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REVIEW PAPER

SAFETY AND RUNAWAY PREVENTION IN BATCHAND SEMIBATCH REACTORS—A REVIEW

K. R. WESTERTERP1 and E. J. MOLGA2Ã1 Ramon Llull University, Institut Quimic de Sarria , Barcelona, Spain

2Warsaw University of Technology, Chemical and Process Engineering Department, Warsaw, Poland

In this paper a review of recent developments on safety and runaway prevention in batchand semibatch reactors is given. To prevent thermal runaways in chemical reactorsusually three lines of defense have to be considered: choice of the right operating con-

ditions, early warning detection system and system to handle running away reactions. Becauseof its too specific nature, the last line of defense is not discussed in this review, while theformer two are considered in detail. Firstly the capability and applicability of the reactioncalorimeter for safety assessments are reviewed, then fundamental safety criteria for safeoperation of batch and semibatch reactors are reported and discussed. A review of the mostuseful and efficient methods for a correct choice of safe operating conditions is split intotwo cases: one, when the reaction kinetics are known, and when kinetic information is notavailable. Also several promising recent developments of an early warning detectionsystem for the on-line detection of unexpected situations leading to a thermal runaway arepresented.

Keywords: safety of chemical reactors; criteria of thermal runaway; reaction calorimetry;early warning detection of runaway; batch and semibatch reactors.

INTRODUCTION

In this paper we will review the developments in the last25 years in the study of safety and runaway prevention of batch and semi-batch reactors. We will do so from theview point of the science of reaction engineering and there-fore, we will leave a number of relevant studies untouchedthat belong to the fields of chemistry, mechanical engineer-ing and/or organizational sciences. In Table 1 we give stat-istical data on the prime causes of batch reactor incidents asthey have been reported in three different studies (Verwijs,

1994). We can observe that at least more than 60% of theincidents could probably be avoided, if a proper design of the reactor plant and choice of the safe operating conditionshas been performed. The number of incidents per monthseems to increase in time according to Table 1, this is notthe case in reality: the numbers of reports and methods of reporting have increased and improved very much overthe period from 1960 to 1990. We may feel that anumber of two incidents per month for a few thousandsof reactors considered in the surveys leads to a rathersmall percentage of incidents. However, more than 80%

of the reactions executed daily do not have a heat effectlarge enough to cause a runaway, so that the chance of arunaway, nevertheless, is not hypothetical.

To prevent reactor incidents and runaways in generalthree lines of defense have to be considered in the designand operation of a (semi-)batch reactor. The first line of defense is the choice of the right operating conditions.This refers to the degree of mixing, the cooling capacity,the choice of the coolant temperature, the dosing rate of the reactant(s) and so on. In the course of the years manypapers have been written on the choice of the operating

conditions; moreover, we should realize that the studieson tubular reactors also can be translated to batch reactors.Most recommendations are based on the knowledge of thekinetics of the reaction. Regretfully batch reactors arealmost exclusively used in the fine chemicals industry,where usually time and money are serious constraints forthe costly and time-consuming study of reaction kinetics.For highly exothermic reactions the use of inaccurate kin-etic information often leads to a too prudent selection of operating conditions with low reactor productivities. Inthe last decennia the Reaction Calorimeter has becomewidely accepted as a tool for the selection of operating con-ditions, so that we will also dedicate some space to the dis-cussion of this piece of very useful laboratory equipment.

The second line of defense is an early warning detectionsystem. As is clear from Table 1, a correct choice of

ÃCorrespondence to: Professor E. J. Molga, Warsaw University of Tech-nology, Chemical and Process Engineering Department, ul. Warynskiego1, 00-645 Warsaw, Poland.E-mail: [email protected]

543

0263–8762/06/$30.00+0.00# 2006 Institution of Chemical Engineers

www.icheme.org/cherd Trans IChemE, Part A, July 2006doi: 10.1205/cherd.05221 Chemical Engineering Research and Design, 84(A7): 543– 552



operating conditions is not enough for the safe running of areactor section in the plant. Human errors like mischargingof reactants, maintenance troubles, agitator break down andso on always may occur. Therefore, it would be a god sendif we could provide industry with a piece of equipment or aprocedure, that can give an early warning to the operator toanticipate a runaway to occur within a shorter period, sayfor example, 20 to 200 min in advance of reaching themaximum runaway temperatures. In this field in the lastten years great advances have been made.

The third line of defense is a suitable system to handlerunning away reactions. Such systems depend on the reac-tants and reactions at hand. If vapors are developed, we

need a blow down system with catch tanks; or in anothercase, reactor contents must be discharged to refrigeratedcellars loaded with ice to stop the reaction by freezing. Inpractice, many different approaches can be found. We willnot discuss this aspect in this paper, because the measuresto be taken to handle a reaction mass, that is heating uptowards a runaway, are too specific for each particular case.

