proyecto de panesso

Chemical Engineering and Processing 41 (2001) 59–77

Runaway behavior and thermally safe operation of multipleliquid–liquid reactions in the semi-batch reactor

The nitric acid oxidation of 2-octanol

B.A.A. van Woezik, K.R. Westerterp *Chemical Reaction Engineering Laboratories, Department of Chemical Engineering, Twente Uni�ersity of Technology, P.O. Box 217,

7500 AE Enschede, The Netherlands

Received 2 August 2000; received in revised form 27 December 2000; accepted 27 December 2000

Abstract

The thermal runaway behavior of an exothermic, heterogeneous, multiple reaction system has been studied in a cooledsemi-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 reactiontowards acids takes place accompanied by a temperature runaway. An experimental set-up was build, containing a 1-l glassreactor, followed by a thermal characterization of the equipment. The operation conditions, e.g. dosing time and coolanttemperature, to achieve a high yield under safe conditions are studied and discussed. The reaction conditions should rapidly leadto the maximum yield of intermediate product 2-octanone under safe conditions and stopped at the optimum reaction time. Theappropriate 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 reactortemperature will always be maintained between well-known limits. The boundary diagram of Steensma and Westerterp [1990] forsingle reactions can be used to determine the dosing time and coolant temperature required for safe execution of the desiredreaction. For suppression of the undesired reaction, it led to too optimistic coolant temperatures. © 2002 Elsevier Science B.V.All rights reserved.

Keywords: Semi-batch reactor; Liquid-liquid reaction; Nitric acid oxidation; Multiple reaction; Runaway; Safe operation

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1. Introduction

To reduce the risk associated with exothermic chemi-cal reactions, in a semi-batch operation, one of thereactants is fed gradually to control the heat generationby chemical reaction. In practice, the added compoundis not immediately consumed and will partly accumu-late in the reactor. The amount accumulated is a directmeasure for the hazard potential. A definition of acritical value of accumulation, to discern between safeand unsafe conditions, may be rather arbitrary. From asafety point of view, an accurate selection of operation

and design parameters is required to obtain the mini-mum accumulation.

Hugo and Steinbach [1] started investigations on thesafe operation of semi-batch reactors for homogeneousreaction systems. Steensma and Westerterp [2,3] studiedsemi-batch reactors for heterogeneous liquid-liquid re-actions. They demonstrated that it is important toobtain a smooth and stable temperature profile in thereactor. These authors dealt with single reactions. How-ever, many problems of runaway reactions encounteredin practice are caused by multiple and more complexreaction systems.

The usual objective is to suppress side reactions,whose rates are negligible at initial conditions but maybecome significant at higher temperatures, see e.g.Hugo et al. [4], Koufopanos et al. [5], Serra et al. [6]. Inthese works, a maximum allowable temperature is

* Corresponding author. Tel.: +31-53-48922879; fax: +31-53-4894738.

E-mail address: [email protected] (K.R.Westerterp).

0255-2701/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S 0 2 5 5 -2701 (01 )00106 -4

B.A.A. �an Woezik, K.R. Westerterp / Chemical Engineering and Processing 41 (2002) 59–7760

defined as the temperature, where decomposition orsecondary reactions are not yet initialized. Limiting thetemperature increase is usually very effective in sup-pressing side reactions. It is a rather conservative ap-proach, but necessary to obtain an inherently safeprocess, see e.g. Stoessel [7,8]. No work has been pub-lished on safe operation of exothermic multiple reac-tions in which, an unwanted reaction is kept in handand partially is allowed to take place.

To prevent a runaway, we have to operate outsideregions of high sensitivity of the maximum reactortemperature towards the coolant temperature. In caseof a multiple reaction system, complications arise andone has to discern between the heat production rates ofthe different reactions, see e.g. Eigenberger and Schuler[9]. The extension of the theory of temperature sensitiv-ity to multiple, more complex, kinetic schemes is notobvious; the interaction of parameters in a multiplereaction system makes the development of an unam-biguous criterion impossible. Each reaction networkrequires an individual approach and the optimum tem-perature strongly depends on the kinetic and thermalparameters of all the reactions involved.

The present work focuses on the thermal dynamics ofa semi-batch reactor, in which multiple exothermicliquid– liquid reactions are carried out. The runawaybehavior has been experimentally studied for the nitricacid oxidation of 2-octanol to 2-octanone, and furtheroxidation products like carboxylic acids. The kinetics ofthese reactions have been discussed in an earlier article,see van Woezik and Westerterp [10]. It will further beevaluated, whether the mathematical model as devel-oped by Steensma and Westerterp [2] is sufficientlyaccurate to predict the reactor behavior and to stop thereaction at the appropriate moment in time.

2. Nitric acid oxidation in a semi-batch reactor

The nitric acid oxidation of 2-octanol to 2-octanoneand the further oxidation of 2-octanone to carboxylicacids have been studied by van Woezik and Westerterp[10]. The reaction system was found to be suitable tostudy the thermal behavior of a semi-batch reactor inwhich, slow multiple liquid-liquid reactions are carriedout. The oxidation reaction system will be describedhere briefly.

2.1. Reaction system

The oxidation of 2-octanol takes place in a two-phasereaction system: a liquid organic phase, which initiallycontains 2-octanol, is in contact with an aqueous nitricacid phase in which the reactions takes place. Thereaction system with simultaneous mass transfer andchemical reaction is represented with Fig. 1.

Fig. 1. Schematic representation of mass transfer with chemicalreaction during the oxidation with nitric acid of 2-octanol to 2-oc-tanon and carboxylic acids.

The oxidation of 2-octanol (A) to 2-octanone (P) andfurther oxidation products (X) can be described withthe following reaction equations:

A+B�rnol

P+2B (1)

P+B �rnone

X (2)

where B is the nitrosonium ion, which also causes anautocatalytic behavior. The reaction rates in the acidphase can be expressed on the basis of a second orderreaction:

rnol=knolmACA,OrgCB,Aq(1−�d) (3)

rnone=knonempCP,OrgCB,Aq(1−�d) (4)

where CA,Org, CP,Org and CB,Aq are the bulk concentra-tions of 2-octanol (A), 2-octanone (P) and nitrosoniumion (B) in the organic phase (Org) and Aqueous phase(Aq), respectively. The kinetic constants knol and knone

can be described with:

k=k� exp�

−E

RT− (mH0H0)

�(5)

where k�, E/R and mH0 are the pre-exponential factor,the activation temperature and the Hammett’s reactionrate coefficient, respectively. H0 is Hammett’s acidity

Fig. 2. Hammett’s acidity function H0 as a function of the nitric acidsolution concentration.

B.A.A. �an Woezik, K.R. Westerterp / Chemical Engineering and Processing 41 (2002) 59–77 61

Table 1Kinetic parameters and reaction heats for the nitric acid oxidation of2-octanol and 2-octanone, respectivelya

Parameter

m3/kmol/s1×105mA k�,nol

Enol/R 11 300 K–6.6mHo,nol

160×106�Hnol J/kmolm3/kmol/smP k�,none 1×1010

K12 000Enone/R2.2mH0,none –

�Hnone J/kmol520×106

a Taken from van Woezik and Westerterp [10].

