How t o *am= DANGEROUS For the chemist and chemical engineer who w o r k with exothermic reactions, wherever you are, remember t h a t .
...
Stable operation, with heat rem oval balancing heat of reaction, is possible only if temperature rise due to reaction i s only a f e w degrees above surrounding temperature. Allowable temperature of operation goes down as reactor volume goes up. Storage vessels should be filled with cold material.
D. E. BOYNTON, W. B. NICHOLS, and H. M. SPURLIN Research Center, Hercules Powder Co., Wilmington, Del.
IN
THE laboratory, pilot plant, and plant highly exothermic reactions are increasingly common. Many reaction mixtures have more potential energy than smokeless powder (700 to 1300 cal. per gram). Extreme examples are those containing high percentages of ethylene. butadiene, acetylene, or carbon monoxide. The dangers of working with such systems are universally recognized, and safety devices are usually adequate to prevent injury to personnel. However, barricades and pressure relief devices do not help to secure a successful reaction. yielding useful data and products suitable for evaluation and sale. This article points out some generalizations that enable conservative estimates of the operability of a proposed process, and gives hints to facilitate the design of an operable process. Always in the discussion it is implied that the reaction is sufficiently exothermic to heat the total mixture up to a dangerous point. This usually implies an adiabatic temperature rise of 200’ C. or more, if all the reagent present should react without loss of heat. Some very fine studies on chemical reactor stability have been published. Bilous and Amundson ( 3 ) presented an elaborate mathematical analysis of the stability of a chemical system. They used “parametric sensitivity” to refer to the large effect in some regions of operation of the parameters such as wall temperature, heat transfer coefficient, feed rate, and feed concentration on the
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APRIL 1959
489
maximum temperature and the composition of the product. Many numerical calculations on an analog computer illustrated these effects. Aris and Amundson ( 7 ) extended these calculations and introduced the effect of various control devices. Gee and others (6) and Beutler (2) described the use of a large, high speed digital computer for kinetic calculations. Analytical expressions were presented by Frank-Kamenetskii ( 5 ) and ChambrC and Grossman (4) for the maximum temperature of the reactants in a solid bed, or in a flow reactor when the only mechanism of heat transfer is conduction normal to the direction of flow. Recently, Thomas analyzed the situation where resistance to heat dissipation through the walls and by conduction through the mass of reacting material is important (9). Van Heerden (7) considered operation a t the upper stable point which exists for reactions of order greater than zero, with particular attention to the case of a retarding shift in equilibrium with increasing temperature. Because the general applicability of these results is poorly understood, this
article emphasizes a general and less complex treatment, which is a satisfactory guide in many cases.
The Stirred Reactor According to Semenov (8): Van't Hoff recognized as early as 1886 that stable operation of an exothermic reaction. with the heat removal balancing the heat of reaction, is possible only if the rise of temperature due to reaction is only a few degrees above ambient. Very few chemists and engineers seem to realize this, and there are repeated, and often disastrous, attempts to do such things as run a highly exothermic reaction in a coil reactor with a AT of 50' C. or more between the coil contents and a surrounding bath. Typical Example. The reaction mixture in question doubles in reaction rate for a 10' C. rise in temperature a t about 120' C., corresponding to an activation energy, E, of 23,000 cal. per mole. T h e rate of heat production then will be an Arrhenius function of the temperature, dQ/dt = Ae
- EIRT
(1 1
plotted as the heavy curve of Figure 1. This mixture is put in a jacketed kettle, for which the rate of heat transfer is given by the equation ( T o is jacket temperature) d Q ' / d t = B( T
-
To)
(2 1
