No More Runaways in Fine Chemical Reactors - ACS Publications

Ind. Eng. Chem. Res. 2004, 43, 4585-4594

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No More Runaways in Fine Chemical Reactors K. Roel Westerterp*,† and Eugeniusz J. Molga‡ Institut Quimic de Sarria´ , Barcelona, Ramon Llull University, via Augusta 390, 08017 Barcelona, Spain, and Chemical and Process Engineering Department, Warsaw University of Technology, ul. Warynskiego 1, 00-645 Warsaw, Poland

In this paper after a literature surveysin which we describe previous development of the theory and the experimental work to prove the theoriesswe discuss the so-called safety diagram and practical values of the relevant parameters in laboratory and plant equipment. We explore when operating conditions are inherently safe and prove that the findings of the safety diagram also apply to batch reactors. We explain the safety diagram data can also be applied to reactions with orders different from 1 for each component and to multiple reactions. All criteria in the literature, developed to determine safe operating conditions to prevent runaway in semibatch and batch reactors, are based on the knowledge of the kinetics of the reactions concerned. In fine chemical industries, however, usually it is impossible to determine kinetics due to economic and time constraints. Previous work on so-called safety diagrams, therefore, has been extended to the full range of all practical cooling number values as they occur in plant reactor operations. From the results obtained two diagrams are presented for the minimum value of the so-called exothermicity, below which no runaway will occur, as well as for the minimum reactivity, above which no runaways are possible, both as a function of the cooling number: one diagram is for the reactions taking place in the dispersed phase, and the other is for those in the continuous phase. With these diagrams inherently safe operating conditions can be determined for high reactor productivities. It is demonstrated that the data obtained can be used also for a multiplereaction scheme, except for autocatalytic reactions. Further it is discussed how the necessary information can be obtained by reactor tests in the plant, by experiments in standard laboratory equipment, and from the literature. A rapid procedure is developed which leads to safe operating conditions without costly and time-consuming kinetic studies. 1. Introduction Since the accident in 1976 in Seveso, Italy, runaways in chemical batch and semibatch reactors for the production of fine chemicals have received much attention. Much progress has been made in the understanding of such phenomena and in the practical laboratory analysis of runaway-prone reactions, but regretfully the problem has not been solved yet for practice, so that runaways still occur. In one of the countries of the European Union statistics of safety authorities reveal that on a total number of around 2000 installed batch and semibatch reactors an average of around 110 runaways occur annually.1 Most of these runaways, of course, lead only to production loss and perhaps some equipment damage. Nevertheless, some runaways lead to more serious consequences with loss of life and release of dangerous chemicals, accompanied sometimes by damage to the surrounding properties and negative health effects to the inhabitants of the neighborhood. The mentioned number of runaways may seem low, but we should realize that around 80% of the reactions executed in fine chemical plants have so low heat release potential that a runaway is impossible. Therefore, the frequency of runaways for reactions with high exothermicity is much higher than the numbers above may indicate. * To whom corresspondence should be addressed. Fax: + 34 972 152 525. E-mail: [email protected]. † Ramon Llull University. ‡ Warsaw University of Technology.

Further, according to Barton and Nolan in ref 1, a number of runaways occur due to human factors, raw material quality control, maintenance, agitator breakdowns, etc. These fall outside of the scope of this paper, which is concerned with defining adequate operating conditions to avoid runaways. In the case of a chemical reaction with a high heat effect in a batch production, the reaction is carried out in the semibatch mode: one of the reactants is slowly added to the second component, which has already been fully loaded to the reactor. By the addition rate of the first reactant the heat evolution can be kept controlled and be set at such a value that the reactor cooling system is able to remove all the reaction heat. We will discuss in this paper semibatch reactors and will demonstrate that the batch reactor is just an extreme of the semibatch reactor, where the addition rate of the dosed reactant is instantaneous. Runaways in liquid-liquid systems usually occur in slow reaction systems, where mass transfer is not yet enhanced by chemical reaction. It has been demonstrated also that rapid reactions in heterogeneous systems may exhibit runaways.4 In this case the reactant, which is being transferred to the other phase, is consumed in the boundary layer where it cannot accumulate, but it may accumulate in its own phase. However, slow reactions in practice exhibit much more frequent runaways, and therefore, in this paper we will only discuss the slow reactions. In this paper after a literature survey we elaborate on the safety diagram and give practical parameter

10.1021/ie030725m CCC: $27.50 © 2004 American Chemical Society Published on Web 06/10/2004

4586 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

values for laboratory and plant equipment. We discuss when the operating conditions are inherently safe. In the fine chemical industry with production programs of widely varying quantities of a wide range of chemicals, it usually is not possible to determine the kinetics of these reactions, because of time and money constraints. Therefore, in the second part we discuss how the values of the relevant parameters can be obtained from the literature and in laboratory experiment and translated to those for plant equipment. We explain the safety diagram data can also be applied to reactions with orders different from 1 for each component and to multiple reactions. Eventually a procedure to choose inherently safe operating conditions will be developed.

Figure 1. Characteristic phenomena in a boundary diagram. Slow reaction in the dispersed phase. RH ) 1 and U*(Da)/ ) 10.