CA,Org�nA

Vdos1�=

(�−�P−�X)nA1

Vdos1�(6)

CB,Aq�nB

Vr0

=(�P+�B0)nA1

Vr0

(7)

CP,Org�nP

Vdos1�=

�PnA1

Vdos1�(8)

CX,Org�nX

Vdos1�=

�XnA1

Vdos1�(9)

CN,Aq�nN

Vr0

=nN0− (�B0+�P+2�X)nA1

Vr0

(10)

The dimensionless time � is obtained by dividing thetime t by the dosing time tdos, and after dosing iscompleted �=1. Vdos1� is the volume of the dispersed,organic phase. The initial concentrations at �=0 of2-octanol CA,Org, 2-octanone CP,Org and carboxylic acidsCX,Org, respectively, are equal to zero. The reaction willonly start after addition of an initiator. The initiatorwill produce the initial concentration of nitrosoniumion: CB0,Aq=nB0/Vr0=�B0nA1/Vr0 . The addition of ini-tiator will consume a small amount of nitric acid equalto �B0nA1. Thus the yield �P starts at zero at the start ofthe reaction, reaches a maximum and after that de-creases. At the end of the secondary reaction �P is againequal to zero.

Due to the low solubilities, we can neglect theamount of the organic components A, P and X presentin the aqueous phase and assume for the macroscopicmass balance that CA,Aq=0, CP,Aq=0 and CX,Aq=0.The mass balances for the oxidations have been derivedby substitution of the concentrations Eqs. (6)– (8) andusing the reaction rates Eqs. (3) and (4), see vanWoezik and Westerterp [10]:

d�P

d�=mAknoltdosCA,dos(�−�P−�X)

�P+�B0

�−

d�X

d�(11)

d�X

d�=mPknonetdosCA,dos(�P)

�P+�B0

�(12)

where CA,dos is the concentration of reactant 2-octanolin the feed as dosed to the reactor vessel. The initialboundary conditions will be discussed later.

Steensma and Westerterp [2] have derived the basicequations and definitions describing the thermal phe-nomena in a cooled semi-batch reactor, in which asingle liquid– liquid reaction is carried out. Their ex-pression for the heat balance has been written in a moregeneral way and can easily be extended to multiplereactions and take into account the additional heatsources like agitation, etc.:

dTr

dt=

1�tot

(QR+Qdos+Qcool+Qstir+Q�) (13)

where �tot is the total heat capacity of the system, beingthe sum of the heat capacities of the reaction mixture

function, see Rochester [11]. The value of H0 is plottedas a function of the nitric acid concentration in Fig. 2.The values of the kinetic constants and the heat effectsare listed in Table 1, see also van Woezik and Westert-erp [10].

2.2. Mathematical model

The reaction will be executed in an indirectly cooledSBR in which aqueous nitric acid is present right fromthe start and the organic component 2-octanol (A)added at a constant feed rate until a desired molar ratioof the reactants has been reached. The 2-octanol reactsto 2-octanone and to carboxylic acids. The heat ofreaction is removed by a coolant, which flows throughan internal coil and/or an external jacket. The tempera-ture in the reactor and the concentrations of the reac-tants and products as a function of time can be foundby solving the heat and mass balances over the reactor,using the appropriate initial conditions.

In the model for the semi-batch reactor considered inthis work, it is assumed that the following conditionsholds:� 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 notoccur.

� No change in the volume of the separate phases.� A low mutual solubility of the reactants.

2.2.1. Mass and energy balancesThe yields of 2-octanone �P and of carboxylic acids

�X, respectively, are defined on the basis of the totalamount of 2-octanol fed nA1, see notation, and can beused to obtain dimensionless concentrations of thecomponents in Eqs. (1) and (2) and of the nitric acidconcentration CN,Aq:


mCp and the effective heat capacity �eff, which consistsof the heat capacities of the devices wetted and the heatcapacity of the reactor wall. The different heat flowsincluded are the QR: chemical reaction heat, Qdos: heatinput due to reactant addition, Qcool: heat exchangedwith the coolant, Qstir: heat supplied by the agitator,and Q�: heat exchanged with the surroundings. Theheat released by chemical reaction is the sum of theheat released by the oxidation of 2-octanol, Qnol, and2-octanone, Qnone, respectively, and can be written as:

QR=Qnol+Qnone

=nA1

tdos

�d�P

d�+

d�X

d�

��Hnol+

nA1

tdos

d�X

d��Hnone (14)

where the dimensionless conversion rates d�P/d� andd�X/d� are taken from the mass balances, Eqs. (11) and(12).

During a semi-batch process the added mass is notnecessarily at the same temperature as the reactor andso contributes to cooling or heating of the reactantmass. In that case this temperature difference must betaken into account in the energy balance.

Qdos=��,dos(�CP)dos(Tdos−Tr) (15)

where ��,dos is the volumetric flow rate of the feeddosed into the reactor. The heat exchanged with theheat transfer fluid can be expressed with:

Qcool=UAcool(Tcool−Tr) (16)

where UAcool is the product of the effective heat trans-fer coefficient and the area of the cooling jacket orcooling coil. UAcool usually depends on the volume ofthe reaction mixture.

The power introduced by the stirrer can be correlatedin the turbulent flow regime by:

Qstir=Po�disN3D stir

5 (17)

In reactor used the power number Po is constant andequal to Po=4.6. The importance of the amount ofheat exchanged with the surroundings increases withthe temperature difference between the system and thesurroundings, the heat flow can be expressed with:

Q�=UA�(T�−Tr) (18)

where T� the ambient temperature and UA� is theeffective heat transfer per unit of temperature differencefor heat losses of the reactor.

The main contribution to the heat removal rate fromthe reactor is the cooling by the coolant. The coolingcan also be expressed as a dimensionless cooling inten-sity, which is equivalent to U*Da/�, as defined bySteensma and Westerterp [2]:

U*Da�

=� UA

�CPVr

�0

tdos

�(19)

in which (UA/�CPVr)0−1 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 tobe determined experimentally for the reactor configura-tion used. This will be discussed in a following section.The mass balances Eqs. (11) and (12) together with theheat balance Eq. (13) have to be solved simultaneously.The resulting temperature profile can be compared witha target temperature as defined by Steensma and West-erterp [2].

2.2.2. Target temperatureAnalogously to Steensma and Westerterp [2] a target

temperature can be defined as the steady-state tempera-ture for an well-ignited reaction:

Ttarget=Tcool+1.05(QR+Qdos+Qstir+Q�)

UAcool

(20)

The target temperature is the temperature that will beattained in the reactor, in case the reaction is infinitelyfast and the reactant added is immediately consumed.This is usually not the case and one has to allow forsome accumulation of the dosed reactant in the reactor.Therefore, the factor 1.05 is introduced into Eq. (20).

In our case the heat released by chemical reaction isthe sum of the heats released by the oxidation of2-octanol Qnol and of 2-octanone Qnone. For 2-octanoneas the only product, we can calculate the heat flow bychemical reaction QR when we assume the reaction isinfinitely fast. Under such conditions the rate of forma-tion is equal to the dosing rate, because the consump-tion rate of the ketone is equal to zero. Thus theconversion rate d�P/d� is equal to unity throughout thesupply period until dosing is stopped at �=1 and,because no carboxylic acids are formed, d�X/d�=0.The heat flow by the chemical reaction QR becomes inthis case:

Qnol=nA1

tdos

�Hnol (21)

In case only the carboxylic acids are produced, hencefor d�P/d�=0 and d�X/d�=1, the heat flow by chemi-cal reaction is equal to:

Qnol+Qnone=nA1

tdos

(�Hnol+�Hnone) (22)

For the oxidations two target temperatures can bedefined: one for 2-octanone and one for the carboxylicacids. To this end we substitute Eqs. (21) and (22),respectively, in Eq. (20). In this way two pre-definedtarget temperature profiles are obtained, which can beused to evaluate the reaction temperature.

