the autocatalytic
behavior. The reactions with the nitrosonium ion take place in the aqueous nitric
22
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
acid phase, so also the mass transfer rates of the organic compounds have to be
taken into account.
This process is schematically represented in Figure 3. The liquid-liquid system
consists of an aqueous acid phase (Aq) with nitric acid and the reacting
nitrosonium ion (B), and an organic phase (Org) containing mainly 2-octanol
(A), 2-octanone (P) and further oxidation products (X).
Aqueous
phase
Interface*
CA,Org
CB,Aq
Organic
phase
CA,Org
JA
JP
*
CP,Org
CP,Org
*
CA,Aq
CA,Aq
*
CP,Aq
CP,Aq
x=δ
x=0
film
Figure 3: Schematic representation of mass transfer with chemical reaction
during the oxidation with nitric acid. Concentration profiles near the liquidliquid interface for a slow reaction and low solubility.
The 2-octanol (A) diffuses through the organic phase via the interface into the
aqueous acid phase. In the boundary layer and/or bulk of the aqueous phase it
reacts with the nitrosonium ion (B) to form 2-octanone (P). The 2-octanone may
react with the nitrosonium ion (B) to form carboxylic acids (X) or it is extracted
to the organic phase.
In case the transport of the organic compound in the reaction phase is not
chemically enhanced and the concentration drop over the film in the reaction
23
Chapter 2
phase being relatively small, it is possible to derive an overall reaction rate
expression, see Steensma and Westerterp [1990]:
ri = (1 − ε )keff Ci , Aq CB, Aq
(6)
where (1 − ε ) refers to the volume fraction of the aqueous reaction phase; keff is
the effective reaction rate constant. Equation (6) can be used under the following
conditions:
• The rate of chemical reaction is slow with respect to the rate of mass transfer,
the rate of mass transfer is not enhanced by reaction, and the reaction mainly
proceeds in the bulk of the reaction phase. One must check that the consumption
by reaction in the thin boundary layer is negligible, which is justified if Ha < 0.3
holds, see Westerterp et al. [1987]. The Hatta number Ha is defined as:
Ha =
keff CB, Aq Di
kL , Aq
(7)
and Di is the diffusivity of the organic compound A and kL , Aq the mass transfer
coefficient for A, both in the aqueous phase.
• The solubility of the organic compound in the aqueous phase is so low, that
mass transfer limitations in the organic phase can be neglected. At the interface
holds Ci*. Aq = mCi*.Org .
• The concentration drop over the film of the organic component transferred is
less than 5%, see Steensma and Westerterp [1990], so Ci*, Aq ≈ Ci , Aq can be
assumed.
If these conditions are fulfilled the conversion rate is independent of the
hydrodynamic conditions and interfacial area, hence independent of the stirring
rate. The conversion rates are determined by the kinetics of the homogeneous
chemical reactions, which can be described by the effective reaction rate
constants keff,nol and keff,none for the oxidations of 2-octanol and 2-octanone,
respectively.
24
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
Kinetic expressions
The effective reaction rate expressions should also account for the effect of
temperature and the acid concentration. Oxidation reactions with nitric acid
solutions are usually very sensitive towards the acid strength, see Ogata [1978].
The influence of the acid strength can be accounted for with the Hammett’s
acidity function, H0, see e.g. Rochester [1970]. So the kinetic constant becomes:
%&
'
keff (T , H0 ) = k∞,eff exp −
2
Eeff
− mHo,eff H0
RT
7()*
(8)
For this expression the preexponential factor, k∞,eff , the energy of activation,
Eeff / R , and Hammett’s coefficient, mHo,eff , have to be determined
experimentally.
Conversion rates in a semi-batch reactor
In a semi-batch operation, where 2-octanol is fed to a reactor initially loaded
with nitric acid, the overall balances list:
- for the 2-octanol, A:
dnA
= ϕ dos CA,dos − rnol Vr
dt
(9)
where ϕ dos is the volumetric flow rate of the feed dosed into the reactor.
- for the 2-octanone, P:
dnP
= rnol Vr − rnoneVr
dt
(10)
- for the carboxylic acids, X:
dnX
= rnoneVr
dt
(11)
- for the nitrosonium ion, B:
dnB
= rnol Vr − rnoneVr
dt
(12)
- for the nitric acid, N:
dnN
= − rnol Vr − rnoneVr
dt
(13)
25
Chapter 2
The yields are defined, on the basis of the total amount of 2-octanol fed, nA1:
n
n
n
ζP = P
ζX = X
ζB = B
nA1
nA1
nA1
The mass balances above can be made dimensionless, see Chapter 3 for the
derivation, as follows:
1
6
dζ P
ζ + ζ B 0 dζ X
= mA keff ,nol tdos CA,dos θ − ζ P − ζ X P
−
dθ
dθ
θ
(14)
1 6
(15)
dζ X
ζ + ζ B0
= mP keff ,none tdos CA,dos ζ P P
dθ
θ
in which θ is the dimensionless dosing time t/tdos. After the end of the dosing
θ =1 in Equations (14) and (15) and the reaction proceeds as in a batch reactor.
ζ B0 is the initial concentration of nitrosonium ion which will be formed after
addition of the initiator. The boundary conditions for these differential equations
and the corresponding heat balance will be discussed later.
It is assumed the volumes of the aqueous phase and the organic phase are not
affected by reaction. During the oxidation of 2-octanol and 2-octanone the
average molecular weight of the organic compounds does not change much, so
this assumption is justified. The assumption of low solubility of reactants and
products in the aqueous phase, which also may result in a change in volume, has
to be validated.
In the simplified representation of the oxidation reactions, Equations (4) and (5),
the reactions can be described with only two dimensionless partial mass
balances. The model of Equations (9)-(15) will be used to obtain the relevant
kinetic parameters and to simulate the experimental conversion rates.
26
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
2.4
Experimental set-up
Reaction calorimeter
The oxidation reactions have been studied in a reaction calorimeter RC1 of
Mettler Toledo, which contains a jacketed reactor vessel. Using the reaction
calorimeter the flow of the heat Qcool is determined, which is transferred through
the wall of the vessel and which is proportional to the temperature difference
between the reactor contents Tr and the coolant temperature Tcool :
1
Qcool = UA ⋅ Tcool − Tr
6
(16)
The proportionality factor UA has to be determined by calibration, which is done
by introducing via an electrical heating element a known amount of energy QC :
UA =
1
QC
Tr − Tcool
6
(17)
The reaction calorimeter enables an accurate measurement of the temperatures
of the reactor contents and of the coolant. The heat balance for the reactor
operating in the semi-batch mode can be written as:
dTr
dT
Γr + w Γw = QR + Qdos + Qcool + Qstir + Q∞
dt
dt
(18)
where Γr is the thermal capacity of the reaction mixture and internal devices in
the reactor, and Γw is the thermal capacity of the reactor wall. The wall
temperature is estimated by: Tw = 1 2 Tr + Tcool . The different heat flows taken
into account are QR by the chemical reaction, Qdos by mass addition, Qcool to the
coolant, Qstir by the agitation and Q∞ to the surroundings.
1
6
27
Chapter 2
Experimental set-up and experimental procedure
The experimental set-up is shown in Figure 4. The RC1 (1) contains a jacketed
1-liter glass vessel of the type SV01. The main dimensions of the reactor are
given in Figure 5. The reactor content is stirred by a propeller stirrer with a
diameter of 0.04 m. The stirring speed is adjusted to 700 rpm. For further details
and drawings of the RC1 see Reisen and Grob [1985] and Mettler-Toledo
[1993].
6
Ti
FC
7
H2O
4
Ti
5
1
2
H2O
3
8
Figure 4: Simplified flowsheet of experimental set-up. Ti: temperature
indicator; FC: flow controller.
The reactor is operated in the semi-batch mode under isothermal conditions. To
operate below room temperature an external cryostatic bath (2) of the type
Haake KT40 has been installed. Before the experiment is started, the equipment
is flushed with N2. The reactor is initially filled with 0.4 kg of HNO3-solution.
First the effective heat transfer coefficient is determined with the electrical
heater with a thermal power of 5 W. After that a small amount of 0.1 g NaNO2 is
added as initiator. As soon as the temperature of the reactor has reached a
constant value, the feeding of reactant 2-octanol is started by activating the
dosing system. The dosing system contains the supply vessel, which is located
28
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
on a balance of the type Mettler pm3000 (3), a Verder gear pump (4) and a
Mettler dosing controller RD10 (6). The feed rate is kept constant in the range of
0.05 to 0.4 kg/h. The nitric acid and organic solutions are immiscible and form a
dispersion. The nitric acid remains the continuous phase during the whole
experiment. During the oxidation of 2-octanol NOX-gases are formed, which
accumulate above the reaction mixture and are let off through an opening in the
reactor lid to the scrubber (5) to be washed with water. After addition of 0.1 kg
2-octanol the dosing is automatically stopped and the experiment is continued
for at least two times the total dosing time. The experiment is then brought to an
end by heating up the reactor contents to complete the conversion and after that
again a determination of the effective heat transfer coefficient.
Also the temperatures of the feed and of the surroundings are measured and
together with the feed flow rate monitored and stored by a computer. When the
reactor temperature exceeds a certain value the computer automatically triggers
an emergency cooling program and opens the electric valve in the reactor
bottom to dump the reactor content and quench it in ice (8). During an
experiment 4 to 10 samples of the dispersion are taken via a syringe, as
indicated by (7) in Figure 4.
Dbaffles
Dstirrer = 0.04 m
Dvessel, min = 0.06 m
hcone
Dbaffles = 0.1Dvessel
αcone
hcone = 0.16 m
αcone = 18º
Dstirrer
Dvessel, min
Figure 5: Dimensions of the SV01 glass reactor.
29
Chapter 2
Chemical treatment and chemical analysis
During an experiment samples of the dispersion are taken of approximately 1
ml, using a syringe. The dispersion, once in the syringe, separates directly in two
phases. The total amount of strong and weak acids in the aqueous phase is
determined by titration with a 0.1 M NaOH-solution in an automatic titration
apparatus of the type Titrino 702 SM of Metrohm. During the reaction some
unstable and unidentified compounds are formed and the composition of an
untreated sample changes with time. Therefore, the samples of the organic phase
are contacted with demineralized water to stabilize the sample and remove the
nitric acid from the organic phase. The organic phase is then analyzed by gas
chromatography using a Varian 3400 with a FID detector. The injector and
detector temperatures are set at 240 ºC. The column is packed with Carbopack C
and is operated at 190 ºC with N2 as carrier gas. The concentrations of 2-octanol,
2-octanone, hexanoic acid and heptanoic acid are determined using reference
samples and an integrator of type HP3392A.
To study the influence of temperature the oxidation reaction has been
investigated in the temperature range of 0 ºC to 40 ºC, for dosing times of 900 to
7200 s, for 100 g of 2-octanol and an initial nitric acid concentration of 60 wt%.
Furthermore a series of experiments has been carried out in the range of 50 to 65
wt% with a dosing time of 1800 s to study the influence of the initial nitric acid
concentration. A total of 33 runs were carried out to obtain kinetic data.
An example of an experimental run is shown in Figure 6. Two peaks can be
observed in the temperature of the reactor as a function of time. The first peak is
small and is caused by the addition of the initiator. The second one is caused by
the start of the reaction; its deviation from the temperature set remains usually
below 2 ºC for a dosing times of 30 minutes and longer. Deviations from
isothermicity were larger for experiments with a short dosing time of 15
minutes. In this case, at temperatures above 25 ºC the heat production rate was
so large that isothermal operation became impossible. In Figure 6b the
calculated heat production rate is plotted as function of time. The maximum in
the heat production rate is an easily to be detected, sensitive measure of the
course of the reaction. It will be used in some comparisons further on.
30
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
25
addition initiator
Temperature [ºC]
start dosing
Treactor
20
15 Treactor setpoint
Tcooling
10
5
stop dosing
0
-2000
a.
0
2000
4000
6000
8000
6000
8000
time [s]
Heat flow QR [W]
100
Qmax
75
stop dosing
50
25
0
start dosing
-25
-2000
0
2000
4000
time [s]
b.
Figure 6: Example of an isothermal semi-batch experiment at 20 ºC with an
initial load of 0.4 kg 60 wt% HNO3 and 0.1 g NaNO2. Addition of 0.1 kg 2octanol in a dosing time of 30 min.
a. Measured temperature of reactor contents and cooling jacket
b. Measured heat flow
31
Chapter 2
For the same experiment the molar amounts of the organic compounds in the
organic phase and the total molar amounts of weak and strong acids in the
aqueous nitric acid solution are given as a function of time in Figure 7. 2Octanol accumulates in the reactor and a part of the dosed 2-octanol reacts to 2octanone, which is partly converted into carboxylic acids. As a result, the yield
of 2-octanone exhibits a maximum.
The distribution of 2-octanol and 2-octanone has been estimated on the basis of
TOC analysis of a saturated 60 wt% nitric acid solution and mA = 0.005 and mP
= 0.006 for 2-octanol and 2-octanone, respectively. The distribution coefficients
of the carboxylic acids are estimated on the basis of gas chromatography
analysis and m ≈ 0.01 for both heptanoic acid and hexanoic acid and m ≈ 1.5 for
acetic acid. Thus, in view of the low solubilities for 2-octanol, 2-octanone,
heptanoic acid and hexanoic acid, the amounts of organic compounds in the
aqueous phase can be neglected. The simultaneously formed acetic and formic
acids will be distributed over both the organic phase and aqueous phase and, as a
result, the volume of aqueous phase will increase as the reaction proceeds. At
the same time a considerable quantity of nitric acid will dissolve into the organic
phase. The overall effect on the volume ratio is small, since hardly any change
in volume is observed during the experiments.
The aqueous phase contains strong and weak acids. The strong acid is nitric
acid, the different weak acids could not be distinguished in the titration method
used. The weak acids probably consist of acetic and formic acids as well as an
amount of inorganic acids like HNO2.
Due to the extraction of nitric acid a part is not available for reaction. The
amount of nitric acid in the organic phase is determined by titration with a 0.1 M
NaOH solution and is approximately 2.5 mol/kg organic phase for 50 to 60 wt%
HNO3. Therefore the amount of strong acid in the aqueous phase, determined by
titration as shown in Figure 7b, appears to decrease faster then one may expect
based on the stoichiometry of the reactions.
32
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
Number of moles
0.8
0.6
2-Octanone
0.4
2-Octanol
Carboxylic acids
0.2
0
0
2000
a.
4000
time [s]
6000
8000
Number of moles
4
Strong acids (e.g. HNO3)
3
2
1
Weak acids (e.g. HNO2, organic acids)
0
0
2000
4000
time [s]
6000
8000
b.
Figure 7: Molar amount as function of time for same run as in Figure 6.
a. Organic compounds in the organic phase;
b. Weak and strong acids in the aqueous nitric acid phase.
33
Chapter 2
2.5
Experimental results
The kinetic parameters of the proposed model can be found by measuring the
conversion rates by means of thermokinetic measurements in the calorimeter in
combination with chemical analyses. Before the kinetic parameters are evaluated
the reaction regime has to be identified.
Identification of reaction regime
Effect of agitation
If the conversion rate in a liquid-liquid reaction is not influenced at all by mass
transfer resistances, it should be independent of the interfacial area and, hence,
of the degree of agitation. The influence of the stirring rate on the conversion
rate has been experimentally determined at 20, 30 and 40 ºC.
In Figure 8 the measured maximum heat production rate is plotted against the
stirring speed. The maximum heat production initially increases with stirring
speed, but becomes independent of the agitation above 300 rpm. At a stirring
speed below 150 rpm the reaction mixture separates into two liquid phases and it
becomes well dispersed at stirring rates above 500 rpm, as can be visually
observed. Between 150 and 500 rpm a certain volume of undispersed organic
phase is visible above the dispersion and the heat production rates fluctuate in
time. For a stirring rate of above 500 rpm evidently the mass transfer resistance
1/kLa does not play a role anymore. Therefore, a stirring rate of 700 rpm has
been chosen for all experiments.
Effect of phase volume ratio
By assuming the nitrosonium ion being the reactive species it is likely that the
reaction takes only place in the aqueous acid phase. The conversion rate is
usually proportional to the volume of reacting phase, according to: R = kCACBVR ,
where CA and CB are the concentrations of the reacting compounds in the
reaction phase with volume VR. On the other hand, the reaction phase can be
identified by varying the volume of the phases and keeping all other parameters
constant, see e.g. Atherton [1993] and Hanson [1971].
34
Maximum heat production rate [W]
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
200
40ºC
30ºC
20ºC
150
100
50
0
0
200
400
600
800
1000
1200
Stirring speed [rpm]
Figure 8: Maximum heat production rate versus stirring speed at 20, 30 and 40
ºC. Isothermal semi-batch experiments with an initial load of 0.4 kg 60 wt%
HNO3 and 0.1 g NaNO2. Addition of 100 g 2-octanol in a dosing time of 30 min.
However, for the autocatalytic reaction, complications arise when the
concentration of nitrosonium ion CB has to be kept constant, while the volume of
the aqueous phase VR is changed. The number of moles of nitrosonium ion nB =
CBVR is equal to the number of moles of product in the non-reaction phase nP =
CPVd. The concentration of nitrosonium ion is therefore equal to CB = CPVd/VR
and consequently the conversion rate is also equal to R = kCACPVd. Thus a larger
initial volume of aqueous phase VR will be accompanied by a lower
concentration of nitrosonium ion CB and as a result there is no change in
conversion rate.
35
Chapter 2
Run
1
2
3
4
5
6
7
Volume of acid
phase
[ml]
293
450
525
295
295
295
295
Volume of
organic phase
[ml]
120
120
120
150
173
225
278
Feed concentration
2-octanol
[mol/l]
6.40
6.40
6.40
4.98
4.33
3.64
2.77
Table 1: Experimental conditions of isothermal experiments with
varying concentration and volumes. All experiments with
initially 60 wt% HNO3 and 0.1 g NaNO2 at 25 ºC, in the semibatch mode with a dosing time of 30 minutes.
The oxidation reaction has been carried out with different volumes of the
aqueous reaction phase as is shown in Table 1. The experimental results are
plotted in Figure 9 and show an increase in heat production rate with an
increasing volume of nitric acid. This increase in the maximum heat production
rate can be explained entirely by the effect of the acid strength on the kinetic
constant k: the nitric acid remains at a higher concentration level for a larger
initial volume, as its excess is larger. Thus a larger volume of reaction phase VR
has no effect on the part CACBVR as mentioned above. This confirms nitric acid
being the reaction phase.
This can be double-checked by changing the volume of the organic phase, which
can be increased by diluting the 2-octanol with inert hexane, keeping the total
amount of 2-octanol constant. The results of these experiments are shown in
Figure 10. The maximum conversion rate decreases, when the amount of
organic non-reacting phase is increased. This can be explained, partly by the
lower concentration of the 2-octanol and 2-octanone in the aqueous phase and
partly, by a lower concentration of the nitrosonium ion, as also mentioned by
Ogata et al. [1967].
The above phenomena also support the assumed ionic mechanism via NO+ in
the aqueous acid phase. Thus, although some reaction may take place in the
organic phase its contribution to the overall rate will be neglected. So it is
assumed that the reaction only takes place in the aqueous, nitric acid phase.
36
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
Qmax. [W]
120
100
80
60
0.1
0.3
0.5
0.7
Volume of aqueous phase [l]
Figure 9: Maximum heat production rate versus volume aqueous nitric acid
phase. Isothermal semi-batch experiments with an initial load of 60 wt% HNO3
and 0.1 g NaNO2. Addition of 0.1 kg 2-octanol in a dosing time of 30 min.
100
Qmax. [W]
80
60
40
20
0.1
0.15
0.2
0.25
0.3
Volume organic phase [l]
Figure 10: Maximum heat production rate versus volume organic phase.
Isothermal semi-batch experiments with an initial load of 0.4 kg 60 wt% HNO3
and 0.1 g NaNO2. Addition of 2-octanol in hexane as indicated in Table 1.
37
Chapter 2
Determination of kinetic parameters
Now the kinetic parameters can be determined using the conversion rate
expressions for slow liquid-liquid reactions, provided the heats of reaction are
known.
Determination of effective heats of reaction
The heat production is determined by the chemical reactions and physical
phenomena like dilution, etc. The heat production rate by n chemical reactions
can be written as:
n
QR = ∑ ri ∆Hi Vr
(19)
i
The amount of heat released by the reaction ∆Ε is determined by integrating the
experimentally measured heat generation rate QR over the reaction time:
I
t
I1
6
t
∆Ecalorimeter = QR dt =
0
Qnol + Qnone dt
0
(20)
where Qnol and Qnone are the heat generated by the oxidation of 2-octanol and 2octanone, respectively. The results of the chemical analyses are used to calculate
the amounts of heat generated by both reactions separately:
1
6
∆Eanalyses = ∆Heff ,nol ⋅ ζ P + ζ X ⋅ nA1 + ∆Heff ,none ⋅ ζ X ⋅ nA1
(21)
The effective heats of reaction ∆Heff,nol and ∆Heff,none are obtained using the
complete set of isothermal experiments and by minimizing the deviation
between the amount of heat measured by the calorimeter, ∆Εcalorimeter, and the
amount of heat calculated using the yields, ∆Εanalyses. The results are listed in
Table 2.
Reaction
Æ 2-octanone, ∆H
Æ products, ∆H
2-octanol
2-octanone
eff,nol
eff,none
∆ H eff
[kJ/mol]
160
520
∆ Hcalc
[kJ/mol]
150
620
Table 2: Experimentally determined effective heats of reaction
∆Heff and calculated ∆Hcalc based on the heats of formation.
38
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
∆Εnol+∆Enone
500
∆Ηeff, none/∆Ηeff, nol = H = 3.25
1.1•H
∆Ε [kJ]
400
∆Εcalorimeter
0.9•H
300
∆Εnone
200
100
∆Εnol
0
0
1800
3600
5400
7200
Time [s]
Figure 11: Amount of heat generated as a function of time by the oxidation of
2-octanol ∆Enol and 2-octanone ∆Enone as measured in the calorimeter, and as
calculated on the basis of the concentration time profiles.
The heat generated as a function of time is shown for a single run in Figure 11,
where the heat generated by the separate reactions ∆Enol and ∆Enone and the total
amount of heat generated ∆Eanalyses = ∆Enol + ∆Enone using Eq.(21) or ∆Ecalorimeter
using Eq.(20), respectively, are displayed. The ratio of the effective heats of
reaction, H = ∆Heff ,none / ∆Heff ,nol , is equal to H = 3.25. In the same figure are
shown the calculated amount of heat ∆Ε with 0.9H and 1.1H respectively. For
this single run the amount of heat ∆Eanalyses calculated with the conversions is in
agreement with ∆Ecalorimeter measured by the calorimeter, during the time of the
experimental run.
A comparison between the calculated heat production and the experimental
determined heat production for all runs is given in Figure 12. Although the
points do not seem completely random by distribution, the deviations are small
and the values of ∆Heff,nol and ∆Heff,none are acceptable.
39
Chapter 2
Amount of heat ∆Qcalorimeter [kJ]
1000
100
10
10
100
1000
Amount of heat ∆Qanalyses [kJ]
Figure 12: Parity plot of calculated amount of heat generated according to
Eq.(21) and in the calorimeter experimentally determined amount of heat
produced, Eq.(20), for all runs.
An approximate estimate of the heats of reaction can be made using the heats of
formation of the reacting species as depicted in Figure 1 and Figure 2. For the
oxidation of 2-octanol to 2-octanone the calculated heat of formation is in good
agreement with the experimentally determined reaction heat. For the oxidation
of 2-octanone to carboxylic acids a 16% difference was found; this is probably
the result of endothermic decomposition reactions, which produce NOX-gases,
and which have not been taken into account.
Determination of the model parameters
The kinetic constants for the proposed model can now be found by comparing
the experimental conversion rates of 2-octanol and 2-octanone and the proposed
model equations. During an experiment the conversion rates can be determined
by evaluating the heat flow measurements or the results of the chemical
40
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
analyses, using Equation (19) and the determined effective heats of reaction as
listed in Table 2. The total heat production rate in the reactor QR is equal to:
QR = Qnol + Qnone = rnol Vr ⋅ ∆Heff ,nol + rnoneVr ⋅ ∆Heff ,none
(22)
On the basis of the chemical analyses the conversion rates can be obtained by
differentiation of a polynomial fit of the measured data points, as is shown in
Figure 13 and using the following equations:
1r V 6 = tn ddζθ
A
P
nol r
dos
1r V 6 = tn
A
none r
dos
+
dζ X
dθ
and
(23)
dζ X
dθ
(24)
Concentration [-]
1
nX
nA1
0.8
0.6
nP
nA1
0.4
0.2
0
0
0.5
1
1.5
2
θ = t/tdos [-]
Figure 13: Measured concentrations by chemical analysis (dots) and polynomial
function (lines) for a single run.
The sampling frequency during an experiment was usually once per 15 minutes,
which results in 5 to 10 samples per run. Due to this limited amount of sampling
data points, not always a useful polynomial expression could be obtained for the
41
Chapter 2
2-octanone (P) concentration. The concentration of the further oxidation
products (X) increases approximately linearly with time under the experimental
conditions applied and good polynomial functions could be found, as shown in
Figure 13. To improve upon the accuracy of the conversion rate of 2-octanol
rnolVr the total conversion rate from the heat flow measurements QR is combined
with the information of chemical composition of the further oxidation products
(X) as function of time. The conversion rate of 2-octanol rnolVr can also be
expressed as:
1 r V 6 = 2Q
R
− rnoneVr ⋅ ∆Heff ,none
nol r
7
(25)
∆Heff ,nol
For every run in the reaction calorimeter first the conversion rate of 2-octanone
rnoneVr is evaluated using Equation (24) and the polynomial expression. Then the
conversion rate of 2-octanol rnol Vr is evaluated by Equation (25).
The conversion rates can also be found after combining the conversion rates
from Equation (23) and (24) with the mass balances Equation (14) and (15):
1r V 6 = tn m k
A
nol r
dos
1r V 6 = tn
A
none r
1
t CA,dos θ − ζ P − ζ X
A eff ,nol dos
1 6ζ
mP keff ,nonetdos CA,dos ζ P
dos
P
6ζ
P
+ ζ B0
θ
(26)
+ ζ B0
θ
(27)
All parameters in the Equations (26) and (27) are known, except mAkeff,nol and
mPkeff,none. The kinetic constants of the proposed expression of Equation (8) are
obtained by non-linear regression using the complete set of isothermal
experiments and fitting the Equations (26) and (27) to the results of Equations
(24) and (25). The results determined in the range of 0 to 60 ºC and acid strength
of H0 = 2.4 to 3.5 are listed in Table 3. The standard deviation of the
experimentally determined reaction rate constants compared to the calculated
ones is 60%. The accuracy will be visualized in the following.
Reaction
Æ
Æ
2-octanol 2-octanone
2-octanone
products
mk‡,eff
[l/mol s]
1 · 105
1 · 1010
Eeff/R
[K]
11300
12000
mHo,eff
[-]
6.6
2.2
Table 3: The effective reaction rate constants for the
oxidation reactions.