2. Literature Survey Hugo and Steinbach2 were in 1986 the first to demonstrate that, in a semibatch reactor, in which a homogeneous reaction is executed, the reactant added accumulates in the reactor in cases where the reaction rate is not infinitely fast. This, e.g., may be caused by too low reaction temperatures. In the course of time the accumulation may become so high and consequently also the concentration of the accumulated component that the reaction rate becomes sufficiently fast to consume the added reactant faster than the addition rate, whichsif the cooling capacity of the reactor is not sufficiently highsleads to a temperature increase in the reactor. After a long accumulation this may lead to very high temperature increases and eventually to a runaway. Hugo and Steinbach2 produced a boundary line in a diagram separating regions with conditions where the reactions are sufficiently fast and with conditions where runaways may occur. Many semibatch reactions also occur in two-phase systems, where the two reactants are not miscible. In such a case not only too low reaction temperatures but also low mass transfer rates or insufficient interfacial areas between the two phases may lead to accumulation. Steensma and Westerterp3,4 were the first to study semibatch reactions in heterogeneous systems. They defined a target temperature, which the reaction mixture will assume at given operating conditions provided the reaction rate is infinitely fast, and they developed a full boundary diagram, in which a region of runaways was separated from regions with fully ignited reactions, a region with insufficient ignition, and a region of practically isothermal operation. The region of runaways itself was divided into a region where runaway occurs already during the period of addition of the second reactant or where it occurs after the addition period. The boundary diagrams depended on the cooling intensity number, which will be discussed later. Steensma and Westerterp made a distinction between slow3 and rapid reactions:4 for rapid reactions the reaction is so fast that it already takes place in the boundary layer of the reaction phase, whereas for slow reactions the reactant is supplied to the whole bulk of the reaction phase. In the case of fully ignited reactions the reaction shows a quick onset of the reaction rapidly after the addition starts, after that a fair conversion takes place and almost all reactant added no longer accumulates but is converted, and as a consequence the temperature profile developed as a function of time is smooth. The authors called this the QFS reaction, for which the accumulation of the added reactant remains harmless.

Both groups studied only single reactions in the mentioned publications.2-4 Moreover, they restricted themselves to second-order reactions. Hugo and coworkers2 further studied the influence of the reaction order on the temperature profile. They also demonstrated experimentally that reactions of different orders can be handled by the models developed for second-order reactions. This is because runaway usually occurs already in the beginning or in the middle of the addition period and in that case the concentration of the first reactant has not changed much yet. Recently van Woezik and Westerterp5,6 studied multiple reactions in heterogeneous systems both theoretically and experimentally. They determined for a nitric acid oxidation of 2-octanol the kinetics and also the interfacial areas as a function of the operating conditions in an agitated semibatch reactor; they used these data to check the applicability of the model equations developed for multiple reactions. They proved this to be the case. The desired product is 2-octanone, whereas the consecutive products are the corresponding carboxylic acids. The heat effect of the second reaction is 3.25 times higher than that of the desired reaction, so the first reaction must be executed to a conversion as high as possible and the consecutive reactions suppressed as much as possible both for selectivity reasons and to avoid a runaway caused by the second reaction. They demonstrated this to be possible and also showed that in the region of practically isothermal reactions a high reactor productivity still can be achieved, provided the reaction is stopped at reaching the highest desired product concentration for this consecutive reaction system. The reactor productivity, expressed as the production in moles of desired product per hour and per unit of reactor volume, as a function of the coolant temperature exhibited a maximum, values of which for much different dosing times were almost equal at the optimum coolant temperature. This observation led to further studies as will be reported in this paper. First we will discuss the safety diagram for single reactions. 3. Safety Diagram for Single Reactions In Figure 1 we present the safety boundary diagram as developed by Steensma and Westerterp.3 The coordinates as used in this diagram are dimensionless groups called by the authors the reactivity number and the exothermicity number or the reactivity, Ry, and the

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exothermicity, Ex. These groups are defined as

Reactivity Ry )

(

νA mκ (Da) νB c

)

(1)

U*(Da)

RH +

Exothermicity Ex )

(

2

Tc

E ∆Tad,o R U*(Da) RH +

)

(2)

The Damko¨hler number at the coolant temperature is given by Da ) kccBotD. In these expressions νA and νB are the stoichiometric coefficients in the reaction equation

νAA + νBB f νCC + νDD

(3)

In this reaction component B is loaded completely already before the start of the reaction, and after the start, component A is slowly added at a constant rate to the reactor contents during the dosing period tD. In a liquid-liquid system A is present in the dispersed phase and B in the continuous phase. The distribution coefficient relates to the phase in which the reaction takes place, so we use mA for a reaction in the dispersed phase and mB for one in the continuous phase. For low solubilities m is much smaller than 1. kc is the value of the kinetic coefficient at the coolant temperature, κc ) kc/kR is the kinetic coefficient kc related to the kinetic constant at the reference temperature TR, RH is the ratio of the heat capacities per unit volume of the dispersed phase over that of the continuous phase, and is the relative volume increase of the reaction mixture after the addition: ) (Vend - Vo)/Vo. ∆Tad,o is the adiabatic temperature rise at the initial state of the reactor given by ∆Tad,o ) (-∆HrnB,o)/(νBFocP,oVo). The boundary lines have been calculated for a number of assumptions: (i) volumes are additive, (ii) the reaction rate is first order in both reactants and given by r ) kcAcB, (iii) the components remain in their phases, A and C in the dispersed phase and B and D in the continuous one, (iv) the mixing enthalpy is zero, (v) the starting temperature is equal to the coolant temperature, which remains constant during the whole reaction, (vi) the addition rate remains constant during the addition, (vii) a stoichiometric amount of A is added to the batch, and (viii) m here is mB. Deviations of these conditions lead to minor changes in the boundary line; only RH and U*(Da)/ influence its shape and location significantly. By overdosing one of the reactants, we may speed up the reaction considerably toward the end of the reaction; in practice this is not often done because of the later separation of the overdosed reactant from the product mixture. The expression U*(Da)/ is called the cooling number (Co) and is defined by