Consider a jacket temperature of 116' C. and a heat-transfer constant, B, such that the line to the left in Figure 1 represents the rate of heat loss from the kettle to the jacket. This line intersects the reaction heat curve at 123' and 143' C. T h e intersection at 123' C. is marked "stable solution" on Figure 1, because the temperature will tend to return to this point if displaced slightly above or below. T h e upper intersection is unstable, however. The slighest drop in temperature would cause the contents to drop to 123' C., and the slightest rise would cause the temperature to go up until exhaustion of reagents or explosion of the vessel brought a halt. Thus, operation at 7' C. temperature differential represents stable operation. As the jacket temperature is raised, the heat loss line moves to the right. T h e second line of Figure 1, corresponding to a jacket temperature of 119' C., is tangent to the heat production curve at 133' C., a AT of 14' C. This is the maximum stable temperature of operation possible for the reaction mixture and vessel described. By increasing the heat-transfer surface, operation at higher temperatures is possible, as shown by the third line of Figure 1, Here, jacket temperature is 134' C. and the point of tangency 148' C.; again, the maximum AT for stable operation is 14' C. This is a result of the utmost generality, for a reaction which doubles in rate for a 10' C. rise in temperature. For activation energies leading to other temperature coefficients, Equations 1 and 2 may be equated and differentiated to demonstrate that the maximum stable temperature differential, ( T - To)orit, is given by
(T
- T,),,it
= RT2/E
(3)
Because reaction rate data, rather than activation energies, are often available? another relationship is often useful :
2(ln 2 ) T o = 1.4 T D (4)
Thermal data from the laboratary can be used to ensure safe operation of large scale equipment
490
INDUSTRIAL AND ENGINEERING CHEMISTRY
Here, T D is the temperature increase required to double the reaction rate. Because reactions seldom require as much as 20" C. to double in rate, and operation near the critical point leaves no safety factor, an unknown exothermic reaction should never be operated at rates demanding a AT of more than about 10' C. for heat removal, unless rapid and effective means for added
E X OTH E R M I C R E A C T I O" S cooling or quenching the reaction are available. I n general, the safe way to proceed with an unknown mixture is to have a well-defined jacket or bath temperature; raise this temperature slowly or add catalyst until the reaction temperature rises about 5" C. above the cooling medium temperature; and finish the run under conditions such that this rise is never exceeded. Reaction Control above Critical Point I t is desirable to operate a t higher values of AT than the 10' C. (approximately) allowable for stable conditions. 'Io facilitate visualization of the problem, the reaction temperatures for equal heat production and dissipation for all ambient or jacket temperatures have been plotted in Figure 2. If both initial reaction temperature and jacket temperature are lo\v, as a t point A , the temperature rises to jacket temperature. and the reaction rate is negligibly slo\v. Over a narrow range of jacket temperatures. froni 100" to 120' C., an appreciable rate is obtained, but conditions are perilously close to a runaivay reaction. If the reaction mixture is initially hot as a t B but not above the upper, unstable branch of the curve. the temperature will fall; a t C the initial temperature is so high that the reaction will run a\vay even if the cooling medium is reduced to 20" C.. as a t C'. A jacket temperature of above 123' C. (point D) must be avoided, as the reaction will run away. 200
60 >
Figure
1.
HEAT PRODUCTION
Rates
of heat production (curve) and heat loss (straight line)
50
-
c
0 z
Stable operation i s 110 possible only i f the rise o f temperature = due to exothermic re- ," action i s only a few 30 degrees above ambient 4
UNSTABLE SOLLITION
-
*
0
2OSTABLE SOLUTION
w
t* o z
IO
-
TANGENTS ABSCISSA
The problem of control with a large
A T is to operate near the unstable branch of the curve, continuously changing ambient temperature or other means of cooling. The danger lies in letting the temperature attain a point corresponding to C, for then the reaction cannot be brought under control with the cooling surface provided. The feasibility of this method of operation depends primarily on the time required for the reaction. If the rate is slo~v, the reaction cannot heat up much before corrective methods can be applied. Butadiene emulsion polymerizations can be controlled if the reaction time is 12 hours per batch, and ivith good instrumentation the reaction should be controllable for a total reaction time of about 30 minutes.
OF REACTION MIXTURF
0
120 r
4 CL.
e
100
z Y c z
-
0
80
0 c
u
60
CL
40
20
0 AMBIENT TEMPERATURE.
OC.
Figure 2. Temperature for heat production equal to heat loss A jacket temperature above 123' C. must b e avoided Activation energy, 23,000 cal. per mole A / B = 4.314 X 1 013 C. (corresponds to a 7' temperature rise at 120' C.)