42
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
The effective kinetic constant depends on temperature and acid strength. To
discuss the influence of these parameters on the kinetic constants the value of
mkeff is measured for both reactions. The kinetic constant is very sensitive to the
nitric acid concentration: below 40 wt% the reaction is so slow that hardly any
heat production is measurable, while above 65 wt% the reaction becomes too
fast. Expressed as an exponential order in the concentration of HNO3, the
exponent would be as high as 12 for the oxidation of 2-octanol. This has no
physical or chemical meaning, so Hammett’s acidity function is used, see
Rochester [1970]. Figure 14 shows a plot of mkeff at 20 ºC as a function of
Hammett’s acidity function H0. The slope of ln(mkeff) versus -H0 is 1.25 and 0.41
for the oxidations of 2-octanol and 2-octanone, respectively. These values can
be compared to those reported in literature. Ogata et al. [1966] found a slope of
0.95 for the nitric acid oxidation of benzyl alcohol, while for the oxidation of
benzaldehyde a value of 0.43 has been reported, see Ogata et al. [1967]. The
oxidation of 2-octanol depends more strongly on the nitric acid concentration
then the oxidation of 2-octanone. This has also been found for the oxidation of
benzyl alcohol and benzaldehyde respectively as described above. Therefore, to
increase the yield of 2-octanone the concentration of nitric acid should be high.
The term mHo,eff accounts for the acidity effect on the conversion rate including
the acidity influence on the solubility, which is known to increase with
increasing HNO3 concentration, see Rudakov et al. [1994].
0
1.E+00
10
3
mkeff [m /kmol s]
-1
1.E-01
10
2-octanol
2-octanone
-2
10
1.E-02
-3
1.E-03
10
-4
1.E-04
10
-5
1.E-05
10
-6
1.E-06
10
2-octanone
carboxylic acids
-7
1.E-07
10
2.1
2.6
3.1
3.6
-H0 [-]
Figure 14: Effect of acid strength on the reaction rate constants for the
oxidation of 2-octanol and 2-octanone, respectively. Lines calculated according
to Eq.(8) and parameters from Table 3 for T = 20 ºC.
43
Chapter 2
In Figure 15 the value of mkeff is plotted at 60 wt% HNO3 as a function of
temperature. The term Eeff/R accounts for the temperature influence on the
conversion rate, including the temperature influence on the solubility and, more
important, the Hammett acidity. The latter is only well tabulated for HNO3solutions at 25 ºC, see Rochester [1970], but some data points at 20 ºC indicate
an increasing acidity with increasing temperature, hence the value of Eeff/R is
overestimated.
Although no experimental data on the oxidation of 2-octanol or 2-octanone have
been published, comparable data can be found in literature for other nitric acid
oxidations. The reported data on energy of activation vary from 9000 K for the
oxidation of methoxyethanol, see Strojny [1971], to 14230 K for benzyl alcohol,
see Ogata et al. [1966]. The same range is found for aldehydes or ketones: from
8000 K for cyclohexanone, see van Asselt and van Krevelen [1963c] to 14400 K
for benzaldehyde, see Ogata et al [1967]. When the determined values of mkeff
for both reactions are compared, an equal trend is observed with respect to
temperature. As the energy of activation has comparable values for the oxidation
of alcohols, aldehydes or ketones, selectivity can not be influenced by
temperature.
1
3
mkeff [m /kmol s]
10
1.E+01
2-octanol
0
1.E+00
10
-1
10
1.E-01
-2
10
1.E-02
2-octanone
-3
10
1.E-03
-4
1.E-04
10
-5
1.E-05
10
-6
2-octanone
1.E-06
10
carboxylic acids
-7
1.E-07
10
2.8
3.0
3.2
3.4
3.6
3.8
1000/T [1/K]
Figure 15: Effect of temperature on the reaction rate constants for the
oxidation of 2-octanol and 2-octanone, respectively. Lines calculated according
to Eq.(8) and parameters from Table 3 for 60 wt% HNO3.
44
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
2.6
Simulation of isothermal runs
The mathematical model for the oxidation rates has been tested using the kinetic
parameters as described above. The mass balances Equation (14) and (15) are
expressed as two differential equations and can be solved simultaneously using a
fifth order Runge-Kutta method with an adaptive step size control, see Press et
al. [1986]. In view of the autocatalytic behavior, whereby some reaction product
must be present before the reaction can start, an initiator has to be added. For all
experiments an addition of 0.1 g NaNO2 has been chosen. This is, as
experimentally found, the minimum amount to be added to ensure the reaction
starts immediately. To solve the differential equations and to account for the
initial reaction rate, an initial concentration of nitrosonium ion ζB0 has to be
taken, which is an optimizing problem. The initial reaction rates as
experimentally determined and calculated are in good agreement provided an
initial concentration of nitrosonium ion equal to 3.5% is taken. Thus, the
boundary conditions for these differential equations are: ζP0 = 0, ζX0 = 0 and ζB0
= 0.035 at θ = 0. The differential equations together with the kinetic parameters
in Table 3 can now be used to simulate the experiments.
Figure 16 shows the experimentally determined and simulated heat production
rates as a function of time. The simulated heat production rates Qnol and Qnone are
plotted for the separate reactions. Also both, the simulated and experimental,
total heat production rates QR = Qnol + Qnone are plotted. The measured and
simulated conversion-time profiles for 2-octanol, 2-octanone and carboxylic
acids are shown in Figure 17 for the same series. The 2-octanol was added in 30
minutes to 60 wt% HNO3 at a temperature of 10, 20 and 40 ºC respectively. One
can observe that the heat generation rate increases with increasing temperature,
which is the result of both the increasing conversion rate of 2-octanol as well as
the increasing rate of the more exothermic oxidation of 2-octanone.
45
Heat production rate, Q [W]
Chapter 2
100
75
Qnol + Qnone
50
QR, experimental
25
Qnol
Qnone
0
0
1800
3600
5400
7200
Heat production rate, Q [W]
Time [s]
100
Qnol + Qnone
75
QR, experimental
50
Qnol
25
Qnone
0
0
1800
3600
5400
7200
5400
7200
Heat production rate, Q [W]
Time [s]
200
Qnol + Qnone
QR, experimental
150
100
Qnone
50
Qnol
0
0
1800
3600
Time [s]
Figure 16: Experimental total heat production rate QR,experimental (thick line) and
simulated (thin lines) heat production rates Qnol, Qnone and QR,simulated= Qnol+Qnone.
Isothermal semi-batch experiments at a temperature of 10, 20 and 40 ºC
respectively, with an initial load of 0.4 kg 60 wt% HNO3 and 0.1 g NaNO2.
Addition of 0.1 kg 2-octanol in a dosing time of 30 min.
46
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
Number of moles
1
0.8
0.6
0.4
0.2
0
0
1800
3600
5400
7200
5400
7200
5400
7200
Time [s]
Number of moles
1
0.8
0.6
0.4
0.2
0
0
1800
3600
Time [s]
Number of moles
1
0.8
0.6
0.4
0.2
0
0
1800
3600
Time [s]
Figure 17: Experimental (dots) and simulated (lines) conversions of 2-octanol
(●,
), 2-octanone (■,
) and carboxylic acids (▲,
). Isothermal semibatch experiments with experimental conditions as for Figure 16.
47
Concentration 2-octanone [-]
Chapter 2
1
0.8
nP
nA1
( )
0.6
20 ºC
max
40 ºC
0.4
0.2
60 ºC
0
0
1
2
3
4
Dimensionless time θ = t/tdos [-]
Figure 18: Concentration of 2-octanone as a function of time for isothermal
semi-batch experiments and the maximum concentration of 2-octanone as
obtained during each run. Simulations with a temperature of 20, 40 and 60 ºC
and further conditions as for Figure 16.
The conversion of 2-octanol increases with increasing temperature and as a
result the location of the maximum concentration of 2-octanone in the
conversion-time profile shifts towards shorter reaction times. The concentration
profiles of 2-octanone for simulations of isothermal runs at 20, 40 and 60 ºC are
plotted in Figure 18. In the same figure, the line is plotted connecting all the
maximum concentrations of 2-octanone. The maximum concentration of 2octanone is found after a long reaction time when the reactor temperature is low.
The energy of activation has comparable values for both reactions. Therefore,
the maximum concentration is hardly affected by the reactor temperature and
will be practically constant as long as the reaction time is sufficiently long.
At higher temperatures the location of the maximum concentration of 2octanone shifts towards shorter reaction times. The influence of dosing becomes
visible when the maximum concentration is obtained just after the dosing has
been stopped at θ = 1. In that case the maximum concentration decreases.
A comparison between simulations and experimental results shows the proposed
model is sufficiently accurate to describe the conversion and heat production
48
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
rates of the oxidation reactions. Especially, when one takes into account the
complexity of the oxidations reaction and the simplicity of the model.
2.7
Model validation and limitations
The process of mass transfer with chemical reaction during the oxidations of 2octanol and 2-octanone with nitric acid has been modeled by assuming that the
conversion rate is not affected by mass transfer rates. The verification of the
assumptions described in Section 2.3 regarding these mass transfer rates is
discussed below:
Slow reaction, Ha<0.3
The Hatta numbers are calculated for both reactions and listed in Table 4 as a
function of temperature. These values have been obtained for CNaNO2 , 0 is 4.9·10-3
M, CHNO3 , 0 is 13.0 M and the stirring rate is 700 rpm. The diffusivity coefficients
have been calculated using the relation of Wilke and Chang [1955] together with
the relation of Cox and Strachan [1972] to correct for nitric acid mixtures. The
estimation of the mass transfer coefficients will be discussed in the next
paragraph.
Temperature
[ºC]
0
10
20
30
40
Hanol, max.
Hanone, max.
0.2
0.3
0.4
0.5
0.6
0.02
0.02
0.06
0.07
0.09
Calculated maximum Hatta numbers,
Table 4:
Hamax, for the isothermal oxidation experiments with
N = 700 rpm. Initial: 60 wt% HNO3, 0.1 g NaNO2.
The calculated Hatta numbers for the oxidation of 2-octanol to 2-octanone
indicate that the transfer rates are not enhanced by chemical reaction as long as
the temperature is below 20 ºC. The conversion rate of 2-octanone to further
oxidation products is not chemically enhanced in the whole range of applied
temperatures. If the reaction is not slow compared to mass transfer, the
49
Chapter 2
enhancement can be estimated by the expression of Danckwerts, see e.g.
Westerterp et al. [1987]:
EA = 1 + Ha 2
(28)
The deviations are within 5% and 10% up to a temperature of 10 ºC and 20 ºC
respectively. The deviation is slightly higher at 40 ºC: 17%, but still reasonably
small as also experimentally demonstrated by the influence of stirring speed.
Mass transfer resistance in the organic phase negligible
The mass transfer resistance in the organic phase is zero if the phase consists of
pure reactant without solvent as in the case of the oxidation of 2-octanol. As the
reaction proceeds, 2-octanone is formed and dilutes the organic phase. Thus the
validity of the neglect of the mass transfer resistance in the organic phase must
be examined. This assumption holds, see Westerterp [1987], if:
kL ,Org
>> 1
kL , Aq m
(29)
The mass transfer coefficients kL,Aq for 2-octanol and 2-octanone in the
continuous, aqueous phase can be estimated with the empirical correlation of
Calderbank and Moo-Young [1961] as discussed in detail in Chapter 4. A
typical value of the mass transfer coefficients for both 2-octanol and 2-octanone
in the continuous phase is kL,Aq = 20·10-6 m/s for the range of experimental
conditions. This value is in agreement with the value reported by Chapman et al.
[1974]. They found experimentally kL = 10.3·10-6 m/s for toluene in a
HNO3/H2SO4 solution.
In view of the low solubility of the organic compounds in nitric acid with mA =
0.005 and mP = 0.006 for 2-octanol and 2-octanone, respectively, and the mass
transfer coefficient in liquid-liquid dispersions of the same order of magnitude,
see e.g. Laddha and Degaleesan [1976] and Heertjes and Nie [1971], this gives
for kL,Org ( kL , Aq m) a value of approximately 200. Therefore, the mass transfer
resistance in the organic phase is negligible for the transport of both 2-octanol
and 2-octanone.
The concentration drop over the film is negligible
The concentration drop from Ci*, Aq to Ci , Aq is relatively more important if mass
transfer resistance in the aqueous phase is higher. When the concentration drop
is more than say 5%, the simple approximation Ci*, Aq ≈ Ci , Aq starts to lead to
50
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
inaccuracies, see Steensma and Westerterp [1990]. To check this approximation
it is possible to compare the rate of mass transfer with the chemical reaction, see
Zaldivar et al. [1995]:
2
7
Ja = kL Ci*, Aq − Ci , Aq a
(30)
Ja = (1 − ε )keff Ci , Aq CB, Aq
(31)
where a is the interfacial area per unit volume of reactor content. The
combination of both equations gives:
(1 − ε )keff CB, Aq Ci*, Aq
=
−1
kL a
Ci , Aq
(32)
Hence, in the case where Ci*, Aq ≈ Ci , Aq it must be checked whether
(1 − ε )keff CB, Aq kL a << 1. The total interfacial area is estimated by means of the
Sauter mean drop diameter, d32, which is defined as:
d32 = 6ε / a
(33)
where ε is volume fraction of dispersed phase and a the interfacial area per unit
volume of reactor content. The average drop size depends upon the conditions of
agitation and the physical properties of the liquids. For baffled stirred tank
reactors the Sauter mean drop diameter d32 can be estimated using the
correlation:
d32
= A(1 + Bε ) We−0.6
Dstir
(34)
where Dstir is the impeller diameter, ε is the volume fraction of dispersed phase,
A and B are empirical constants, which must be determined experimentally for a
given reactor set-up and liquid-liquid system, see Chapter 4. We is the Weber
number, defined as:
We =
3
N 2 Dstir
ρc
σ
(35)
where N is the stirring rate, ρ c is the density of the continuous phase and σ is
the interfacial tension. Equation (34) has been used by numerous workers,
51
Chapter 2
whereby the values of A and B depend on the geometry. With the used values for
A and B reasonable values have been obtained for the drop size. This is
sufficiently accurate to estimate the validity of the concentration drop over the
film.
The interfacial tension is predicted using the empirical correlation of Good and
Elbing [1970]:
σ 12 = γ 1 + γ 2 − 2φ 12 γ 1γ 2
(36)
where φ 12 is an experimentally determined interaction parameter and γ 1 and γ 2
are the surface tensions of the pure components. The interaction parameter φ 12 is
not known for 2-octanol. Therefore the value for n-octanol has been used, see
Good and Elbing [1970], which is equal to φ 12 =0.97. The surface tensions for
both 2-octanol and 2-octanone are equal to 0.026 N/m at 20 ºC, see Daubert et
al. [1989], and for a 60 wt% HNO3 solution it is equal to 0.063 N/m, see
Zaldivar et al. [1996]. The liquid-liquid interfacial tension between 2-octanol, 2octanone or a mixture of both with a 60 wt% nitric acid solution is thus equal to
σ = 0.010 N/m. This can be compared to the experimental value between
octanol and water of σ = 0.0085 N/m, as measured by van Heuven and Beek
[1971].
Temperature (1 − ε )keff , nol CB, Aq kL a (1 − ε )keff ,none CB, Aq kL a
[ºC]
0
0.02
0.0001
10
0.05
0.0004
20
0.07
0.001
30
0.15
0.004
40
0.20
0.006
Table 5: Validity of the assumption of a negligible
concentration drop over film for 2-octanol (reaction ‘nol’)
and 2-octanone (reaction ‘none’), respectively. Isothermal
oxidation experiments with N = 700 rpm and initially
60wt% HNO3 and 0.1 g NaNO2.
The Weber-number is now equal to We =1175. The interfacial area increases
with the hold-up of the organic phase for the used system from 8000 to 15000
m2/m3. Typical values of (1 − ε )keff CB, Aq kL a are listed in Table 5 as a function of
52
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
temperature. The assumption of a negligible concentration drop over the film for
2-octanone is valid. For 2-octanol this is not true and the simple approximation
Ci*, Aq ≈ Ci , Aq leads to inaccuracies. The deviations are within 5% and 10% up to a
temperature of 10 ºC and 20 ºC respectively.
As can be concluded from Table 4 and Table 5, all assumptions are valid with
deviations below 10% as long as temperature is lower than 20 ºC. At a higher
temperature the description of the oxidation of 2-octanol using the reaction rate
expression of Equation (6) may lead to deviations of up to 20% at 40 ºC.
Fortunately, the deviations are small and still within the experimental error.
Thus the model based on the slow liquid-liquid reaction regime can be used
without introducing larger inaccuracies.
Model verification with isoperibolic experiments
The data from the isothermal experiments, being the concentrations versus time
and heat production rate versus time, were used to fit the reaction rate equations.
Data from isoperibolic experiments can be used to test the accuracy of the
derived kinetic expressions. The data from experiments with a constant jacket
temperature have not been used to determine the kinetic expressions.
The mathematical model with the mass balances Equation (14) and (15) together
with the heat balance Equation (18) now can be used to describe the temperature
profile. The isoperibolic experiments were carried out in the same way as the
isothermal runs, except that the calorimeter now is operated with a constant
jacket temperature. In Figure 19 the temperature profiles are plotted for five
isoperibolic experiments with different jacket temperatures: the experimental
profiles are in good agreement with the simulations. In Figure 20 the
temperature profiles are plotted for four isoperibolic experiments with different
jacket temperatures and a faster dosing rate. As can be seen one is working in a
parametric sensitivity region, where the maximum reactor temperature, Tmax, is
sensitive towards the cooling temperature Tcool.
Under these conditions even a small deviation between model and actual
parameters will lead to large discrepancies. At higher temperatures the model
overestimates the reactor temperature, which can be attributed to evaporation of
the nitric acid solution, which has not been incorporated in the model. However,
the simulated and the experimental results show the same thermal behavior. This
thermal behavior of the oxidation reaction will be discussed in more detail and
under varying experimental conditions in Chapter 3.
53
Chapter 2
Temperature [ºC]
60
50
40
30
20
10
0
0
0.5
1
1.5
2
theta [-]
Figure 19: Experimental (continuous line) and simulated (dotted lines) reactor
temperatures in some isoperibolic semi-batch experiments with varying coolant
temperature with T0 = Tcool. Initial load of 60 wt% HNO3 and 0.1 g NaNO2.
Addition of 100 g 2-octanol in a dosing time of 120 min.
Temperature [ºC]
120
100
80
60
40
20
0
0
0.5
1
1.5
2
theta [-]
Figure 20: Experimental (continuous line) and simulated (dotted lines) reactor
temperatures in some isoperibolic semi-batch experiments with varying coolant
temperature with T0 = Tcool. Initial load of 60 wt% HNO3 and 0.1 g NaNO2.
Addition of 100 g 2-octanol in a dosing time of 30 min.
54
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
2.8
Discussion and conclusions
The main objective of this chapter is to determine the kinetic parameters of the
model proposed to describe the heterogeneous oxidation of 2-octanol to 2octanone and the unwanted, further oxidation reactions to carboxylic acids. The
oxidation of 2-octanol and 2-octanone with nitric acid exhibits the typical
features of nitric acid oxidation reactions, like a long induction time without
initiator; autocatalytic reaction; strong dependence of mineral acid concentration
and high energy of activation, see Ogata [1978]. Although the main phenomena
of nitric acid oxidation reactions are well known the exact mechanism is still not
elucidated. There is a limited knowledge of the exact chemical structure of the
compounds in the aqueous reaction phase and of a number of unknown, unstable
compounds in the organic phase. As a consequence of this a strong model
reduction was necessary to describe the overall reaction rates. The model
reduction in this case gave satisfactory results, as also demonstrated by Hugo
and Mauser [1983].
The observed conversion rates of the complex reactions of 2-octanol and 2octanone with nitric acids can be correlated using only two kinetic equations, in
which the effect on temperature is described through the Arrhenius equation and
the effect on acid strength through Hammett’s acidity function. The
experimental results and simulations are in good agreement, hence the employed
film model is satisfactory.
The oxidation reactions have been studied in the range 0 to 40 ºC, with initial
nitric acid concentrations of 50 to 65 wt% and a stirring rate of 700 rpm. The
results indicate the oxidation of 2-octanol is operated in the non-enhanced
regime when nitric acid is below 60 wt% or when the temperature is below 25
ºC at 60 wt% HNO3, while the oxidation of 2-octanone is operated in the nonenhanced regime for the whole range of experimental conditions considered.
Under these conditions the mass transfer resistance does not influence the
overall conversion rate, so the governing parameters are the reaction rate
constant and the solubility of the organic compounds in the nitric acid solution.
This has also been experimentally confirmed by determining the influence on
stirring rate.
Even though the kinetic constants have been determined only up to a
temperature of 40 ºC, the simulated results for isoperibolic experiments at higher
temperatures are still acceptable. Therefore it can be concluded that it has been
possible to describe the thermal behavior of the semi-batch reactor for the nitric
acids oxidation reactions with the film model for slow liquid-liquid reactions
55
Chapter 2
and a simplified reaction scheme. In Chapter 3 the thermal behavior of this
consecutive heterogeneous liquid-liquid reaction system will be further
evaluated.
Acknowledgements
The author wishes to thank S.E.M. Geuting, R.H. Berends, V.B. Motta, E.A.H.
Ordelmans and S.P.W.M. Lemm for their contribution to the experimental work,
and F. ter Borg, G.J.M. Monnink and A.H. Pleiter for technical support. W.
Lengton and A. Hovestad are acknowledged for the assistance in the analysis.
Notation
a
A
C
CP
D
DI
d32
EA
EAct
h
H
H0
Ha
J
kLaq
kLorg
keff
k∞,eff
M
m
mHo
n
N
Q
R
r
56
Interfacial area per volume of reactor content = 6ε / d32
Effective cooling area
Concentration
Specific heat capacity
Diameter
Diffusivity coefficient component i
Sauter mean drop diameter
Enhancement factor
Energy of activation
Height
∆Heff ,none / ∆Heff ,nol
Hammett’s acidity function
Hatta number
Mole flux
Mass transfer coefficient in the aqueous phase
Mass transfer coefficient in the organic phase
Effective second order reaction rate constant
Effective preexponential constant
Molecular weight
Molar distribution coefficient
Hammett’s coefficient
Number of moles in the reactor
Stirring rate
Heat flow
Gasconstant = 8315
Rate of reaction per volume of reactor content
[m2/m3]
[m2]
[kmol/m3]
[J/Kg K]
[m]
[m2/s]
[m]
[-]
[J/kmol]
[m]
[-]
[-]
[-]
[kmol/m2·s]
[m/s]
[m/s]
[m3/kmol·s]
[m3/kmol·s]
[kg/kmol]
[-]
[-]
[kmol]
[s-1]
[W]
[J/kmol·K]
[kmol/m3s]
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
t
tdos
T
U
V
Time
Dosing time
Temperature
Overall heat transfer coefficient
Volume
[s]
[s]
[K]
[W/m2K]
[m3]
Greek symbols
α
∆H
∆E
ε
ϕ
Γ
µ
θ
ρ
σ
ζi
ζ B0
Angle of cone
Heat of reaction
Amount of heat
Volume fraction dispersed phase = Vd (Vd + Vc )
Flow
Effective heat capacity
Viscosity
Dimensionless dosing time = t/tdos
Density
Interfacial tension
Yield of component i = ni/nA1
Initial concentration of nitrosonium ion = 0.035
[º]
[kJ/mol]
[kJ]
[-]
[m3/s]
[J/K]
[Ns/m2]
[-]
[kg/m3]
[N/m]
[-]
[-]
Dimensionless groups
Q
5
ρ dis N 3 Dstir
Po
Power number
Re
Reynolds number
We
Weber number
2
ρ dis NDstir
µ dis
3
ρc
N 2 Dstir
σ
[-]
[-]
[-]
57
Chapter 2
Subscripts and superscripts
0
1
nol
none
A
Aq
B
c
C
cool
d
dis
dos
eff
f
i
max
Org
P
R
r
stir
w
X
∗
¯
∞
58
Initial, at t = 0
Final (after dosing is completed)
Reaction of 2-octanol, see Equation (4)
Reaction of 2-octanone, see Equation (5)
Component A (2-octanol)
Aqueous phase (nitric acid solution)
Component B (nitrosonium ion)
Continuous (aqueous) phase
Calibration
Cooling
Dispersed (organic) phase
Dispersion
Dosing
Effective
Formation
Component i
Maximum
Organic phase
Component P (2-octanone)
Reaction
Reactor
Stirring
Reactor wall
Component X (carboxylic acids)
At interface
Average
Ambient
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
References
van Asselt, W.J. and van Krevelen, D.W., Preparation of adipic acid by
oxidation of cyclohexanol and cyclohexanone with nitric acid. Part I
Reaction mechanism., Rec. Trav. Chim. Pays-Bas 82 (1963) 51-67.
van Asselt, W.J. and van Krevelen, D.W., Preparation of adipic acid by
oxidation of cyclohexanol and cyclohexanone with nitric acid. Part II
Reaction kinetics of the decomposition of 6-hydroxyimino-6-nitrohexanoic acid. Rec. Trav. Chim. Pays-Bas 82 (1963) 429-437.
van Asselt, W.J. and van Krevelen, D.W., Preparation of adipic acid by
oxidation of cyclohexanol and cyclohexanone with nitric acid. Part III
Reaction kinetics of the oxidation. Rec. Trav. Chim. Pays-Bas 82 (1963)
438-449.
van Asselt, W.J. and van Krevelen, D.W., Adipic acid formation by oxidation of
cyclohexanol and cyclohexanone with nitric acid, measurements in a
continuous stirred tank reactor, reactor stability. Chem. Eng. Sci. 18
(1963) 471-483.
Atherton, J.H., Methods for study of reaction mechanisms in liquid/liquid and
liquid/solid reaction systems and their relevance to the development of
fine chemical processes., Trans. Inst. Chem. Eng. 71 (1993) 111-118.
Calderbank, P.H. and Moo-Young, M.B., The continuous phase and heat and
mass transfer properties of dispersions, Chem. Eng. Sci. 16 (1961) 39-54.
Camera, E., Zotti, B., and Modena, G., On the behaviour of nitrate esters in acid
solution. Chim. Ind. 61 (1979) 179-183.
Camera, E., Modena, G. and Zotti, B., On the behaviour of nitrate esters in acid
solution. III. Oxidation of ethanol by nitric acid in sulphuric acid.
Propellants, Explos., Pyrotech. 8 (1983) 70-73.
Castellan, A., Bart, J.C.J. and Cavallaro, S., Nitric acid reaction of cyclohexanol
to adipic acid, Catal. Today 9 (1991) 255-283.
Chapman, J.W., Cox, P.R. and Strachan, A.N., Two phase nitration of toluene
III, Chem. Eng. Sci. 29 (1974) 1247-1251.
Cox, P.R. and Strachan, A.N., Two-phase nitration of toluene, Part II. Chem.
Eng. J. 4 (1972) 253-261.
Daubert, T.E., Danner, R.P., Sibul, H.M. and Stebbins, C.C., Physical and
thermodynamic properties of pure chemicals: data compilation, Taylor &
Francis, London, 1989.