The temperature and concentration versus time profi-les of the nitric acid oxidation of 2-octanol can becalculated when the mass balances Eqs. (11) and (12)


and the heat balance Eq. (13) are solved simultaneouslyusing a fifth order Runge–Kutta’s method with anadaptive step size control. The division by � in Eqs.(11) and (12) with �=0 can be solved numerically aftersubstitution of � plus a very small number equal to10−15: �=�+10−15. The initial boundary conditionsfor these differential equations are: �P0=0, �X0=0 and�B0=0.035 at �=0 and Tr=T0=Tcool at �=0. Theinitial concentration of nitrosonium ion has been set at�B0=0.035 to compensate for the autocatalytic behav-ior, whereby it is necessary to have some of the reactionproduct nitrosonium ion present directly at the start.The value of �B0 has been chosen by van Woezik andWesterterp [10] in such a way that a good agreementbetween the initial reaction rates as experimentally de-termined and the calculated ones is obtained. The exactvalue of �B0 has a strong influence on the calculatedresults, in case the initial reaction rate is very low. Inthis work, we use rather long dosing times and operateat high temperatures, hence the initial reaction rate islarge and will be less sensitive towards �B0.

The characteristic behavior of the nitric acid oxida-tion of 2-octanol will be explained in the followingsection using the results of simulations. For the simula-tions, a small industrial reactor has been chosen. In thisway, the characteristics will be pointed out for the nitricacid oxidation carried out in an industrial reactor. Thereactor, having a total volume of Vr=3 m3, is equippedwith a cooling jacket for the heat transfer. The jackethas a total surface area Acool of 7.5 m2 with U=400W/m2/K. The parameters as listed in Table 2 are used.In the second part of the paper, the model will beadapted to a laboratory reactor and it will be provedthat the simulation covers the experimental data well.

3. Thermal behavior of the nitric acid oxidation of2-octanol, simulations

To give insight into the reaction behavior of thenitric acid oxidation of 2-octanol, it is assumed that thereaction is executed in a SBR and only the coolanttemperature, which is the most important control vari-able, is varied. Three typical reaction regimes can bedistinguished with increasing operation temperatures:

Fig. 3. Reaction behavior in case of oxidation of 2-octanol to2-octanone under conditions that the target line of 2-octanone isapproached: (A) reactor temperature; (B) heat production rates; and(C) molar amounts. Simulation of an isoperibolic semi-batch experi-ment with a coolant temperature of −12°C and an initial load of1500 l of 60 wt.% HNO3. Addition of 600 l of 2-octanol in a dosingtime of 10 h.

1. Oxidation of 2-octanol to 2-octanone.2. Simultaneously the reaction of 2-octanol to 2-oc-

tanone and the further oxidation of 2-octanone tocarboxylic acids.

3. Oxidation of 2-octanol to carboxylic acids.The calculated temperature profile, heat production

rates and molar amounts as a function of time areshown in Figs. 3–5.1. Production of 2-octanone

At a low coolant temperature and for the chosenfurther operating conditions, mainly 2-octanone isformed, see Fig. 3. The reaction has a good start,followed by a period of a practically constant reac-tion temperature. The reactor temperature curveapproaches the target temperature of 2-octanone,

Table 2Process and equipment parameters of the oxidation reaction carriedout in a small industrial reactor having a total volume of Vr=3 m3

and equipped with a cooling jacket for the heat transfer

Parameter Parameter

1.5UAcool,0 (kW/K) UAcool,1 (kW/K) 2.11.5Vr0 (m3) 2.1Vr1 (m3)

�0 (J/K) �Cp,dos (J/m3/K) 2.0×1065.4 106

3.8NA1 (kmol)10tdos (h)


Ttarget,2-octanone, and the yield of 2-octanone is high.This type of profile is called a QFS profile-with aQuick onset, Fair conversion and Smooth tempera-ture profile-by Steensma and Westerterp [2]. Thechosen regime is usually the optimal operating regimefor semi-batch processes. One can observe that in Fig.3 the maximum concentration of 2-octanone, wherethe reaction has to be stopped, has not yet beenreached. In practice the coolant temperature wouldbe increased as soon as the reactor temperaturebecomes lower than Ttarget,2-octanone.

The reactor operation as depicted in Fig. 3 mayappear reasonably safe. There is no temperaturejump, no sudden conversion of 2-octanol and no largeaccumulation of 2-octanol. However, a large quantityof 2-octanone accumulates, which creates a potentialfor extra heat production as it can be further oxidizedby nitric acid. This can be seen in Fig. 4.

Fig. 5. Reaction behavior as in Fig. 3, but a coolant temperature of30°C. The target line of carboxylic acids is approached.

Fig. 4. Reaction behavior as in Fig. 3, but a coolant temperature of−5°C. The target line is undesirable exceeded.

2. Transition of the oxidation reactionsAs the temperature is increased also the simulta-

neous production of carboxylic acids takes place. Theconditions in this case are critical so that, after a goodstart of the first reaction, they lead to a temperaturerunaway: the target temperatures of 2-octanone andof the carboxylic acids are both undesirably exceeded.During such an experiment larger amounts of 2-oc-tanone accumulate in the reactor before the sec-ondary reaction is triggered. The produced2-octanone is then very rapidly consumed by furtheroxidation reactions. The heat of reaction of thesecondary reaction is liberated in a short timeresulting in a large temperature peak. The heatproduction rate then decreases, as the concentrationof the reactants has dropped to a low level, whilethe heat removal rate by cooling is still


high due to the high temperature difference betweenthe reaction mixture and the coolant, so the reactortemperature decreases rapidly. When the reactiontemperature decreases the heat production rates ofboth reactions decrease very fast and, hence, thereaction rates. This is due not only to the influenceof the temperature, but above all to influence of theacid strength on the reaction rates. The nitric acidconcentration decreases in this case from 60 to 45wt.%, which corresponds to H0= −3.38 and−2.68, respectively, see Fig. 2. This lowers thekinetic constant knol, see Eq. (5), with a factor 100.Thus, the reaction is practically extinguished.

3. Production of carboxylic acidsWhen the temperature is further increased, practi-

cally no 2-octanone accumulates during the wholereaction period, it reacts away immediately to acids.The system again behaves as a single reaction, inwhich 2-octanol reacts to carboxylic acids and againone can observe a good start of the reaction with asmooth temperature profile, see Fig. 5. Such a situa-tion is thermally safe but is undesirable, because ahigh yield of 2-octanone is desired. Also in this casethe strong influence of the nitric acid is visible. Atthe moment dosing is stopped the nitric acid con-centration is only 40 wt.%, i.e. H0= −2.39, andagain, the reaction rate is drastically reduced.

The nitric acid oxidation of 2-octanol can beinterpreted as a reaction system with two mainreactions in which 2-octanone is produced at lowtemperatures and carboxylic acids at high tempera-tures. At very low and at very high temperatures,the system behaves as if only a single reactionoccurs. The intermediate region is of interest be-cause there runaways may occur, as is demonstratedin Fig. 4, but also reaction rates are high, so alsoreactor capacity is high and still high yields of theketone must be feasible.

3.1. Sudden reaction transition

The temperature profiles, as shown in Figs. 3–5, arethe result of operating the SBR under such conditionsthat production shifts from producing 2-octanone, Fig.3, to producing carboxylic acids, Fig. 5, via a largeundesired temperature overshoot as a result of thesudden reaction transition, Fig. 4. This will take place,in case the operator only increases the coolant tempera-ture, keeping all other conditions constant.

For a series of simulations with a dosing time of 10h, i.e. U*Da/�=25, the temperature profiles are plottedas (Tr−Tcool) as a function of time, in Fig. 6A. In thisfigure, the (Tr−Tcool) goes through a maximum as thecoolant temperature increases.

The temperature overshoot as a function of coolanttemperature can best be visualized when the maximumtemperature obtained in the reactor is plotted as afunction of the coolant temperature. A typical exampleis shown in Fig. 6B. At a very low coolant temperature,we observe a region of insufficient ignition. Under theseconditions the reactor temperature does not approachthe target temperature for 2-octanone. The reactionrate is much lower than the dosing rate, the reactoroperates as a batch reactor and a long time is needed tocomplete the reaction, so dosing has no use.