Much trouble arises in practice from scaling u p from laboratory experiments, w-ithout regard for the proper balance between heat-transfer area and volume. As sho\vn in Figure 3, the allowable temperature of operation goes down as the volume goes up. if the reactors are geometricallv similar and have the same heat-transfer coefficient per unit of surface; the allowable reaction rate per unit of surface is roughly constant. if stable operation is to be maintained. I t is a common error to attempt to compensate for a reduction in surfacevolume ratio by using a larger A T . Another point of considerable practical importance can be demonstrated by Figure 3. A reaction may be controllable a t a fairly high temperature, say 140' C., in a small piece of equipment, yet in a large storage tank, it may run away. An esterification reaction on a polyrnerizable monomer could be a case in point. I n actual practice, this type
OC.
of trouble arises most often from loading dry powders into storage bins, where atmospheric oxidation is the exothermic reaction. T h e cure is to cool the product before putting it in storage. Reaction Order
T h e underlying thesis of the discussion so far is that a given reaction mixture. in a given environment, cannot get out of control if the exothermic rise above the environment is less than RT2,E. If this limitation is exceeded, the temperature will continue to rise until most of the reagent is consumed, unless the decline in concentration due to reaction offsets the increase in rate due to higher tem200 I
Scale Factors
& 1110
INTERSECT 14' BELOW
I 0
TEMPERATURE
I80 I60
-
;I6O 140
1
v
=
I .
v
=
1000.
VIS =
1
vis =
AMBIENT TEMPERATURE,
OC,
Figure 3. A proper balance between heat-transfer area and volume must b e maintained V. Volume. S. Heat-transfer surface. Same shape and reaction mixture as in Figures 1 and 2
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APRIL 1959
491
havior, with a runaway (exothermic peak hot spot) if this rise is exceeded. This rise at the center for incipient runaway reaction is giv-n, for the various configurations, in Table I. The tolerable rise is thus somewhat greater for the unstirred cases. However, this rise is a t the center, and the temperature declines to ambient a t the boundary, so that thr average temperature is smaller. The temperature a t the center for an unstirred cylinder as a function of ambient temperature is compared with that of a stirred reactor in Figure 5. The general course of the two curves is similar.
Table 1.
Maximum Exothermic Rise for Stable Operation
The tolerable rise is somewhat greater for unstirred cases
Reactor Type Stirred reactor
Slab Cylinder
Sphere
In jacketed reaction vessels such as those in picture above, surface to volume ratio is critical
perature. Unless the reaction is only mildly exothermic, so little reaction is required to throw it ivell over the critical limit that the effect of decline of concentration due to reaction cannot compete with the exponential rise in reaction rate. To investigate this problem quantitatively, some calculations for a coil reactor were made on a Bendix G-15A digital computer. First-order reactions with adiabatic rises of looo, 2OOo, 400', and 1000' K . were chosen, so that the effect of the fraction of the batch that had to react to bring the temperature u p from bath temperature to the highest point could be studied. Other parameters Ivere selected so that temperature rises would be comparable a t the same ambient temperature level. As is evident from the results of these calculations (Figure 4), there was a very sudden instability when the ambient temperature was increased only 1' with the two more exothermic reactions (Figure 4. C and
D).
A 1' rise in the cooling bath temperature resulted in a complete runaway. T h e instability was not so marked in the other cases. Apparently stable operation can be obtained a t a temperature somewhat above the figure of 2 T L / E (14' in this case)t but control would have to be so close that even in the mild case of a 400'-adiabatic rise it would be preferable to design fgr a 10' A T , particularly where the yield or quality of product is dependent on fairly close temperature control.