Cooling number Co )

(UA)otD U*(Da) ) (FcP)oVo

(4)

In the safety boundary diagram of Figure 2 the different regions are indicated. These regions have been defined on the basis of the maximum temperature of the reactor contents during the course of the reaction and comparing that temperature with a target temper-

Figure 2. Types of thermal behavior in semibatch reactors.

ature. The target temperature Tta is the temperature that the reaction mixture would have in cases where all reactant A added immediately reacts away. This Tta slowly drops during the addition period, because the volume of the reaction mixture and consequently also the cooling area increases. The target temperature is defined by

Tta ) Tc +

1.05∆Tad,o [RH + Co(1 + θ)]

(5)

The reaction temperature profile is used to define the regions in the safety boundary diagram. In the case of a runaway the temperature increase (Tta - Tc) is overrun at least by 5%, as accounted for by the factor 1.05. A measure for the seriousness of this overrun is given by the factor ψ defined as

ψmax )

Tmax - Tc Tta - Tc

(6)

Realistically, in practice ψmax may reach values such as 2-3, but in the low range ψmax values of say 1.1-1.3 occur, so a value only slightly higher than 1.05 may be found. Anyway, in Figure 2 in the runaway region the value of ψmax is 1.05 or higher, and serious, dangerous runaways occur at the higher Ex values. This overrun of the Tta may occur somewhere during the reaction, either during the addition of reactant A or after the addition has been completed. If the time t is divided by the dosing time tD, we obtain a dimensionless time θ. If Tmax is reached before the end of the addition period, it is reached at θ smaller than 1. Characteristic temperature profiles are given in Figure 3 for the main regions in the safety diagram. The region of insufficient or no ignition is separated from the runaway region by the marginal ignition line. On this line the conditions are represented, where the reactor temperature profile just approaches the target line. For coolant temperatures below this line the reactor temperatures remain too low and the reactant added is not completely consumed or, less precisely, the reactor is not sufficiently ignited. This region has no meaning in practice, because of the low conversion of the reactants. It may seem safe, but due to a large accumulation it is potentially dangerous: in the case of an occasional increase of the reactor temperature a serious runaway can be provoked. In the region of full ignition the reactor temperature curve rapidly approaches the target temperature line and remains high without overrunning that line. This


Figure 5. Boundary diagram for a slow reaction in the continuous phase, with RH ) 1.

Figure 3. Characteristic temperature profiles.

Figure 4. Influence of the cooling number on the boundary lines for a slow reaction in the dispersed phase, with RH ) 1 and < 0.6.

is the region of QFS reactions, in which the reaction is quickly ignited, the conversion increases almost linearly during the addition, and the temperature profile remains smooth. In the fourth region of practically isothermal operation the reactor temperature changes remain small, because either the heat effect is too low for large temperature excursions or the cooling intensity is so high that the operation approaches isothermal conditions. 3.1. Influence of the Cooling Number. The cooling number influences the position of the boundary diagram. Steensma and Westerterp3 demonstrated that with increasing values of the cooling number the boundary lines move toward lower exothermicities in the safety diagram; see, e.g., Figure 4, where the safety diagram is shown for slow reactions in liquid-liquid systems with the reaction taking place in the dispersed phase. The boundary lines are also influenced by the value of RH; see the original paper for further details. In Figure 5 we show the results of Steensma and Westerterp3 for liquid-liquid systems with the reaction

taking place in the continuous phase. The shapes of the boundary lines are similar to those for the reaction in the dispersed phase, but the values of Ry required for fully ignited reactions of the QFS type are now more than 10 times lower than for reactions in the dispersed phase. This is understandable. If the reaction takes place in the dispersed phasesthe addition of which only begins at the start of the reactionsin the beginning only very small volumes of dispersed phase are present and the heat evolved in this small volume must be so large that it heats the total reaction mass: this evidently results in much higher reaction rates than when the reaction occurs over the total continuous-phase volume. 3.2. Practical Values for the Dimensionless Groups. A number of dimensionless groups have been introduced to make the balance equations dimensionless and to obtain more general conclusions, which also can be applied in other, similar cases. It is important to know how these groups vary in practice to have an impression of their relative importance. In the denominators of the reactivity number and of the exothermicity number appears the sum RH + Co. The term RH represents the ratio of the specific heats of the dosed liquid over that of the batch already present in the reactor at the start. This ratio depends on the type of liquid. If an aqueous solution is originally present and an organic phase added, this ratio is around 0.4, and if an organic solution is present at the start and an aqueous solution is added, this ratio is 2.5. Co, see eq 4, may vary over a much larger range. U is the overall heat transfer coefficient for the heat transfer of the reaction mixture toward the coolant. In Perry’s Chemical Engineers’ Handbook of Perry et al.7 typical values can be found for jacketed vessels and vessels equipped with a jacket and with a coil. For good agitation with turbine impellers and the vessel equipped with baffles, we find, for example, values around 750 W/(m2 K) for a coil and 450 W/(m2 K) for the jacket. The cooling area per unit of volume depends on the diameter of the vessel. For a vessel of a height twice its diameter D and filled at the start at 60% of the total volume, we find 4.0/D (m2/m3) for a jacketed vessel, and if also equipped with a coil of a diameter 0.7D, we have about 5.6/D (m2/m3). We further assume the volume added to be 0.3Vo. If we now need 1/4 h to add the second reactant, we can estimate the values of the cooling number for such a rapid filling. For a 10 m3 vessel originally filled with an aqueous solution, we find that Co ≈ 2.4, and if originally an organic solution is present in the reactor, we find Co ) 6 for vessels equipped with both a jacket and a coil. Without a coil, typical values such as 0.7 and