At a somewhat higher coolant temperature the maxi-mum temperature and the yield of 2-octanone increase.The conversion rate of the alcohol is close to the dosing

Fig. 6. Transition of the reactions accompanied by a large tempera-ture overshoot. Simulation of isoperibolic semi-batch experimentswith the parameter values from Table 2 and U*Da/�=25. (A)Temperature profiles as a function of time, Tcool= −10, 0, 10 and30°C, respectively. (B) Maximum temperature of the reactor as afunction of the coolant temperature. (C) Maximum molar amount of2-octanone as a function of the coolant temperature, together withthe corresponding molar amount of carboxylic acids and the reactiontime, when the reaction is stopped.


rate and only a small amount of 2-octanol will accumu-late. The semi-batch process now operates under QFSconditions and 2-octanone is produced. The coolanttemperature is in this case lower than the coolanttemperature that leads to a temperature runaway.

At −6°C, we can observe a sharp increase in themaximum temperature. At this temperature also car-boxylic acids are produced and a temperature runawayoccurs.

Further increasing the coolant temperature results inearlier ignition of the further oxidation to acids. Themaximum temperature is lower and is reached at anearlier stage. At very high Tcool, the maximum tempera-ture approaches the target temperature for the car-boxylic acids and the oxidation can be regarded as asingle reaction, but the undesired one.

The nitric acid oxidation of 2-octanol and 2-octanoneis a consecutive reaction system in which the intermedi-ate product 2-octanone is the one desired. Thus, theyield of 2-octanone reaches a maximum and after acertain reaction time all 2-octanol has been converted,while 2-octanone is still being converted into the unde-sired carboxylic acids. In order to obtain a high yield of2-octanone the reaction should be stopped as soon asthe concentration of 2-octanone has reached its maxi-mum value. This can be done for this heterogeneousreaction system by stopping the stirrer, so that thedispersion separates and the interfacial area becomes sosmall that the reaction rate is practically negligible, orby diluting the nitric acid with water, which also effec-tively reduces the reaction rate.

The necessary reaction time to reach the maximumyield of 2-octanone depends on the reactor tempera-ture. The conversion rate of 2-octanol increases withincreasing temperature and as a result the location ofthe maximum yield of 2-octanone in the conversion-time profile shifts towards shorter reaction times. Themaximum yield of 2-octanone and the necessary time toreach it are shown in Fig. 6C as a function of thecoolant temperature together with the amount of car-boxylic acids formed.

When the coolant temperature is increased the timeto obtain the maximum yield of 2-octanone decreases,which increases the reactor capacity. On the other handthe amount of carboxylic acids increases, which leads toloss of raw materials. The time until the maximumincreases just before the runaway reaction is triggered,which can be attributed to the large amount of car-boxylic acids formed during the dosing period. Conse-quently, more nitric acid is consumed and reaction ratedecreases. At a coolant temperature of higher than−6°C, one can also observe a sharp decrease in themaximum yield of 2-octanone together with a rapidreduction of the reaction time. At higher coolant tem-peratures, the maximum yield of 2-octanone is obtainedbefore the dosing is stopped, which of course, is anundesired situation.

Fig. 7. Simulation of isoperibolic semi-batch experiments as in Fig. 6with the parameter values from Table 2, but a dosing time of 20 h,U*Da/�=50 and Tcool= −15, −5, 3 and 30°C, respectively.

3.2. Gradual reaction transition

The use of a longer dosing time may reduce or evenavoid an undesired temperature overshoot. To this endthe dosing time is doubled, compared with the condi-tions in Fig. 6, and the value of U*Da/� increases from25 to 50. In Fig. 7A, the temperature profiles areplotted, as (Tr−Tcool) as a function of time for thiscase and, again, only the coolant temperature is varied.

The maximum temperature as a function of thecoolant temperature is shown in Fig. 7B for the case ofa gradual reaction transition; the production shiftsfrom producing 2-octanone to producing carboxylicacids, while the maximum temperature increases onlymoderately. For this series with a dosing time of 20 h,no temperature overshoot takes place. The consecutivereaction has a heat of reaction 3.25 times that of themain, desired reaction. Therefore, there will always be a


region where the maximum temperature is more sensi-tive towards the coolant temperature, when the produc-tion of 2-octanone shifts to the production ofcarboxylic acids, in this case between −10 and 10°C.The maximum in Tmax has disappeared in Fig. 7; norunaway occurs anymore. During the transition, thereactor temperature is always limited between the targettemperature of 2-octanone and the target temperatureof the carboxylic acids. This we call invariably safe asno sudden temperature jump occurs for any coolanttemperature chosen. However, the reaction is not inher-ently safe because, for example in case of coolingfailure, further oxidation reactions will be triggered.

The maximum yield of 2-octanone, the amount ofcarboxylic acids and the necessary time to reach themaximum are for this case shown in Fig. 7C as afunction of the coolant temperature: for higher coolanttemperatures the maximum yield of 2-octanone and thetime to obtain the maximum yield decrease gradually.At a high coolant temperature, only carboxylic acidsare produced.

Due to the plant economics, one must achieve a highyield of 2-octanone in a short time under safe condi-tions. For a time tidle for filling, emptying and cleaningof the reactor, the productivity is (�p·nA,1/Vr,1)/(treac+tidle). For the two dosing times, the productivities areplotted in Fig. 8, as well as the relative loss of rawmaterial defined as the amount of raw material Aconverted into X per unit of P produced. For a coolanttemperature below Tcool= −15°C, the maximum yieldof 2-octanone is obtained a long time after the dosinghas been stopped. For this low coolant temperature ahigh yield is obtained and it is for both U*Da/�=25and 50 equal to �p=90%. Thus, for a high yield bothdosing times give similar productivities. A larger dosingtime makes the process invariably safe, while the totaltime for reaction is not much longer, so for this case thelonger dosing period of tdos=20 h must berecommended.

Fig. 9. Boundary diagram for a slow reaction in the continuous phasefor U*Da/�=5, 10 and 20, respectively. From Steensma and Westert-erp [12].

The most economical operating conditions dependon numerous parameters, and should be determined foreach individual case.

4. Recognition of a dangerous state

In the oxidation of 2-octanol, one focuses on the firstreaction because high yields of ketone are required,while the danger of a runaway reaction must be at-tributed to the ignition of the secondary reaction. Thereaction system can be considered as two single reac-tions and, therefore, the boundary diagram developedby Steensma and Westerterp [2] for single reactionsmay be helpful to estimate critical conditions for themultiple reaction system. Their boundary diagram for aslow reaction in the continuous phase is given in Fig. 9.The area enclosed by the boundary lines is whereoverheating i.e. a runaway will occur and, therefore, itshould be avoided. For reaction conditions locatedbelow the boundary area the reaction does not ignite.The discontinuous line in Fig. 9 is the route through thediagram, if only the coolant temperature is increased.The insufficiently ignited reaction will, in that case, firstchange into a runaway reaction and eventually becomea QFS reaction when the coolant temperature is furtherincreased. The coolant temperature should, therefore,preferably be chosen such that: (1) the oxidation of2-octanol to 2-octanone is a QFS reaction; and (2) thesecondary reaction remains insufficiently ignited.

When Ex�Exmin, no runaway will take place for anycoolant temperature. In that case, at higher values ofthe reactivity number, the reaction will be a QFSreaction. The minimum exothermicity number Exmin

corresponds to the invariably safe operation as dis-cussed in the earlier paragraph.