In this paper we will discuss first the capabilities of thereaction calorimeter, then the criteria based on known kin-etics to operate a batch reactor safely and after that themethods developed to achieve safe operation withoutknowing reaction kinetics. At the end we will dedicatesome space to the promising recent developments of anearly warning detection system.

THE REACTION CALORIMETER

The reaction calorimeter has been developed and now isin full use at almost every process development laboratoryin fine chemicals industry. In commercial applications of reaction calorimetry the operation of batch and semibatchreactions is supported in many ways apart from controlledheating and cooling, stirring and mixing, distillation andrefluxing, dosing of reactants and measurement and controlof process parameters (pressure, pH, turbidity, chemicalcontent by FTIR analysis and so on).

An extensive review of the application of the reaction

calorimetry is given in the special issue of Thermochimica Acta 289, 1996, edited by R.N. Landau. In this issue

entitled Reaction Calorimetry, in a series of contributionsthe expanding role of reaction calorimetry is demonstratedand its theoretical principles, methods of modelling aswell as areas of application are indicated and widelydiscussed—see a.o. Landau (1996), Rowe (1996) andZaldivar et al. (1996). Following Landau (1996), threebasic areas of application of reaction calorimetry can be

distinguished: Process Safety, Process Development and Basic Research. All of them contribute significantly tothe evaluation of safety aspects of batch and semibatchreactors by thermal and kinetic analysis of chemical reac-tions. In a more recent review by Zogg et al. (2004), themost important calorimetric principles are presented anddiscussed—including heat flow, heat balance, powercompensation and the Peltier principle—as well as aclassification and a comparison of the available reactioncalorimeters. Among numerous relevant papers on thecontribution of reaction calorimetry to safe operation of chemical reactors, e.g., the following publications shouldbe mentioned: Ubrich et al. (2001) and Gesthuisen et al.

(2005). A few commercial applications of standard heat-flow reaction calorimeters are available on the market forboth laboratory and research purposes. To avoid promotingany particular producer the reader is referred to the paperscited above as well as to the webpage HarsNet (HarsBook).

In principle each heat-flow reaction calorimetermeasures the heat evolution with time of a reaction underisothermal, isoperibolic or adiabatic conditions. A sche-matic diagram of a typical bench-scale reactor is shownin Figure 1.

The principles of reaction calorimetry are based on thedetermination of mass and energy balances carried outover the reaction vessel. In the general case—taking intoaccount the behaviour of a semi-batch reactor, even with

evaporation of solvent or reactants—the molar balancefor each reactant in the reacting mixture has to be formu-lated, including the molar flow rates due to evaporationand refluxing of certain components. Their flow rateshave to be determined from a heat balance around the con-denser as well as from a mass balance around the refluxcollector (see Figure 1).

The reaction heat-flow rate qR(t ) can be found easilyusing only temperatures measured inside the reactor andin the coolant jacket. Values of parameters such as theoverall heat transfer coefficient U and the specific heatcapacity of the reaction mixture C P, can be determined ina separate series of calibration experiments.

An accurate estimation of heat flow through the reactorwall is essential for this type of reaction calorimeters andcan be found from the following relationship:

qflow ¼ UA T R À T Að Þ (1)

where T A is a corrected jacket temperature, T c, to take intoaccount the heat capacity of reactor walls (Zaldivar et al.,1996; Molga, 1997).

Having determined the power generated due to the reac-tion progress, qR(t ), the total heat effect, QT, can be calcu-lated as well as the reaction enthalpy:

D H A ¼ QTDnA

¼ Ð t F

0 qR(t )dt DnA

(2)

Table 1. Prime causes of batch reactor incidents (Verwijs, 1994).

1962–1984 1962–1987 1986–1990

ReferencesÃ

Incident causeNolan and

Barton (1987)Barton and

Nolan (1989) Etchells (1993)

Thermo-reactionchemistry

21.4% 20.1% 14.8%

Raw material quality 7.9% 8.9% 9.8%Maintenance/other

factors22.3% 21.3% 22.2%

Temperature control 22.2% 18.9% 13.9%Loss of

mixing/agitation9.5% 10.1% 13.1%

Mischarging of reactants

16.7% 20.7% 26.2%

Incident rate(#/month)

0.46 0.54 2.03

ÃData obtained from Health and Safety Executive records (HSE, UK).