and the dimensionless temperature difference (Tta - Tc):

Ex )

Figure 6. (a) Typical values of the cooling number as a function of the reactor volume in well-agitated reactors with a dosing time of 1 h and the organic phase already present at the start of the reaction. (b) Typical values of the cooling number as a function of the reactor volume in well-agitated reactors. Conditions as for part a, except the aqueous phase is already present at the start.

1.8, respectively, would be found. In Figure 6 data are given for Co values as a function of the gross reactor volume for reactors with H ) 2D, with a cooling jacket only or a cooling jacket plus a cooling coil and depending on the phase of the batch originally loaded into the reactor. With a dosing time of 1 h, practical values for Co range from 0.9 to 20 for originally an aqueous phase and from 2 to 50 for originally an organic phase loaded to the reactor. We should realize that the typical values given hold for well-agitated vessels. Vessels with bad agitators of low rotational speeds and without baffles give much lower values for Co. In that case we must carefully check whether we really have a good liquidliquid dispersion. In the numerator of the exothermicity number appear the adiabatic temperature rise and the activation temperature, both divided by the coolant temperature. Really dangerous adiabatic temperature rises start at 150 K and upward; at the usual reactor temperatures between say -10 and +90 °C, this leads to ∆Tad,o/Tc values from 0.4 and higher. Activation temperatures vary between 6000 and 40 000 K; this leads to values of the dimensionless activation temperature γ ) E/RTc between 16 and 150. For a 10 m3 vessel originally filled to 60% with an aqueous solution and an value of 0.30, we obtain Ex values of 10-70. The realistic maximal value of the exothermicity number can also be estimated taking into account the definition of eq 2 and the target temperature as it is calculated from eq 5 at the start of the addition where θ ) 0. Then the exothermicity number can be expressed in terms of the dimensionless activation temperature

1 E Tta - Tc 1.05 RTc Tc

(7)

The maximum realistic value of Tta is about 425 K: above this value most of the solvents already boil, while organic reactants also may start to decompose. For Tc ) 273 K, Tta ) 425 K, and an activation temperature E/R ) 40 000 K, we obtain an exothermicity number of about 80. In a similar way we find a minimum of around 2 for the exothermicity number. In the numerator of the reactivity number we find the product of the Damko¨hler number Da ) kcnB,otD/Vo and the distribution coefficient m. In measuring reaction rates, we always obtain data on the product km, because the concentration in the reaction phase is difficult to determine, whereas the concentration in the nonreaction phase will be well-known indeed. For reaction in the dispersion phase the value of the reactivity number must be on the order of 0.7, whereas for reactions in the continuous phase it must be on the order of 0.03, to obtain QFS reactions in semibatch reactors. It is of interest to estimate at what Damko¨hler numbers the reaction takes place under QFS conditions. We refer to a paper by Steensma and Westerterp,3 where data are given for a synthesis of a peroxide with the reaction taking place in the dispersed phase. In this example the value of (Da)mB ) 1.8 at Tc, and the target temperature in the case of QFS reactions is reached at θ ) 0.3. From the definition of Tta and the data in that paper, we can calculate that Tta - Tc ) 38.7 K at those conditions. At reaching the target line temperature the value of the Damko¨hler number times the solubility is 131. If the reaction could have been executed isothermally in a homogeneous system at such a high Damko¨hler number, the conversion reached after a period equal to the dosing time would have been 99.2%. So for heterogeneous reaction systems and reaction in the dispersed phase, the reaction rates have to be really high to reach QFS conditions. We also refer to a paper by van Woezik and Westerterp6 for data on a nitration reaction, where the reaction takes place in the continuous phase. From the data given in that paper we can calculate that at those reaction conditions the Damko¨hler number is around 8. At such a value for a homogeneous, second-order reaction, a conversion of around 88% would be reached, so the reaction rate can be much lower in cases where the reaction takes place in the continuous phase and QFS conditions are required. 3.3. Inherently Safe Operation. Van Woezik and Westerterp6 showed that in certain areas of the safety diagram operating conditions are represented where a runaway can never occur and still high reactor productivities are achieved. In this paper at hand we will determine this region and analyze it further. In Figure 7, for the given value of U*(Da)/, we have indicated with a line the values of RyQFS,min above which we always will find QFS conditions. Also we have indicated the value of Exmin below which we always will have an exothermicity not sufficiently high for a dangerous runaway reaction. A horizontal line and a vertical line, respectively, isolate the area where we have both QFS conditions and still too low values of Ex for dangerous reactions. We have called this the region of inherently safe conditions. The boundaries of this region still


Figure 7. Determination of the values of RyQFS,min and Exmin for inherently safe operation conditions. Slow reaction in the continuous phase.