Later on, the experimental results will used to verifywhether the boundary diagram as developed bySteensma and Westerterp [2] is sufficiently accurate topredict the reactor behavior of a multiple reactionsystem.

Fig. 8. Productivity and raw material loss as a function of the coolanttemperature for the oxidation of 2-octanol carried out in a semi-batchreactor with dosing times of 10 and 20 h, respectively. Furtherparameter values taken from Table 2.


5. Experimental set-up and procedure

The experimental set-up is shown in Fig. 10. Thereactor (1) is a jacketed 1-l glass vessel of the type HWSMainz. The glass reactor has a diameter of 0.10 m. andis equipped with four equally spaced stainless steelbaffles with a width of 10 mm. The reactor content isagitated by a stainless steel turbine stirrer with a diame-ter of 36 mm and six blades of 7.4×9.4 mm2 each. Thestirrer is driven by a Janke and Kunkel motor and itsspeed is kept constant at 1000 rpm.

The reactor is operated in the semi-batch mode witha constant coolant temperature. To study the influenceof different heat transfer coefficients, two separate cool-ing circuits are used — one via the cooling jacket andone via a cooling coil. The coolant is pumped from acryostat (2) of the type Julabo FP50 through the cool-ing jacket by a Pompe Caster gear pump or through thecooling coil by a Verder gear pump. The coil consists oftubes made of stainless steel with a diameter of 6 mmand wall thickness of 1 mm. The reactor is initiallyloaded with 0.5 l of 60 wt.% HNO3-solution. Before theexperiment is started, a small amount of 0.12 g NaNO2

is added as initiator. When the temperature of thereactor has become constant, the feeding of pure 2-oc-tanol is started. The supply vessel has been located ona balance of the type Mettler pm1200 (3) to measurethe mass of the feed. The organic compound is fed tothe reactor by a Verder gear pump (4) with a constantfeed rate in the range of 0.03–0.33 kg/h. The nitric acidand the organic solutions are immiscible and form adispersion in the reactor, provided the mixing rates arehigh. The nitric acid is taken in excess and forms thecontinuous phase during the whole experiment. Before

an experiment is started, the equipment is flushed withN2. During the oxidation NOX-gases are formed, whichare allowed to escape through a hole in the reactor lidtowards a scrubber (5), where they are washed withwater. After an amount of 0.16 kg 2-octanol has beenadded, the dosing is stopped manually. After that theexperiment is continued till at least t=2 tdos. Theexperiment is then brought to an end by heating up thereactor contents, so that the remaining reactants areconverted to carboxylic acids.

The temperatures of the reaction mixture, coolantinlet and outlet, feed and surroundings are measured bythermocouples. The temperatures and the feed massflow rate are monitored and stored by a Data Acquisi-tion and Control Unit in combination with a computerof the type HP486-25 of Hewlett Packard. When thereactor temperature exceeds a certain unacceptablevalue, the computer in an emergency procedure acti-vates actuators to open: (a) the valve in the reactorbottom to dump the reactor content and quench it onice in a container (6) and (b) The valve on the reactorlid to dump an amount of 0.5 l water into the reactorfrom the container (7). During an experiment, samplesof the dispersion are taken manually via a syringe.Approximately five samples are taken during each run.In the syringe, the dispersion separates immediately intwo phases; both phases are analyzed. The nitric acidconcentration in the aqueous phase is determined bytitration and the organic phase is analyzed by gaschromatography, see van Woezik and Westerterp [10].

An example run is shown in Fig. 11, with the temper-atures as measured and the number of moles of thecompounds as determined via the chemical analysis.

Fig. 10. Simplified flowsheet of experimental set-up. Ti, temperature indictor. See text for further details.


Fig. 11. Isoperibolic semi-batch experiment with jacket and spiralcooling at 10°C with an initial load of 0.5 l of 60 wt.% HNO3 and0.12 g NaNO2. Addition of 0.2 l of 2-octanol in a dosing time of 42min. (A) Measured temperatures of the feed, ambient, reactor con-tents, cooling spiral and cooling jacket. (B) Molar amounts asfunction of time of the nitric acid in the aqueous phase and of2-octanol, 2-octanone and carboxylic acids, respectively, in the or-ganic phase.

5.1.2. UAThe product of the overall heat transfer coefficient

and the cooling area UAcool of the cooling jacket andcooling coil are determined by introducing an amountof energy with a cartridge heater of the type Superwatt7310 put into the reaction mixture. A heat flow ofapproximately Qelement�10 W is adequate. The coolingcircuit removes the heat and the temperature of thereaction mixture and coolant are measured as a func-tion of time: a steady state will be reached as soon asthe heat production rate by the electrical heater is equalto the heat flow to the coolant Qcool. Under theseconditions the temperature difference between the reac-tion mixture and cooling medium (Tr−Tcool) can beused to determine the value of UAcool according to:

UAcool=Qelement

(Tr−Tcool)(24)

UAcool has been determined for different volumes ofdispersion in the reactor and increases linearly with thevolume dosed.

5.1.3. Heat losses to the surroundingsA good estimate can be obtained by introducing a

known amount of energy with the electrical heater intothe reaction mixture without cooling. The heat input isset at approximately Qelement�5 W and the tempera-ture of the reaction mixture Tr and of the surroundingsT� are measured as a function of time. The tempera-ture of the reaction mixture will increase until a steadystate is reached, where the heat production rate equalsthe heat flow to the surroundings Q�. This leads to:

UA�=Q�

(T�−Tr)=

Qelement

(T�−Tr)(25)

5.1.4. Power input by stirringThe power supplied by stirring can be determined by

measuring the torque transmitted by the shaft. If this isnot possible the power generated can be estimated bycalorimetric measurements with only heat transfer tothe surroundings. When the stirrer is the only powerinput source and UA� has been determined as de-scribed earlier, it is possible to calculate the powerinput in the steady state:

Qstir=Po�disN3D stir5 =Q�=UA�(Tr−T�) (26)

Typical values of the various parameters are listed inTable 3 for the different cooling configurations.

The thermal characterization was first carried outwith the reactor containing only water. The results wereused to describe experiments in which hot water isadded semi-batch-wise to cold water initially in thereactor. During such an experiment the temperature ofthe reactor contents will increase during the dosing andafter that, it will be brought back by the cooling to the

5.1. Thermal characterization of equipment

To describe the thermal dynamics of the reactorset-up a proper equipment characterization is necessary,see also Barcons [13]. It is carried out by determiningheat capacities and heat flows as enumerated in Eq. (13)as follows.

5.1.1. Thermal capacitiesThe effective heat capacity �eff involves the heat

capacities of the vessel wall and inserts, like the coolingcoil, baffles, and stirrer; it is determined by a rapidaddition to the reactor vessel of an amount of hot waterof a temperature Tw,0 and a mass m and measure thetemperature of the liquid phase as a function of time.The temperature of the added water will decrease fromTw,0 to T1 and heat-up the system from Tr,0 to T1. Thetotal heat capacity �tot follows from:

�tot=�eff+ (mCP)w=(mCP)w(Tw,0−T1)

(T1−Tr,0)+ (mCP)w

(23)


Table 3Thermal characteristics of the experimental set-up as obtained by determining the heat capacities and heat flows as enumerated in Eq. (13)

Jacket cooling Spiral cooling Jacket and spiral cooling Jacket and spiral coolinga

380�eff (J/K) 380380 3808.8 13.1 13.5UAcool,0 (W/K) 4.3

11.8 17.25.4 18.2UAcool,1 (W/K)0.1UA� (W/K) 0.3b 0.1 0.1

Po (−) 4.64.6 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.

initial value. For a series of experiments the tempera-ture profiles are plotted in Fig. 12: the experimental andsimulated profiles show a good agreement. The thermalcharacterization is adequate. Then UA values weredetermined with nitric acid and with dispersions ofnitric acid and final organic reaction product. Theresults of the thermal characterization as listed in Table3, should be sufficiently accurate to simulate the heateffects in our reactor.