Trans IChemE, Part A, Chemical Engineering Research and Design, 2006, 84(A7): 543–552

544 WESTERTERP and MOLGA



Then, for a single reaction, the conversion rate of the com-pound A can be estimated as a function of the reactiontime:

RA t ð Þ ¼ qR t ð ÞD H A

(3)

and further the conversion of the compound A as:

X A t ð Þ ¼Ð

t 0

qR t ð Þdt

QT

(4)

Based on the mass balance and the stoichiometric reactionequation as well as using the conversion rate, the concen-tration of the ith reactant in the reacting mixture can befound as a function of the reaction time.

So, based on data for the reaction rate and the reactant con-centrations, both as a function of time, the reaction kineticscan be studied and the safety of the process can be analysed.As can be seen from equations (2)–(4), even with a singlerun the reaction enthalpy can be determined, while by carry-ing out the reaction at isothermal conditions at least at two

different temperatures, the activation energy can beobtained. So, with the reaction calorimeter the parametersD H R, E , DT ad and C p, required for process safety assessment,can be estimated. They can be directly used for safe design-ing of the reactor performance on an industrial scale.

Apart from the references mentioned before in thissection, some other representative examples of practicalapplications of reaction calorimetry are listed below.They have been here arbitrarily grouped according to thecategories proposed by Landau (1996), although all of them can be directly related to safety of processes:

. Process Safety (Zaldivar et al., 1992; Schuler andSchmidt, 1992; Regenass, 1997a, b; Serra et al., 1997;

Lerena et al., 1996; De Filippis et al., 2002; Molgaet al., 2004).

. Process Development (Schmidt and Reichert, 1988; amEnde et al., 1996; Ferguson and Puga, 1997; Erwinet al., 2001; Clark et al., 2001).

. Basic Research (Nomen et al., 1997; Stoessel, 1997;Singh, 1997; LeBlond et al., 1996; Ubrich et al., 1999;Nogent and Le Tacon, 2002).

CRITERIA FOR SAFE OPERATION AND RUNAWAY

PREVENTION OF (SEMI-)BATCH REACTORS, BASEDON KNOWN KINETICS

Runaway prevention has drawn the attention of chemicalengineers for many decennia. We refer to the early work of Semenov and others already before the Second World War,specially in the field of combustion engineering, and also tothe work of Barkelew (1959). He demonstrated that for firstorder reactions in a batch reactor the reactor remains ther-mally stable provided the temperature difference betweencoolant and reacting mixture is not higher than:T R À T c RT 2c =E .

Provided this condition is fulfilled a runaway will notoccur. Later Van Welsenaere and Froment (1970) demon-

strated this also holds for a temperature difference smallerthan RT R

2 / E and that an even somewhat higher (T R2 T c)can be applied without a runaway. In the period under con-sideration Balakotaiah et al. (1995) demonstrated that theabove criterion must be corrected for the heat taken upby the mass of the reactor vessel. They introduced theratio of the heat capacity of the reactor vessel and its con-tents compared to that of the reactor mixture only andcalled this arbitrarily a Lewis number

Le ¼ ðmcpÞR

ðmcpÞf

¼ 1 þ ðm cpÞw

ðm cpÞf

This factor, called also thermal inertia, had been used ear-lier—e.g. see the paper by Townsend and Tou (1980),

Figure 1. Schematic diagram of a typical bench-scale (semi-)batch reactor or a reaction calorimeter: 1—basic unit containing reactor control and regulationsystems, 2—reactor vessel with jacket, head assembly and stirrer, 3—dosing pumps, 4—electronic weights, 5—computer for controlling the system andacquisition of data, 6—cryostat, 7—distillation and reflux set.


SAFETY AND RUNAWAY PREVENTION 545



where its influence on runaway trajectories as well as onthermal stability is also discussed. So, the acceptable adia-batic temperature rise for the batch wise executed reactioncan be a factor Le higher. In practice it is difficult to esti-mate the value of Le: for instance the agitator will havethe same temperature as the reaction mixture, but thewall of the reactor not so, because it will have a tempera-

ture somewhere in between T R and T c. These authors con-sidered a well mixed batch reactor with a homogeneous,single and irreversible, exothermic reaction A ! B, witha rate given by r ¼ k (T )cn

A. Assuming that the reactionheat generated is removed only by cooling, they gave thefollowing operation equation, which can be easily derivedfrom the set of general mass and heat balance equationsafter introducing dimensionless variables and parameters:

Le

B

d u

dX ¼ 1 À a u À u cð Þ

B 1 À X ð Þnexp u =1 þ u =g ½ (5)

It holds for the reactant conversion 0

X , 1 and after

integration with u ¼ 0 at X ¼ 0 gives the reaction pathsin the temperature-conversion plane. Particularly usefulcan be an observation of the reactor temperature trajectoryat assumed operating conditions in relation to the adiabatictrajectory. A typical plot is shown in Figure 2.