Figure 8. Boundary diagram for the slow reaction taking place in the continuous phase.

Figure 9. Boundary diagram for the slow reaction taking place in the dispersed phase.

depend on the value of the cooling number. We, therefore, extended our calculations of the safety diagrams to lower and much higher Co values. In Figures 8 and 9 we give representative plots of such diagrams. For systems with the reaction in the continuous phase, we give the values of RyQFS,min and Exmin of the boundaries of the inherently safe region as a function of the value of the cooling number in Figure 10. For a certain cooling number we find here the value of Ex below which a runaway can never occur. If we do operate our reactor at a value of Ex higher than Exmin, we should achieve values of the reactivity number above RyQFS,min for a given Co number to avoid runaways

Figure 10. (a) Inherently safe operating conditions for a slow reaction in the continuous phase: RyQFS,min and Exmin as a function of the cooling number. (b) Enlargement of a part of a.

forever. We observe that for high values of the cooling number Exmin approaches a limit value of around 2.9, whereas RyQFS,min keeps decreasing with increasing cooling numbers. For systems with the reaction in the dispersed phase, a somewhat different behavior has been found, as can be seen in Figure 11. Similarly, the Exmin values for the inherently safe operation region decrease for increasing Co. A limit value of around 1 is observed for Exmin at high values of the cooling number. However, an increase of the cooling number demands higher values of the limiting reactivity number RyQFS,min. For high values of the cooling number RyQFS,min approaches a limit value of around 0.86, while for Co < 20 it decreases rapidly with a decrease of Co. 3.4. Batch Reactor. For the extreme case of the Co number going toward zero, we have, of course, the ideal batch reactor. In that case we only find the term RH in the denominators of the expressions for Ry and Ex. We have shown before that, in industrially sized batch reactors, to which the second reactant is dosed rapidly within 1/4 h, we find Co numbers on the order of 1-5. For the case of a reaction with Tc ) 20 °C and E/(RTc) ) 35 taking place in the aqueous phasesdata relevant for the synthesis of peroxidessand on the basis of the data calculated before, we would find for the denominator (RH + Co) ) 0.3(0.4 + 1.5) ) 0.57 for the case where the aqueous phase has been charged at the start. Here Exmin ) 13, so we find ∆Tad,o/Tc ) 0.21, which implicates that ∆Tad,o must be 61 °C or lower to be able to execute the reaction in the batch mode. For the same data, but the reaction taking place in the organic phase and the organic phase being loaded directly at the start, we


Figure 11. (a) Inherently safe operating conditions for a slow reaction in the dispersed phase: RyQFS,min and Exmin as a function of the cooling number. (b) Enlargement of a part of a.

would find for the denominator 2.55, Exmin ) 6.2, and a maximum adiabatic temperature rise of 130 °C. For the organic phase originally loaded to the reactor we can accept much higher adiabatic temperature rises. This is understandable, because in that case an aqueous phase with a much higher heat absorption capacity (RH ) 2.5) is added; please note that ∆Tad,o is based on the FcP of the organic phase. 4. How To Obtain the Values of the Relevant Parameters Now that the entire safety diagram has been evaluated, it is important to study what the significance is for the practice of the production of fine chemicals in semibatch and batch reactors. 4.1. Exothermicity. We have seen that a low exothermicity is of great importance to avoid a runaway. To determine its value, a number of properties of the reaction mixtures and of the plant equipment have to be determined. This requires for practice that the plant engineer first determine the cooling properties of his reactors, that is, the value of UA/FocP,oVo for the reactors he uses. This can be easily done by determining a cooling curve for the reactant batch originally present in the reactor or after the reaction has been completed. This cooling curve has to be determined for a number of different reaction mixtures, depending on how their properties influence the heat transfer coefficients, and for the maximum flow rate of the coolant. Also this has to be done at good mixing conditions in the reactor, so that a good dispersion is obtained as well as a high heat transfer coefficient. If mixing conditions are bad, an-

other reactor with a better agitator has to be selected or a better agitator has to be installed, including the baffles. Also the reaction heat has to be known. This is no problem, because several methods have been developed to estimate with sufficient accuracy the heat effect of a reaction, e.g., the method of the additive groupcontribution scheme. It must be made sure that all reactions involved are included in such calculations, especially in the case of side reactions. On the basis of these heat effects, the adiabatic temperature rise ∆Tad,o of the originally loaded batch has to be determined. The activation energy of the main reaction has to be known. Many methods are available for the determination of this property in the laboratory, such as reaction calorimetry or DSC. Now, with the already known values of RH and of , the exothermicity can be calculated for a number of reasonable dosing times. If the reaction can be executed in the region of low exothermicity, a practical dosing time has to be selected on the basis of the reactor productivity. If this is not possible, we have to ensure that the reactivity is high enough for a QSF reaction; see also Figure 7. To this end we have to do experiments in a reaction calorimeter. We will discuss this in the next section. 4.2. Reactivity. In a reaction calorimeter we can determine the reaction rate. We usually do such experiments in the batch mode. For liquid-liquid reactions we actually determine values of the product of the kinetic constant times the solubility of the reactants in the reaction phase. We have to ensure that the dispersion is good. This can be done by determining these rates at different agitator speeds: as soon as the rate does not change anymore with an increase in agitator speed, we can be sure that the drop sizes are small enough and the interfacial area between the phases is large enough. In this case the mass transfer rate of the reactant to the reaction phase is so fast that it does not influence the conversion rate anymore. Further, it has to be checked that the reaction is slow or that the Hatta number is smaller than 0.3; see, e.g., papers by van Woezik and Westerterp.5,6 We also have to do experiments in a reaction calorimeter in the semibatch mode and isothermally. The heat evolution measured under isothermal conditions must be evaluated on the basis of a second-order reaction taking into account the decrease of the concentration of reactant B with the progress of the conversion. As soon as the reaction rate changes linearly with the concentration of component Assay after a conversion of 10-30% has been reachedswe can be sure that hardly any accumulation in the reaction phase takes place anymore. The shape of the heat removal curve for a QFS reaction for Tc, Tta, and intermediate temperatures has been discussed in the paper of Steensma and Westerterp,3 where also more details can be found on the evaluation of the data and the required checks. In Figure 12 we present for a single reaction heat evolution curves at different temperature levels: we see that at the target temperature the heat evolution curve approaches the shape of a rectangular block. By executing the reaction at different temperatures, we can determine also the real or apparent activation energy of the reaction. If the data over the temperature range of interest are consistent, we have found the real activation energy; if not, it will be an apparent one based