5.2. Check on the �alidity of the model for slowreactions

The mass balances for the oxidations, Eqs. (11) and(12), have been derived by assuming the rate of masstransfer is not enhanced by reaction, and the reactionmainly proceeds in the bulk of the reaction phase. Thishas to be validated for the current reactor set-up andthe applied experimental conditions. For such situa-tions, we must check that Ha�0.3 holds, see Westert-erp et al. [14], where the Hatta number Ha is defined as:

Ha=�kDi CB,Aq

kL

(27)

The mass transfer coefficients kL,Aq for 2-octanol and2-octanone in the continuous, aqueous phase is typi-cally kL,Aq=40·10−6 m/s, which has been discussed inmore detail by van Woezik and Westerterp [10,15]. Thisvalue is larger than the value reported by Chapman etal. [16]. They found experimentally kL=10.3·10−6 m/sfor toluene in a HNO3/H2SO4 solution with an acidstrength of 76%. The acid strength used in the presentwork is much lower and, therefore, at the lower viscos-ity a larger value of the mass transfer coefficient isfound. The Hatta number for the oxidation of 2-oc-tanone is always below 0.3, for the whole experimentalrange. The calculated Hatta numbers for the oxidationof 2-octanol indicate that this is also the case as long asthe temperature is below 40°C as Ha�0.3. This in-cludes the temperature range for high yields of 2-octanone.

Furthermore, we can neglect the mass transfer resis-tance in the organic phase, as the solubility of theorganic compounds in the nitric acid solution is low

and the mass transfer coefficients are of the same orderof magnitude, see van Woezik and Westerterp [10].

If the conversion rate for a liquid– liquid reaction isnot influenced by a mass transfer resistance, it shouldbe independent of the stirring rate. The influence of thestirring rate on the conversion rate has been experimen-tally determined in the temperature range of 10–60°Cat 720, 1000 and 1400 rpm. The maximum heat produc-tion rate is plotted against the stirring speed in Fig. 13and is independent of the stirring speed. For the chosenstirring rate of 1000 rpm in our experiments masstransfer resistance 1/kLa does not play a role. Visuallyit can be observed that above N=600 rpm the mixturebecomes well dispersed.

6. Experimental results

6.1. Temperature profiles

The nitric acid oxidation of 2-octanol has been exper-imentally studied under isoperibolic conditions i.e. witha constant coolant temperature, at different values ofthe coolant temperature. The semi-batch reactor is ini-tially charged with 0.5 l of a 60 wt.% HNO3 solution,after that 0.2 l of 2-octanol is added at ambient temper-ature, in all experiments. First, a series of semi-batchexperiments has been carried out with a constant feed

Fig. 12. Experimental (continuous lines) and simulated (dashed lines)temperature profiles for verifying the thermal characterization. Addi-tion of 0.25 l water with Tdos�60°C in a dosing time of 75, 225 and475 s, respectively, to an initial reactor load of 0.5 l water of 10.8°C.


Fig. 13. Maximum heat production rate versus stirring speed forsemi-batch experiments at a temperature of 15, 30 and 60°C. Reactorinitial loaded with 0.7 kg 60 wt.% HNO3 and 0.12 g NaNO2.Addition of 0.16 kg of 2-octanol in a dosing time of 42 min.

ature overshoot. For a higher cooling capacity —U*Da/�=65 — in Fig. 14B the transition is gradualand no sudden temperature jumps can be observed.

6.2. Thermally safe operation of the nitric acidoxidation of 2-octanol

The objective is to produce 2-octanone with a highyield and under safe conditions. To this end the nitricacid oxidation of 2-octanol is experimentally studiedtogether with the region of a high yield of 2-octanone.

6.2.1. Influence of dosing timeIncreasing dosing time makes it possible to spread

the produced heat of reaction over a longer period oftime and should, therefore, reduce or avoid temperatureovershoots. A series of experiments has been carriedout at different coolant temperatures with dosing timesof 60, 135 and 170 min, respectively, which is equiva-lent to U*Da/� values of 21, 48 and 61. The maximumtemperature obtained during a run is plotted versus thecoolant temperature in Fig. 15A.

Increasing U*Da/� from 21 to 48 effectively reducesthe temperature overshoot, which even disappears forU*Da/�=61. Thus, for a long dosing time an increasein coolant temperature leads to a gradual transition ofthe reactions and no runaway occurs anymore for anycoolant temperature chosen; the process is invariablysafe.

The calculated maximum yield of 2-octanone, to-gether with the corresponding reaction time are givenas a function of coolant temperature for U*Da/� of 21and 61, respectively, in Fig. 15B and C together withsome experimentally determined values. Due to a lim-ited amount of sampling data points it is for mostexperiments impossible to determine the value of themaximum yield exactly, nevertheless the agreement be-tween the calculations and experiments is good.

When the dosing time is increased threefold from 60to 170 min, we may observe for the same high yield,thus at low coolant temperatures, that the total reactiontime increases with about 2 h, meanwhile, the processhas become invariably safe.

6.2.2. Influence of cooling capacityWith larger UA/Vr values the temperature effects are

moderated and the reaction becomes more isothermal.A reactor equipped with both a cooling jacket and acooling coil can be operated with either one or the twosystems simultaneously. This enables us to operate thereactor with three different cooling capacities. A seriesof experiments has been carried out at different coolanttemperatures and different UA-values and a dosingtime of 60 min, which are equivalent to U*Da/� valuesof 21, 44 and 65. The same typical behavior of themaximum temperature is found, as in the case of

rate during 1 h and with cooling only via the coolingjacket. Second, a series of experiments has been exe-cuted with both cooling jacket and cooling coil in use.The temperature profiles are shown in Fig. 14, a goodagreement between the experimental and simulated val-ues can be observed, except for high temperatures. Forthe reaction system the upper temperature limit is ap-proximately 90°C, where the mixture starts to boil.

In Fig. 14A the temperature profiles are shown forexperiments with U*Da/�=21 whereby, as a result ofincreasing coolant temperature, the transition to theconsecutive reaction is accompanied by a large temper-

Fig. 14. Experimental (continuous lines) and simulated (dashed lines)temperature profiles of isoperibolic semi-batch experiments with aninitial load of 0.5 l of 60 wt.% HNO3 and 0.12 g NaNO2. Addition of0.2 l of 2-octanol in a dosing time of 60 min with (A) U*Da/�=21,the transition of the reaction is accompanied by a large temperatureovershoot; and (B) U*Da/�=65, a gradual temperature increase.


Fig. 15. Influence of the dosing time on (A) the maximum tempera-ture; (B) the yield of 2-octanone; and (C) the reaction time asfunction of the coolant temperature. Experimental (dots) and simu-lated (lines) isoperibolic semi-batch experiments with an initial loadof 0.5 l of 60 wt.% HNO3 and 0.12 g NaNO2. Addition of 0.2 l of2-octanol in a dosing time of 60 (�), 135 (�) and 170 (�) min,which is equivalent to U*Da/� values of 21, 48 and 61.

For this example, in which U*Da/� is increased from 21to 65 by increasing the UA-values, for the same highyield the total reaction time is shortened by about 3 hand at the same time the process has become invariablysafe. These high effective heat transfer coefficients areusually not feasible for reactors of a large size andconsequently one has to accept longer reaction times.