Davis, D.D., Adiptic acid, in: Ullmann’s Encyclopedia of Industrial chemistry,
Volume A1, VCH, Weinheim, 5th edn. 1985, pp. 269-278.
Good, R.J. and Elbing, E., Generalization of theory for estimation of interfacial
energies, Ind. Eng. Chem., 62 (1970) 54-78.
59
Chapter 2
Haldar, R. and Rao, D.P., Experimental studies on parametric sensitivity of a
batch reactor, Chem. Eng. Technol. 15 (1992), 34-38.
Haldar, R. and Rao, D.P., Experimental studies on semibatch reactor parametric
sensitivity, Chem. Eng. Technol. 15 (1992), 39-43.
Hanson, C. Mass transfer with simultaneous chemical reaction, in: C. Hanson
(ed.), Recent advances in liquid-liquid extraction, Pergamon Press,
Oxford 1971, p. 429-453.
Heertjes, P.M. and de Nie, L.H., Mass transfer to drops, in: C. Hanson (ed.),
Recent advances in liquid-liquid extraction, Pergamon Press, Oxford,
1971, p. 367-406.
van Heuven, J.W. and Beek, W.J., Power input, drop size and minimum stirrer
speed for liquid-liquid dispersions in stirred vessels, Proc. Int. Solv. Extr.
Conference, Society of Chemical Industries, 1971, pp. 70-81.
Horvath, M., Lengyel, I. and Bazsa, G., Kinetics and mechanism of autocatalytic
oxidation of formaldehyde by nitric acid, Int. J. Chem. Kinet., 20 (1988)
687-697.
Hugo, P. and Mauser, H., Detaillierte und modellreduzierte Beschreibung der
chemischen Wärmeentwicklung am Beispiel der Oxidation von
Acetaldehyd mit Salpetersäure. Chem. Ing. Tech. 55 (1983) 984-985.
Laddha, G.S. and Degaleesan, T.E., Transport phenomena in liquid extraction,
McGraw-Hill, New Delhi, 1976.
Longstaff, J.V.L. and Singer, K., The kinetics of oxidation by nitrous acid. Part
II. Oxidation of formic acid in aqueous nitric acid, J. Chem. Soc. (1954)
2610-2617.
Mettler-Toledo AG, Operating instructions RC1 Reaction Calorimeter, MettlerToledo AG, Switzerland 1993.
Ogata, Y., Sawaki, Y., Matsunaga, F. and Tezuka, H., Kinetics of the nitric acid
oxidation of benzyl alcohols to benzaldehydes. Tetrahedron 22 (1966)
2655-2664.
Ogata, Y., Tezuka, H. and Sawaki, Y., Kinetics of the nitric acid oxidation of
benzaldehydes to benzoic acid. Tetrahedron 23 (1967) 1007-1014.
Ogata, Y., Oxidations with nitric acid or nitrogen oxides, in: Oxidation in
organic chemistry, part C, ed. W.S. Trahanovsky, Academic press, New
York, 1978, pp. 295-342.
Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., Numerical
recipes, Cambridge University Press, Cambridge, 1986.
Reisen, R. and Grob, B., Reaction calorimetry in chemical process development,
Swiss Chem., 7 (1985) 39-43.
Rochester, C.H., Organic chemistry, A series of monographs: Acidity functions,
Academic press, London, 1970.
60
The Nitric Acid Oxidation of 2-Octanol and 2-Octanone
Rudakov, E.S., Lutsyk, A.I. and Gundilovich, G.G., Propane solubility in
aqueous mineral acids (0-100%): a significant difference in the solvating
properties of H2SO4, HNO3 and H3PO4. Mendeleev Commun. 1 (1994)
p.27-28.
Snee, T.J. and Hare, J.A., Development and application of pilot scale facility for
studying runaway exothermic reactions, J. Loss Prev. Process Ind. 5
(1992) 46-54.
Steensma, M. and Westerterp, K.R., Thermally safe operation of a semi-batch
reactor for liquid-liquid reactions. Slow reactions, Ind. Eng. Chem. Res.
29 (1990) 1259-1270.
Strojny, E.J., Iwamasa, R.T. and Frevel, L.K., Oxidation of 2-methoxyethanol to
methoxyacetic acid by nitric acid solutions, J. Am. Chem. Soc. 93 (1971)
1171-1178.
Westerterp, K.R., van Swaaij, W.P.M. and Beenackers, A.A.C.M., Chemical
reactor design and operation, Wiley, Chichester, student edn., 1987.
Wilke, C.R. and Chang, P., Correlation of diffusion coefficients in dilute
solutions, AIChE J. 1 (1955) 264-270.
Zaldivar, J.M., Molga, E., Alos, M.A., Hernandez, H. and Westerterp, K.R.,
Aromatic nitrations by mixed acid. Slow liquid-liquid reaction regime,
Chem. Eng. Process. 34 (1995) 543-559.
Zaldivar, J.M., Molga, E., Alos, M.A., Hernandez, H. and Westerterp, K.R.,
Aromatic nitrations by mixed acid. Fast liquid-liquid reaction regime,
Chem. Eng. Process. 35 (1996) 91-105.
61
Chapter 2
62
3
Runaway Behavior and Thermally Safe
Operation of Multiple Liquid-Liquid
Reactions in the Semi-Batch Reactor
Chapter 3
Abstract
The thermal runaway behavior of an exothermic, heterogeneous, multiple
reaction system has been studied in a cooled semi-batch reactor. The nitric acid
oxidation of 2-octanol has been used to this end. During this reaction 2-octanone
is formed, which can be further oxidized to unwanted carboxylic acids. A
dangerous situation may arise when the transition of the reaction towards acids
takes place accompanied by a temperature runaway.
An experimental set-up was build, containing a 1-liter glass reactor, followed by
a thermal characterization of the equipment. The operation conditions, e.g.
dosing time and coolant temperature, to achieve a high yield under safe
conditions are studied and discussed.
The reaction conditions should rapidly lead to the maximum yield of
intermediate product 2-octanone under safe conditions and stopped at the
optimum reaction time. The appropriate moment in time to stop the reaction can
be determined by model calculations. Also operation conditions are found which
can be regarded as invariably safe. In that case no runaway reaction will occur
for any coolant temperature and the reactor temperature will always be
maintained between well-known limits.
The boundary diagram of Steensma and Westerterp [1990] for single reactions
can be used to determine the dosing time and coolant temperature required for
safe execution of the desired reaction. For suppression of the undesired reaction
it led to too optimistic coolant temperatures.
64
Runaway Behavior and Thermally Safe Operation
3.1 Introduction
To reduce the risk associated with exothermic chemical reactions, in a semibatch operation one of the reactants is fed gradually to control the heat
generation by chemical reaction. In practice the added compound is not
immediately consumed and will partly accumulate in the reactor. The amount
accumulated is a direct measure for the hazard potential. A definition of a
critical value of accumulation, to discern between safe and unsafe conditions,
may be rather arbitrary. From a safety point of view an accurate selection of
operation and design parameters is required to obtain the minimum
accumulation.
Hugo and Steinbach [1985] started investigations on the safe operation of semibatch reactors for homogeneous reaction systems. Steensma and Westerterp
[1990,1991] studied semi-batch reactors for heterogeneous liquid-liquid
reactions. They demonstrated that it is important to obtain a smooth and stable
temperature profile in the reactor. These authors dealt with single reactions.
However, many problems of runaway reactions encountered in practice are
caused by multiple and more complex reaction systems.
The usual objective is to suppress side reactions whose rates are negligible at
initial conditions but may become significant at higher temperatures, see e.g.
Hugo et al. [1988], Koufopanos et al. [1994], Serra et al. [1997]. In these works
a maximum allowable temperature is defined as the temperature, where
decomposition or secondary reactions are not yet initialized. Limiting the
temperature increase is usually very effective in suppressing side reactions. It is
a rather conservative approach, but necessary to obtain an inherently safe
process, see e.g. Stoessel [1993,1995]. No work has been published on safe
operation of exothermic multiple reactions in which an unwanted reaction is
kept in hand and partially is allowed to take place.
To prevent a runaway one has to operate outside regions of high sensitivity of
the maximum reactor temperature towards the coolant temperature. In case of a
multiple reaction system complications arise: one has to discern between the
heat production rates of the different reactions, see e.g. Eigenberger and Schuler
[1986]. The extension of the theory of temperature sensitivity to multiple, more
complex, kinetic schemes is not obvious: the interaction of parameters in a
multiple reaction system makes the development of an unambiguous criterion
impossible. Each reaction network requires an individual approach and the
optimum temperature strongly depends on the kinetic and thermal parameters of
all the reactions involved.
65
Chapter 3
The present work focuses on the thermal dynamics of a semi-batch reactor, in
which multiple exothermic liquid-liquid reactions are carried out. The runaway
behavior has been experimentally studied for the nitric acid oxidation of 2octanol to 2-octanone, and further oxidation products like carboxylic acids. The
kinetics of these reactions have been discussed in Chapter 2. It will further be
evaluated, whether the mathematical model as developed by Steensma and
Westerterp [1990] is sufficiently accurate to predict the reactor behavior and to
stop the reaction at the appropriate moment in time.
3.2 Nitric acid oxidation in a semi-batch reactor
The nitric acid oxidation of 2-octanol to 2-octanone and the further oxidation of
2-octanone to carboxylic acids are described in Chapter 2. The reaction system
was found to be suitable to study the thermal behavior of a semi-batch reactor in
which slow multiple liquid-liquid reactions are carried out. The oxidation
reaction system will be described here briefly.
Interface
Aqueous nitric acid Phase
2-Octanol
Organic Phase
2-Octanol
rnol
2-Octanone
2-Octanone
rnone
Carboxylic acids
Carboxylic acids
Figure 1: Schematic representation of mass transfer with chemical reaction
during the oxidation with nitric acid of 2-octanol to 2-octanon and carboxylic
acids.
66
Runaway Behavior and Thermally Safe Operation
Reaction system
The oxidation of 2-octanol takes place in a two-phase reaction system: a liquid
organic phase, which initially contains 2-octanol, is in contact with an aqueous
nitric acid phase in which the reactions takes place. The reaction system with
simultaneous mass transfer and chemical reaction is represented with Figure 1.
The oxidation of 2-octanol (A) to 2-octanone (P) and further oxidation products
(X) can be described with the following reaction equations:
rnol
A + B  → P + 2 B
(1)
rnone
→ X
P + B 
(2)
where B is the nitrosonium ion, which also causes an autocatalytic behavior. The
reaction rates in the acid phase can be expressed on the basis of a second order
reaction:
1
rnol = knol mACA,Org CB, Aq 1 − ε d
1
6
rnone = knone m p CP ,Org CB, Aq 1 − ε d
(3)
6
(4)
where CA,Org, CP,Org and CB,Aq are the bulk concentrations of 2-octanol (A), 2octanone (P) and nitrosonium ion (B) in the organic phase (Org) and Aqueous
phase (Aq), respectively. The kinetic constants knol and knone can be described
with:
%&
'
k = k∞ exp −
1
E
− mHo H0
RT
6()*
(5)
where k∞, E/R and mH0 are the pre-exponential factor, the activation temperature
and the Hammett’s reaction rate coefficient, respectively. H0 is Hammett’s
acidity function, see Rochester [1970]. The value of H0 is plotted as a function
of the nitric acid concentration in Figure 2. The values of the kinetic constants
and the heat effects are listed in Table 1, see also Chapter 2.
67
Chapter 3
4
- H0 [-]
3
2
1
0
-1
0
10
20
30
40
50
60
70
Concentration HNO3 [wt%]
Figure 2: Hammett’s acidity function H0 as a function of the nitric acid solution
concentration.
Parameter
mA k nol
Enol/R
mHo,nol
∆Hnol
1·105
11300
6.6
160·106
m3/kmol·s
K
J/kmol
mP k ,none
Enone/R
mHo,none
∆Hnone
1·1010
12000
2.2
520·106
m3/kmol·s
K
J/kmol
‡
‡
Table 1: Kinetic parameters and reaction heats for
the nitric acid oxidation of 2-octanol and 2octanone, respectively. Taken from Chapter 2.
68
Runaway Behavior and Thermally Safe Operation
Mathematical model
The reaction will be executed in an indirectly cooled SBR in which aqueous
nitric acid is present right from the start and the organic component 2-octanol
(A) added at a constant feed rate until a desired molar ratio of the reactants has
been reached. The 2-octanol reacts to 2-octanone and to carboxylic acids. The
heat of reaction is removed by a coolant, which flows through an internal coil
and/or an external jacket. The temperature in the reactor and the concentrations
of the reactants and products as a function of time can be found by solving the
heat and mass balances over the reactor, using the appropriate initial conditions.
In the model for the semi-batch reactor considered in this work it is assumed,
that the following conditions holds:
- Uniform reaction temperature
- Volumes and heat capacities are additive
- The reactions take place in the aqueous nitric acid phase only
- The nitric acid phase is the continuous phase throughout the experiment, phase
inversion does not occur
- No change in the volume of the separate phases
- A low mutual solubility of the reactants
Mass and energy balances
The yields of 2-octanone ζ P and of carboxylic acids ζ X respectively, are defined
on the basis of the total amount of 2-octanol fed nA1, see notation, and can be
used to obtain dimensionless concentrations of the components in Equations (1)
and (2) and of the nitric acid concentration CN,Aq:
1
6
CA,Org ≈
θ − ζ P − ζ X nA1
nA
=
Vdos1θ
Vdos1θ
(6)
CB, Aq ≈
nB (ζ P + ζ B 0 )nA1
=
Vr 0
Vr 0
(7)
CP,Org ≈
nP
ζ n
= P A1
Vdos1θ Vdos1θ
(8)
CX ,Org ≈
nX
ζ n
= X A1
Vdos1θ Vdos1θ
(9)
69
Chapter 3
CN , Aq ≈
1
6
nN nN 0 − ζ B 0 + ζ P + 2ζ X nA1
=
Vr 0
Vr 0
(10)
The dimensionless time θ is obtained by dividing the time t by the dosing time
tdos, and after dosing is completed θ = 1. Vdos1θ is the volume of the dispersed,
organic phase. The initial concentrations at θ = 0 of 2-octanol CA,Org, 2-octanone
CP,Org and carboxylic acids CX,Org respectively, are equal to zero. The reaction
will only start after addition of an initiator. The initiator will produce the initial
concentration of nitrosonium ion: CB 0, Aq = nB 0 Vr 0 = ζ B 0 nA1 Vr 0 . The addition of
initiator will consume a small amount nitric acid equal to ζ B 0 nA1 . Thus the yield
ζP starts at zero at the start of the reaction, reaches a maximum and after that
decreases. At the end of the secondary reaction ζP is again equal to zero.
Due to the low solubilities one can neglect the amount of the organic
components A, P and X present in the aqueous phase and assume for the
macroscopic mass balance that CA, Aq = 0, CP, Aq = 0 and CX , Aq = 0. The mass
balances for the oxidations have been derived by substitution of the
concentrations Equations (6)-(8) and using the reaction rates Equations (3) and
(4):
1
6
dζ P
ζ + ζ B0 dζ X
= mA knol tdos CA,dos θ − ζ P − ζ X P
−
dθ
dθ
θ
(11)
1 6
(12)
dζ X
ζ + ζ B0
= mP knonetdos CA,dos ζ P P
dθ
θ
where CA,dos is the concentration of reactant 2-octanol in the feed as dosed to the
reactor vessel. The initial boundary conditions will be discussed later.
Steensma and Westerterp [1990] have derived the basic equations and
definitions describing the thermal phenomena in a cooled semi-batch reactor, in
which a single liquid-liquid reaction is carried out. Their expression for the heat
balance has been written in a more general way and can easily be extended to
multiple reactions and take into account the additional heat sources like
agitation, etc.:
1
1
dTr
QR + Qdos + Qcool + Qstir + Q∞
=
dt Γtot
70
6
(13)
Runaway Behavior and Thermally Safe Operation
where Γtot is the total heat capacity of the system, being the sum of the heat
capacities of the reaction mixture mCp and the effective heat capacity Γeff, which
consists of the heat capacities of the devices wetted and the heat capacity of the
reactor wall. The different heat flows included are the QR: chemical reaction
heat, Qdos: heat input due to reactant addition, Qcool: heat exchanged with the
coolant, Qstir: heat supplied by the agitator, and Q∞: heat exchanged with the
surroundings. The heat released by chemical reaction is the sum of the heat
released by the oxidation of 2-octanol, Qnol, and 2-octanone, Qnone, respectively
and can be written as:
QR = Qnol + Qnone =
nA1 dζ P dζ X
n dζ
+
∆Hnol + A1 X ∆Hnone
tdos dθ
dθ
tdos dθ
(14)
where the dimensionless conversion rates dζ P dθ and dζ X dθ are taken from
the mass balances, Eq.(11) and Eq.(12).
During a semi-batch process the added mass is not necessarily at the same
temperature as the reactor and so contributes to cooling or heating of the
reactant mass. In that case this temperature difference must be taken into
account in the energy balance.
1 6 1T
Qdos = ϕ v ,dos ρ CP
dos
dos
− Tr
6
(15)
where ϕ v ,dos is the volumetric flow rate of the feed dosed into the reactor. The
heat exchanged with the heat transfer fluid can be expressed with:
1
Qcool = UAcool ⋅ Tcool − Tr
6
(16)
where UAcool is the product of the effective heat transfer coefficient and the area
of the cooling jacket or cooling coil. UAcool usually depends on the volume of the
reaction mixture. The power introduced by the stirrer can be correlated in the
turbulent flow regime by:
5
Qstir = Po ρ dis N 3 Dstir
(17)
In reactor used the power number Po is constant and equal to Po = 4.6. The
importance of the amount of heat exchanged with the surroundings increases
with the temperature difference between the system and the surroundings, the
heat flow can be expressed with:
71
Chapter 3
1
Q∞ = UA∞ T∞ − Tr
6
(18)
where T∞ the ambient temperature and UA∞ is the effective heat transfer per unit
of temperature difference for heat losses of the reactor.
The main contribution to the heat removal rate from the reactor is the cooling by
the coolant. The cooling can also be expressed as a dimensionless cooling
intensity, which is equivalent to U*Da/ε, as defined by Steensma and Westerterp
[1990]:
U * Da = UA
ε
ρCPVr
1
in which UA ρCPVr
6
−1
0
t
dos
/ε
(19)
0
is the cooling time and tdos, the dosing time.
The heat capacity of the equipment and heat transfer coefficients to the coolant
and the surroundings have to be determined experimentally for the reactor
configuration used. This will be discussed in a following section. The mass
balances Eq.(11) and Eq.(12) together with the heat balance Eq.(13) have to be
solved simultaneously. The resulting temperature profile can be compared to a
target temperature as defined by Steensma and Westerterp [1990].
Target temperature
Analogously to Steensma and Westerterp [1990] a target temperature can be
defined as the steady-state temperature for an well-ignited reaction:
Tta rget = Tcool +
1
1.05 ⋅ QR + Qdos + Qstir + Q∞
UAcool
6
(20)
The target temperature is the temperature that will be attained in the reactor, in
case the reaction is infinitely fast and the reactant added is immediately
consumed. This is usually not the case and one has to allow for some
accumulation of the dosed reactant in the reactor. Therefore the factor 1.05 is
introduced into Eq.(20).
In this case the heat released by chemical reaction is the sum of the heats
released by the oxidation of 2-octanol Qnol and of 2-octanone Qnone. For 2octanone as the only product one can calculate the heat flow by chemical
reaction QR when it is assumed that the reaction is infinitely fast. Under such
72
Runaway Behavior and Thermally Safe Operation
conditions the rate of formation is equal to the dosing rate, because the
consumption rate of the ketone is equal to zero. Thus the conversion rate
dζ P dθ is equal to unity throughout the supply period until dosing is stopped at
θ = 1 and, because no carboxylic acids are formed, dζ X dθ = 0. The heat flow
by the chemical reaction QR becomes in this case:
Qnol =
nA1
∆Hnol
tdos
(21)
In case only the carboxylic acids are produced, hence for dζ P dθ = 0 and
dζ X dθ = 1, the heat flow by chemical reaction is equal to:
Qnol + Qnone =
1
nA1
∆Hnol + ∆Hnone
tdos
6
(22)
For the oxidations two target temperatures can be defined: one for 2-octanone
and one for the carboxylic acids. To this end Equation (21) or Equation (22) is
substituted in Equation (20). In this way two pre-defined target temperature
profiles are obtained, which can be used to evaluate the reaction temperature.
The temperature and concentration versus time profiles of the nitric acid
oxidation of 2-octanol can be calculated when the mass balances Equations (11)
and (12) and the heat balance Equation (13) are solved simultaneously using a
fifth order Runge-Kutta method with an adaptive step size control. The division
by θ in Equations (11) and (12) with θ = 0 can be solved numerically after
substitution of θ plus a very small number equal to 10-15: θ = θ + 10-15. The
initial boundary conditions for these differential equations are: ζP0 = 0, ζX0 = 0
and ζB0 = 0.035 at θ = 0 and Tr = T0 = Tcool at θ = 0. The initial concentration of
nitrosonium ion has been set at ζB0 = 0.035 to compensate for the autocatalytic
behavior, whereby it is necessary to have some of the reaction product
nitrosonium ion present directly at the start. The value of ζB0 has been chosen in
such a way that a good agreement between the initial reaction rates as
experimentally determined and the calculated ones is obtained. The exact value
of ζB0 has a strong influence on the calculated results, in case the initial reaction
rate is very low. In this work rather long dosing times are used and is operated at
high temperatures, hence the initial reaction rate is large and will be less
sensitive towards ζB0.
The characteristic behavior of the nitric acid oxidation of 2-octanol will be
explained in the following section using the results of the simulations. It will
73
Chapter 3
also be proved that the simulation covers the experimental data well. For the
simulations a small industrial reactor has been chosen. The reactor, having a
total volume of Vr = 3 m3, is equipped with a cooling jacket for the heat transfer.
The jacket has a total surface area Acool of 7.5 m2 with U = 400 W/m2K. The
parameters as listed in Table 2 are used.
parameter
UA cool,0 [kW/K]
Vr0 [m3]
Γ0 [J/K]
tdos [h]
1.5
1.5
5.4·106
10
parameter
UA cool,1 [kW/K]
Vr1 [m3]
ρCp,dos [J/m3K]
nA1 [kmol]
2.1
2.1
2.0·106
3.8
Table 2: Process and equipment parameters of the oxidation
reaction carried out in a small industrial reactor having a total
volume of Vr = 3 m3 and equipped with a cooling jacket for the
heat transfer.
74
Runaway Behavior and Thermally Safe Operation
3.3 Thermal behavior of the nitric acid oxidation of 2-octanol
To give insight into the reaction behavior of the nitric acid oxidation of 2octanol, it is assumed that the reaction is executed in a SBR and only the coolant
temperature, which is the most important control variable, is varied. Three
typical reaction regimes can be distinguished with increasing operation
temperatures:
i) Oxidation of 2-octanol to 2-octanone
ii) Simultaneously the reaction of 2-octanol to 2-octanone and the further
oxidation of 2-octanone to carboxylic acids
iii) Oxidation of 2-octanol to carboxylic acids
The calculated temperature profile, heat production rates and molar amounts as a
function of time are shown in figures 3-5.
i) Production of 2-octanone
At a low coolant temperature and for the chosen further operating conditions,
mainly 2-octanone is formed, see Figure 3. The reaction has a good start,
followed by a period of a practically constant reaction temperature. The reactor
temperature curve approaches the target temperature of 2-octanone,
Ttarget, 2-octanone, and the yield of 2-octanone is high. This type of profile is called a
QFS profile - with a Quick onset, Fair conversion and Smooth temperature
profile - by Steensma and Westerterp [1990]. The chosen regime is usually the
optimal operating regime for semi-batch processes. One can observe that in
Figure 3 the maximum concentration of 2-octanone, where the reaction has to be
stopped, has not yet been reached. In practice the coolant temperature would be
increased as soon as the reactor temperature becomes lower than Ttarget ,2-octanone.
The reactor operation as depicted in Figure 3 may appear reasonably safe. There
is no temperature jump, no sudden conversion of 2-octanol and no large
accumulation of 2-octanol. However, a large quantity of 2-octanone
accumulates, which creates a potential for extra heat production as it can be
further oxidized by nitric acid. This can be seen in Figure 4.
75
Chapter 3
Temperature, T [ºC]
40
T target carboxylic acids
20
T target 2-octanone
0
Tcool = -12 ºC
-20
0
5
10
15
20
15
20
Heat production rate [W/kg]
Time [h]
12
QR = Qnol + Qnone
8
Qnol
4
Qnone
0
0
5
10
Time [h]
Number of moles [kmol]
21
5
HNO3
18
16
4
3
13
2-octanone
8
2
2-octanol
3
1
carboxylic acids
0
-2
0
5
10
15
20
Time [h]
Figure 3: Reaction behavior in case of oxidation of 2-octanol to 2-octanone
under conditions that the target line of 2-octanone is approached: a) reactor
temperature; b) heat production rates, and c) molar amounts. Coolant
temperature of -12 ºC and an initial load of 1500 l. 60wt% HNO3. Addition of
600 l. 2-octanol in a dosing time of 10 hours.
76
Runaway Behavior and Thermally Safe Operation
ii) Transition of the oxidation reactions
As the temperature is increased also the simultaneous production of carboxylic
acids takes place. The conditions in this case are critical so that, after a good
start of the first reaction, they lead to a temperature runaway: the target
temperatures of 2-octanone and of the carboxylic acids are both undesirably
exceeded. During such an experiment larger amounts of 2-octanone accumulate
in the reactor before the secondary reaction is triggered. The produced 2octanone is then very rapidly consumed by further oxidation reactions. The heat
of reaction of the secondary reaction is liberated in a short time resulting in a
large temperature peak. The heat production rate then decreases, as the
concentration of the reactants has dropped to a low level, while the heat removal
rate by cooling is still high due to the high temperature difference between the
reaction mixture and the coolant, so the reactor temperature decreases rapidly.
When the reaction temperature decreases the heat production rates of both
reactions decrease very fast and, hence, the reaction rates. This is due not only to
the influence of the temperature, but above all to influence of the acid strength
on the reaction rates. The nitric acid concentration decreases in this case from 60
wt% to 45 wt%, which corresponds to H0 = -3.38 and –2.68, respectively, see
Figure 2. This lowers the kinetic constant knol, see Equation (5), with a factor
100. Thus, the reaction is practically extinguished.
iii) Production of carboxylic acids.
When the temperature is further increased practically no 2-octanone accumulates
during the whole reaction period, it reacts away immediately to acids. The
system again behaves as a single reaction in which 2-octanol reacts to carboxylic
acids and again one can observe a good start of the reaction with a smooth
temperature profile, see Figure 5. Such a situation is thermally safe but is
undesirable, because a high yield of 2-octanone is desired. Also in this case the
strong influence of the nitric acid is visible. At the moment dosing is stopped the
nitric acid concentration is only 40 wt%, i.e. H0 = -2.39, and again, the reaction
rate is drastically reduced.