Figure 12. Normalized heat production rate in an isothermal reactor with cooling number Co ) 5. Single reaction at three representative temperatures.

on the apparent behavior of a combination of reactions. It has to be assured that the accumulation is negligible during the period of evaluation of the reaction rates. We have to realize that in reaction calorimeters the cooling area per unit of reaction volume is much larger than in the industrial reactor, at least a factor of 10. Cooling numbers of easily 100-400 can be found. To compensate for this, manufacturers of such calorimeters intentionally install an inefficient agitator with a low rotational speed; consequently, the cooling numbers are comparable to those in industry, because of the low overall heat transfer coefficients in such laboratory reactors. For liquid-liquid reactions this is dangerous, because the agitation often is too bad to achieve a good dispersion. So for the experiments in the reaction calorimeter and in the semibatch mode, also the agitation must be good. 4.3. Reaction Order. The boundary lines in the safety diagram have been developed on the basis of the behavior of second-order reactions in semibatch reactors. For reactions of an order lower than 2 the reaction rates will decrease less rapidly with the decrease of the concentration of the reactants; therefore, also accumulation will increase less rapidly. This implicates that the boundary diagram for orders lower than 2 will be conservative and can be used as such. We have to make an exception for autocatalytic reactions, which show a completely different behavior and therefore cannot be explained on the basis of the developed safety diagram. 4.4. Multiple Reactions. Multiple reactions are more difficult to evaluate. The usual objective is to produce a certain component and suppress the side reactions. At the same time we have to avoid runaways and achieve the highest possible selectivities. Only recently the first complete study on a system of multiple reactions has been published by van Woezik and Westerterp,5,6 in this case of consecutive reactions. They determined the kinetics of their reaction system and demonstrated that the set of dimensionless balance equations as developed by them adequately and accurately describes the experimentally observed temperatures, conversions, and selectivities as a function of time. We do not need to worry much in the case of parallel reactions. The heat evolved is caused by either one of the reactions. With data on the selectivity a good estimate can be made of the effective heat evolution. Over a temperature range of a few tens of degrees the selectivity will not vary too much. So the conditions

where QFS reactions are executed can be found by reaction calorimetry. In the case of consecutive reactions the situation is much more dangerous, because now the heat effects are additive. The intermediate product, which is the desired one, is itself also converted to an unwanted, consecutive product. The heat effect of this secondary reaction may be much higher; e.g., in the nitric acid oxidations of van Woezik and Westerterp,5,6 the heat effect of the secondary reaction was more than 3 times higher than that of the desired one. We also have to stop the reaction as soon as the concentration of the desired reaction in the reaction mixture has reached its highest value, or at a lower concentration when a recycle of nonconverted reactants is applied. So we have to find conditions where the first reaction is carried out at QFS conditions and the secondary reaction is suppressed as much as possible during the reaction. The extension of the theory of temperature sensitivity to multiple, more complex kinetic schemes is not obvious: the interaction of parameters in a multiple-reaction system makes the development of an unambiguous criterion impossible. Each reaction network requires an individual approach, and the optimum temperature strongly depends on the kinetic and thermal parameters of all the reactions involved. In the above-mentioned work of van Woezik and Westerterp the target temperatures of the two reactions were usedsas well as the exothermicities and reactivities of both reactionssto find the safe operating conditions for the production of the intermediate product; meanwhile simultaneously a good selectivity and a good reactor productivity had to be achieved. For the reaction system studied by van Woezik and Westerterp,5,6 it has been demonstrated experimentally and also confirmed by calculation that the reaction system is inherently safe already at a cooling number of 45. From Figure 10a we can read that at this value of Co the exothermicity number has to have a value of 3.0. For the desired reaction the adiabatic temperature rise is 110 K and for the undesired one 354 K. Further data are given by van Woezik and Westerterp.5,6 We can now determine at Exmin ) 3.0 what values of Co are required for the given ∆Tad,o. We find for the desired reaction a value of 14.2, for the undesired one 46.6. So in this case it is practically possible to keep the reaction inherently safe for the Exmin value of the undesired reaction. The selectivity of the given reaction system is high, on the order of 90%. If the selectivity would have been much lower and both reactions would have occurred to a considerable extent, we could have taken the sum of the two adiabatic temperature rises to estimate the minimum value of Co to operate in the inherently safe region. Under such conditions the reactor temperature is always limited between predefined and known temperature limits. These predefined temperatures are based on the target temperature developed by Steensma and Westerterp3,4 and can be applied successfully in the case of a multiple-reaction system. In Figure 13 a number of calculated heat production curves for consecutive reactions carried out in the semibatch mode are sketched for different selectivities of the reaction system. The reactions are executed isothermally, and the heat evolution is made dimensionless by dividing the heat evolution by that obtained for the first reaction.