Because in many practical cases the adiabatic tempera-ture is unacceptably high as the limiting temperature, Bala-kotaiah et al. (1995) referred to the work of Adler and Enig(1964) to have a sharp and realistic criterion for the preven-tion of runaway. At some special conditions—i.e., for u c ¼0 and g ¼ 1—the results are presented in an operating dia-gram, in which the lines separating runaway and saferegions are plotted in a plane with the coordinates a / Band B / Le (see figure 2 in the cited paper).

Heiszwolf and Fortuin (1996) executed an experimentalstudy with a first order reaction and demonstrated that thepredictions of Adler and Enig (1964) are on the dot to pre-dict for a certain set of operating and design conditions atwhat reactant concentration in the feed a runaway willoccur in a batch reactor with a homogeneous reactionmixture.

In general the batch reactor can be applied only for reac-tions with a low adiabatic temperature rise. For moreexothermic reactions the semi-batch reactor is used, inwhich one or more reactants are loaded into the reactorand the balance of the recipe items are fed with a desiredmass rate profile (usually but not always linear with time)over a defined period. Doing so, we can keep the heat evol-

ution by a very exothermic reaction in hand by the dosingrate of the second reactant.

After the Seveso incident in 1976 much research wasstarted to understand what the real cause of the runawayin a semi-batch reactor may have been. The authors Hugoand Steinbach (1985, 1986) deserve the honour for theobservation that an accumulation of the dosed componentat too low reactor temperatures is the cause of the runawayin homogeneous semi-batch reactors. They presented a linein a diagram, which separates the region with a runawayfrom the region with a smoothly operating semi-batchreactor with only a small harmless accumulation of thedosed reactant. They did so for modified Stanton numbers

of 5, 10 and 15, where this number reads asSt ¼ (U A t dos=V r cP). They also determined empiricallyfrom their calculations that—in their range of Stantonnumbers—in the boundary between the two regions theDamkohler number Da ¼ kcBo t dos must be equal to orhigher than the modified Stanton number.

In their paper Hugo and Steinbach (1986) derivedempirical relations for the operating conditions in a homo-geneous semi-batch reactor. They found that the thermal

reaction number B ¼ (E DT ad= R T 2R) must be smaller than

the limit value B ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSt þ 2G

p þ 1:2À Á2

, where G ¼ mA / mis the ratio of the mass of the reactant A to the final massof the reactor content, which represents the volumeincrease due to the dosage of the second reactant, andthat the coolant temperature must be higher than thelimit value T d, which can be found from the followingequation:

Da T dð Þ ¼ St (6)

Specially their last relation is very simple.Hugo et al. (1988) studied the danger of a runaway after

an agitator breakdown, because after a breakdown the reac-tion proceeds adiabatically. They demonstrate that the mostdangerous situation prevails if the breakdown occurs at themoment of just reaching the stoichiometric dosage of the

second reactant, because at that condition the concen-trations of the two reactants reach such values that the reac-tion rate of a second order reaction just has its highestvalue, that is the highest value of the product cA Ã cB.They found that the final temperature of the adiabatic reac-tion mixture will exhibit a minimum value as a function of the reaction temperature chosen in a particular case, pro-vided the value for B is larger than 2.

Steensma and Westerterp (1990, 1991) developed fullsafety diagrams for the same range of cooling numbersfor heterogeneous liquid–liquid semi-batch reactions andfor reactions both in the dispersed phase as well as in thecontinuous phase. They have studied slow reactions andalso fast reactions, where the mass transfer is enhanced

by the chemical reaction. They show that also for chemi-cally enhanced reactions, where the supplied reactant is

Figure 2. Temperature trajectories calculated with the operation equation[Equation (5)] according to the criterion by Balakotaiah et al. (1995). Cal-culations carried out at: Le¼ 1, B ¼ 2, n ¼ 1, u c ¼ 0, g ¼ 20 for differentvalues of dimensionless external heat transfer coefficient a.





already consumed in the film around the drops, still adangerous accumulation can occur in its own phase, caus-ing a runaway.