77
Chapter 3
Temperature, T [ºC]
130
80
T target carboxylic acids
30
T target 2-octanone
Tcool = -5 ºC
-20
0
5
10
15
20
15
20
Time [h]
Heat production rate [W/kg]
75
Qmax = 494 W/kg
50
QR = Qnol + Qnone
Qnone
25
Qnol
0
0
5
10
Time [h]
Number of moles [kmol]
21
4
HNO3
18
15
3
13
2
carboxylic acids
2-octanone
8
1
3
2-octanol
0
-2
0
5
10
15
20
Time [h]
Figure 4: Reaction behavior as in Figure 3, but a coolant temperature of -5 ºC.
The target line is undesirable exceeded.
78
Runaway Behavior and Thermally Safe Operation
Temperature, T [ºC]
80
T target carboxylic acids
60
T target 2-octanone
40
Tcool = 30 ºC
20
0
5
10
15
20
15
20
Time [h]
Heat production rate [W/kg]
50
QR = Qnol + Qnone
25
Qnone
Qnol
0
0
5
10
Time [h]
Number of moles [kmol]
21
6
HNO3
17
14
5
12
4
7
2
3
carboxylic acids
-3
2
2-octanone
1
-8
2-octanol
-13
-18
0
0
5
10
15
20
Time [h]
Figure 5: Reaction behavior as in Figure 3, but a coolant temperature of 30 ºC.
The target line of carboxylic acids is approached.
79
Chapter 3
The nitric acid oxidation of 2-octanol can be interpreted as a reaction system
with two main reactions in which 2-octanone is produced at low temperatures
and carboxylic acids at high temperatures. At very low and at very high
temperatures the system behaves as if only a single reaction occurs. The
intermediate region is of interest because there runaways may occur, as is
demonstrated in Figure 4, but also reaction rates are high, so also reactor
capacity is high and still high yields of the ketone must be feasible.
Sudden reaction transition
The temperature profiles, as shown in Figures 3-5, are the result of operating the
SBR under such conditions that production shifts from producing 2-octanone,
Figure 3, to producing carboxylic acids, Figure 5, via a large undesired
temperature overshoot as a result of the sudden reaction transition, Figure 4.
This will take place, in case the operator only increases the coolant temperature,
keeping all other conditions constant. For a series of simulations with a dosing
time of ten hours, i.e. U*Da/ε = 25, the temperature profiles are plotted as (TrTcool) as a function of time, in Figure 6. In this figure the (Tr-Tcool) goes through a
maximum as the coolant temperature increases.
Tr - Tcool [ºC]
100
75
Tcool
50
25
0
0
5
10
15
20
Time [h]
Figure 6: Transition of the reactions accompanied by a large temperature
overshoot. Simulation of isoperibolic semi-batch experiments with the
parameter values from Table 2 and U*Da/ε = 25. Temperature profiles as a
function of time, Tcool = -10, 0, 10 and 30 ºC, respectively.
80
Runaway Behavior and Thermally Safe Operation
The temperature overshoot as a function of coolant temperature can best be
visualized when the maximum temperature obtained in the reactor is plotted as a
function of the coolant temperature. A typical example is shown in Figure 7a. At
a very low coolant temperature one can observe a region of insufficient ignition.
Under these conditions the reactor temperature does not approach the target
temperature for 2-octanone. The reaction rate is much lower than the dosing
rate, the reactor operates as a batch reactor and a long time is needed to
complete the reaction, so dosing has no use.
At a somewhat higher coolant temperature the maximum temperature and the
yield of 2-octanone increase. The conversion rate of the alcohol is close to the
dosing rate and only a small amount of 2-octanol will accumulate. The semibatch process now operates under QFS conditions and 2-octanone is produced.
The coolant temperature is in this case lower then the coolant temperature that
leads to a temperature runaway. At -6 ºC one can observe a sharp increase in the
maximum temperature. At this temperature also carboxylic acids are produced
and a temperature runaway occurs.
Further increasing the coolant temperature results in earlier ignition of the
further oxidation to acids. The maximum temperature is lower and is reached at
an earlier stage. At very high Tcool the maximum temperature approaches the
target temperature for the carboxylic acids and the oxidation can be regarded as
a single reaction, but the undesired one.
The nitric acid oxidation of 2-octanol and 2-octanone is a consecutive reaction
system in which the intermediate product 2-octanone is the one desired. Thus,
the yield of 2-octanone reaches a maximum and after a certain reaction time all
2-octanol has been converted, while 2-octanone is still being converted into the
undesired carboxylic acids. In order to obtain a high yield of 2-octanone the
reaction should be stopped as soon as the concentration of 2-octanone has
reached its maximum value. This can be done for this heterogeneous reaction
system by stopping the stirrer, so that the dispersion separates and the interfacial
area becomes so small that the reaction rate is practically negligible, or by
diluting the nitric acid with water, which also effectively reduces the reaction
rate.
The necessary reaction time to reach the maximum yield of 2-octanone depends
on the reactor temperature. The conversion rate of 2-octanol increases with
increasing temperature and as a result the location of the maximum yield of 2octanone in the conversion-time profile shifts towards shorter reaction times.
81
Maximum temperature [ºC]
Chapter 3
170
Insuf.
ignition
120
70
QFS
2-octanone
QFS
carboxylic acids
Thermal
Runaway
TTarget, carboxylic acids
20
TTarget, 2-octanone
-30
-30
-20
a
-10
0
10
20
30
Coolant temperature [ºC]
100
2-octanone
0.8
80
0.6
60
0.4
40
carboxylic acids
0.2
20
0
0
-30
b
Time until maximum [h]
Relative molar amount [-]
1
-20
-10
0
10
Coolant temperature [ºC]
20
30
Figure 7: Transition of the reactions accompanied by a large temperature
overshoot. Simulation as Figure 6. a: Maximum temperature of the reactor as a
function of the coolant temperature. b: Maximum molar amount of 2-octanone
as a function of the coolant temperature, together with the corresponding molar
amount of carboxylic acids and the reaction time, when the reaction is stopped.
The maximum yield of 2-octanone and the necessary time to reach it are shown
in Figure 7b as a function of the coolant temperature together with the amount of
carboxylic acids formed. When the coolant temperature is increased the time to
obtain the maximum yield of 2-octanone decreases, which increases the reactor
82
Runaway Behavior and Thermally Safe Operation
capacity. On the other hand the amount of carboxylic acids increases, which
leads to loss of raw materials. The time until the maximum increases just before
the runaway reaction is triggered, which can be attributed to the large amount of
carboxylic acids formed during the dosing period. Consequently, more nitric
acid is consumed and reaction rate decreases. At a coolant temperature of higher
than -6 ºC one can also observe a sharp decrease in the maximum yield of 2octanone together with a rapid reduction of the reaction time. At higher coolant
temperatures the maximum yield of 2-octanone is obtained before the dosing is
stopped, which, of course, is an undesired situation.
Gradual reaction transition
The use of a longer dosing time may reduce or even avoid an undesired
temperature overshoot. To this end the dosing time is doubled, compared to the
conditions in Figures 6 and 7, and the value of U*Da/ε increases from 25 to 50.
In Figure 8 the temperature profiles are plotted, as (Tr - Tcool) as a function of
time for this case and, again, only the coolant temperature is varied.
30
Tr - Tcool [ºC]
Tcool
20
10
0
0
10
20
30
40
Time [h]
Figure 8: Transition of the reactions accompanied by a gradual temperature
increase. Simulation of isoperibolic semi-batch experiments as in Figure 6 with
the parameter values from Table 2, but a dosing time of 20 hours, U*Da/ε = 50
and Tcool = -15, -5, 3 and 30 ºC, respectively.
83
Chapter 3
Maximum temperature [ºC]
90
60
Insuf.
QFS
ignition 2-octanone
30
TTarget, carboxylic acids
QFS
carboxylic acids
TTarget, 2-octanone
0
-30
-30
-20
a
-10
0
10
20
30
Coolant temperature [ºC]
1
100
carboxylic acids
0.8
80
0.6
60
0.4
40
tdos
0.2
20
0
0
-30
b
Time until maximum [h]
Relative molar amount [-]
2-octanone
-20
-10
0
10
Coolant temperature [ºC]
20
30
Figure 9: Transition of the reactions accompanied by a gradual temperature
increase. Simulation as Figure 8. a: Maximum temperature of the reactor as a
function of the coolant temperature. b: Maximum molar amount of 2-octanone
as a function of the coolant temperature, together with the corresponding molar
amount of carboxylic acids and the reaction time, when the reaction is stopped.
The maximum temperature as a function of the coolant temperature is shown in
Figure 9a for the case of a gradual reaction transition: the production shifts from
producing 2-octanone to producing carboxylic acids, while the maximum
temperature increases only moderately. For this series with a dosing time of 20
84
Runaway Behavior and Thermally Safe Operation
hours no temperature overshoot takes place. The consecutive reaction has a heat
of reaction 3.25 times that of the main, desired reaction. Therefore there will
always be a region where the maximum temperature is more sensitive towards
the coolant temperature when the production of 2-octanone shifts to the
production of carboxylic acids, in this case between -10 and 10 ºC. The
maximum in Tmax has disappeared in Figure 9a; no runaway occurs anymore.
During the transition the reactor temperature is always limited between the
target temperature of 2-octanone and the target temperature of the carboxylic
acids. This is now called invariably safe as no sudden temperature jump occurs
for any coolant temperature chosen. However, the reaction is not inherently safe
because, for example in case of cooling failure, further oxidation reactions will
be triggered.
The maximum yield of 2-octanone, the amount of carboxylic acids and the
necessary time to reach the maximum are for this case shown in Figure 9b as a
function of the coolant temperature: for higher coolant temperatures the
maximum yield of 2-octanone and the time to obtain the maximum yield
decrease gradually. At a high coolant temperature, only carboxylic acids are
produced.
tdos = 10 h
50
tdos = 20 h
0.8
40
0.6
30
tdos = 20 h
20
0.4
tdos = 10 h
0.2
10
0
0
-30
-25
-20
-15
-10
-5
Coolant temperature [ºC]
0
5
10
Figure 10: Productivity and raw material loss as a function of the coolant
temperature for the oxidation of 2-octanol carried out in a semi-batch reactor
with dosing times of 10 and 20 hours, respectively. Further parameter values
taken from Table 2.
85
Loss of raw material [-]
1
3
Productivity [mol/m /h]
60
Chapter 3
Because of the plant economics one must achieve a high yield of 2-octanone in a
short time under safe conditions. For a time tidle for filling, emptying and
cleaning of the reactor the productivity is (ζ p · nA,1/Vr,1) / (treac + tidle). For the
two dosing times the productivities are plotted in Figure 10, as well as the
relative loss of raw material defined as the amount of raw material A converted
into X per unit of P produced. For a coolant temperature below Tcool = -15 ºC the
maximum yield of 2-octanone is obtained a long time after the dosing has been
stopped. For this low coolant temperature a high yield is obtained and it is for
both U*Da/ε = 25 and 50 equal to ζ p = 90%. Thus, for a high yield both dosing
times give similar productivities. A larger dosing time makes the process
invariably safe, while the total time for reaction is not much longer, so for this
case the longer dosing period of tdos = 20 hours must be recommended. The most
economical operating conditions depend on numerous parameters, and should be
determined for each individual case.
3.4 Recognition of a dangerous state
In the oxidation of 2-octanol one focuses on the first reaction because high
yields of ketone are required, while the danger of a runaway reaction must be
attributed to the ignition of the secondary reaction. The reaction system can be
considered as two single reactions and, therefore, the boundary diagram
developed by Steensma and Westerterp [1990] for single reactions may be
helpful to estimate critical conditions for the multiple reaction system.
Their boundary diagram for a slow reaction in the continuous phase is given in
Figure 11. The area enclosed by the boundary lines is where overheating, i.e. a
runaway, will occur and therefore it should be avoided. For reaction conditions
located below the boundary area the reaction does not ignite. The discontinuous
line in Figure 11 is the route through the diagram if only the coolant temperature
is increased. The insufficiently ignited reaction will, in that case, first change
into a runaway reaction and eventually become a QFS reaction when the coolant
temperature is further increased. The coolant temperature should therefore
preferably be chosen such that:
1) the oxidation of 2-octanol to 2-octanone is a QFS reaction, and
2) the secondary reaction remains insufficiently ignited.
When Ex < Exmin, no runaway will take place for any coolant temperature. In
that case at higher values of the Reactivity number the reaction will be a QFS
reaction. The minimum exothermicity number Exmin corresponds to the
invariably safe operation as described in the previous paragraph.
86
Runaway Behavior and Thermally Safe Operation
Later on, the experimental results will be used to verify whether the boundary
diagram as developed by Steensma and Westerterp [1990] is sufficiently
accurate to predict the reactor behavior of a multiple reaction system.
Ry = Reactivity [-]
0.04
increasing
Tcool
U*Da/ε = 10
0.03
U*Da/ε = 5
QFS
0.02
U*Da/ε = 20
Runaway
0.01
Exmin
Insufficient ignition
0
0
2
4
6
8
10
12
Ex = Exothermicity [-]
Figure 11: Boundary diagram for a slow reaction in the continuous phase for
U*Da/ε = 5, 10 and 20, respectively. From Steensma and Westerterp [1988].
87
Chapter 3
3.5 Experimental set-up and procedure
The experimental set-up is shown in Figure 12. The reactor (1) is a jacketed 1liter glass vessel of the type HWS Mainz. The glass reactor has a diameter of
0.10 m and is equipped with four equally spaced stainless steel baffles with a
width of 10 mm. The reactor content is agitated by a stainless steel turbine
stirrer with a diameter of 36 mm and six blades of 7.4 x 9.4 mm2 each. The
stirrer is driven by a Janke and Kunkel motor and its speed is kept constant at
1000 rpm.
7
Ti
Ti
H2O
4
Ti
Ti
5
Ti
Ti
1
Ti
H2O
3
6
2
Figure 12: Simplified flowsheet of experimental set-up. Ti, temperature
indictor. See text for further details.
88
Runaway Behavior and Thermally Safe Operation
The reactor is operated in the semi-batch mode with a constant coolant
temperature. To study the influence of different heat transfer coefficients two
separate cooling circuits are used: one via the cooling jacket and one via a
cooling coil. The coolant is pumped from a cryostat (2) of the type Julabo FP50
through the cooling jacket by a Pompe Caster gear pump or through the cooling
coil by a Verder gear pump. The coil consists of tubes made of stainless steel
with a diameter of 6 mm and wall thickness of 1 mm. The reactor is initially
loaded with 0.5 liter of a 60 wt% HNO3-solution. Before the experiment is
started a small amount of 0.12 g NaNO2 is added as initiator. When the
temperature of the reactor has become constant, the feeding of pure 2-octanol is
started. The supply vessel has been located on a balance of the type Mettler
pm1200 (3) to measure the mass of the feed. The organic compound is fed to the
reactor by a Verder gear pump (4) with a constant feed rate in the range of 0.03
to 0.33 kg/h. The nitric acid and the organic solutions are immiscible and form a
dispersion in the reactor, provided the mixing rates are high. The nitric acid is
taken in excess and forms the continuous phase during the whole experiment.
Before an experiment is started, the equipment is flushed with N2. During the
oxidation NOX-gases are formed, which are allowed to escape through a hole in
the reactor lid towards a scrubber (5), where they are washed with water. After
an amount of 0.16 kg 2-octanol has been added, the dosing is stopped manually.
After that the experiment is continued till at least t = 2 tdos. The experiment is
then brought to an end by heating up the reactor contents, so that the remaining
reactants are converted to carboxylic acids.
The temperatures of the reaction mixture, coolant inlet and outlet, feed and
surroundings are measured by thermocouples. The temperatures and the feed
mass flow rate are monitored and stored by a Data Acquisition and Control Unit
in combination with a computer of the type HP486-25 of Hewlett Packard.
When the reactor temperature exceeds a certain unacceptable value, the
computer in an emergency procedure activates actuators to open: a) The valve in
the reactor bottom to dump the reactor content and quench it on ice in a
container (6) and b) The valve on the reactor lid to dump an amount of 0.5 liter
water into the reactor from the container (7). During an experiment samples of
the dispersion are taken manually via a syringe. Approximately 5 samples are
taken during each run. In the syringe the dispersion separates immediately in
two phases; both phases are analyzed. The nitric acid concentration in the
aqueous phase is determined by titration and the organic phase is analyzed by
gas chromatography, see Chapter 2.
An example run is shown in Figure 13, with the temperatures as measured and
the number of moles of the compounds as determined via the chemical analysis.
89
Chapter 3
25
Tfeed
Temperature [ºC]
Tambient
20
15
Treactor
Tspiral
Tjacket
10
start
dosing
stop
dosing
5
-1000
0
1000
2000
3000
4000
5000
6000
Time [s]
a
Number of moles
72
6
1.5
5
HNO3
2-Octanone
1
2-Octanol
0.5
Carboxylic acids
0
-1000
b
0
1000
2000
3000
4000
5000
6000
Time [s]
Figure 13: Isoperibolic semi-batch experiment with jacket and spiral cooling at
10 ºC with an initial load of 0.5 liter of 60 wt% HNO3 and 0.12 gram NaNO2.
Addition of 0.2 liter 2-octanol in a dosing time of 42 minutes. a) Measured
temperatures of the feed, ambient, reactor contents, cooling spiral and cooling
jacket. b) Molar amounts as function of time of the nitric acid in the aqueous
phase and of 2-octanol, 2-octanone and carboxylic acids, respectively in the
organic phase.
90
Runaway Behavior and Thermally Safe Operation
Thermal characterization of equipment
To describe the thermal dynamics of the reactor set-up a proper equipment
characterization is necessary, see also Barcons [1991]. It is carried out by
determining heat capacities and heat flows as enumerated in Equation (13) as
follows:
Thermal capacities
The effective heat capacity Γeff involves the heat capacities of the vessel wall
and inserts, like the cooling coil, baffles, and stirrer: it is determined by a rapid
addition to the reactor vessel of an amount of hot water of a temperature Tw,0 and
a mass m and measure the temperature of the liquid phase as a function of time.
The temperature of the added water will decrease from Tw,0 to T1 and heat-up the
system from Tr,0 to T1. The total heat capacity Γtot follows from:
Γtot = Γeff + ( mC P )w =
2
( mCP )w Tw , 0 − T1
2T − T 7
1
7 + ( mC )
P w
(23)
r,0
UA
The product of the overall heat transfer coefficient and the cooling area UAcool of
the cooling jacket and cooling coil are determined by introducing an amount of
energy with a cartridge heater of the type Superwatt 7310 put into the reaction
mixture. A heat flow of approximately Qelement ≈ 10 Watt is adequate. The
cooling circuit removes the heat and the temperature of the reaction mixture and
coolant are measured as a function of time: a steady state will be reached as
soon as the heat production rate by the electrical heater is equal to the heat flow
to the coolant Qcool. Under these conditions the temperature difference between
the reaction mixture and cooling medium (Tr -Tcool) can be used to determine the
value of UAcool according to:
UAcool =
1
Qelement
Tr − Tcool
6
(24)
UAcool has been determined for different volumes of dispersion in the reactor and
increases linearly with the volume dosed.
Heat losses to the surroundings
A good estimate can be obtained by introducing a known amount of energy with
the electrical heater into the reaction mixture without cooling. The heat input is
set at approximately Qelement ≈ 5 Watt and the temperature of the reaction
91
Chapter 3
mixture Tr and of the surroundings T∞ are measured as a function of time. The
temperature of the reaction mixture will increase until a steady state is reached,
where the heat production rate equals the heat flow to the surroundings Q∞. This
leads to:
UA∞ =
1
Q∞
Q
= element
T∞ − Tr
T∞ − Tr
6 1
6
(25)
Power input by stirring
The power supplied by stirring can be determined by measuring the torque
transmitted by the shaft. If this is not possible the power generated can be
estimated by calorimetric measurements with only heat transfer to the
surroundings. When the stirrer is the only power input source and UA∞ has been
determined as previously described, it is possible to calculate the power input in
the steady state:
1
5
= Q∞ = UA∞ Tr − T∞
Qstir = Po ρ dis N 3 Dstir
6
(26)
Typical values of the various parameters are listed in Table 3 for the different
cooling configurations.
jacket
spiral
jacket and
jacket and
cooling
cooling
spiral cooling spiral coolinga
380
380
380
380
Γeff [J/K]
UA cool0 [W/K]
4.3
8.8
13.1
13.5
UA cool1 [W/K]
5.4
11.8
17.2
18.2
b
0.1
0.3
0.1
0.1
UA∞ [W/K]
Po [-]
4.6
4.6
4.6
4.6
a
Values for the reactor containing only water
b
Heat losses are larger when jacket is empty, i.e. only spiral cooling
Table 3: Thermal characteristics of the experimental set-up as obtained by
experimentally determining the heat capacities and heat flows as enumerated in
Equation (13).
92
Runaway Behavior and Thermally Safe Operation
The thermal characterization was first carried out with the reactor containing
only water. The results were used to describe experiments in which hot water is
added semi-batch-wise to cold water initially in the reactor. During such an
experiment the temperature of the reactor contents will increase during the
dosing and after that, it will be brought back by the cooling to the initial value.
For a series of experiments the temperature profiles are plotted in Figure 14: the
experimental and simulated profiles show a good agreement. The thermal
characterization is adequate.
Then also UA values were experimentally determined for the reactor containing
only a 60 wt% nitric acid solution, and a dispersion of nitric acid and final
organic reaction product, respectively. The thermal characteristics data obtained
in this way have typically a standard deviation of 3.5%. The results of the
thermal characterization are listed in Table 3 and should be sufficiently accurate
to simulate the heat effects in the reactor.
Temperature [ºC]
30
25
20
15
10
0
600
1200
1800
Time [s]
Figure 14: Experimental (continuous lines) and simulated (dashed lines)
temperature profiles for verifying the thermal characterization. Addition of 0.25
liter water with Tdos ≈ 60 ºC in a dosing time of 75, 225 and 475 s., respectively
to an initial reactor load of 0.5 liter water of 10.8 ºC.
93
Chapter 3
Check on the validity of the model for slow reactions
The mass balances for the oxidations, Equation (11) and (12), have been derived
by assuming the rate of mass transfer is not enhanced by reaction, and the
reaction mainly proceeds in the bulk of the reaction phase. This has to be
validated for the current reactor set-up and the applied experimental conditions.
For such situations, one must check that Ha < 0.3 holds, see Westerterp et al.
[1987], where the Hatta number Ha is defined as:
Ha =
kCB, Aq Di
kL
(27)
The mass transfer coefficients kL,Aq for 2-octanol and 2-octanone in the
continuous, aqueous phase is typically kL,Aq = 40·10-6 m/s, which has been
discussed in more detail in Chapter 2. This value is larger than the value
reported by Chapman et al. [1974]. They found experimentally kL = 10.3·10-6
m/s for toluene in a HNO3/H2SO4 solution with an acid strength of 76%. The
acid strength used in the present work is much lower and, therefore, at the lower
viscosity a larger value of the mass transfer coefficient is found. The Hatta
number for the oxidation of 2-octanone is always below 0.3, for the whole
experimental range. The calculated Hatta numbers for the oxidation of 2-octanol
indicate that this is also the case as long as the temperature is below 40 ºC as Ha
< 0.3. This includes the temperature range for high yields of 2-octanone.
Furthermore, the mass transfer resistance in the organic phase can be neglected
as the solubility of the organic compounds in the nitric acid solution is low and
the mass transfer coefficients are of the same order of magnitude, see Chapter 2.
If the conversion rate for a liquid-liquid reaction is not influenced by a mass
transfer resistance, it should be independent of the stirring rate. The influence of
the stirring rate on the conversion rate has been experimentally determined in
the temperature range of 10 to 60 ºC at 720, 1000 and 1400 rpm. The maximum
heat production rate is plotted against the stirring speed in Figure 15 and is
independent of the stirring speed. For the chosen stirring rate of 1000 rpm in the
experiments mass transfer resistance 1/kLa does not play a role. Visually it can
be observed that above N = 600 rpm the mixture becomes well dispersed.
94
Maximum heat production rate [W]
Runaway Behavior and Thermally Safe Operation
500
60 ºC
30 ºC
15 ºC
400
300
200
100
0
500
700
900
1100
1300
1500
Stirring speed [rpm]
Figure 15: Maximum heat production rate versus stirring speed for semi-batch
experiments at a temperature of 15, 30 and 60 ºC. Reactor initial loaded with 0.7
kg 60 wt% HNO3 and 0.12 g NaNO2. Addition of 0.16 kg 2-octanol in a dosing
time of 42 min.
3.6
Experimental results
Temperature profiles
The nitric acid oxidation of 2-octanol has been experimentally studied under
isoperibolic conditions i.e. with a constant coolant temperature, at different
values of the coolant temperature. The semi-batch reactor is initially charged
with 0.5 liter of a 60 wt% HNO3 solution, after that 0.2 liter of 2-octanol is
added at ambient temperature, in all experiments. First, a series of experiments
has been carried out with a constant feed rate during one hour and with cooling
only via the cooling jacket. Second, a series of experiments has been carried out
with both cooling jacket and cooling coil in use. The temperature profiles are
shown in Figure 16: a good agreement between the experimental and simulated
values can be observed, except for high temperatures. For the reaction system
the upper temperature limit is approximately 90 ºC, where the mixture starts to
boil. In Figure 16a the temperature profiles are shown for experiments with
U*Da/ε = 21 whereby, as a result of increasing coolant temperature, the
transition to the consecutive reaction is accompanied by a large temperature
overshoot. For a higher cooling capacity – U*Da/ε = 65 – in Figure 16b the
transition is gradual and no sudden temperature jumps can be observed.
95
Chapter 3
Temperature [ºC]
100
80
60
40
20
0
0
1800
3600
5400
7200
Time [s]
a
Temperature [ºC]
80
60
40
20
0
0
1800
3600
5400
7200
Time [s]
b
Figure 16: Experimental (continuous lines) and simulated (dashed lines)
temperature profiles of isoperibolic semi-batch experiments with an initial load
of 0.5 liter 60 wt% HNO3 and 0.12 gram NaNO2. Addition of 0.2 liter 2-octanol
in a dosing time of 60 minutes with (a) U*Da/ε = 21: the transition of the
reaction is accompanied by a large temperature overshoot, and (b) U*Da/ε = 65:
a gradual temperature increase.
96
Runaway Behavior and Thermally Safe Operation
Thermally safe operation of the nitric acid oxidation of 2-octanol
The objective is to produce 2-octanone with a high yield and under safe
conditions. To this end the nitric acid oxidation of 2-octanol is experimentally
studied together with the region of a high yield of 2-octanone.
Influence of dosing time
Increasing dosing time makes it possible to spread the produced heat of reaction
over a longer period of time and should therefore reduce or avoid temperature
overshoots. A series of experiments has been carried out at different coolant
temperatures with dosing times of 60, 135 and 170 minutes, respectively, which
is equivalent to U*Da/ε values of 21, 48 and 61. The maximum temperature
obtained during a run is plotted versus the coolant temperature in Figure 17.
Maximum temperature [ºC]
100
21
48
60
61
U*Da/ε
20
-20
-20
0
20
40
60
Coolant temperature [ºC]
Figure 17: Influence of the dosing time on the maximum temperature.