5. Procedure for Choosing Inherently Safe Operating Conditions

Figure 13. Dimensionless heat production rate as a function of the dimensionless time for consecutive reactions. ∆Hr,X ) 3.25∆Hr,P.

In this figure we may observe that even at higher selectivities already at the start of the dosification the contribution of the undesired reaction to the heat evolution is noticeable. For larger κ the heat evolution is determined by the sum of the heat effects of the two reactions. For the considered case the yield of the intermediate product P decreases from 41% to 7% for κ going from 0.007 to 0.05. These yields are far too low to be ever accepted in a commercial production scheme. We refer to the work of van Woezik and Westerterp,5,6 who discuss a consecutive reaction with a yield of 90%, where it was sufficient to take only the heat effect of the undesired reaction into account to avoid runaways. 4.5. Reactor Productivity. The reactor productivity is the most important factor for the economical use of the investments in the reactor section. In the foregoing we have shown that the most important factor for scaleup is the cooling number. For a certain reactor the cooling number can be unnecessarily low, because of bad design of the cooling system and of the agitator. The flow of coolant through the cooling part of the reactor has to be so high that at maximum flow rate the temperature increase of the coolant is only a few degrees. Further, the circulation at the coolant side has to be forced in such a way that no free convection can occur. The agitator in the reactor has two tasks to perform: ensure a good dispersion and a good heat transfer coefficient, both at the jacketed wall and at the coil installed around the agitator. In cases where the reactor productivity is too low, the additional installation of a cooling coil in the reactor vessel can be considered and/or a better agitator with a higher rotational speed. Once these two conditions are fulfilled, for reactions with a high heat effect, we have to choose a dosing time which warrants a safe operation and an acceptable productivity of the reactor. In the first instance we aim at conditions with Ex < Exmin. If dosing times must be too long for an acceptable productivity, we can change to fully ignited reactions in the QFS regime, where lower values of Co can be tolerated. In that case we must ensure that the reaction is really fast as can be ascertained by laboratory experiments in a reaction calorimeter.

On the basis of the discussion in the previous paragraphs we now must adhere to the following procedure to determine safe operating conditions for the execution of reactions in a semibatch reactor. We determine (i) whether in the laboratory calorimeter the agitation is sufficiently high (no increase of the reaction rate at higher agitation rates) for a good dispersion, (ii) the adiabatic temperature rise on the basis of the batch of liquid originally loaded (this can be done experimentally or by calculation based on the reaction scheme and thermodynamic data), (iii) the activation energy of the reaction by reaction calorimetry or DSC, (iv) the ratio RH of the heat capacities of the two phases, (v) the fraction of the dispersed phase after completion of the dosing, (vi) the cooling number of the industrial reactor to be used by measuring the cooling curve for the batch of liquid originally loaded to the vessel at full coolant flow, (vii) the value of Ex as a function of the dosing times for the industrial reactor to be used at realistic coolant temperatures, (viii) the course of the target temperatures during the dosing in a reaction calorimeter and also the cooling number of the reaction calorimeter, and (ix) the reactor productivity at the chosen dosing times (choose the economically optimum dosing time, provided that Ex < Exmin on the basis of Figures 10 and 11). In cases where we cannot meet the requirement Ex < Exmin for economically acceptable reactor operating conditions, we have to go for QFS conditions. The procedure above can be extended as follows: (i) determine in a reaction calorimeter in the semibatch mode under what conditions we obtain QFS conditions. (ii) on the basis of the cooling numbers of the laboratory as well as the industrial reactor, extrapolate the cooling temperature of the laboratory reactor to Tc to be chosen in the industrial reactor; see Figures 10 and 11. The relevant relation is Tc,ind - Tc,lab ) (RTc,lab2/E) ln(Ryind/ Rylab). If we suspect multiple reactions to occur of the parallel type, we determine an apparent activation energy. In cases where consecutive reactions occur, we determine as a function of the temperature in the reaction calorimeter in the semibatch mode (i) heat evolution curves, (ii) the selectivities and when to stop the reaction to achieve the maximum yield, (iii) Ex values for the first reaction, the second reaction, or the sum of the heat effects of all reactions, depending on the selectivities obtained, (iv) the ratio of the activation energies, and (v) the RyQFS conditions, if Ex remains >Exmin. With these data we can find realistic Ex values and, if QFS conditions are required, extrapolate the laboratory data to those required for the operation of the industrial reactor. In this evaluation we have to be aware of possible autocatalytic reactions. The analysis given in this paper does not hold for autocatalytic reactions. In a following paper we will discuss how autocatalytic reactions have to be handled to operate them safely in semibatch reactors. 6. Summary and Conclusions Runaway events in chemical reactors occur in chemical industry rather frequently, leading sometimes to serious losses and release of dangerous chemicals. The