In their safety diagrams they plotted the Reactivity, Ry,as a function of the Exothermicity, Ex, and surroundedthe region of runaways by a boundary line. These dimen-sionless groups are defined as:

Ex ¼ DT ad,o E = R

T 2c RH þ U Ã Da=1ð Þ1 (7)

Ry ¼ (nA=nB)mDac

RH þ U Ã Da=1ð Þ1 (8)

Further regions with no accumulation, harmless reactionsand insufficient ignitions are distinguished. The boundarydiagrams (see Figure 3) depend on the value of the coolingnumber—which is similar to the modified Stanton numberof Hugo and Steinbach (1986)—and on whether the reac-tion takes place in the continuous phase or in the dispersed

phase in the reactor.Van Woezik and Westerterp (2000, 2002) publish exper-imental work on a very exothermic nitration reactionsystem with consecutive reactions and with a secondaryheat effect, which is 3.25 times higher than that of thedesired reaction. They determined very accurately the kin-etics of their consecutive reaction scheme. They also deter-mined the interfacial areas in the reactor. They concludethat the set of differential equations as used by Westerterpand coworkers to describe the behaviour of such reactorsare confirmed accurately by their experiments. For safeoperation much higher Cooling numbers are required thanin the previous work (Steensma and Westerterp, 1990,1991) and they introduce the concept of the inherently

safe operating region, in which the heat evolution is stillharmless and the accumulation of the dosed reactantremains very small (see Figure 3).

Maestri and Rota (2005a and 2005b) calculate safety dia-grams for kinetics different from those used by Hugo, Wes-terterp and coworkers. The diagrams are influenced indeedby a difference in kinetics, regretfully they do not discusswhen and where their kinetics occurs in practical semi-batch reactor operations. Hugo (1990) determined that adescription by second order reaction always gives satisfac-tory results, except for autocatalytic reactions. A special

caution about blindly applying of each safety criteria toreactions that may be autocatalytic, is very important.

SAFE OPERATION OF (SEMI-)BATCH REACTORS

WITHOUT KINETIC INFORMATION

Gygax (1988, 1990) discusses in two concise papers theavailable methods to determine the danger of runaways inbatch and semi-batch reactors and how we can use chemi-cal engineering principles to cope with these dangers.

Stoessel and Ubrich (2001) for homogeneous reactorsdemonstrate how the operation of a semi-batch reactorcan be improved by modulating the feed rate to a semi-batch reactor, proving that the reactor productivity can besharply increased. They also demonstrate how in theircase the appropriate information can be obtained with areaction calorimeter and without knowing the kinetics of the reactions involved. They illustrate their method withan example of a set of consecutive reactions.

Westerterp and Molga (2004a) demonstrate that theCooling number is the key parameter, that determines thedifference in behavior of the large scale, industrial reactorand the laboratory reactor. The Cooling number is definedas:

Co ¼ U Að Þot dos

1 V r cPð Þo

(9)

They indicate how this Co number must be determinedfor laboratory reactors as well as for industrial reactors.Further they elaborate on the concept of inherently safereactor operation and how this must be achieved in prac-tice. See Figure 3 for the indication of the inherently safe

operation region in a safety diagram for a slow liquid–liquid reaction in the continuous phase.

They determine the full range of values of Cooling num-bers for all liquid– liquid reactors of all sizes in a laboratoryor in an industrial plant. They also determine the maximumof the Exothermicity values below which, and the mini-mum values of the Reactivity above which, never a run-away can occur. They state that the necessary informationcan be obtained in a few days in a laboratory in a reactioncalorimeter, provided the calorimeter is used in thesemi-batch mode. They argue that their method forliquid–liquid reactions can be used for single as well asfor multiple reactions of any reaction scheme with the

exception of autocatalytic reactions. They also discusshow incidents like agitator breakdown can be handled with-out any danger of a runaway. The elaborated practical pro-cedure to determine the inherently safe operatingconditions in semi-batch reactors is summarized inTable 2 (Westerterp and Molga, 2004b). Westerterp andMolga (2004a) in their paper give data on the practicalvalues of the dimensionless groups of the Reactivity, theExothermicity and the Cooling numbers for both laboratoryand industrial reactors. We should realize that laboratoryreactors usually have much higher Cooling numbers thanindustrial reactors. Specially, for heterogeneous liquid–liquid and gas–liquid reactions Cooling numbers necess-arily are high in order to achieve good dispersions with

large interfacial areas. In order to simulate industrialconditions often reaction calorimeters are equipped with

Figure 3. Inherently safe operating conditions for slow reaction in the con-tinuous phase.





stirrers with low agitation speeds to reduce the Coolingnumbers. This helps indeed for homogeneous reactions,but is unacceptable for heterogeneous reactions leading tophase separations.

EARLY WARNING DETECTION SYSTEMS

As has been mentioned before, even a correct choice of reactor operating conditions does not totally protect theplant against a thermal runaway. So, apart from the off-

line activities, which help to define safe operatingconditions, also on-line prevention measures are necessaryto detect any unexpected situation leading to a runawayscenario (see Figure 4). Among others under the on-linesafety measures as listed in Figure 4, an early warningdetection system (EWDS) is indispensable to detectand evaluate unexpected dangerous situations, whichmay occur in batch and semibatch reactors e.g., due to afailure of the cooling or stirring systems or to a humanmistake.