Experimental (dots) and simulated (lines) isoperibolic semi-batch experiments
with an initial load of 0.5 liter of 60 wt% HNO3 and 0.12 gram NaNO2. Addition
of 0.2 liter 2-octanol in a dosing time of 60(●), 135(❍) and 170(▲) minutes,
which is equivalent to U*Da/ε values of 21, 48 and 61.
97
Chapter 3
1
Maximum yield [-]
61
0.8
U*Da/ε
21
0.6
0.4
0.2
0
0
10
20
30
40
50
Coolant temperature [ºC]
a
Reaction time [h]
10
8
61
6
4
U*Da/ε
21
2
0
0
b
10
20
30
40
50
Coolant temperature [ºC]
Figure 18: Influence of the dosing time on (a) the yield of 2-octanone and (b)
the reaction time as function of the coolant temperature. Parameters as in Figure
17.
Increasing U*Da/ε from 21 to 48 effectively reduces the temperature overshoot,
which even disappears for U*Da/ε = 61. Thus, for a long dosing time an
increase in coolant temperature leads to a gradual transition of the reactions and
no runaway occurs anymore for any coolant temperature chosen; the process is
invariably safe.
98
Runaway Behavior and Thermally Safe Operation
The calculated maximum yield of 2-octanone, together with the corresponding
reaction time are given as a function of coolant temperature for U*Da/ε of 21
and 61 respectively in Figure 18a and 18b together with some experimentally
determined values. Due to a limited amount of sampling data points it is for
most experiments impossible to determine the value of the maximum yield
exactly, nevertheless the agreement between the calculations and experiments is
good.
When the dosing time is increased threefold from 60 to 170 minutes, one can
observe for the same high yield, thus at low coolant temperatures, that the total
reaction time increases with about 2 hours, meanwhile the process has become
invariably safe.
Maximum temperature [ºC]
100
60
21
U*Da/ε
44
65
20
-20
-20
0
20
40
60
Coolant temperature [ºC]
Figure 19: Influence of the cooling capacity UA/Vr on the maximum
temperature. Experimental (dots) and simulated (lines) isoperibolic semi-batch
experiments with an initial load of 0.5 liter of 60 wt% HNO3 and 0.12 gram
NaNO2. Addition of 0.2 liter 2-octanol in a dosing time of one hour and UA0’s of
4.3(●), 8.8(❍) and 13.1(▲) W/K respectively, which is equivalent to U*Da/ε
values of 21, 44 and 65.
99
Chapter 3
1
Maximum yield [-]
U*Da/ε
0.8
65
0.6
21
0.4
0.2
0
-10
0
10
20
30
20
30
Coolant temperature [ºC]
a
20
Reaction time [h]
16
12
65 U*Da/ε
8
21
4
0
-10
b
0
10
Coolant temperature [ºC]
Figure 20: Influence of the cooling capacity UA/Vr on (a) the yield of 2octanone and (b) the reaction time as function of the coolant temperature.
Parameters as in Figure 19.
Influence of cooling capacity
With larger UA/Vr values the temperature effects are moderated and the reaction
becomes more isothermal. A reactor equipped with both a cooling jacket and a
cooling coil can be operated with either one or the two systems simultaneously.
This enables one to operate the reactor with three different cooling capacities. A
series of experiments has been carried out at different coolant temperatures and
100
Runaway Behavior and Thermally Safe Operation
different UA-values and a dosing time of 60 minutes, which are equivalent to
U*Da/ε values of 21, 44 and 65. The same typical behavior of the maximum
temperature is found, as in the case of change in the dosing time, see Figure 19.
One should be aware that for U*Da/ε = 21 and coolant temperatures above 8 ºC
the maximum yield is reached even before the dosing has been completed. In
this runaway situation the reactor temperatures become so high that the
secondary reaction starts to dominate the reaction process.
The maximum yield of 2-octanone and the corresponding reaction time are
plotted in Figure 20a and 20b, respectively. The influence of the cooling
capacity on the total reaction time follows from comparing the yield. For
example, a maximum yield of 90% is obtained in a shorter reaction time when
the reaction is carried out in a reactor with a larger cooling capacity. For this
example, in which U*Da/ε is increased from 21 to 65 by increasing the UAvalues, for the same high yield the total reaction time is shortened by about 3
hours and at the same time the process has become invariably safe. These high
effective heat transfer coefficients are usually not feasible for reactors of a large
size and consequently one has to accept longer reaction times.
Maximum temperature [ºC]
80
dosing
time
60
40
TTarget, 2-octanone
TTarget, carboxylic acids
20
UA0
0
-20
-20
0
20
40
60
Coolant temperature [ºC]
Figure 21: Comparison of different dosing times with U*Da/ε ≈ 46 for the
same data as Figure 19, but dosing times of 135, 60 and 42 minutes,
respectively.
101
Chapter 3
Maximum yield [-]
1
0.8
UA0
0.6
dosing
time
0.4
0.2
0
0
10
20
30
40
50
60
50
60
Coolant temperature [ºC]
a
Reaction time [h]
8
6
dosing
time
4
UA0
2
0
0
b
10
20
30
40
Coolant temperature [ºC]
Figure 22: Comparison of different dosing times with U*Da/ε ≈ 46 for the
same data as Figure 21.
A series of experiments has been carried out with different cooling
configurations, while a dosing time has been chosen in such way that the
U*Da/ε-values are the same. The values are tabulated in Table 4. For these
series the maximum temperature obtained during a run is plotted in Figure 21 as
a function of the coolant temperature. Above a coolant temperature of 5 ºC one
can observe a region where the transition of the reaction products takes place.
102
Runaway Behavior and Thermally Safe Operation
When the coolant temperature is increased, the resulting maximum temperature
approaches the target temperature of 2-octanone, for all series, as QFS of 2octanone is reached. Finally, above a coolant temperature of 40 ºC, for all series
the same maximum temperature is obtained: that of the target temperature of the
carboxylic acids as QFS of the carboxylic acids is reached. Thus, for U*Da/ε ≈
46, the reactor temperature is always limited between the target temperature of
2-octanone and the target temperature of the carboxylic acids and the process
can be considered as invariably safe.
The maximum yield of 2-octanone and the time to obtain this maximum are
plotted in Figure 22a and 22b, respectively. For the same maximum yield and
the same values of U*Da/ε, an increase in tdos leads to an increasing reaction
time, whereas an increase in UA0 leads to a reduction of the reaction time.
(UA)0
[W/K]
4.3
8.8
13.1
tdos
[s]
8100
3600
2520
U*Da/ε
[-]
48
44
46
Table 4: Different cooling configurations
with a constant value of U*Da/ε as used for
the experimental series.
(UA/ρCpVr)0
[h-1]
8.2
16.8
25.0
tdos,min
tdos,min
simulations
experimental
[h]
2.1
1.0
0.7
[h]
2.8
≈1
0.7
Table 5: Experimental and calculated
minimum dosing time for different cooling
capacities UA/Vr to achieve invariably safe
operation.
103
Chapter 3
Invariably safe operation
The process can be regarded as invariably safe when no runaway can occur for
any coolant temperature. This can be achieved for large values of U*Da/ε, that
is for a long dosing time tdos or a large cooling capacity UA/Vr, as has been
shown. When this is one of the conditions to be fulfilled the minimum dosing
time tdos,min should be found that just meets this requirement. It can be
determined experimentally by carrying out experiments with different coolant
temperatures and different dosing times. This demands much experimental
effort. First a dosing time was chosen and a series of experiments was carried
out with different coolant temperatures. When one of the experiments led to a
runaway a second series was carried out with a longer dosing time. This was
repeated, until the dosing time was found that led to invariably safe operation.
This has been done for the different cooling capacities of the reactor set-up. The
resulting minimum dosing times tdos,min are tabulated in table 5 and plotted in
Figure 23. The process is invariably safe for U*Da/ε > 45. As can be seen in
Figure 23, the experimental and simulated results are in reasonable agreement in
predicting the boundary region. This region is very critical, as it is very sensitive
towards small changes. The experimental and calculated results suggest that
scale-up can be done, for a given cooling capacity of the reactor, by selecting the
minimum dosing time from Figure 23. Consequently, a few laboratory-scale
experiments should be enough to establish conditions for a large-scale reactor to
achieve an invariably safe operation.
100
Safe
Boundary line
U*Da/ε = 45
U*Da/ε > 45
tdos [h]
10
Experimental
points
1
Runaway
U*Da/ε < 45
0.1
0.1
1
10
100
-1
(UA/ρCpVr)0 [h ]
Figure 23: Boundary line for invariably safe operation of the nitric acid
oxidation of 2-octanol for U*Da/ε = 45. Results of the simulations (solid line)
and the experimentally determined points.
104
Runaway Behavior and Thermally Safe Operation
3.7 Prediction of safe operation based on the individual reactions
Now the boundary diagram developed by Steensma and Westerterp [1990] will
be used to estimate the QFS conditions of the oxidation of 2-octanol to 2octanone, as well as the critical conditions at which the further oxidation
reaction will be triggered.
Æ
Prediction of QFS conditions for the oxidation of 2-octanol to 2-octanone
In case 2-octanone is produced with a high yield, the reaction is: A + B
P+
2B. This reaction is considered as a slow single reaction in the continuous phase.
The boundary diagram can be used to determine the coolant temperature at
which QFS conditions are obtained. This will be explained with the oxidation of
2-octanol as an example. To obtain a value of U*Da/ε = 20 for a reactor initially
loaded with HNO3 and UA0 = 4.3 W/K a dosing time has to be chosen equal to
tdos = 0.93 hour, which can be compared to the experiments with U*Da/ε = 21 in
Figure 17.
The required coolant temperature can be found after iteration. For Tcool = -1 ºC
one can calculate the Exothermicity number to be Ex = 2.0. The corresponding
reactivity number, for QFS conditions, can be read from Figure 11: Ry = 0.02.
The coolant temperature Tcool follows from the definition for Ry, see notation,
provided the other initial reaction conditions are known. After rewriting:
Tcool = E / R
−m
H0
H0 − ln
Ry 1εR + U * Da6 C t mk H
B 0 dos
(28)
∞
The initial concentration of nitrosonium ion has been set at ζ B0 = 0.035 , thus
CB 0 = nA1 ⋅ ζ B 0 / V0 = 0.088 M. So, for the oxidation of 2-octanol and the relevant
parameters as listed in Tables 1 and 6 it follows that QFS conditions will be
obtained for Tcool > -1 ºC. The oxidation of 2-octanol was experimentally found
to be under QFS conditions for a coolant temperature of Tcool > -5 ºC, see Figure
17, which is close to the calculated value.
Prediction of runaway conditions for the oxidation of 2-octanone
Now is has to be verified that the unwanted reaction will not be triggered as a
result of the first reaction. When the conversion to 2-octanone is complete and
no carboxylic acids are formed, one obtains: CB 0 = nA1 ⋅ ζ P 0 / V0 = 2.46 M and the
acid strength of the nitric acid will drop to a value of H0 = -2.86. With a coolant
temperature of Tcool = -1 ºC for the first reaction, a maximum temperature of Tmax
= 12 ºC is found experimentally, see Figure 17. Using these conditions as initial
105
Chapter 3
conditions for the oxidation of 2-octanone, one can calculate that: Ex = 6.35 and
Ry = 0.003. When this is compared to the boundary diagram with U*Da/ε = 20
in Figure 11, it is located in the area of insufficient ignition. Thus the further
oxidation reaction will not be triggered for Tcool = -1 ºC, which was also
experimentally found.
The critical coolant temperature, for the same experimental series, at which the
runaway reaction of the second reaction is just not triggered is Tcool = 8 ºC, see
Figure 17. The maximum temperature obtained by the first reaction is in that
case T = 30 ºC. In the boundary diagram the critical coolant temperature will be
the one where the insufficient ignition changes to a runaway condition. Using
the same conditions as above, one can find the runaway to be triggered for Ex =
5.1, Ry = 0.008 and Tcool > 45 ºC, while experimentally a runaway reaction was
already triggered for T = 30 ºC. This dangerous overestimation of Tcool, using the
boundary diagram for single second order reactions, is the result of treating the
oxidation reactions as two single independent reactions. The reaction to the
carboxylic acids can only start when the intermediate reaction product 2octanone has been formed. Thus the second oxidation step strongly depends on
the first one, which makes it difficult to determine the exact starting condition
for the further oxidation reaction.
Initial reactor load
ρ0 [kg/m3]
CP0 [J/kg K]
H0 [-]
V0 [m3]
1360
2660
-3.42
0.5⋅10-3
Feed
ρ [kg/m3]
CP [J/kg K]
nA1 [mol]
Vdos1 [m3]
817
2523
1.23
0.2⋅10-3
Table 6: Relevant parameters of reaction system at T = 25 ºC
with a 60 wt% HNO3 solution as initial load and pure 2-octanol
as feed.
106
Runaway Behavior and Thermally Safe Operation
Prediction of invariably safe operation conditions using Exmin
The boundary diagram can also be used to determine the minimum dosing time
tdos,min, which leads to invariably safe operation. This corresponds to the
minimum exothermicity number Exmin. Exmin can be read from the boundary
diagram for a single reaction in the continuous phase in Figure 11 and is equal to
Exmin = 4.3, 6 and 8.6 for U*Da/ε = 20, 10 and 5, respectively. For the oxidation
of 2-octanone one can calculate, using the relevant parameters as listed in Tables
1 and 6, ∆Tad0 = 354 K, ε = 0.4 and RH =0.57. For Tcool = 20 ºC one can
calculate Ex = 6.0, 11.7 and 18.4 for U*Da/ε = 20, 10 and 5, respectively, which
now can be compared to the Exmin-values taken from Figure 11. This is done in
Figure 24. When U*Da/ε is increased the exothermicity Ex decreases faster than
Exmin and consequently there exist a point where Ex = Exmin and hence tdos equals
tdos,min. In this case Exmin = 2.8 can be found and for U*Da/ε > 47 no runaway
will take place for any coolant temperature and the process has become
invariably safe. This value can be compared to U*Da/ε > 45, which was found
experimentally.
100
Exothermicity [-]
Calculated Ex
Ex = Exmin
10
Exmin
from Figure 11
1
1
10
100
U*Da/ε [-]
Figure 24: Exothermicity number Ex for the oxidation of 2-octanone to
carboxylic acids as a function of U*Da/ε to determine the minimum
exothermicity number Exmin.
107
Chapter 3
3.8 Discussion and conclusions
The nitric acid oxidation of 2-octanol has been studied experimentally in a 1liter glass reactor. The reaction rates of the oxidation reactions as experimentally
determined and modeled, see Chapter 2, have been successfully applied to
simulate the experiments and a satisfactory agreement has been obtained
between experiments and calculations.
Thermally safe operation of a semi-batch reactor usually implies that under
normal operating conditions a runaway is avoided. To this end one has to avoid
accumulation of the dosed reactant in the reaction phase. However, in case the
intermediate is the required product, accumulation of the reactant for the
consecutive reaction necessarily occurs. So for the second reaction, conditions
must be such that the reaction will not occur at all or at least remains
insufficiently ignited. The reaction conditions should rapidly lead to the
maximum yield of 2-octanone under safe conditions and stopped at the optimum
reaction time.
The process can be regarded as invariably safe when no runaway takes place for
any coolant temperature. This is possible for a large value of U*Da/ε, and hence
a long dosing time or a large cooling capacity, which effectively moderates the
temperature effects. For the oxidation of 2-octanol to 2-octanone and carboxylic
acids the process is invariably safe for U*Da/ε > 45. Under such conditions the
reactor temperature is always limited between pre-defined known temperature
limits. These predefined temperatures are based on the target temperature
developed by Steensma and Westerterp [1990] and can be successfully applied
in case of a multiple reaction.
The conditions leading to invariably safe operation correspond with the
minimum exothermicity number Exmin. The value for Exmin can be derived from
the boundary diagram of Steensma and Westerterp [1990]. For the oxidation of
2-octanone and using the boundary diagram a minimum exothermicity number
of Exmin = 2.8 and U*Da/ε > 47, the process was found to be invariably safe.
Experimentally a value of U*Da/ε > 45 was found.
For a single reaction the conditions leading to QFS conditions and to thermal
runaway can be extracted from the boundary diagram. The coolant temperature
leading to a QFS condition for the oxidation of 2-octanol to 2-octanone as
predicted in the boundary diagram agrees with the experimental result.
108
Runaway Behavior and Thermally Safe Operation
However, it is not possible to predict with sufficient accuracy the conditions
leading to a runaway of the secondary oxidation reaction. This reaction can only
start when the intermediate reaction product 2-octanone has been formed.
Regretfully, it is difficult to determine the exact starting conditions for the
further oxidation reaction, which is necessary for an accurate estimation.
The reaction conditions should rapidly lead to the maximum yield of 2-octanone
under safe conditions and stopped at the optimum reaction time. The
mathematical model as developed by Steensma and Westerterp [1990], and
extended in this work to a multiple reaction system, can be used to predict the
reactor behavior and the moment to stop the reaction. The most economical
operation condition depends on a number of parameters and must be determined
for each specific case.
Acknowledgements
The author wishes to thank A.B. Wonink and S.J. Metz for their contribution to
the experimental work, M.T. van Os and A.B. Kleijn for their contribution to the
preliminary calculations and further F. ter Borg, K. van Bree, G.J.M. Monnink
and A.H. Pleiter for the technical support.
Notation
a
A
C
CP
D
Di
d32
E
H0
Ha
kL
k
k∞
mi
m
mHo
n
N
Interfacial area per volume of reactor content = 6ε / d32
Surface area
Concentration
Specific heat capacity
Diameter
Diffusivity coefficient of component i
Sauter mean drop diameter
Energy of activation
Hammett’s acidity function
Hatta number
Mass transfer coefficient in the aqueous phase
Second-order reaction rate constant
Pre-exponential constant
Molar distribution coefficient of component i=Ci , Aq Ci ,Org
Mass
Hammett’s reaction rate coefficient
Number of moles
Stirring rate
[m2/m3]
[m2]
[kmol/m3]
[J/Kg·K]
[m]
[m2/s]
[m]
[J/kmol]
[-]
[-]
[m/s]
[m3/kmol·s]
[m3/kmol·s]
[-]
[kg]
[-]
[kmol]
[s-1]
109
Chapter 3
Q
Heat flow
R
Gas constant = 8315
RH Heat capacity ratio = ( ρCP )dos ( ρCP )0
r
Rate of reaction per volume of reactor content
t
Time
tdos Dosing time
tdos,min Minimum dosing time
T
Temperature
U
Overall heat transfer coefficient
V
Volume
[W]
[J/kmol·K]
[-]
[kmol/m3·s]
[s]
[s]
[s]
[K]
[W/m2·K]
[m3]
Greek symbols
∆H
∆Tad0
εd
ε
ϕv
Γ
ρ
θ
ζi
ζ B0
Heat of reaction
Adiabatic temperature rise = ∆H nA1 ( ρCPVr )0
Volume fraction of dispersed phase = Vdos1 (Vdos1 + V0 )
Relative volume increase at end of dosing = Vdos1 V0
Flow
Heat capacity
Density
Dimensionless dosing time = t/tdos
Yield of component i = ni nA1
Initial concentration of nitrosonium ion = 0.035
[J/kmol]
[K]
[-]
[-]
[m3/s]
[J/K]
[kg/m3]
[-]
[-]
[-]
Dimensionless groups
Ex
Exothermicity number =
Ry
Reactivity number =
Po
Power number =
∆Tad ,0 E / R
1
2
Tcool
εRH + U * Da
1
CB 0 tdos mk∞ exp − E / RT0 − mH 0 H0
εRH + U * Da
Q
5
ρ dis N 3 Dstir
U*Da Cooling number =
110
6
[-]
[-]
UA t
ρC V P r
[-]
0
dos
[-]
Runaway Behavior and Thermally Safe Operation
Subscripts and superscripts
0, 1
A
Aq
B
cool
dis
dos
element
i
N
nol
none
Org
P
R
r
stir
tot
w
X
∞
Initial, Final (after dosing is completed)
Component A (2-octanol)
Aqueous phase (nitric acid solution)
Component B (nitrosonium ion)
Coolant
Dispersion
Dosing
Electrical heater element
Component i
Component N (nitric acid)
Reaction of 2-octanol, see Equation (1)
Reaction of 2-octanone, see Equation (2)
Organic phase
Component P (2-octanone)
Reaction
Reactor
Stirring
Total
Water
Component X (carboxylic acids)
Ambient
111
Chapter 3
References
Barcons I Ribes, C., Equipment characterisation, in: A. Benuzzi, J.M. Zaldivar
(eds.), Euro Courses, Reliability and Risk Analysis, Vol.1: Safety of
Chemical Batch Reactors and Storage Tanks, Kluwer Academic,
Dordrecht 1991, pp. 99-123.
Chapman, J.W., Cox, P.R. and Strachan, A.N., Two phase nitration of toluene
III, Chem. Eng. Sci. 29 (1974) 1247-1251.
Eigenberger, G. and Schuler, H., Reaktorstabilität und sichere
Reaktionsführung, Chem. Ing. Tech. 58 (1986) 655-665.
Hugo, P. and Steinbach J., Praxisorientierte Darstellung der thermischen
Sicherheitsgrenzen fur den indirekt gekühlten Semibatch-Reaktor, Chem.
Ing. Tech. 57 (1985) 780-782.
Hugo, P., Steinbach, J. and Stoessel, F., Calculation of the maximum
temperature in stirred tank reactors in case of a breakdown of cooling,
Chem. Eng. Sci. 43 (1988) 2147-2152.
Koufopanos, C.A., Karetsou, A. and Papayannakos, N.G., Dynamic response
and safety assessment of a batch process on cooling breakdown, Chem.
Eng. Technol. 17 (1994) 358-363.
Rochester, C.H., Organic chemistry, A Series of Monographs: Acidity
Functions, Academic press, London, 1970.
Serra, E., Nomen, R. and Sempere, J., Maximum temperature attainable by
runaway of synthesis reaction in semi-batch processes, J. Loss Prev.
Process Ind. 10 (1997) 211-215.
Steensma, M. and Westerterp, K.R., Thermally safe operation of a cooled semibatch reactor. Slow liquid-liquid reactions, Chem. Eng. Sci. 43 (1988)
2125-2132.
Steensma, M. and Westerterp, K.R., Thermally safe operation of a semi-batch
reactor for liquid-liquid reactions. Slow reactions, Ind. Eng. Chem. Res.
29 (1990) 1259-1270.
Steensma, M. and Westerterp, K.R., Thermally safe operation of a semi-batch
reactor for liquid-liquid reactions. Fast reactions, Chem. Eng. Technol. 14
(1991) 367-375.
Stoessel, F., What is your thermal risk? Chem. Eng. Progress 89 (1993) 68-75.
Stoessel, F., Design thermally safe semi-batch reactors, Chem. Eng. Progress 91
(1995) 46-53.
Westerterp, K.R., van Swaaij, W.P.M. and Beenackers, A.A.C.M., Chemical
Reactor Design and Operation, student edition, Wiley, Chichester, 1987.
112
4
Determination of Interfacial Areas with
the Chemical Method for a System with
Alternating Dispersed Phases
Chapter 4
Abstract
The interfacial area for a liquid-liquid system has been determined by the
chemical reaction method. The saponification of butyl formate ester with 8 M
sodium hydroxide has been used to this end. A correlation has been derived to
describe the mole flux of ester through the interface and the kinetic rate
constants have been calculated.
For a continuously operated reactor a correlation has been derived for the Sauter
mean drop diameter for both reaction in the dispersed phase as well as reaction
in the continuous phase. A viscosity factor had to be incorporated to obtain one
single correlation. The validation for this chemically enhanced reaction regime
is presented and discussed.
114
Determination of Interfacial Areas with the Chemical Method
4.1
Introduction
Many industrially important reactions such as nitrations, sulfonations,
saponifications, and oxidations are often performed under conditions whereby
two immiscible phases coexist. The knowledge of the effective interfacial area is
essential for an accurate prediction of the mass transfer and chemical reaction
rates. Numerous methods, see Tavlarides and Stamatoudis [1981], have been
developed for the determination of the interfacial area, such as withdrawal of a
sample of the dispersion, immobilization by encapsulation and then analysis, see
e.g. van Heuven and Beek [1971] or photography of the dispersion via a probe
or through a window in a vessel, see e.g. Giles et al. [1971], or light
transmittance, measuring the fraction of a light beam which is not scattered by
the dispersion, see e.g. Calderbank [1958]. In all these methods a local value of
the interfacial area is determined.
Absorption accompanied by a fast pseudo-first order reaction has first been used
by Westerterp et al. [1963] to evaluate the effective interfacial area. Since then
this method has been used extensively for gas-liquid systems to determine
interfacial areas of absorbers, see Sharma and Danckwerts [1970]. The chemical
method also has been employed to determine the interfacial areas in liquidliquid systems e.g. in an extraction column, first by Nanda and Sharma [1966].
Overviews of different reaction systems have been given by Tavlarides and
Stamatoudis [1981] and Doraiswamy and Sharma [1984]. The saponification of
butyl formate was found to be a suitable reaction system by Nanda and Sharma
[1966], Santiago and Trambouze [1971a,b] and Onda et al. [1975]. In all these
methods the total interfacial area in the entire apparatus is determined.
Contradictory observations have been reported in literature as to the phase to be
dispersed in order to obtain the largest interfacial area. The difference in
interfacial area has been explained by the density difference and viscosity
difference between the two phases. Fernandes and Sharma [1967] examined the
hydrolysis of 2-ethylhexyl formate with 2 M NaOH in an agitated contactor.
They found smaller droplets for the aqueous phase being dispersed. This was
explained by the hindrance to coalescence of drops with a higher viscosity. Lele
et al. [1983] examined the effect of emulsifiers on the rate of alkaline hydrolysis
of tridecyl formate. They also found smaller droplets for an aqueous reaction
phase being dispersed as expected: the aqueous phase had a higher viscosity. On
the other hand, Zaldivar et al. [1996] studied the reaction between diisobutylene
in toluene and H2SO4 and found larger droplets for the aqueous phase being
dispersed. This was explained by the density of the continuous phase, which was
smaller when the aqueous phase was dispersed compared to the organic phase
115
Chapter 4
dispersed. Godfrey et al. [1989] found a larger drop size for the system
cumene/water when the aqueous phase was dispersed. This could not only be
explained by the smaller density of the continuous phase; they also had to take
into account the effect of the viscosity.
Although drop sizes in dispersions have been studied extensively, experimental
data for the same system and alternating phases dispersed are scarce. The
present work presents experimental data for the two dispersion types. The first
objective of this work is to find a correlation to describe the interfacial area in
the used experimental set-up using the saponification of butyl formate.
4.2
Measurement of interfacial area, the theory
The average drop size depends upon the conditions of agitation as well as the
physical properties of the liquids. The Sauter mean drop diameter, d32, is defined
as:
d32 = 6ε / a
(1)
where ε is volume fraction of dispersed phase and a the interfacial area per unit
volume of reactor content.