problem is particularly significant in the fine chemical industry, where we work in the batch and semibatch production mode and where an evaluation of the reaction kinetics usually is not possible due to time pressures in a widely diversified production. Runaways are observed, both in homogeneous and in heterogeneous systems, for chemical reactions with a high heat effect carried out in semibatch reactors, when the addition rate is higher than the reaction rate. It has been found that runaways occur particularly frequently in heterogeneous systems with a slow reaction rate, so in this study we focused on these systems. First, the safety diagram for single heterogeneous reactions has been characterized and discussed. Then values of the cooling number have been calculated for realistic situations. The concept of an inherently safe operating region has been discussed and demonstrated for reactions taking place in the continuous and dispersed phases, respectively. Also the batch production mode, as a limiting case of the semibatch method with an instantaneous addition rate of the reactant, has been shortly discussed. Previous work on safety diagrams has been extended to the full range of all practical cooling number values as they occur in plant reactor operations. From the results obtained two diagrams are presented for the minimum value of the exothermicity as well as the minimum reactivity, both as a function of the cooling number. With these diagrams inherently safe operating conditions can be determined for high reactor productivities. It is demonstrated that the data obtained can be used also for multiple-reaction schemes, except for autocatalytic reactions. The necessary information can be obtained by reactor tests in the plant, by experiments in standard laboratory equipment, and from the literature. A rapid procedure is developed which leads to safe operating conditions without costly and time-consuming kinetic studies. Acknowledgment This work was partially supported by the EU-funded project AWARD (Advanced Warning and Runaway Disposal), Contract G1RD-CT-2001-00499, in the frame of the 5th Frame Programme of the European Commission. Nomenclature A ) cooling surface area, m2 c ) concentration, mol/m3 cP ) specific heat capacity, (J/kg)/K Co ) cooling number (eq 4) Da ) kccB,otD ) Damko¨hler number at the reference temperature Tc E ) activation energy, J/mol Ex ) exothermicity number (eq 2) ∆Hr ) enthalpy of reaction, J/mol k ) reaction rate constant, m3/(mol s) m ) distribution coefficient mA ) cA,c/cA,d ) distribution coefficient for component A mB ) cB,d/cB,c ) distribution coefficient for component B ni ) amount of compound i, mol QP ) kPcAV∆Hr,P ) power generated due to the progress of the desired reaction, W QX ) kXcPV∆Hr,X ) power generated due to the progress of the undesired reaction, W Ry ) reactivity number (eq 1) tD ) dosing time, s r ) reaction rate, mol/(m3 s)

RH ) (FcP)d/(FcP)c ) ratio of the heat capacities t ) time, s T ) temperature, K ∆Tad,o ) adiabatic temperature rise, K U* ) (UA)o/(FcPVRcB)o kR ) dimensionless cooling capacity V ) reactor volume, m3 Greek Symbols ) relative volume increase γ ) E/RT ) dimensionless activation energy θ ) t/tD ) dimensionless time kc ) kc/kR ) reaction rate constant kc related to kR at the reference temperature TR κ ) kX/kP ) ratio of the rate constant for the undesired reaction to the rate constant of the desired reaction νi ) stoichiometric coefficient in the reaction equation F ) density, kg/m3 ψ ) temperature overrun factor (eq 6) ΘH ) (QP + QX)/QP ) dimensionless heat production rate Subscripts and Superscripts A, B, C, D ) reactants c ) cooling (at cooling temperature) c ) continuous phase d ) dispersed phase D ) dosing (dosed) QFS ) fully ignited reaction (quick onset, fair conversion, smooth temperature profile) P ) desired reactant (reaction) r ) reaction R ) reference ta ) target X ) undesired reactant (reaction) o ) initial (at the start of the dosing period)

Literature Cited (1) Safety of Chemical Reactors and Storage Tanks; Benuzzi, A., Zaldivar, J. M., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1991. (2) Hugo, P.; Steinbach, J. A comparison of the limits of safe operation of a SBR and a CSTR. Chem. Eng. Sci. 1986, 41, 10811087. (3) Steensma, M.; Westerterp, K. R. Thermally safe operation of a semibatch reactor for liquid-liquid reactions. Slow reactions. Ind. Eng. Chem. Res. 1990, 29, 1259-1270. (4) Steensma, M.; Westerterp, K. R. Thermally safe operation of a semibatch reactor for liquid-liquid reactions. Fast reactions. Chem. Eng. Technol. 1991, 14, 367-375. (5) van Woezik, B. A. A.; Westerterp, K. R. The nitric oxidation of 2-octanol. A model reaction for multiple heterogeneous liquidliquid reactions. Chem. Eng. Process. 2000, 39, 521-537. (6) van Woezik, B. A. A.; Westerterp, K. R. Runaway behaviour and thermally safe operation of multiple liquid-liquid reactions in the semibatch reactor. The nitric acid oxidation of 2-octanol. Chem. Eng. Process. 2002, 41, 59-77. (7) Perry, R. H., Green, D. W., Eds. Perry’s Chemical Engineers’ Handbook, 7th ed.; McGraw-Hill International Editors: New York, 1998; Section 19.

Received for review September 22, 2003 Revised manuscript received February 2, 2004 Accepted February 3, 2004 IE030725M

No More Runaways in Fine Chemical Reactors - ACS Publications

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