The development of an efficient and robust EWDS forbatch and semi-batch reactors is very difficult due to thecomplexity of the processes carried out in such reactorsand their strongly nonlinear dynamics. The main problem

of a detection of dangerous situations in discontinuousreactors is the fast recognition of deviations from safe

operation, because we must provide sufficient time for theplant operator or an automatic protection system to takeappropriate protective countermeasures to stop a thermalexcursion. Such countermeasures may be a pressurerelief, full cooling or quenching (i.e., addition of inhibitoror cold inert liquid as well as dumping of the reactorcontent into a cold catch tank). At the same time toavoid false alarms, a warning system must be able to pre-cisely distinguish between dangerous and non-dangerousreactor states. So, an essential element of any EWDS isa robust safety criterion, which works on-line and ispractically independent of the actual process carried outin the reactor.

Numerous criteria for the safe operation of batch andsemibatch reactions have been developed and can befound in literature, some of them are discussed in thispaper in the sections above. The sensitivity towards theinitial and the operating parameters has been extensivelystudied—(see Varma et al. 1999)— and a new series of safety criteria based on parametric sensitivity has beendeveloped (e.g., see Morbidelli and Varma, 1986, 1988,1989; Vajda and Rabitz, 1992; Shukla and Pushpavanam,1994). Unfortunately, these criteria can not be used for anon-line early warning detection of a runaway. A detailed

discussion of the applicability of the existing safety criteriafor an early detection system can be found in a series of

Table 2. Procedure for the determination of safe operating conditions

Value (or group) determined

Method used to determine

In laboratory reactor In industrial reactor

I. The Exothermicity criterion for a single reaction

DT ad,o Measured or calculated

E Measured in reaction calorimeteror DSC

R H Calculated1 CalculatedCo Measured (cooling curve for

originally loaded batch)Measured (cooling curve for

originally loaded batch)Ex Calculated as a function of t dos, and

at realistic T cYield For Ex Exmin check for the reactor

productivity at the chosen t dos

II. The Reactivity criterion for a single reaction

Co Measured (cooling curve for batch originally loaded)T ta ¼ f (t ) Calculated Calculated

RyQFS,min Calculated Calculated

T c T c,ind - see below Eq. T1

III. Multiple reactions

See original article. The following holds:(a) for parallel reactions an apparent activation energy should be determined, then the procedure above can be directly applied;

(b) for consecutive reactions the following method should be applied:

Heat evolution curves Measured as a function of T Yield MeasuredEx For the first reaction, the second reaction or for the sum of heat effectsE 1 / E 2 EstimatedEx criterion Calculated

RyQFS criterion Calculated Calculated

T c,ind ¼ T c,lab þ RT 2c,lab

E ln

RyQFS,min

À Áind

RyQFS,minÀ Álab

" # (T1)





papers by Strozzi and Zaldivar (e.g., see Strozzi et al.,

1999; Zaldivar et al., 2003). The general conclusion arisingfrom this analysis indicates that most of the existing safetycriteria can not be directly used for an EWDS, becauseeither they work off-line or they are model-based; soexpensive and time consuming kinetic studies are required,which are seldom applied to processes carried out in batchand semi-batch reactors.

A simple on-line safety criterion has been based onmeasurements of the reactor and cooling jacket tempera-tures and some their derivatives: for the recognition of adangerous situation it is enough to check the followingexpressions (Hub and Jones, 1986):

d 2T R

dt 2 . 0 (10a)

and

d T R À T cð Þdt

. 0 (10b)

This criterion does not require any detailed information onthe process carried out in the reactor and it can be alsoapplied for the detection of thermal runaway in other equip-ment, e.g., in storage tanks. Its main disadvantage is thatthe noise, always measured in experimental signals, is

amplified and significantly affects the results of evalu-ations, so false alarms may be triggered. A very useful dis-cussion of practical tests of this method as well as theresults obtained is given by (Zaldivar, 1991b).