Drops in an agitated dispersion are subject to shear stresses and to turbulent
velocity and pressure variations along their surfaces. These processes cause a
drop to deform and to break into smaller parts if these dissipative forces exceed
the restoring forces, which consist of interfacial tension forces and viscous
forces in the drop. On the other hand drops also collide with each other. They
will coalesce when they remain together for a time long enough to overcome the
resistance of the continuous phase separating the drops. Breakage and
coalescence take place simultaneously and after a certain time the dispersion
reaches a dynamic equilibrium, containing drops of different sizes. The
microscopic phenomena occurring in an agitated vessel are extremely complex
and are still not very well understood.
Semi-empirical correlations are usually based on the theory of Kolmogorov for
drops in locally isotropic, turbulent fields. The theory is reviewed by Peters
[1992] and Davies [1992]. The basic assumption in this theory is that for a drop
to become unstable and break, the kinetic energy of the drop oscillations must be
sufficiently high. Hinze [1955] characterized the maximum drop size by a
critical Weber number, defined as the ratio of the kinetic energy to the surface
116
Determination of Interfacial Areas with the Chemical Method
energy. Assuming that under specified conditions the local rate of energy
dissipation is proportional to the total power input per unit of volume of mixture
in the whole tank, the maximum stable drop size has been correlated through the
expression, see e.g. Davies [1992]:
σ P =C ⋅
ρ ρ V
0 .6
dmax
−0 . 4
1
c
(2)
dis
Introducing the Power number and Weber number one obtains:
dmax
Po 3
D
= C1 We−0.6
D
V
−0 . 4
(3)
For a baffled stirred tank reactor operated under fully turbulent conditions with
Re>104, the Power number is constant. Sprow [1967] showed that d32 was
directly proportional to the maximum drop size, therefore also holds under full
turbulence:
d32
= AWe −0.6
D
(4)
Here A has to be determined experimentally. This relation has been used to
correlate a wide range of experimental results at a low dispersed phase hold-up
for mixing in stirred tank reactors, see e.g. Sprow [1967], Shinnar [1961] and
Chen and Middleman [1967].
For increasing volume fractions of the dispersed phase, the drop size increases
due to coalescence. This is explained by a damping effect of an increased
content dispersed phase on the local intensity of turbulence, see Godfrey et al.
[1989] or an increasing collision frequency, see Coulaloglou and Tavlarides
[1976]. This effect is usually accounted for by a linear factor (1 + Bε ) :
d32
= A(1 + Bε ) We −0.6
D
(5)
This equation has been used to correlate data for higher dispersed phase holdups by numerous workers, e.g. by Calderbank [1958], van Heuven and Beek
[1971] and Coulaloglou and Tavlarides [1976]. The value of A varies between
0.04 and 0.4 and between 2 and 10 for B. The values of these constants must be
determined experimentally for a given reactor set-up and liquid-liquid system.
117
Chapter 4
Many researchers have mentioned the influence of the viscosity on the drop size.
The viscosity is believed to hinder coalescence and therefore leads to smaller
droplets. If the dispersed phase is significantly more viscous than the continuous
phase, the drop size correlation has to be corrected. Calderbank [1958] and more
recently Godfrey et al. [1989] have introduced an empirical viscosity factor
C
f µ = µ d µ c in which C has to be determined experimentally.
05 1
6
Aqueous
phase
Organic
phase
Interface
*
CA,Org
CB,Aq
CA,Org
JA
*
CA,Aq
x=δ
*
= mACA,Org.
x=0
film
Figure 1: Concentration profiles for chemically enhanced mass transfer.
Determination by the chemical method
The liquid-liquid system consists of an aqueous phase (Aq) containing sodium
hydroxide (B) and an organic phase (Org) containing n-butyl formate ester (A).
The reaction between n-butyl formate and the NaOH-solution takes place in the
aqueous phase according to:
O
HCOC4H9 + OH
118
O
HCO + C4H9OH
Determination of Interfacial Areas with the Chemical Method
The reaction products are butanol and the salt of the acid. The application of the
chemical method to this reaction is based on the chemical enhanced extraction
of ester (A) from the organic phase to the aqueous phase in which an irreversible
reaction takes place with sodium hydroxide (B), see Figure 1. Sodium hydroxide
is insoluble in the organic phase. The film theory, see Westerterp et al. [1987],
gives for the extraction rate in the reactor:
J A = kL , Aq CA* , Aq EA
(6)
The enhancement factor E A equals the Hatta number:
Ha =
k11CB, Aq DA
kL, Aq
(7)
when the following conditions holds:
• The solubility of ester A in the aqueous phase is very low, so mass transfer
limitations in the organic phase can be neglected. At the interface holds:
CA* , Aq = mACA,Org .
• The reaction is sufficient fast to consume all ester A in the film and no A will
reach the bulk of the reaction phase, CA, Aq = 0. In fact the reaction is so fast that
the following holds: Ha > 3
• No diffusion limitation of sodium hydroxide B occurs in the reaction zone.
Concentration B at the interface CB* , Aq is approximately equal to the bulk
concentration CB, Aq . The pseudo-first-order rate constant can be assumed to be
k1 = k11CB, Aq .
• Ha << EA∞ , the maximum possible enhancement factor for instantaneous
reactions, given by:
E A∞ = 1 +
DBCB, Aq
DA mACA* ,Org
(8)
If these conditions are fulfilled, the mass transfer rate JA is a unique function of
the physico-chemical properties of the system and independent of the
hydrodynamics conditions and is equal to:
J A = mACA,Org k11CB, Aq DA
(9)
119
Chapter 4
The value of the term mA k11 DA for a given system can be determined
separately, for instance in a stirred cell reactor with a well defined interfacial
area. Under these conditions the extraction rate becomes:
J A aVR = mACA,Org k11CB, Aq DA aVR
(10)
With all data in relation (10) known, the interfacial area can be determined, as
long as the same conditions are satisfied, for any piece of equipment by:
a=
2
ϕ V , Aq . CB, Aq . in − CB, Aq. out
7
J AVR
2
(11)
7
in which ϕ V , Aq. CB, Aq . in − CB, Aq . out is the amount of solute extracted per unit of
time.
4.3
Experimental set-up
The extraction rate measurements and the interfacial area determinations have
been carried out in the experimental set-up as shown in Figure 2. The
experimental set-up consists of three sections:
1) The feed section. The supply vessels of 5 liter are located on balances of the
types Mettler-Toledo PG8001 and Mettler PM6000. One of the supply vessels
is filled with sodium hydroxide solution, the other one with pure butyl formate.
Each vessel is stirred by a magnetic stirrer and under a continuous flow of
nitrogen. The nitrogen is used to prevent CO2 to dissolve into the liquids, which
would react with OH − to form CO32− . The chemicals are pumped via a ball valve
to the reactor by two gear pumps of Verder with maximum flow rates of 25 g/s
and 5 g/s respectively.
2) The reactor section. The reactor is a jacketed glass vessel, clamped between
two stainless steel flanges. The inner diameter of the vessel is 85 mm and the
height of the vessel is 88 mm. The reactor content is agitated by a stainless steel
turbine stirrer, driven via a magnetic Medimex coupling by a Janke and Kunkel
motor of the type RW20DZM. The stirring rate of the stirrer is read from the
display with a digital tacho-meter of the type Ebro DT-2234. The temperature of
the reactor content is measured by a thermocouple. The conductivity probe of a
120
Determination of Interfacial Areas with the Chemical Method
Metrohm pH-meter can be placed in the reactor to measure the conductivity of
the dispersion. Different reactor configurations have been used to study the
extraction rate with a known interfacial area and the interfacial area in a
turbulently mixed dispersion respectively. The reactor set-ups are shown in
Figure 3.
3
4
Ti
N2
N2
pH
2
1
Figure 2: Experimental set-up for stirred cell and continuous experiments,
respectively. With: 1) the feed section; 2) the reactor section; 3) the heat
exchange section; and 4) the sampling point.
The first set-up is a stirred cell. To separate the two phases it contains a Teflon
ring with a thickness of 10 mm and an inner diameter of 65.2 mm. In the open
area of the ring the two phases are in contact; the total contact area is 33.4 cm2.
The aqueous phase with the highest density is located in the lower part of the
reactor and is stirred by a turbine stirrer with a diameter of 38 mm and six blades
121
Chapter 4
of 7.6x10 mm2 each. It is placed 20 mm above the bottom. The vessel is
equipped with four equally spaced, 8 mm wide stainless steel baffles. The ring
weakens the interface fluctuations, so that it is possible to have good mixing
without disturbing the interface.
The second reactor set-up is a continuously operated contactor. The ring has
been removed and the turbine stirrer has been replaced by another one with a
diameter of 40 mm, six blades of 8x10 mm2 each. It is now placed 44 mm above
the bottom. The vessel contains four equally spaced, 9 mm wide, glass baffles.
3) The heat exchange section. The experiments are carried out isothermally. To
achieve this, two heat exchangers have been installed made of stainless steal and
with an exchange area of 0.1 m2 each. The reactor has also been equipped with a
cooling jacket. The coolant consists of 50 wt% water in glycol: it is pumped
through the system by the internal pump of the cryostat, which is of the type
Julabo FP50. The coolant first passes through the heat exchangers and then
through the cooling jacket of the reactor and finally is returned to the cryostat.
During all experiments the temperature, conductivity and mass of the chemicals
on the balances are measured and stored by a Data Acquisition and Control Unit
of Hewlett Packard in combination with a computer of the type HP486-33.
85
8
9
65.2
40
88
10
8
38
Teflon
ring
44
7.6
20
a.
10
b.
Figure 3: Dimensions of the reactor in millimeters.
a. Stirred cell.
b. Continuously operated contactor.
122
10
Determination of Interfacial Areas with the Chemical Method
Chemical treatment and chemical analysis
The butyl formate ester is first washed with demineralized water to remove a
small amount of ethyl formate and after that it is dried on molecular sieves. The
butyl formate now contains only small amounts of butanol and water, and has a
purity of 99+ vol%. The solution of sodium hydroxide is prepared by dissolving
NaOH pellets in demineralized water under a continuous flow of nitrogen to
prevent any CO2 to dissolve into the solution. The equipment is also flushed
with N2 before an experiment is started. In this way the concentration of CO32− in
the sodium hydroxide solution at the outlet of the reactor was always kept below
0.08 M.
During each experiment samples are taken. For the stirred cell experiments
samples are taken from the reactor of both phases separately with a syringe via a
septum placed in the lid of the reactor, number 4 in Figure 2. For the
continuously operated contactor samples are taken from the reactor outlet. The
outlet flow consists of the dispersion, which separates directly on standing.
The organic phase is analyzed in a gas chromatograph to determine the
concentrations of butyl formate, butanol, and water. The aqueous phase is
analyzed by titration with trifluoromethanesulfonic acid in acetone/water to
determine the concentrations of OH − , CO32− and HCO2− .
4.4
Measurements in the stirred cell
Experimental procedure
Before each experiment the equipment is flushed with nitrogen. After that the
lower part of the reactor is filled with approximately 0.23 l NaOH-solution till
half way in the Teflon ring. Then a volume pure ester of approximately 0.23 l is
carefully pumped into the upper part of the reactor. After that the experiment is
started by starting the stirrer. The stirring rate is set at 80 – 125 rpm to obtain
good mixing without disturbing the interface. Samples are taken of the aqueous
phase as well as the organic phase with a syringe before and during the run.
123
Chapter 4
Determination of flux equation
The mass balance for sodium hydroxide B in the aqueous phase can be written
as follows:
VAq
d CB, Aq
= − J A A = − mACA,Org k11CB, Aq DA ⋅ A
dt
(12)
After integration of Equation (12) with CB, Aq = CB, Aq 0 and J A = J A 0 at t = 0 the
concentration of NaOH in the aqueous phase can be expressed as function of
time:
CB, Aq (t )
A
A
JA0 t +
JA0
=1−
CB. Aq 0
VAq CB, Aq 0
VAq CB, Aq 0
2
1 2
t
4
(13)
The last term in Equation (13) can be neglected for relatively short reaction
times. When the conversion is kept below 10% the contribution of the last term
is less than 2.5% and the concentration of NaOH in the aqueous phase is given
by:
CB, Aq (t )
A
(14)
J A0 t
≈1−
CB, Aq 0
VAq CB, Aq 0
The amount of OH − consumed equals the amount of HCO2− formed. This leads
to the following expression:
1−
CB, Aq (t ) CC , Aq (t )
A
JA0 t
=
≈
CB, Aq 0
CB, Aq 0
VAq CB, Aq 0
(15)
The flux can thus be calculated from the decrease in concentration of sodium
hydroxide and production of formate salt.
Typical plots for the measured, relative concentration of sodium hydroxide
CB, Aq CB, Aq 0 versus time are shown in Figure 4. The mass transfer rate is
calculated from the slope of these concentration profiles, using the least squares
method, for different temperatures and concentrations of NaOH. The flux is
known to be sensitive towards the ionic strength of the solution, see Nanda and
Sharma [1966, 1967]. This is explained by the change in solubility of the ester in
the aqueous phase, which reduces substantially with an increase in the ionic
strength. This can be seen in Table 1 where the mass transfer rates are listed as
calculated on the basis of the experiments in the stirred cell.
124
Determination of Interfacial Areas with the Chemical Method
1
COH/C OH0 [-]
From OHFrom HCOO0.99
0.98
20 ºC
30 ºC
40 ºC
0.97
0
50
100
A
150
200
250
300
Time [min.]
1
8M
COH/COH0 [-]
6M
0.95
4M
0.9
3M
From OHFrom HCOO-
2M
0.85
0
B
100
200
300
400
500
Time [min.]
Figure 4: Relative concentration of NaOH as calculated from the sodium
hydroxide concentration (▲) and formate ester salt concentration (●)
respectively vs. time in the stirred cell experiments.
a. For different reactor temperatures and 6 M NaOH solution.
b. For different NaOH concentrations at 20 ºC.
125
Chapter 4
The physico-chemical parameters depend on temperature T and ionic strength I
and are usually exponentially related to these. So, one can use the relation:
ln( mA k11 DA ) = A + B / T + C ⋅ I
(16)
to correlate the data. The following constants are found for the experiments as
listed in Table 1, with the ionic strength I calculated as described in appendix
4A:
mA k11 DA = exp( −2.05 − 3350 / T − 0.65 ⋅ I )
(17)
A parity plot is given in Figure 5 to compare the experimental and calculated
values as calculated using Equation (17). The standard deviation for the data is
3.5%. In the same figure the flux of butyl formate is given as reported in
literature by Nanda and Sharma [1967], Santiago and Bidner [1971] and
Santiago and Trambouze [1971a]. The data in this work and data from literature
are in good agreement, as long as the reaction takes place in the fast reaction
regime.
Temperature
[ºC]
19.0
20.1
20.0
20.0
20.2
20.0
20.1
20.0
20.0
25.0
25.0
30.6
35.1
40.2
Ionic strength
[kmol/m3]
2.02
2.02
3.05
4.00
4.00
5.01
6.02
8.08
8.00
5.99
6.00
5.99
5.92
5.95
COH,average
[kmol/m3]
1.93
1.90
2.98
3.91
3.92
4.91
5.96
8.04
7.96
5.92
5.90
5.93
5.84
5.89
Jester ·106
[kmol/m2s]
4.65
4.25
2.63
1.61
1.64
0.89
0.54
0.186
0.184
0.67
0.67
0.80
1.03
1.25
Table 1: Experimental conditions and results for the flux
measurements in the stirred cell.
126
Determination of Interfacial Areas with the Chemical Method
10
Nanda & Sharma '67
Santiago & Trambouze '71
2
Experimental flux x10 [kmol/m s]
Santiago & Bidner '71
6
this work
1
0.1
0.1
1
10
6
2
Calculated flux x10 [kmol/m s]
Figure 5: Parity plot of the calculated flux according to Equation (9) with (17)
and experimental flux as obtained in stirred cell experiments.
Calculation of kinetics
With a description of the flux and estimation of the solubility and diffusivity of
butyl formate in aqueous NaOH, see appendix 4A, one can calculate the kinetic
rate constants for the reaction using Equation (9). The saponification reactions
are known to be affected by the amount of ions in the solution, see Bell [1949].
The reaction rate coefficient k11 can be enhanced as well as reduced by
increasing ionic strengths, as shown by Nanda and Sharma [1967] for different
127
Chapter 4
types of esters. The reaction rate constant is therefore described by an extra term
in the usual Arrhenius equation to account for this effect of the ionic strength:
k11 = k∞ exp −
E + k I
RT Act
(18)
I
The effect of temperature on the reaction rate constant is shown in Figure 6. The
energy of activation is found to be 36.2·106 J/kmol, which can be compared to
the value reported by Leimu et al. [1946] of 33.5·106 J/kmol. The effect of the
ionic strength on the reaction rate is shown in Figure 7. The ionic rate constant kI
= +0.33 m3/kmol, thus the reaction rate coefficient is reduced by an increased
ionic strength, which was also found by Nanda and Sharma [1966]. This leads to
the following equation for the second order reaction rate constant:
k11 = 9.02 ⋅ 10 7 exp −
4350 + 0.33 I
T
(19)
The calculated kinetic rate constant is in agreement with the data reported by
Nanda and Sharma [1966], see Table 2. In the same table the data for the flux of
ester can be found as reported by Nanda and Sharma [1966]. The deviations in
the kinetic rate constant is larger then the deviations in the flux. The main reason
for this is that Nanda and Sharma [1966] used the average concentration of the
NaOH-solution to estimate the properties that depend on the ionic strength. In
this work the ionic strength was found to be constant during the reaction.
Therefore, using the ionic strength, should lead to a better estimation of the
physical properties.
Temperature
[K]
Ionic
strength
[kmol/m3]
283
293
303
313
303
303
2.04
2.04
2.04
2.04
3.98
5.98
Jester ·106
[kmol/m2s]
Nanda &
Sharma ‘66
3.08
4.27
5.79
8.75
2.59
0.78
Jester ·106
[kmol/m2s]
this work
2.94
4.51
6.74
9.81
2.41
0.84
k11
[m3/kmol ·s]
Nanda &
Sharma ’66
13.1
18.6
26.0
42.4
21.8
9.7
k11
[m3/kmol ·s]
this work
9.7
16.4
26.8
42.4
14.1
7.3
Table 2: Reaction rate constants and extraction rates for the hydrolysis of butyl
formate compared to the data reported by Nanda and Sharma [1966].
128
Determination
Determination of
of Interfacial
Interfacial Areas
Areas with
with the
the Chemical
Chemical Method
Method
3
k11 [m /kmols]
20
10
10
8
6
4
3
3.15
3.2
3.25
3.3
3.35
3.4
3.45
1000/T [1/K]
100
1
Figure 6: Effect of temperature on the reaction rate constant for the alkaline
3.2 with
3.25
3.3
3.35
3.4
3.45
hydrolysis 3.15
of butyl formate
6 M NaOH.
3
k11 [m /kmols]
20
10
10
7
5
3
2
1
3
5
3
Ionic strength [kmol/m ]
7
9
1
1
3
5
7
9
Figure 7: Effect of ionic strength on the reaction rate constant for the alkaline
hydrolysis of butyl formate with a NaOH solution at 20 ºC.
129
Chapter 4
4.5
Determination of interfacial area
Experimental procedure
For a complete dispersion a minimum stirring speed is required. The minimum
stirring speed is estimated on the basis of the correlation of van Heuven and
Beek [1971]: it is for the used set-up 700 rpm. For the determination of the
interfacial area steady state conditions in the continuously operated reactor
should be reached as soon as possible in order to minimize the consumption of
chemicals. Therefore the reactor is first operated for a short time in the batch
mode. While the reaction proceeds, the system approaches the steady state and
then close to steady state the feed flows are started. An example run is shown in
Figure 8. The steady state condition is obtained as soon as temperature, pH, and
hold-up have reached a constant value. The temperature and pH are measured
online, while the hold-up of dispersed phase is calculated from the measured
volumes of both phases at the outlet of the reactor. The volumes are determined
in a measuring cylinder of 10 ml after filling it with the dispersion at the reactor
outlet.
Determination of drop size correlation
The mass balance for NaOH, respectively formed formiate salt, in the aqueous
phase under steady state conditions reads:
2
7
2
J A aVR = ϕ OH , Aq . COH , Aq. in − COH , Aq. out = ϕ OH , Aq . CC , Aq . out
= mACA,Org. out k11COH , Aq. out DA aVR
7
(20)
So the interfacial area is equal to:
a=
2
ϕ OH , Aq . COH , Aq. in − COH , Aq. out
7
VR mACA,Org.out k11COH , Aq. out DA
(21)
In this relation all data are known or have been experimentally determined. With
d32 = 6ε / a one can calculate the drop size.
With increasing conversion the composition of the phases will change. Santiago
and Trambouze [1971a] observed the interfacial area to be independent of the
amount of butanol in the organic phase, as long as the conversion of sodium
hydroxide as well as of butyl formate is kept below 15%.
130
Determination of Interfacial Areas with the Chemical Method
12
Temperature
10
20
pH
8
15
10
flow continous phase
5
flow dispersed phase
6
4
Flow [g/s]
Temperature [ºC], pH [-]
25
2
0
0
0
start batch
5
10
15
20
25
20
25
Time [min.]
start flow
A
Conversion [-]; Hold-up [-]
0.4
0.3
Hold-up dispersed phase
0.2
0.1
Conversion
0
0
start batch
5
start flow
10
15
Time [min.]
B
Figure 8: Example of a run with started as a batch operation and switched to
continuous operation after 4 min.
a. On-line measured variables.
b. Indirectly measured variables.
131
Chapter 4
The experimental conditions for the runs in the continuously operated reactor
and the conversion of NaOH are listed in Table 3. The influence of the stirring
rate on the drop size can be seen in Figure 9. Within the experimental accuracy a
slope of –1.2 can be found, which is expected on the basis of the Equation (5).
The effect of the hold-up of the dispersed phase on the drop size is shown in
Figure 10: the drop size increases linearly with increasing hold-up.
run
1
2
3
4
5
6
7
8
9
10
11
N
[rpm]
1115
1108
1102
1108
1113
900
1009
1203
1305
1312
1410
12
13
14
15
16
17
18
19
20
1113
1114
1102
1105
918
1003
1115
1315
1516
ϕ NaOH ·106 ϕ ester ·106
[m3/s]
[m3/s]
8.83
1.50
5.60
3.02
7.14
2.98
8.95
2.34
5.22
3.54
7.21
2.95
7.23
3.00
5.34
2.37
7.41
2.72
8.22
3.47
8.30
3.80
3.85
2.70
2.08
1.69
2.42
2.60
2.88
2.87
2.86
5.95
5.10
6.38
6.91
6.01
6.13
7.02
7.04
7.03
T
[ºC]
19.6
20.1
20.2
19.8
21.2
18.9
20.9
20.3
21.3
20.6
19.3
COH 0
[kmol/m3]
7.92
8.00
8.00
8.00
8.00
8.00
8.00
8.01
7.83
7.95
7.89
1-COH1 COH 0
[-]
0.028
0.031
0.046
0.072
0.066
0.034
0.036
0.069
0.056
0.056
0.060
19.2
20.4
19.6
19.6
19.5
19.2
19.1
19.4
19.9
8.06
7.82
7.94
7.87
7.89
7.98
7.75
7.88
7.88
0.046
0.087
0.078
0.082
0.061
0.064
0.070
0.084
0.103
Table 3: Experimental runs in the continuously operated reactor, all with pure
butyl formate and a concentrated sodium hydroxide solution of around 8M. Run
1-11: NaOH as the continuous phase; Run 12-20: NaOH as the dispersed phase.
132
Determination
Determinationof
ofInterfacial
InterfacialAreas
Areaswith
withthe
theChemical
ChemicalMethod
Method
100
Droplet diameter d32 [µ m]
200
150
NaOH dispersed phase
100
70
50
slope: -1.2
NaOH continuous phase
30
12
14
20
16
24
30
Stirring rate N [1/s]
10
10
Figure 9: Influence of the stirring rate on the drop size for a sodium hydroxide
solution as the dispersed or continuous phase respectively.
Droplet diameter d 32 [µ m]
150
NaOH dispersed phase
125
100
75
50
NaOH continuous phase
25
0
0
0.1
0.2
0.3
0.4
0.5
Hold-up dispersed phase [-]
Figure 10: Influence of the hold-up of the dispersed phase on drop size for a
sodium hydroxide solution as the dispersed or continuous phase respectively.
133
Chapter 4
The data will now be correlated in accordance with Equation (5) without or with
the viscosity factor. The Weber number is calculated with the estimated value of
interfacial tension between sodium hydroxide and butyl formate, which is
according to Puranik and Sharma [1970] σ = 0.009 N/m. The optimal values of
the constants A and B are found via non-linear regression, fitting the proposed
expression to the experimental data. In this way one obtains for:
- sodium hydroxide solution as continuous phase:
d32
= 0.049(1 + 7.77ε )We−0.6
D
(22)
- and for sodium hydroxide solution as dispersed phase:
d32
= 0.16(1 + 2.29ε )We −0.6
D
(23)
Introducing the viscosity factor to account for which phase is the dispersed one,
the experimentally determined drop size can be correlated by a single
expression:
µ
d32
= 0.09(1 + 4.30ε )We −0 .6 d
µc
D
0 .12
(24)
The exponent of the viscosity term is 0.12. Calderbank [1958] found 0.25 and
Godfrey et al. [1989] found a value even as high as 0.4. The constant seems to
vary between 0 and 0.4; the value of 0.12 is within the range found in literature.
A parity plot of Equation (22) and (23) is given in Figure 11. The standard
deviation of the experimentally determined drop size compared to the size using
these equations is 7.7%. The standard deviation for the data calculated with the
second method is 8.3%. Both methods produce similar errors.
Santiago and Trambouze [1971a] have determined the effective interfacial area
in their reactor using the same reaction system with only the ester phase as the
dispersed phase. They have found the following expression with the ratio of the
diameter of the baffles to the reactor diameter dbaffles / dreactor equal to 0.1:
d32
= 0.172(1 + 3ε )We −0.6
D
134
Determinationof
ofInterfacial
InterfacialAreas
Areaswith
withthe
theChemical
ChemicalMethod
Method
Determination
200
d32 calculated [µm]
NaOH dispersed phase (x)
Aqueous phase dispersed (▲)
+15%
-15%
100
70
50
NaOH continuous
phase((■s))
Organic
phase dispersed
30
30
50
70
100
200
d32 experimental [µm]
Figure 11: Parity plot of calculated droplets diameter according to Equation
(22) and (23) and experimental droplets diameter in the continuous contactor.
The drop size is calculated for the same conditions as function of the hold-up of
the dispersed phase, see Figure 12, to compare the drop size correlation found
100The drop size calculated
by Santiago and Trambouze [1971a] with this work.
from their results is larger. Santiago and Trambouze [1971a] have used a 0.8
liter batch reactor with a relatively smaller turbine stirrer: Their ratio of the
diameter of the turbine to the reactor diameter dturbine / dreactor = 0.33, compared to
0.47 in this work. Fernandes and Sharma [1967] found experimentally that the
interfacial area is independent of the agitator height above the bottom and
practically independent of its diameter. Konno et al. [1987] concluded it takes
135
Chapter 4
long agitation times to reach a steady-state dispersion: they found smaller drops
after longer contact times. This time dependence of the average drop size is also
reported by Yoshida and Yamada [1970]. Bouyatiotis and Thornton [1967]
found no significant difference when batch was compared to continuous
operation. Care should be taken in comparing experimentally determined drop
sizes to literature data, because of the variety of operating conditions, range of
physical properties and effects of trace of impurities.