A series of experiments has been carried out withdifferent cooling configurations, while a dosing time hasbeen chosen in such way that the U*Da/�-values arethe same. The values are tabulated in Table 4. For theseseries the maximum temperature obtained during a runis plotted in Fig. 17A, as a function of the coolant

Fig. 16. Influence of the cooling capacity UA/Vr on (A) the maximumtemperature; (B) the yield of 2-octanone; and (C) the reaction time asfunction of the coolant temperature. Experimental (dots) and simu-lated (lines) isoperibolic semi-batch experiments with an initial loadof 0.5 l of 60 wt.% HNO3 and 0.12 g NaNO2. Addition of 0.2 l of2-octanol in a dosing time of 1 h and UA0’s of 4.3 (�), 8.8 (�) and13.1 (�) W/K respectively, which is equivalent to U*Da/� values of21, 44 and 65.

change in the dosing time, see Fig. 16A. The readershould be aware that for U*Da/�=21 and coolanttemperatures above 8°C, the maximum yield is reachedeven before the dosing has been completed. In thisrunaway situation, the reactor temperatures become sohigh that the secondary reaction starts to dominate thereaction process.

The maximum yield of 2-octanone and the corre-sponding reaction time are plotted in Fig. 16B and C,respectively. The influence of the cooling capacity onthe total reaction time follows from comparing theyield. For example, a maximum yield of 90% is ob-tained in a shorter reaction time when the reaction iscarried out in a reactor with a larger cooling capacity.


Table 4Sets of the dosing time tdos and cooling capacity UA/Vr with aconstant value of U*Da/� as used for the experimental series

U*Da/� (−)(UA)0 (W/K) tdos (s)

4.3 8100 48448.8 360046252013.1

Table 5Experimental and calculated minimum dosing time for differentcooling capacities UA/Vr to achieve invariably safe operation

(UA/�CpVr)0 (h−1) tdos,min experimentaltdos,min simulations (h)(h)

2.88.2 2.11.016.8 �1

25.0 0.7 0.7

temperature. Above a coolant temperature of 5°C, onecan observe a region where the transition of the reac-tion products takes place. When the coolant tempera-ture is increased, the resulting maximum temperatureapproaches the target temperature of 2-octanone, forall series, as QFS of 2-octanone is reached. Finally,above a coolant temperature of 40°C, for all series thesame maximum temperature is obtained: that of the

target temperature of the carboxylic acids as QFS ofthe carboxylic acids is reached. Thus, for U*Da/��46,the reactor temperature is always limited between thetarget temperature of 2-octanone and the target temper-ature of the carboxylic acids and the process can beconsidered as invariably safe.

The maximum yield of 2-octanone and the time toobtain this maximum are plotted in Fig. 17B and C,respectively. For the same maximum yield and the samevalues of U*Da/�, an increase in tdos leads to an in-creasing reaction time, whereas an increase in UA0

leads to a reduction of the reaction time.

6.2.3. In�ariably safe operationThe 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/�, that isfor a long dosing time tdos or a large cooling capacityUA/Vr, as has been shown. When this is one of theconditions to be fulfilled the minimum dosing timetdos,min should be found that just meets this require-ment. It can be determined experimentally by carryingout experiments with different coolant temperaturesand different dosing times. This demands much experi-mental effort. First a dosing time was chosen and aseries of experiments was carried out with differentcoolant temperatures. When one of the experiments ledto a runaway a second series was carried out with alonger dosing time. This was repeated, until the dosingtime was found that led to invariably safe operation.This has been done for the different cooling capacitiesof our reactor set-up. The resulting minimum dosingtimes tdos,min are tabulated in Table 5 and plotted inFig. 18. The process is invariably safe for U*Da/��45.As can be seen in Fig. 18, the experimental and simu-lated results are in reasonable agreement in predictingthe boundary region. This region is very critical, as it isvery sensitive towards small changes. The experimentaland calculated results suggest that scale-up can bedone, for a given cooling capacity of the reactor, byselecting the minimum dosing time from Fig. 18. Con-sequently, a few laboratory-scale experiments should beenough to establish conditions for a large-scale reactorto achieve an invariably safe operation.

Fig. 17. Comparison of different dosing times with U*Da/��46 forthe same data as Fig. 16, but dosing times of 135, 60 and 42 min,respectively.


7. Prediction of safe operation based on the individualreactions

Now the boundary diagram developed by Steensmaand Westerterp [2] will be used to estimate the QFSconditions of the oxidation of 2-octanol to 2-octanone,as well as the critical conditions at which the furtheroxidation reaction will be triggered.

7.1. Prediction of QFS conditions for the oxidation of2-octanol to 2-octanone

In case 2-octanone is produced with a high yield, thereaction is: A+B�P+2B. This reaction is consideredas a slow single reaction in the continuous phase. Theboundary diagram can be used to determine the coolanttemperature at which QFS conditions are obtained.This will be explained with the oxidation of 2-octanolas an example. To obtain a value of U*Da/�=20 for areactor initially loaded with HNO3 and UA0=4.3 W/K, a dosing time has to be chosen equal to tdos=0.93 h,which can be compared with the experiments withU*Da/�=21 in Fig. 15.

The required coolant temperature can be found afteriteration. For Tcool=272 K one can calculate theexothermicity number to be Ex=2.0. The correspond-ing reactivity number, for QFS conditions, can be readfrom Fig. 9: Ry=0.02. The coolant temperature Tcool

follows from the definition for Ry, see notation, pro-vided the other initial reaction conditions are known.After rewriting we obtain:

Tcool=E/R

(−mH0H0− ln(Ry(�RH+U*Da)/CB0tdosmk�))(28)

The initial concentration of nitrosonium ion has beenset at �B0=0.035, thus CB0=nA1 �B0/V0=0.088 M. So,for the oxidation of 2-octanol and the relevant parame-ters as listed in Table 1 and 6 it follows that QFSconditions will be obtained for Tcool�272 K. Theoxidation of 2-octanol was experimentally found to be

under QFS conditions for a coolant temperature ofTcool�268 K, see Fig. 15, which is close to the calcu-lated value.

7.2. Prediction of runaway conditions for the oxidationof 2-octanone

Now we have to verify that the unwanted reactionwill not be triggered as a result of the first reaction.When the conversion to 2-octanone is complete and nocarboxylic acids are formed, we obtain: CB0=nA1·�B0/V0=2.46 M and the acid strength of the nitric acid willdrop to a value of H0= −2.86. With a coolant temper-ature of Tcool=272 K for the first reaction, a maximumtemperature of Tmax=285 K is found experimentally,see Fig. 15. Using these conditions as initial conditionsfor the oxidation of 2-octanone, we can calculate that:Ex=6.35 and Ry=0.003. When this is compared withthe boundary diagram with U*Da/�=20 in Fig. 9, it islocated in the area of insufficient ignition. Thus, thefurther oxidation reaction will not be triggered forTcool=272 K, which was also experimentally found.

The critical coolant temperature, for the same experi-mental series, at which the runaway reaction of thesecond reaction is just not triggered is Tcool=281 K,see Fig. 15. The maximum temperature obtained by thefirst reaction is in that case T=303 K. In the boundarydiagram the critical coolant temperature will be the onewhere the insufficient ignition changes to a runawaycondition. Using the same conditions as above, we findthe runaway to be triggered for Ex=5.1, Ry=0.008and Tcool�318 K, while experimentally a runawayreaction was already triggered for T=303 K. Thisdangerous overestimation of Tcool, using the boundarydiagram for single second order reactions, is the resultof treating the oxidation reactions as two single inde-pendent reactions. The reaction to the carboxylic acidscan only start when the intermediate reaction product2-octanone has been formed. Thus, the second oxida-tion step strongly depends on the first one, whichmakes it difficult to determine the exact starting condi-tion for the further oxidation reaction.