Strozzi and Zaldivar developed a new method for asses-sing the thermal stability of batch and semibatch chemicalreactors (e.g., see Strozzi and Zaldivar, 1994a; Strozziet al., 1994b; Alos et al., 1996a,b). In their method theLyapunov exponents were used to calculate the sensitivityand to formulate a new safety criterion. An essential advan-tage of this method, in comparison to the previous ones, isthat it can be applied for on-line runaway detection. Thiswas made possible by applying a phase-space reconstruc-tion technique and resulted in the fact that the divergence

of the system can be evaluated from the measurement of one system variable only. The background of this method

can be found in the paper by Strozzi et al. (1999), whilefurther theoretical developments as well as practical appli-cations and considerations are published in a series of papers by Strozzi, Zaldivar and their coworkers, whichreport on the results obtained in an EU funded projectAWARD (2001– 2005) (see Zbilut et al., 2002; Boschet al., 2004c; Zaldivar et al., 2005, 2003; Bosch et al.,

2004 a, b, d), respectively. Based on the results of thestudies carried out within the frame of the AWARDproject, several prototypes of an Early Warning DetectionSystem for batch and semibatch reactors have beenproduced (for details see AWARD, 2001–2005).

In the mentioned method a new runaway criterion hasbeen defined and the onset of loss of control has been ident-ified at the point where the divergence of the reactor beha-vior becomes positive on a segment of the reaction path:

div F u , X 1, X 2 Á Á Áð Þ . 0 (11)

The research group led by Strozzi and Zaldivar developed a

method to calculate the divergence on-line, using onerepresentative measurable variable of the system. Statereconstruction techniques and a theory of embeddinghave been applied for this purpose. The method based ona delayed temperature vector turned out as the mostrobust one with respect to noised experimental data, butalso pressure measurements have been successfully tested(e.g., see Bosch et al., 2004d and a). The divergence cri-terion developed has been tested and successfully validatedfor different types of reactors (batch, semibatch and CSTR),different operating modes (isothermal, isoperibolic andadiabatic) as well as for different schemes of reactionkinetics—a.o. for simple and complex (parallel, consecu-tive, mixed and equilibrium) reactions, homogenous liquid

and heterogeneous liquid–liquid reactions, polymerizationreactions and so on (see the references cited above).

Several methods employing the state reconstruction tech-nique with use of one or more temperature sensors havebeen developed and successfully tested for early detectionof runaway (see Bosch et al., 2004b; Zaldivar et al.,2005). It has been found that for all considered batch andsemi-batch runs only one temperature sensor is usually suf-ficient to reconstruct the divergence with a reasonablyaccuracy, so to detect runaway.

The developed method of runaway detection, employingonly one temperature sensor, simplifies considerably anapplication of the EWDS in industrial practice. In case of

one single temperature sensor we have to be sure that themeasured temperature is representative for the entire reac-tor, i.e., that perfect mixing has been achieved. In case of failure of the stirring system significant non-uniformitiesof temperature and reactants concentrations inside the reac-tor will occur, so a proper location of the required numberof the temperature sensors is essential. Computational fluiddynamics (CFD) have been used to investigate this EWDSmethod and to identify ‘hot-spots’ appearing in the reactionmass (see Rudniak et al., 2004; Molga et al., 2004;Milewska et al., 2005). The CFD models of stirred tank reactors for bench and industrial scale reactors and alsofor both homogeneous and heterogeneous reaction systems,enable a determination of local and instantaneous values of

reactor temperatures and reactant concentrations in badlymixed vessels.

Figure 4. Prevention measures developed to avoid situations that may leadto loss of thermal control and runaway scenario, see also Zaldivar (1991a)as well as Westerterp and Molga (2004a).





In off-line applications the results from CFD simulationscan be directly converted into a spatial map of the localdivergence of the system so, a detection of local ‘hotspots’ and their propagation into a global runaway maybe indicated. It can be particularly important for a so-called ‘computer experimentation’, during which differenttypes of failures occurring in industrial reactors can be

safely investigated. However, it must be clearly distin-guished, that for industrial reactors of complex geometrylocal CFD predictions are difficult for experimental verifi-cations, so the results of CFD simulations should be treatedas preliminary indications.

SUMMARY AND CONCLUSIONS

From statistical data, which report on the prime causes of incidents in batch and semibatch chemical reactors carryingout strongly exothermic reactions, the general conclusionarises that a thermal runaway in these reactors is still a pro-blem of great importance. So, a robust safety assessment is

always indispensable. Usually three lines of defense haveto be considered to prevent thermal runaways in chemicalreactors: choice of the right operating conditions, applicationof early warning detection system and methods to handlerunning away reactions. Because of its too specific nature,the last line of defense was not discussed in this review,while the former two have been considered in detail. Thechoice of safe or inherently safe reactor operating conditionsis usually performed in an off-line analysis. Two mainapproaches can be here distinguished: the model-basedanalysis in which a detailed knowledge of the reaction kin-etics is indispensable and the most recent approach basedon the boundary diagram, which is particularly useful forthe reacting systems with unknown reaction kinetics. In