Droplet diameter d 32 [µ m]
130
This work, NaOH
as dispersed phase
110
Santiago and
Trambouze '71
90
70
50
This work, NaOH as
continuous phase
30
10
0
0.1
0.2
0.3
0.4
0.5
Hold-up dispersed phase [-]
Figure 12: Comparison of calculated drop sizes of NaOH-solution as continuous
phase from Santiago and Trambouze [1971a] and this work.
The droplet size of the organic liquid dispersed in the aqueous phase is under
equal operating conditions approximately two times larger than the aqueous
droplets. The physical property that changes most in case the dispersed phase
changes, is the ratio of the density to the viscosity ρ dis µ dis , which increases
from 133 to 726·103 s/m2. This changes the Reynolds number for the dispersion
with a factor 5.5. However, in the range of Reynolds numbers operated in this
work the Power number does not change significantly and can be regarded as
being constant. Zaldivar et al. [1996] could explain the increase in drop size for
their system -toluene with 5 mol% diisobutylene as the organic and 77 wt%
H2SO4 as the aqueous phase- with only the change in density of the continuous
1
136
6
Determination of Interfacial Areas with the Chemical Method
phase. In this work the density of the continuous phase decreases from 1272 to
892 kg/m3, for the aqueous phase and organic phase respectively, which changes
the Weber number from 3620 to 2540. With the drop size proportional to the
Weber number to the power –0.6, this would increase the droplet by a factor
1.24. Using the viscosity factor, which changes from 0.77 to 1.29 if one changes
from organic phase dispersed to aqueous phase dispersed, a two-fold increase is
obtained, which was also found experimentally. The increase in drop size seems
to be influenced by the change in density as well as the change in viscosity ratio.
Although drop sizes in dispersions have been studied extensively, very little data
are available covering both phases as dispersed phase under the same conditions.
4.6
Validity of the assumed conditions
The correlation developed to describe the experimentally determined drop size is
based on the mass transfer rate of ester through the interface as determined in a
stirred cell. The assumptions made have to be verified in order to justify the use
of the drop size correlations and they follow.
Quasi steady state conditions
The non steady state flux can be solved using the Higbie penetration model in
case the bulk concentration of the transferred reactant in the reaction phase is
equal to zero. The average mass transfer rate J A (τ ) reads, see Westerterp et al.
[1987]:
!
J A (τ ) = k11CB, Aq DA 1 +
4
9
1
erf
2k11CB, Aqτ
k11CB, Aqτ +
exp − k11CB, Aqτ
πk11CB, Aqτ
"#C
#$
*
A, Aq
(25)
The mass transfer rate approaches the steady state and becomes independent of
τ within 10% for k11CB, Aqτ > 5 . The deviation from the steady state follows from
the ratio of the time dependent flux and the steady state flux J A (τ ) / J A - 1:
4
J A (τ )
1
erf
−1 = 1+
JA
2 k11CB, Aqτ
9
k11CB, Aqτ +
exp − k11CB, Aqτ
πk11CB, Aqτ
−1
(26)
This ratio is plotted in Figure 13 as a function of contact time. The estimated
reaction rate constant for the saponification of butyl formate with 8 M NaOH is
137
Chapter 4
k11CB, Aq ≈ 20 s −1. In that case the average flux becomes constant after 0.25 s. To
verify the assumptions of steady state conditions one has to estimate the contact
time. From the same theory it follows that the contact time τ can be written as:
2
2
D
τ= A
π kL , Aq
(27)
The mass transfer coefficients are for ester in NaOH kL , Aq = 13·10-6 m/s and
kL , Aq = 15·10-6 m/s for NaOH as the continuous phase and dispersed phase,
respectively, see appendix 4A. The diffusivity coefficient of butyl formate in
8M NaOH at 20 ºC is 0.23·10-9 m2/s, see appendix 4A. With Equation (27) one
finds a contact time, for the used set-up under the applied experimental
conditions, of approximately 1.5 s. Therefore, the assumptions of the quasi
steady state conditions is justified.
10
JA (τ)/JA - 1 [-]
8
6
4
2
0
0.01
0.1
1
10
k11CB,Aq τ [-]
Figure 13: Ratio, J A (τ ) J A - 1 defined by equation (26) representing the
deviation from steady state approximation, as a function of the contact time τ.
138
Determination of Interfacial Areas with the Chemical Method
Fast reaction, Ha>3
The enhancement can be calculated by the experimentally determined flux and
the physical transfer rate:
EA = J A, with reaction J A, physical = mACA,Org k11CB, Aq DA
2k
L , Aq
mACA,Org
7
(28)
mACA,Org k11CB, Aq DA is for 8M NaOH at 20 ºC equal to 0.185·10-6 kmol/m2s. The
mass transfer coefficients of ester in NaOH are kL , Aq = 13·10-6 m/s and kL , Aq =
15·10-6 m/s for NaOH as the continuous phase and dispersed phase respectively,
see appendix 4A. The solubility of butyl formate in 8M NaOH solution is equal
to mACA,Org = 2.6 mol/m3. Thus the enhancement factor is equal to around 5,
which implicates operation in the fast reaction regime.
Mass transfer resistance in the organic phase negligible
This holds, see Westerterp et al. [1987] if:
kL ,Org
>> 1
kL , Aq mA EA
(29)
At the start of the run the organic phase consists of pure butyl formate, hence the
resistance to mass transfer in this phase is negligible. As the reaction proceeds,
the reaction product butanol dilutes the organic phase more and more. For all
experiments the conversion is kept below 15%. The distribution coefficient is
about mA ≈ 0.3·10-3, the enhancement factor is around 5 and the kL values of
ester in butanol and ester in NaOH-solution are 30·10-6 m/s and 15·10-6 m/s
respectively. This gives for kL,Org ( kL , Aq mA EA ) a value of 1000. Therefore, mass
transfer resistance in the organic phase is negligible.
Pseudo first order approximation
According to the penetration theory, see Westerterp et al. [1987] , the (1,1)reaction can be regarded as a reaction first order in CA, Aq , if
Ha << EA∞ = 1 +
DBCB, Aq
DA mACA* ,Org
DA
DB
(30)
139
Chapter 4
The initial concentrations of pure butyl formate, CA,Org ≈ 8.6 M, and sodium
hydroxide, CB, Aq ≈ 8 M, are of the same magnitude, while the conversion is kept
below 15%. The ratio between the diffusivities is reported by Onda et al. [1975]
to be 4. The enhancement factor for instantaneous reaction is thus in the order of
104, which is much larger than the estimated Hatta number.
Hinterland ratio, Al>>1
Al is the ratio between the total reaction phase volume and the volume of the
film in which the reaction takes place. For the case that sodium hydroxide is
dispersed, e.g. the reaction takes place in the dispersed phase Al can be
expressed as:
Al =
1
2D 1 − 1 −
k d 3
(31)
A
L , Aq 32
The dispersed phase mass transfer coefficient is estimated by the correlation of
Treybal [1963], see appendix 4A for an evaluation. This leads to Al ≈ 1.5 in case
sodium hydroxide solution is dispersed.
For the case that the ester is dispersed, e.g. the reaction takes place in the
continuous phase Al can be expressed as:
Al =
1− ε
2D − ε 1 +
k d 1
3
(32)
A
L , Aq 32
The continuous phase mass transfer coefficient is estimated by the correlation of
Calderbank and Moo-Young [1961], see appendix 4A for an evaluation. This
leads to Al ≈ 1 in case sodium hydroxide solution is the continuous phase.
The effect of small hinterland ratio on the mass transfer of ester will be
discussed in the next section
140
Determination of Interfacial Areas with the Chemical Method
The effect of small Hinterland ratio
To determine interfacial areas using the chemical reaction method and to
interpret the experimental data the film theory or non-stationary penetration
models of Higbie and Danckwerts are employed, see Westerterp et al. [1987].
The film theory is based on the assumption that near the interface, behind a
stagnant film of thickness δ, a well-mixed bulk exists in which no concentration
gradients occur. The penetration theory of Higbie and Danckwerts describes
non-stationary mass transfer into small stagnant fluid elements. The mass
transfer can in this case be described by non-stationary diffusion into a semiinfinite continuum. Both theories make use of the existence of a well-mixed
bulk either at short distance from the interface (film theory) or at infinity
(penetration model). When the droplets are small and the Hinterland ratio Al
becomes small, hardly any bulk phase exists and these theories can no longer be
used.
6
2
Flux ester x10 [kmol/m s]
0.160
analytical first order
0.155
0.150
depletion
numerical solution
0.145
0.140
0.01
0.1
1
10
100
Contact time [s]
Figure 14: Mass transfer rate of ester A into a droplet of d32 = 50 µm as a
function of contact time. Numerical solution of mass transfer with (1,1)-reaction
compared to the analytical solution for a first order reaction.
141
Chapter 4
For small values of Al and at high conversion of sodium hydroxide, deviations
may be expected due to depletion of reactant sodium hydroxide, see Westerterp
et al. [1987]. Furthermore, the equations derived based on these theories usually
assume a flat interface, which is not found for small droplets. In these cases one
has to solve the mass transfer equations numerically.
The reaction between ester and sodium hydroxide in a single drop has been
described, see appendix 4B for the derivation; the transfer rate of ester A is
calculated as a function of contact time for a small droplet of d32 = 50 µm, see
Figure 14. The flux decreases very fast to a practically constant value in a period
of 0.1 s., after this the steady state flux is JA = 0.153·10-6 kmol/m2s. For long
contact times, the concentration of B in the dispersed phase decreases and
depletion can be observed. The ester flux now again decreases with time. The
effect of depletion is low for short contact time or a large amount of B. The
deviation as a result of depletion is defined as a ratio of the numerical solution
of the flux to the analytical solution for a first order reaction, according to:
J A,numerical / J A,analytical - 1. The analytical solution can be found for spherical polar
coordinates, see e.g. Hoogendoorn [1985]:
J A ( r, t ) =
DA 2 R mACA,org
1 (−1)
r ∑ ! n
(−1)
−∑
! n
∞
n +1
n =1
∞
n =1
n +1
πr
⋅
nπ r k R
cos R ⋅ D
(33)
"# "#
$ #$
!
D n π t "# "#
exp − k +
! R $ $#
1
DA n 2π 2
nπ r
k1 R2
2 2
sin
exp
π
⋅
+
−
+
n
k
t
1
k1 R2 / DA + n 2π 2
R
DA
R2
nπ
3
k1 R / DA + Rn 2π 2
2
1
A
+ n 2π 2
2
2
A
1
2
The ratio J A,numerical / J A,analytical - 1 is shown in Figure 15 for a droplet of d32 = 50
µm. For the experimental set-up and experimental conditions the contact time is
1.5 s., while the smallest droplets found had a size d32 of 65 µm for the NaOH
solution as the dispersed phase. Therefore, deviations due to depletion of NaOH
in the droplet are not to be expected in the experiments.
142
Determination of Interfacial Areas with the Chemical Method
Jnumerical/Janalytical -1 [-]
0.05
0.00
depletion
-0.05
-0.10
-0.15
0.1
1
10
100
Contact time [s]
Figure 15: Ratio J A,numerical / J A,analytical -1 representing the deviation as a result of
depletion of component B in the droplet with d32 = 50 µm.
More important is the assumption of a flat interface, on which the film theory
and Higbie penetration theory are based. The deviation between a plain interface
or a curved interface can best be seen, when the steady state flux through the
interface of a sphere is compared with the flux through a plain interface. The
steady state solution for Equation (33) is with k1 = k11CB, Aq , see Hoogendoorn
[1985], Bird et al. [1960]:
J A ( R) = mACA,Org
k11CB, Aq DA −
DA
R
(34)
The deviation is now calculated as follows:
J A ( R) − J A ( x )
DA
=±
JA ( x)
R k11CB, Aq DA
(35)
in which J A ( x ) is equal to the steady-state flux through a plain interface, see
Equation (9). The value of this ratio is plotted as a function of droplet diameter
in Figure 16. As expected the largest deviations occur for the smallest diameters.
143
Chapter 4
0.25
flux from sphere
J(R)/J(x)-1
0.15
0.05
-0.05
flux to sphere
-0.15
-0.25
10
100
1000
Droplet diameter [µm]
Figure 16: Ratio J A ( R) / J A ( x )-1 as defined by equation (35), representing the
deviation as a result of assuming a flat interface.
For a reaction outside the droplet the mass transfer is directed outwards and the
flux is underestimated (+), when a flat interface is assumed. For a reaction inside
the droplet the flux is overestimated (-). For reaction inside the droplets the
experimentally found droplets were larger in diameter 65 µm: deviations, caused
by assuming a flat interface, are small and lower than 7.5%. For reaction outside
the droplet the smallest droplets found had a d32 larger than 33 µm, resulting in a
maximum deviation of 17%. Thus for the smallest droplets the assumption of a
flat interface results in an underestimate of the mass transfer rate and hence, of
the average drop size. However, for the normal operation conditions the droplets
in general are larger than 35 µm and thus the deviations are smaller than 15%,
which can be accepted within the accuracy of the physical properties.
The effect of a small Hinterland ratio shows itself by the inability of the
penetration theory to allow for eventual depletion of the reactant B within the
sphere. Furthermore, when at the same time the droplet diameter is small, the
assumption of a flat interface is no longer valid. In industrial applications the
contact time generally is relative short, see Brunson and Wellek [1971].
Therefore, in liquid droplets the penetration depth is generally small compared
to the diameter, thus the deviations are small as well.
144
Determination of Interfacial Areas with the Chemical Method
4.7
Discussion and Conclusions
The mass transfer rate of butyl formate through the interface as experimentally
determined in a stirred cell, has been used to predict the interfacial area in a
continuously operated contactor. The Sauter mean diameter can be described by
correlations similar to those in literature, only the constants deviate, because the
specific properties of the system investigated and the reactor configuration are
different. These constants were found to depend also on the phase that is
dispersed. This has been also mentioned by Pacek et al. [1994].
With the organic ester phase dispersed, droplet diameters were found between
35 and 75 µm; between 65 and 135 µm in case the aqueous phase is dispersed.
The drop size seems to be influenced by the density of the continuous phase as
well as the ratio of the viscosities of the two phases. It is not unambiguous
which phase dispersed will give the smallest drop size and, hence, the largest
interfacial area. It is, therefore, recommended to determine the drop size for both
liquids as the dispersed phase.
The simplest approach to describe mass transfer with reaction is the film theory.
This theory can be applied within the uncertainties of the estimated physicochemical parameters. The necessary conditions are all full-filled in all
experiments except that of a large Hinterland ratio. For the smallest droplets the
influence of the curvature of the interface has to be taken into account.
Otherwise the film theory can be used with confidence.
Acknowledgements
The author wishes to thank B.T. Sikkens, R.B.F. Horsthuis, and P. Meulenberg
for their contribution to the experimental work, and F. ter Borg and A.H. Pleiter
for technical support. W. Lengton and A. Hovestad are acknowledged for the
assistance in the analysis.
145
Chapter 4
Notation
A
A
a
Al
B
C
C, C1
D
Di
d32
d
EA
EA∞
EAct
g
Ha
I
J
kLaq
kLorg
k∞
k1
k11
kI
KS
m
N
P
r
R
R
t
T
V
w
Z
146
Cross-sectional area
Constant
Interfacial area per volume of reactor content = 6ε / d32
Hinterland ratio
Constant
Concentration
Constants
Diameter stirrer
Diffusivity coefficient component i
Sauter mean drop diameter
Diameter
Enhancement factor
Maximum enhancement factor
Energy of activation
Gravity constant = 8.91
Hatta number
Ionic strength
Mole flux
Mass transfer coefficient in the aqueous phase
Mass transfer coefficient in the organic phase
Preexponential constant
First-order reaction rate constant
Second-order reaction rate constant
Ionic strength reaction rate constant
Salting-in or salting-out coefficient
Molar distribution coefficient
Stirring rate
Power of stirring
Radial direction
Radius of sphere
Gas constant = 8315
Time
Temperature
Volume
Impeller blade height
Charge of ion
[m2]
[-]
[m2/m3]
[-]
[-]
[kmol/m3]
[-]
[m]
[m2/s]
[m]
[m]
[-]
[-]
[J/kmol]
[m/s2]
[-]
[kmol/m3]
[kmol/m2·s]
[m/s]
[m/s]
[m3/kmol·s]
[s-1]
[m3/kmol·s]
[m3/kmol]
[m3/kmol]
[-]
[s-1]
[J/s]
[m]
[m]
[J/kmol·K]
[s]
[K]
[m3]
[m]
[-]
Determination of Interfacial Areas with the Chemical Method
Greek symbols
ε
ϕ
µ
ρ
σ
τ
Volume fraction dispersed phase = Vd (Vd + Vc )
Flow
Viscosity
Density
Interfacial tension
Contact time
[-]
[m3/s]
[Ns/m2]
[kg/m3]
[N/m]
[s]
Dimensionless groups
Po
Re
We
P
ρ dis N 3 D5
ρ dis ND2
Reynolds number
µ dis
2 3
N D ρc
Weber number
σ
Power number
[-]
[-]
[-]
Subscripts and superscripts
0
Aq
Org
A
B
C
c
d
dis
R
w
max
∗
¯
Initial
Aqueous phase
Organic phase
Component A (ester)
Component B (OH-)
Component C (HCOO-)
Continuous phase
Dispersed phase
Dispersion
Reactor
Water
Maximum
At interface
Average
147
Chapter 4
References
Baker, G.A. and Oliphant, T. A., An implicit, numerical method for solving the
two-dimensional heat equation, Q. Appl. Math., 17 (1960) 361-373.
Bell, P., Acid-base catalysis, Oxford university press, London 1949.
Bidner, M.S. and de Santiago, M., Solubilite de liquides non-électrolytes dans
des solution aqueuses d’électrolytes, Chem. Eng. Sci., 26 (1971) 14841488.
Bird, R.B., Stewart, W.E. and Lightfoot, E.N., Transport phenomena, Wiley,
New York, 1960.
Bouyatiotis, B.A. and Thornton, J.D., Liquid-liquid extraction studies in stirred
tanks. Part I: Droplet size and hold-up measurements in a seven-inch
diameter baffled vessel, Inst. Chem. Eng. Symp. Ser. 26 (1967) 43-51.
Brunson, R.J. and Wellek, R.M., Mass transfer inside liquid droplets and gas
bubbles accompanied by a second order chemical reaction, AIChE J. 17
(1971) 1123-1130.
Calderbank, P.H., Physical rate processes in industrial fermentation, part 1: The
interfacial area in gas-liquid contacting with mechanical agitation., Trans.
Inst. Chem. Eng. 36 (1958) 443-463.
Calderbank, P.H. and Moo-Young, M.B., The continuous phase heat and masstransfer properties of dispersions, Chem. Eng. Sci. 16 (1961) 39-54.
Chen, H.T. and Middleman, S., Drop size distribution in agitated liquid-liquid
systems AIChE J. 13 (1967) 989-995.
Coulaloglou, C.A. and Tavlarides, L.L., Drop size distributions and coalescence
frequencies of liquid-liquid dispersions in flow vessels, AIChE J. 22
(1976) 289-297.
Daubert, T.E., Danner, R.P., Sibul, H.M. and Stebbins, C.C., Physical and
thermodynamic properties of pure chemicals: data compilation, Taylor &
Francis, London, 1989.
Davies, G.A., Mixing and coalescence phenomena in liquid-liquid systems, in:
J.D. Thornton (ed.), Science and practice of liquid-liquid extraction,
Vol.1, Clarendon press, Oxford, 1992, p. 244.
Doraiswamy, L.K. and Sharma, M.M., Heterogeneous reactions: Analysis,
examples and reactor design, Vol. 2: Fluid-fluid-solid reactions, John
Wiley and Sons, New York, 1984.
Fernandes, J.B. and Sharma, M.M., Effective interfacial area in agitated liquidliquid contactors, Chem. Eng. Sci. 22 (1967) 1267-1282.
Giles, J.W., Hanson, C. and Marsland, J.G., Drop size distribution in agitated
liquid-liquid systems with simultaneous interface mass transfer and
chemical reaction, Proc. Int. Solv. Extr. Conference, Society of Chemical
Industries, 1971, pp. 91-111.
148
Determination of Interfacial Areas with the Chemical Method
Godfrey, J.C., Obi, F.I.N. and Reeve, R.N., Measuring drop size in continuous
liquid-liquid mixers, Chem. Eng. Prog. 85 (1989) 61-69.
Heertjes, P.M. and de Nie, L.H., Mass transfer to drops, in: C. Hanson (ed.),
Recent advances in liquid-liquid extraction, Pergamon Press, Oxford,
1971, p. 367.
van Heuven, J.W. and Beek, W.J., Power input, drop size and minimum stirrer
speed for liquid-liquid dispersions in stirred vessels, Proc. Int. Solv. Extr.
Conference, Society of Chemical Industries, 1971, pp. 70-81.
Hinze, J.O., Fundamentals of the hydrodynamic mechanism of splitting in
dispersion processes, AIChE J. 1 (1955) 289-295.
Hoffman, J.D., Numerical Methods for Engineers and Scientists, McGraw Hill,
New York, 1992.
Hoogendoorn, C.J. (in dutch) Fysische transportverschijnselen II, Delftse
Uitgevers, Delft, 2nd edn., 1985.
Konno, M. and Daito, S., Correlation of drop sizes in liquid-liquid agitation at
low dispersed phase volume fractions, J. Chem. Eng. Jpn. 20 (1987) 533535.
Leimu, R., Korte, R., Laaksonen, E. and Lehmuskoski, U., The alkaline
hydrolysis of formic esters, Suom. Kemistil. B. 19 (1946) 93-97.
Lele, S.S., Bhave, R.R. and Sharma, M.M., Fast liquid-liquid reactions: Role of
emulsifiers, Ind. Eng. Chem. Process Des. Dev. 22 (1983) 73-76.
Long, F.A. and McDevit, W.F., Activity coefficients of nonelectrolyte solutes in
aqueous salt solutions, Chem. Rev. 51 (1952) 119-169.
Nanda, A.K. and Sharma, M.M., Effective interfacial area in liquid-liquid
extraction, Chem. Eng. Sci. 21 (1966) 707-713.
Nanda, A.K. and Sharma, M.M., Kinetics of fast alkaline hydrolyses of esters,
Chem. Eng. Sci. 22 (1967) 769-775.
Onda, K., Takenchi, H., Fujine, M. and Takahashi, Y., Study of mass transfer
between phases by a diaphragm cell - alkaline hydrolysis of esters in
aqueous NaOH solution-, J. Chem. Eng. Jpn. 8 (1975) 30-34.
Pacek, A.W., Nienow, A.W. and Moore, I.P.T., On the structure of turbulent
liquid-liquid dispersed flows in an agitated vessel, Chem. Eng. Sci. 49
(1994) 3485-3498.
Perry, R.H. and Chilton, C.H., Chemical engineers’ handbook, McGraw-Hill,
New York, 6th edn., 1984.
Peters, D.C., Dynamics of emulsification, in: N. Harnby, M.F. Edwards and
A.W. Nienow (eds.), Mixing in the process industries, Butterworth,
Oxford, 2nd edn., 1992, pp. 294-317.
Puranik, S.A. and Sharma, M.M., Effective interfacial area in packed liquid
extraction columns, Chem. Eng. Sci. 25 (1970) 257-266.
149
Chapter 4
de Santiago, M. and Trambouze, P., Réacteurs parfaitement agites à deux phases
liquides: mesure de l’aire interfaciale par méthode chimique, Chem. Eng.
Sci. 26 (1971a) 29-38.
de Santiago, M. and Trambouze, P., Applicabilité de la méthode chimique de
mesure de l’aire interfaciale, Chem. Eng. Sci. 26 (1971b) 1803-1815.
de Santiago, M. and Bidner, M.S., Etude de la réaction formiate de n-butylsoude en vue de son emploi pour la mesure des aires interfaciales liquideliquide, Chem. Eng. Sci. 26 (1971) 175-176.
Sharma, M.M. and Danckwerts, P.V., Chemical methods of measuring
interfacial area and mass transfer coefficients in two-fluid systems, Br.
Chem. Eng. 15 (1970) 522-528.
Shinnar, R., On the behaviour of liquid dispersions in mixing vessels. J. Fluid
Mech. 10 (1961) 259.
Sprow, F.B., Distribution of drop sizes produced in turbulent liquid-liquid
dispersion, Chem. Eng. Sci. 22 (1967) 435-442.
Tavlarides, L.L. and Stamatoudis, M., The analysis of interphase reactions and
mass transfer in liquid-liquid dispersions, in: T.B. Drew, G.R. Cokelet,
J.W. Hoopes and T. Vermeulen (eds.), Advances in Chemical
Engineering, Vol.11, Academic Press, New York, 1981, p.199.
Treybal, R.E., Liquid extraction, McGraw-Hill, New York, 2nd edn., 1963,
pp.150-195.
Vermeulen, T., Williams, G.M. and Langlois, G.E., Interfacial area in liquidliquid and gas-liquid agitation, Chem. Eng. Prog. 51 (1955) 85-94.
Wesselingh, J.A., The velocity of particles, drops and bubbles, Chem. Eng.
Process., 21 (1987) 9-14.
Westerterp, K.R., van Dierendonck, L.L. and de Kraa, J.A., Interfacial areas in
agitated gas-liquid contactors, Chem. Eng. Sci., 18 (1963) 157-176.
Westerterp, K.R., van Swaaij, W.P.M. and Beenackers, A.A.C.M., Chemical
reactor design and operation, Wiley, Chichester, student edn., 1987.
Wilke, C.R. and Chang, P., Correlation of diffusion coefficients in dilute
solutions, AIChE J. 1 (1955) 264-270.
Yoshida, F. and Yamada, T., Dispersion of oil in water in gas-bubble columns
and agitated vessels, Chemeca ’70 Conf., Butterworths, Sydney, 1970, pp.
19-26.
Zaldivar, J.M., Molga, E., Alos, M.A., Hernandez, H. and Westerterp, K.R.,
Aromatic nitrations by mixed acid. Fast liquid-liquid reaction regime,
Chem. Eng. Process., 35 (1996) 91-105.