7.3. Prediction of in�ariably safe operation conditionsusing Exmin

The boundary diagram can also be used to determinethe minimum dosing time tdos,min, which leads to invari-ably safe operation. This corresponds to the minimumexothermicity number Exmin. Exmin can be read fromthe boundary diagram for a single reaction in thecontinuous phase in Fig. 9 and is equal to Exmin=4.3,6 and 8.6 for U*Da/�=20, 10 and 5, respectively. Forthe oxidation of 2-octanone one can calculate, using therelevant parameters as listed in Table 1 and Table 6,�Tad0=354 K, �=0.4 and RH=0.57. For Tcool=20°C

Fig. 18. Boundary line for invariably safe operation of the nitric acidoxidation of 2-octanol for U*Da/�=45. Results of the simulations(solid line) and the experimentally determined points.


Table 6Relevant parameters of reaction system at T=25°C with a 60 wt.%HNO3 solution as initial load and pure 2-octanol as feed

Initial reactor load Feed

� (kg/m3)1360 817� (kg/m3)CP0 (J/kg/K)CP0 (J/kg/K) 25232660nA1 (mol)−3.42 1.23H0 (−)

V0 (m3) 0.5×10−3 Vdos1 (m3) 0.2×10−3

The reaction conditions should rapidly lead to themaximum yield of 2-octanone under safe conditionsand stopped at the optimum reaction time.

The process can be regarded as invariably safe whenno runaway takes place for any coolant temperature.This is possible for a large value of U*Da/�, and hencea long dosing time or a large cooling capacity, whicheffectively moderates the temperature effects. For theoxidation of 2-octanol to 2-octanone and carboxylicacids the process is invariably safe for U*Da/��45.Under such conditions, the reactor temperature is al-ways limited between pre-defined known temperaturelimits. These predefined temperatures are based on thetarget temperature developed by Steensma and Westert-erp [2] and can be successfully applied in case of amultiple reaction.

The conditions leading to invariably safe operationcorrespond with the minimum exothermicity numberExmin. The value for Exmin can be derived from theboundary diagram of Steensma and Westerterp [2]. Forthe oxidation of 2-octanone and using the boundarydiagram a minimum exothermicity number of Exmin=2.8 and U*Da/��47, the process was found to beinvariably safe. Experimentally a value of U*Da/��45was found.

For a single reaction the conditions leading to QFSconditions and to thermal runaway can be extractedfrom the boundary diagram. The coolant temperatureleading to a QFS condition for the oxidation of 2-oc-tanol to 2-octanone as predicted in the boundary dia-gram agrees with the experimental result.

However, it is not possible to predict with sufficientaccuracy the conditions leading to a runaway of thesecondary oxidation reaction. This reaction can onlystart when the intermediate reaction product 2-oc-tanone has been formed. Regretfully, it is difficult todetermine the exact starting conditions for the furtheroxidation reaction, which is necessary for an accurateestimation.

The reaction conditions should rapidly lead to themaximum yield of 2-octanone under safe conditionsand stopped at the optimum reaction time. The mathe-matical model as developed by Steensma and Westert-erp [2], and extended in this work to a multiple reactionsystem, can be used to predict the reactor behavior andthe moment to stop the reaction. The most economicaloperation condition depends on a number of parame-ters and must be determined for each specific case.

Acknowledgements

These investigations were supported by the Nether-lands Foundation for Chemical Research (SON) withthe financial aid from the Netherlands TechnologyFoundation (STW). The authors wish to thank A.B.

we can calculate Ex=6.0, 11.7 and 18.4 for U*Da/�=20, 10 and 5, respectively, which now can be comparedwith the Exmin-values taken from Fig. 9. This is done inFig. 19. When U*Da/� is increased the exothermicityEx decreases faster than Exmin and consequently thereexist a point where Ex=Exmin and hence tdos equalstdos,min. In this case, we find Exmin=2.8 and for U*Da/��47 no runaway will take place for any coolanttemperature and the process has become invariablysafe. This value can be compared with U*Da/��45,which was found experimentally.

8. Discussion and conclusions

The nitric acid oxidation of 2-octanol has been stud-ied experimentally in a 1-l glass reactor. The reactionrates of the oxidation reactions as experimentally deter-mined and modeled by van Woezik and Westerterp [10]have been successfully applied to simulate the experi-ments and a satisfactory agreement has been obtainedbetween experiments and calculations.

Thermally safe operation of a semi-batch reactorusually implies that under normal operating conditionsa runaway is avoided. To this end one has to avoidaccumulation of the dosed reactant in the reactionphase. However, in case the intermediate is the requiredproduct, accumulation of the reactant for the consecu-tive reaction necessarily occurs. So for the second reac-tion, conditions must be such that the reaction will notoccur at all or at least remains insufficiently ignited.

Fig. 19. Exothermicity number Ex for the oxidation of 2-octanone tocarboxylic acids as a function of U*Da/� to determine the minimumexothermicity number Exmin.


Wonink and S.J. Metz for their contribution to theexperimental work, M.T. van Os and A.B. Kleijn fortheir contribution to the preliminary calculations andfurther F. ter Borg, K. van Bree and G.J.M. Monninkfor the technical support.

Appendix A. Nomenclature

Interfacial area per volume of reactorAcontent=6�d/d32(m2/m3)

A Surface area (m2)C Concentration (kmol/m3)CP Specific heat capacity (J/Kg/K)

Diameter (m)DDiffusivity coefficient of component iDI

(m2/s)d32 Sauter mean drop diameter (m)E Energy of activation (J/kmol)H0 Hammett’s acidity function (−)

Hatta number (−)HaMass transfer coefficient in the aqueouskL

phase (m/s)Second-order reaction rate constantk, knol, knon

e (m3/kmol/s)k� Preexponential constant (m3/kmol·s)mi Molar distribution coefficient of com-

ponent i=Ci,Aq/Ci,Org (−)M Mass (kg)

Hammett’s reaction rate coefficient (−)mH0

Number of moles (kmol)nN Stirring rate (s−1)

Heat flow (W)QGas constant=8315 (J/kmol/K)R

RH Heat capacity ratio= (�CP)= (�CP)dos/(�CP)0 (−)Rate of reaction per volume of reactorrcontent (kmol/m3/s)Time (s)tDosing time (s)tdos

tdos,min Minimum dosing time (s)Temperature (K)TOverall heat transfer coefficientU(W/m2/K)

V Volume (m3)

Greek symbols�H Heat of reaction (J/kmol)�Tad0 adiabatic temperature rise=�HnA1/

(�CpVr)0 (K)Volume fraction of dispersed phase=�d

Vdos1/(Vdos1+V0) (−)Relative volume increase at end of dos-�

ing=Vdos1/V0 (−)

Flow (m3/s)�v

Heat capacity (J/K)�

� Density (kg/m3)Dimensionless time= t/tdos (−)�

�I Yield of component i=ni/nA1 (−)�B0 Initial concentration of nitrosonium

ion=0.035 (−)

Dimensionless groupsExothermicity number, ((�Tad,0E/R)/ExT cool

2 )(1/(�RH+U*Da)) (−)Reactivity number, CB0tdosmk�exp−(E/RyRT0−mH0H0)/(�RH+U*Da) (−)

Po Power number, Q/�disN3D stir

5 (−)Cooling number, (UA/�CPVr)tdos (−)U*Da

Subscripts and superscripts0, 1 Initial, final (after dosing is completed)A Component A (2-octanol)

Aqueous phase (nitric acid solution)AqB Component B (nitrosonium ion)

CoolantCoolDispersionDisDosingDosElectrical heater elementElement

I Component iComponent N (nitric acid)NReaction of 2-octanol, see Eq. (1)nol

none Reaction of 2-octanone, see Eq. (2)Organic phaseOrgComponent P (2-octanone)PReactionRReactorrStirringStirTotalTotWaterWComponent X (carboxylic acids)XAmbient�

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