the last approach, based on the work of Westerterp and hiscollaborators which are published in the series of citedpapers, safety boundary diagrams are employed to dis-tinguish the inherently safe operating conditions for batchand semibatch reactors with liquid and liquid–liquid react-ing systems, respectively. In these safety diagrams in aplot of the coordinates Reactivity versus Exothermicitynumbers, runaway and non-runaway regions can be easilydistinguished (see Figure 3). In these safety diagrams theboundary lines are still a function of the Cooling number.The most relevant advantage of this approach is that evenfor the case, when a detailed reaction kinetics is not know,the problem of safety assessments can be tackled in a few

days with use of the reaction calorimeter.Also the capability and applicability of the reaction calori-meter for safety assessments have been reviewed. Severalapplications, useful particularly for direct process safetyimprovement as well as for supporting assessments basedon the use of boundary diagrams, have been indicated.

Due to a failure of the cooling/stirring systems or ahuman mistake, different unexpected dangerous situations,which can lead to a runaway scenario, may occur even in areactor operated along a safe trajectory. Taking intoaccount that even a correct choice of safe operating con-ditions does not totally protect the reactor against a thermalrunaway, the recent developments of early warning detec-tion system have been reported. Such a warning detection

system makes possible an early on-line prediction of thereactor states, which may lead to the uncontrolled rise of

reactor temperature. In this area a very promising approach,developed and tested by Zaldivar, Strozzi, Westerterp andtheir collaborators, must be noticed. From this approach,initially based on the divergence criterion and then sub- jected to several modifications, a universal and robustEWDS has been developed. In these transformations thestate space reconstruction has been employed, so the detec-

tion of runaway with the developed EWDS has becomepossible by on-line measurement of one single operatingparameter such as the reactor temperature or the reactorpressure, provided the latter can be considered as a variablerepresenting the state of the reactor.

The presented review can be concluded with the follow-ing corroborations, which are particularly useful and sig-nificant for the fine chemicals industry:

. Off-line safety assessments for batch and semibatchreactors, to determine inherently safe operatingconditions, should be carried out on the basis of theboundary diagram. This approach does not demand fordetailed kinetic investigations, only a few measurements

with a laboratory reaction calorimeter are needed.. For on-line runaway detection in reactors operated

according to the state of the art, the EWDS system ela-borated by Zaldivar, Strozzi and their collaboratorsshould be employed. It is a robust early warning detec-tion system, for which only an on-line, single pointmeasurement of the reactor temperature (and/or the reac-tor pressure) is needed.

NOMENCLATURE

A heat exchange surface area, m2

B ¼ E

RT c

D HcAoV Ro

mcpÀ Áf T c

dimensionless adiabatictemperature rise

ci concentration of the ithcomponent, mol m23

cp mass specific heat capacity, J kg21

K 21

C p molar specific heat capacity, Jmol21K 21

Co Cooling number, see equation (9)for definition

Da ¼ k c cBot dos Damkohler numberE activation energy, J mol21

Ex exothermicity number, see equation(7) for definition

k reaction rate constant, m3 mol21

s21

m mass, kgm distribution coefficient (liquid–

liquid system)n number of moles, reaction orderq heat flow, WQ amount of energy, Jr reaction rate, mol m23 s21

R conversion rate, mol s21

R gas constant, J mol21 K 21

RH ¼ (r cP)d =(r cP)c ratio of heat capacities of thedispersed and the continuous phase

Ry reactivity number, see equation (8)for definition

St ¼ UAt dos=V r C p modified Stanton numbert dos dosing time, sT temperature, K

T ta ¼ T c þ 1:05DT ad,0

1 RH þ Co 1 þ 1t ð Þ½ target temperature, K

U overall heat transfer coefficient,W m22K 21





U Ã ¼ (U A)0 /(r cP V R k cB)0 dimensionless cooling capacityV volume, m3

X conversion

Greek symbols

a ¼ UA

mcPð Þf k T cð ÞcnÀ1Ao

dimensionless external heat transfercoefficient

g ¼ E = RT cdimensionless activation energy

D H reaction enthalpy, J mol21

DT ad adiabatic temperature rise, K 1 relative volume increase

u ¼ E

RT c

T À T c

Tcdimensionless temperature

n stoichiometric coefficientt ¼ t =t dos dimensionless time

Subscripts0 initialc jacket, cooling, at cooling

temperaturef fluid (liquid reactor content)F finalflow flow through the reactor wallQFS quick onset, fair conversion, smooth

temperature profileR reactor, reactionw reactor walls and inserts (stirrer and

baffles)

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The manuscript was received 30 September 2005 and accepted for publication after revision 15 February 2006.



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