150
Determination of Interfacial Areas with the Chemical Method
Appendix 4.A:
Physico-chemical parameters
Diffusivity
The diffusivity of butyl formate in a concentrated sodium hydroxide solution is
calculated by the relation proposed by Onda et al. [1975]. This relation gives the
diffusivity ratio of ester in water and ester in a sodium hydroxide solution:
DA,w
= 1 + 0.118413 ⋅ I + 0.0217124 ⋅ I 2
DA
(36)
The diffusivity of butyl formate in water is estimated by the method of Wilke
and Chang [1955]:
DA,w = 2.67 ⋅ 10 −15
T
µw
(37)
Ionic strength
The ionic strength of the NaOH solution is calculated with the contribution of
small amounts CO32− included, as:
4
2
2
I = 1 2 CNa + Z Na
Z 2 + CCO2 − ZCO
2−
+ + C
OH − OH −
3
3
9
(38)
Viscosity
The viscosity of pure butyl formate µ Org is calculated with the correlation of
Daubert et al. [1989]. The viscosity of the NaOH solution µ Aq is calculated with
the correlation of Onda et al. [1975], which gives the viscosity of sodium
hydroxide in relation to the viscosity of water:
µ Aq = µ w (1 + 0.177 ⋅ I + 0.0527 ⋅ I 2 )
(39)
The viscosity of water µ w is calculated with:
log µ w =
1.3271(29315
. − T ) − 0.001053 (T − 29315
. )2
−3
.
T − 16815
(40)
151
Chapter 4
Viscosity of the dispersion is calculated with the correlation of Vermeulen et al.
[1955]:
µ
εµ d
(41)
µ dis = c 1 + 1.5
1− ε
µd + µc
Density
The density of pure butyl formate ρ Org is calculated with the correlation of
Daubert et al. [1989]. The density of the aqueous NaOH solution ρ Aq is taken
from Perry and Chilton [1984]. The density of the dispersion is calculated with:
ρ dis = ερ d + (1 − ε )ρ c
(42)
Solubility
The solubility of butyl formate in concentrated electrolyte solutions is estimated
by a salting-out parameter Ks, see: Long and McDevit [1952]:
CA∗ , Aq = CAw ⋅10 − Ks I
(43)
The salting-out parameter is taken from Bidner and Santiago [1971], Ks =
0.1793 m3/kmol. The solubility of butyl formate in water is taken from Nanda
and Sharma [1966] who found CA,w =0.075 kmol/m3 for 10 to 30 ºC and a small
increase in solubility for 30 to 40 ºC, according to the correlation:
CA,w = 5.57 ⋅ 10 −2 + 6.32 ⋅ 10 −4 (T − 27315
. )
(44)
Continuous phase mass transfer coefficient
The empirical correlation of Calderbank and Moo-Young [1961] is used to
determine the mass transfer coefficient kL,Aq of ester (A) in the continuous phase
(B):
( P / V )µ "# µ "#
= 0.13
! ρ $ !ρ D $
1/ 4
k L, Aq
C
2
C
C
−2 / 3
C
C
(45)
A
P is the power dissipated by agitator, which can be calculated by:
P = Po ⋅ ρ dis N 3 D5
152
(46)
Determination of Interfacial Areas with the Chemical Method
The power number Po is practically constant and for a turbine stirrer it equals
Po=5.
This gives for the continuous phase mass transfer coefficient kL,Aq= 13·10-6 m/s,
which is in agreement with the value reported by Fernandes and Sharma [1967].
They found experimentally kL= 11.3-16·10-6 m/s for n-hexyl formate in a
NaOH/Na2SO4 solution.
Dispersed phase mass transfer coefficient
The dispersed phase mass transfer coefficient will depend on whether the drop
behaves as a rigid body or not, see: Treybal [1963] and Heertjes and Nie [1971].
The mass transfer coefficient for rigid spheres is, Treybal [1963]:
kL, Aq =
2π 2 DA
3 ⋅ d32
(47)
This relationship is valid for spheres with no circulation and with transfer by
pure molecular diffusion.
In order to evaluate whether the drop behaves as a rigid body, the diameter
number d * is calculated, see Wesselingh [1987]:
d = d32
*
µ "#
! ρ g∆ρ $
2
C
−1/ 3
(48)
C
When d * < 10 the bubbles or drops can be regarded as rigid spheres. For the
experimental range with NaOH as the dispersed phase, the diameter number
varies between 1 and 3, hence the drops behave like rigid spheres. The dispersed
phase mass transfer coefficient can be calculated using Equation (47) and is
equal to kL,Aq = 15·10-6 m/s.
153
Chapter 4
Appendix 4.B:
Numerical model
Very tiny droplets are nearly spherical in shape and non-stationary diffusion is
the main process in the droplet. One therefore can assume the system to be
represented as mass transfer with second order reaction in a stagnant sphere. For
the experimental range, the droplets can be regarded as a stagnant sphere, based
on the criterion of Wesselingh [1987], see appendix 4A. The same reaction
system is considered as shown in Figure 1 of Chapter 4. The following nonlinear, coupled partial differential equations have to be solved:
∂CA, Aq
∂t
∂CB, Aq
∂t
∂C
1 ∂
=
r D
∂r
r ∂r =
− k C
1 ∂ 2 ∂CA, Aq
r DA
− k11CA, Aq CB, Aq
∂r
r 2 ∂r
B , Aq
2
B
2
11
A, Aq
(49)
(50)
CB, Aq
With the following initial and boundary conditions:
t = 0, ∀ r → CB, Aq = CB, Aq (t = 0 )
t = 0, 0 ≤ r < R → CA, Aq = 0
∂C = 0
∂r ∂C = k 2C
r = R, ∀ t → D ∂r r = 0, ∀ t →
B, Aq
r = 0, ∀ t
r=0
A, Aq
A
LA
r=R
A,Org
− CA* ,Org
→
∂C ∂r =0
A, Aq
r =0
7
These partial differential equations are discretised according to the Baker and
Oliphant method, see Baker and Oliphant [1960] and linearised with a NewtonRhapson interation, see e.g. Hoffman [1992]. The model is then numerically
solved for the whole experimental range. As a check of the accuracy of the
program the numerical solution of a first order reaction was compared to its
analytical solution, Equation (33). Deviations never exceeded 0.2 %.
154
Samenvatting en Conclusies
Een aantal ernstige ongelukken in de chemische industrie werd veroorzaakt door
een runaway van een heterogene vloeistof-vloeistof reactie waarbij een
ongewenste reactie optrad. Een van de voornaamste oorzaken van deze
runaways is een gebrek aan inzicht van de fenomenen welke plaatsvinden in
deze reactiesystemen. Om dit type processen veilig en economische te
ontwerpen en te bedrijven is een gedegen kennis van deze processen uiterst
belangrijk. Dit proefschrift gaat over het veilig bedrijven van een meervoudige
vloeistof-vloeistof reactie, uitgevoerd in een semi-batch reactor, met de
salpeterzuur oxidatie van 2-octanol als voorbeeld. Een algemene inleiding tot
runaways in (semi) batch reactoren wordt gegeven in Hoofdstuk 1.
In Hoofdstuk 2 wordt de oxidatie van 2-octanol behandeld. De oxidatie van 2octanol met salpeterzuur is geselecteerd als modelreactie voor een heterogene
vloeistof-vloeistof reactie met een ongewenste zijreactie. Hierbij wordt 2octanol eerst geoxideerd tot 2-octanon dat vervolgens verder geoxideerd kan
worden tot carbonzuren. De oxidatie van 2-octanol met salpeterzuur vertoont de
typische kenmerken van salpeterzuur oxidaties, zoals: lange inductietijd zonder
toevoeging van initiator; autokatalytische reactie, sterke invloed van
zuurconcentratie en hoge activeringsenergie. Er is een beperkte kennis over de
exacte chemische structuur van de componenten in de waterige reactiefase en
over een aantal ongeïdentificeerde, onstabiele verbindingen, in de organische
fase. Daarbij is ook het exacte mechanisme van de reactie nog niet opgehelderd.
Hierdoor was een sterke vereenvoudiging nodig van het model om de
reactiesnelheden te kunnen beschrijven.
Een uitgebreid experimenteel programma is gevolgd met behulp van
reactiecalorimetrie ondersteund met chemische analyses. De oxidatie reacties
zijn uitgevoerd in de reactie calorimeter RC1 van Mettler Toledo welke is
uitgevoerd met een dubbelwandige glazen reactievat ter grootte van 1 liter. De
reacties zijn onderzocht in de temperatuurrange van 0 tot 40 ºC, een
beginconcentratie salpeterzuur van 50 tot 65 massa% en een toerental van 700
tpm. De kinetiekconstanten zijn bepaald voor beide reacties. De waargenomen
omzettingssnelheden van de complexe reacties van 2-octanol en 2-octanon met
salpeterzuur
kunnen
beschreven
worden
met
slechts
twee
kinetiekvergelijkingen. Hierin wordt de invloed van de temperatuur beschreven
155
Samenvatting en Conclusies
met de Arrhenius-vergelijking en de invloed van de zuursterkte met Hammett’s
zuurfunctie.
Salpeterzuur en de organische oplossing zijn onmengbaar. Hierdoor verlopen de
chemische reactie en de stofoverdrachtverschijnselen gelijktijdig. De resultaten
geven aan dat de oxidatie van 2-octanol is uitgevoerd in het niet-chemisch
versnelde regiem, zolang de salpeterzuurconcentratie lager is dan 60 massa% of
de temperatuur beneden 25 ºC is bij een concentratie van 60 massa%. De
oxidatie van 2-octanon is uitgevoerd in het niet-chemisch versnelde regiem voor
alle experimenteel toegepaste condities. Onder deze condities wordt de
omzettingssnelheid niet beïnvloed door de weerstand tegen stofoverdracht. De
heersende parameters zijn in dit geval de reactiesnelheidsconstante en de
oplosbaarheid van de organische componenten in de salpeterzuuroplossing. Dit
is ook experimenteel bevestigd door de invloed van het toerental te bepalen.
Gelijktijdig is een model ontwikkeld waarmee de omzettingssnelheden
beschreven kunnen worden. Hiermee kan het gedrag van de semi-batch reactor,
de concentratie- en temperatuur-tijd profielen, met succes voorspeld worden. De
experimentele resultaten en de simulaties zijn in goede overeenstemming en het
is mogelijk gebleken om het thermische gedrag van de salpeterzuuroxidatie
reacties in de semi-batch reactor te beschrijven met het filmmodel in het
langzame reactie regiem en een vereenvoudigd reactie schema.
In hoofdstuk 3 is het thermisch gedrag van dit heterogene vloeistof-vloeistof
reactie systeem in meer detail beschreven. Een experimentele opstelling is
gebouwd, met een glazen reactor van 1 liter, gevolgd door een thermische
karakterisering van de opstelling. Twee gescheiden koelcircuits zijn
geïnstalleerd, één via een koelspiraal en één via een koelwand, om verschillende
koelcapaciteiten te onderzoeken. De reactor wordt bedreven op semi-batch wijze
onder isoperibole condities, d.i. met constante koeltemperatuur. Een serie
oxidatie experimenten is uitgevoerd om de invloed van verschillende initiële en
operatiecondities te onderzoeken. De reacties zijn uitgevoerd met een
koeltemperatuur van –5 tot 60 ºC, doseertijden van 0.5 tot 4 uur, een initiële
salpeterzuur concentratie van 60 massa% en een toerental van 1000 tpm.
De reactie is uitgevoerd in een gekoelde SBR waarbij salpeterzuur wordt
voorgelegd en de organische component 2-octanol gedoseerd wordt met een
constant debiet. 2-Octanol reageert tot 2-octanon dat vervolgens verder
geoxideerd kan worden tot ongewenste carbonzuren. Een gevaarlijke situatie
kan ontstaan wanneer de overgang van de reactie naar zuren op zo een snelle
wijze plaatsvindt dat de reactiewarmte in zeer korte tijd vrijkomt waardoor een
156
Samenvatting en Conclusies
temperatuur-runaway optreedt. Het toepassen van een langere doseertijd of een
grotere koelcapaciteit is een effectieve manier om de temperatuureffecten te
matigen en uiteindelijk zal een ongewenste temperatuurstijging voorkomen
kunnen worden. In het laatste geval kan het proces beschouwd worden als ‘altijd
veilig’ en zal er voor geen enkele koeltemperatuur een runaway plaatsvinden en
de reactortemperatuur blijft gehandhaafd tussen bekende grenzen. De condities
welke leiden tot een ‘altijd veilig’ proces zijn bepaald met experimenten en met
modelberekeningen.
Voor de winstgevendheid van een fabriek is het gewenst om een hoge opbrengst
te bereiken in een korte tijd en onder veilige omstandigheden. De
reactiecondities moeten zo gekozen worden dat de maximale opbrengst aan
tussenproduct 2-octanon snel bereikt wordt en vervolgens dient de reactie
gestopt te worden bij het bereiken van de optimale reactietijd. Het geschikte
moment om de reactie te stoppen kan bepaald worden met modelberekeningen.
De invloed van de operatiecondities, bijv. doseertijd en koeltemperatuur, op de
maximale opbrengst is bestudeerd en wordt besproken.
Bij de oxidatie van 2-octanol is de aandacht gericht op de eerste gewenste
reactie, terwijl het gevaar van een runaway-reactie toegeschreven kan worden
aan het ontsteken van de tweede reactie. Het reactiesysteem kan worden opgevat
als twee enkelvoudige reacties en daarom is ook het grensdiagram − ontwikkeld
door Steensma en Westerterp [1990] − voor enkelvoudige reacties gebruikt om
de kritische condities te bepalen voor het meervoudige reactiesysteem. Het
grensdiagram kan gebruikt worden om de doseertijd en de koeltemperatuur te
bepalen nodig voor het veilig bedrijven van de gewenste reactie, maar het leidt
tot een te optimistische koeltemperatuur om de ongewenste reactie te
onderdrukken.
Het bestuderen van het dynamische gedrag van vloeistof-vloeistof reactie
systemen gaat gepaard met enkele complicaties, omdat de chemische reactie en
stofoverdracht gelijktijdig optreden. De kennis over het oppervlak van het
fasengrensvlak in een vloeistof-vloeistof systeem is essentieel voor een
nauwkeurige beschrijving van de stofoverdracht en snelheden van de chemische
reacties. In Hoofdstuk 4 is het contactoppervlak van een vloeistof-vloeistof
systeem in een mechanisch geroerde reactor bepaald met behulp van de
chemische reactie methode. Bij deze methode wordt gebruik gemaakt van
absorptie welke gepaard gaat met een snelle pseudo-eerste orde reactie. Als
modelreactie is gekozen voor de verzeping van butylformiaat met een 8 M
natronloog oplossing. De extractiesnelheid van de ester is bepaald in een
geroerde cel met een goed gedefinieerd contactoppervlak van 33.4 cm2 en er is
157
Samenvatting en Conclusies
een correlatie afgeleid om de molflux van de ester door het oppervlak te
beschrijven. De kinetiekconstanten zijn berekend en worden vergeleken met de
literatuurwaarden. De snelheid van de reactie wordt beïnvloed door de
hoeveelheid ionen in de oplossing. Om dit effect van de ion-sterkte te kunnen
beschrijven is de reactiesnelheidconstante beschreven met een extra term in de
gebruikelijke Arrhenius-vergelijking.
Om het contactoppervlak in een turbulent gemengde dispersie te onderzoeken is
de reactor, met een volume van 0.5 liter, continu bedreven. Een correlatie voor
de Sauter gemiddelde druppeldiameter is afgeleid voor zowel reactie in de
disperse fase als voor reactie in de continue fase. Een viscositeitfactor moest
ingevoerd worden om beide situaties met één enkele correlatie te kunnen
beschrijven. De Sauter gemiddelde druppeldiameter kan beschreven worden met
vergelijkbare correlaties als vermeld in de literatuur, alleen de constanten
verschillen. Dit is het gevolg van verschillen in de specifieke eigenschappen van
het onderzochte systeem en verschillen in de configuratie van de reactor. Hierbij
is gevonden dat deze constanten afhangen van welke fase gedispergeerd wordt.
Met de organische fase als de gedispergeerde fase worden diameters van de
druppels gevonden tussen 35 en 75 µm en tussen 65 en 135 µm als de waterige
fase wordt gedispergeerd. De druppelgrootte lijkt af te hangen van de dichtheid
van de continue fase en de verhouding van de viscositeiten van de twee fasen.
Het is niet eenduidig welke fase gedispergeerd de kleinste druppels geeft en
daarmee het grootste contactoppervlak. Het wordt daarom aanbevolen om het
contactoppervlak te bepalen voor beide vloeistoffen als de gedispergeerde fase.
De stofoverdracht met chemische reactie is beschreven met het filmmodel. Deze
theorie kan over het algemeen toegepast worden binnen de onzekerheden van de
geschatte fysische en chemische parameters, terwijl het model eenvoudig is. De
geldigheid van het toepassen van het chemisch versnelde regiem is getoetst. Er
wordt voor alle experimenten voldaan aan de noodzakelijke condities, behalve
de voorwaarde van een grote Achterland verhouding. Hierom is de reactie tussen
ester en natronloog in een druppel beschreven met een numeriek model. Het
effect van een kleine Achterland verhouding manifesteert zich omdat, voor
zowel de filmtheorie als penetratietheorie, het niet mogelijk is om de
uiteindelijke uitputting van reactant in de druppel te beschrijven. Voor de
experimentele opstelling en experimentele condities is de contacttijd relatief kort
en zijn afwijkingen, ten gevolge van uitputting van NaOH in de druppel, niet te
verwachten. Voor de experimenteel gemeten kleinste druppeldiameters is de
aanname van een vlak contactoppervlak niet meer geldig. In dat geval zal de
invloed van de kromming meegenomen moeten worden. In de andere gevallen
kan het filmmodel met vertrouwen worden toegepast.
158
Dankwoord
De totstandkoming van dit proefschrift is het resultaat van de inspanning van
een groot aantal mensen. Iedereen die een bijdrage heeft geleverd wil ik hierbij
bedanken. Een aantal mensen wil ik zeker niet onvermeld laten.
Ik wil allereerst mijn promotor, Professor Westerterp, noemen. Toen ik begon
was ik mij maar ten dele bewust van de moeilijkheid van het voortzetten van een
reeds begonnen onderzoek. Hij heeft vertrouwen getoond en de vrijheid gegeven
om het onderzoek een nieuwe richting te geven. Na het schrijven van de
artikelen werden de discussies gevoerd. Dit moest meestal per fax van en naar
Spanje. Hoewel dat niet altijd even makkelijk is gegaan heeft zijn kritische blik
er voor gezorgd dat het proefschrift aan duidelijkheid heeft gewonnen.
Daarnaast heb ik grootste bewondering voor zijn enthousiasme en gedrevenheid
waarmee hij altijd heeft gezorgd voor een hechte groep met een brede blik.
Een groot gedeelte van het beschreven werk is uitgevoerd door studenten in het
kader van hun afstudeeropdracht. Waarvan Bart Sikkens veruit de eerste. Hij
had de opdracht al gekozen voordat ik in dienst getreden was. Samen zijn we
begonnen met de ‘kinso-opstelling’ en hebben het onderzoek op poten gezet
naar het meten van grensvlakken in vloeistof-vloeistof dispersies. Het werk
werd voortgezet door de eerste van een groep vrienden: Rob Horsthuis, waarmee
het onderzoek snel vorderde. De meeste bezieling in het Hoge Druk
Laboratorium werd ingebracht door Pieter Meulenberg, hij introduceerde de
HDL-shuffle.
Veel tijd is gaan zitten in het vinden van een geschikte modelreactie. De
mogelijke reactiesystemen werden getest door Sander Geuting in de reactie
calorimeter. Altijd begon Sander met een kleurloze oplossing welke vervolgens
groen, blauw, geel, bruin of rood werd. Robert Berends vervolgde het werk met
de oxidatie van alcoholen met salpeterzuur. Wat waren we blij toen de
temperatuur plotseling snel opliep, bruine dampen ontstonden en de stoppen van
de reactordeksel om onze oren vlogen: onze eerste runaway!! Dat was het
systeem dat we zochten. Vincent Motta heeft enkele oriënterende metingen
uitgevoerd in een adiabatisch vat en Emiel Ordelmans heeft het systeem verder
onderzocht in de calorimeter. Ondanks het complexe gedrag van het systeem is
met Sjoerd Lemm een beschrijving verkregen van de kinetiek van de oxidatie
159
Dankwoord
reacties. Hij hield er wel bruine vingers aan over en kreeg er de gaten van in zijn
broek.
Bas Wonink is begonnen met de bouw van een gekoelde semi-batch reactor en
de warmtekarakterisering daarvan. Sybrand Metz heeft deze karakterisering
afgerond en heeft vele malen de salpeterzuuroxidatie in de reactor uitgevoerd.
Het veroorzaken van een runaway werd zijn specialisme, maar ook het veilige
operatiegebied werd ontdekt.
Veel begripsvorming rondom runaways van systemen met meervoudige reacties
is ontstaan door modelleerwerk, waarvan Menno van Os een deel op zich heeft
genomen. Menno is een van de weinige die een kwaliteitselftal weet te
waarderen: En weer trekken wij ten strijde... Dit werk werd voortgezet door
Arnold ‘Mo’ Kleijn die, naar zijn zeggen, enkele handige ‘tools’ heeft bedacht,
maar vooral zijn ‘most worthy models’ hebben indruk gemaakt. Tot slot hebben
Veroniek Joosten, Maurice Prins, Marc Weemer en Jeroen Bouwman als TBKPstudenten metingen verricht in het kader van hun technische opdracht.
Tevens wil ik alle leden van binnen en buiten de vakgroep bedanken, die als
commissielid van het onderzoek hebben deelgenomen: Louis van der Ham, Imre
Rácz, Günter Weickert, Konrad Mündlein, Rahul Vas Bhat, Frank van Veggel,
Maarten Vrijland, en speciale dank gaat naar Wim Brilman en Metske
Steensma. Met Wim heb ik altijd waardevolle discussies kunnen voeren en
Metske van Akzo Nobel Deventer heeft vooral in de beginfase nodige
aanwijzingen gegeven.
Het onderzoek omvatte een groot deel experimenteel werk. Vele opstellingen
zijn gebouwd en vele runaways zijn beheerst opgetreden. Dit was alleen
mogelijk met de hulp van alle technici in het Hoge Druk Laboratorium. Zij
sleutelen niet alleen aan de opstellingen, maar dachten ook altijd mee over
verbeteringen. Arie Pleiter en Fred ter Borg maakten altijd even tijd vrij om iets
te doen. Maar ook zonder de inspanningen van Karst van Bree en in de laatste
periode vooral de bijdrage van Geert Monnik had mijn onderzoek niet continu
kunnen doorlopen. En natuurlijk Gert Banis. Hij weet je het gevoel te geven dat
je rijk bent, terwijl je niks hebt.
Vele analyses zijn uitgevoerd door Wim Lengton en Adri Hovestad. Met name
wil ik hun bedanken voor de hulp en tips om zelf analyse methoden op te
starten. Mijn dank gaat dan ook onvermijdelijk uit naar Bert Kamp, die
vakkundig de gas-chromatograaf repareerde. De glasblazers voor het
vervaardigen van het glaswerk en na intensief gebruik: het herstellen van de
160
Dankwoord
barsten. Henny Bevers dank ik voor het uitvoeren van de TOC-analyses, net
voordat het apparaat ter zielen is gegaan.
Een ieder van Financiële Zaken, Personeels Zaken wil ik bedanken voor al het
werk dat ze voor mij hebben verricht. Het Apparatencentrum, en met name Wim
Platvoet en Jan Jagt die de bestellingen van de juiste apparatuur hebben geregeld
en Henk Bruinsma voor de chemicaliën en laboratorium spullen. Ik heb veel van
het internet mogen genieten omdat ik (bijna) altijd on-line was. Dit was alleen
mogelijk dankzij de hulp van SGA en met name Jan Heezen en Marc Hulshof.
Tevens gaat mijn dank uit naar de gehele vakgroep Industriële Processen en
Produkten: de stafleden, (ex)promovendi, postdoc’s en het secretariaat. Familie
en vrienden wil ik bedanken voor hun morele steun die zij mij gegeven hebben
en de welkome uitjes. Mijn moeder wil ik bedanken voor haar steun en begrip.
Zij wilde altijd op de hoogte blijven van de stand van zaken, maar daar moest ik
soms in teleurstellen. Ik hoop dat ze kan leven met hetgeen dat vermeld is in het
proefschrift. En in het bijzonder Geralda. Zij stond altijd klaar wanneer dat
nodig was, terwijl ze ook begrip had als ik geen tijd had om iets voor haar te
doen zolang het nog niet af was. Maar nu, voor je verjaardag, … het is af!
161
List of Publications
L. van de Beld, R.A. Borman, O.R. Derkx, B.A.A. van Woezik and K.R.
Westerterp, 1994. Removal of volatile organic compounds from polluted air in a
reverse flow reactor: An experimental study. Ind. Eng. Chem. Res. 33 29462956.
B.A.A. van Woezik and K.R. Westerterp, 2000. Measurement of interfacial
areas with the chemical method for a system with alternating phases dispersed.
Chem. Eng. Process. 39 299-314.
(Chapter 4 of this thesis)
E.J. Molga, B.A.A. van Woezik and K.R. Westerterp, 2000. Neural networks for
modelling of chemical reaction systems with complex kinetics: oxidation of 2octanol with nitric acid. Chem. Eng. Process. 39 323-334.
B.A.A. van Woezik and K.R. Westerterp, 2000. The nitric acid oxidation of 2octanol. A model reaction for multiple heterogeneous liquid-liquid reactions.
Chem. Eng. Process. 39 521-537.
(Chapter 2 of this thesis)
B.A.A. van Woezik and K.R. Westerterp, 2000. Runaway behavior and
thermally safe operation of multiple liquid-liquid reactions in the semi-batch
reactor. The nitric acid oxidation of 2-octanol. Accepted for publication in
Chem. Eng. Process.
(Chapter 3 of this thesis)
162
Levensloop
Bob van Woezik is op 6 januari 1969 geboren te Nijmegen. Na de lagere school
bezocht hij de Dukenburg College te Nijmegen waar hij in juni 1986 het
H.A.V.O. diploma behaalde en vervolgens in juni 1988 het V.W.O. diploma.
In augustus van datzelfde jaar begon hij met de studie Chemische Technologie
aan de Universiteit Twente. De propaedeuse werd in augustus 1989 behaald.
Gedurende de opleiding werd een jaar aan extra keuzevakken gevolgd en in april
1994 sloot hij het theoretische deel van deze opleiding af met een onderzoek
binnen de vakgroep Industriële Processen en Produkten naar de invloed van
procesparameters op het bedrijven van een omkeerreactor.
In de zomerperiode beëindigde hij de opleiding met een stage bij de
cementfabriek Adelaide Brighton Cement Ltd. te Angaston, Australië. Hier
onderzocht hij de mogelijkheid om de agglomeraatvorming te regelen en te
controleren aan de hand van geluidsniveaumetingen.
Vervolgens trad hij in december 1994 in dienst als medewerker onderzoek,
vanaf maart 1995 als onderzoeker in opleiding in dienst van het NWO, en vanaf
januari 1997 als assistent in opleiding, bij de vakgroep Industriële Processen en
Produkten. Onder leiding van Prof.dr.ir. K.R.Westerterp heeft hij het in dit
proefschrift beschreven onderzoek verricht. Tegelijkertijd volgde hij de
postdoctorale Ontwerpersopleiding Procestechnologie tot procesontwikkelaar,
waarvan hij het diploma ontving. Sinds 1 november 1999 is hij werkzaam als
procestechnoloog bij Akzo Nobel Functional Chemicals, locatie Herkenbosch.
163
ISBN 90 - 365 14878