.492
It may be concluded that the safe AT of 14' predicted from the simple treatment is somemrhat conservative, compared with the 19' for 400'-adiabatic rise and the 16' for 1000'-adiabatic rise read from the curves. However, the prediction is not far off. and gets better as the reaction mixture becomes more exothermic and therefore more dangerous. The curves of Figure 4 are presented in terms of physical units, although they can be put into dimensionless form simply. By straightforiiard transformations, they may be used as guides for other reaction conditions Unstirred Reactions
In some cases of interest to the chemical engineer. it is impossible to stir the reaction system: bulk polymerization, fixed-bed catalysts, and storage of dry materials. The mathematical treatment. while more complicated than that for t!ie stirred reactor, can be handled Lvith a minor mathematical simplification (4, 5) for flat beds and cylinders. A numerical computation for the case of the sphere has been given by FrankKamenetskii (5). The exact results are of little interest for the chemical engineer, as the simplifying assumptions of independence of temperature of coefficients of heat transfer and zero-wall resistance are never quite fulfilled. The basic, and very important, conclusion is that the unstirred systems also show the same type of critical temperature rise be-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Critical Rise
RFIE 1.19 R P / E 1.39 R F I E 1.61 R P / E
A striking difference becomes apparent when the scale factor is considered. The maximum allowable A T is independent of scale. In the stirred case the maximum reaction rate per unit of volume that can be controlled is inversely proportional to the first power of the linear dimensions. With unstirred reactions, the allowable rate is inversely proportional to the square of the dimensions-the heat output is not only greater in a larger reactor, but has a greater average distance to traverse before reaching the boundary. For the typical case xvhere the reaction rate doubles for 10' C., the temperature of operation must be reduced 20' C. if the reactor is doubled in size. This factor helps to explain why large containers of reactive solids are so much more likely to cause trouble in storage than small containers. Autocatalytic and inhibited Reactions
No simple analysis can cope with all the problems presented by autocatalytic and inhibited reactions. However, even such reactions are characterized by maximum rates that can be attained after autocatalysis has taken hold or the inhibitor has been consumed. From the point of view of the design engineer, the conservative approach is to insist that the rate of heat evolution of the reaction mixture be measured throughout the reaction, a t all temperatures and pressures that come in question for plant process conditions. If the maximum rates so found can be fitted to a simple Arrhenius formula, the design considerations outlined above can be applied. Bulk polymerization of some monomers presents additional complications.
EXOTHERMIC REACTIONS
1
530r
0'
540
I
I
510
'
470
0
I
I
I
2
4
6
I
I
I
12 8 IO TIME, 10-3 HOURS
6. Adiabatic temperature rise, 200' K. 530
-
470 L 0
T o = 976'K.
C
I
I
I
2
9
6
I
I
I
Heat transfer coefficient, 50 cal. per hr.-sq. cm.
I
I
8 10 12 I& T I M E , 10-3 HOURS
16
I
18
I
I
I
I4
16
I8
20
' K.
I 20
C. Adiabatic temperature rise, 400' K. Heat transfer coefficient, 100 cal. per hr -sq. cm.
Figure 4.
K. T I M E , 10-3 HOURS
The safe AT of 14' i s somewhat conservative D.
Diameter, 1.0 cm.
Activation energy, 31,400 cal. per mole
The viscosity rise impairs heat transfer. Furthermore, many bulk polymerizations are autocatalytic. I t is desirable to segregate these two effects-autocatalysis and viscosity increase-when designing a process. Devices for Control of Exothermic Reactions 1. Vse dilute solutions or suspensions. If the amount of reagent present cannot raise the temperature more than
Adiabatic temperature rise, 1000° K. Heat transfer coefficient, 2 5 0 cal. per hr.-sq. cm.
about 100' C., no trouble will be encountered. 2 . Feed the exothermic ingredient slowly, so that it is used u p by reaction, and never reaches a dangerous concentration. T h e dangerous ingredient must react as rapidly as it is fed, and not accumulate. Make sure that the catalyst is present, and that the reaction temperature is reached before feed is started. I n contrast to the batch reaction, a high temperature is safer than a low one. I t is desirable to keep the reaction con-
stantly in a runaway condition to prevent accumulation of the exothermic ingredient. Both methods 1 and 2 require larger reactor volumes than if higher reagent concentrations could be tolerated, and sometimes give poor yields or qua lit!^ because of the longer reaction time, or the different ratio of reagent concentrations present. 3. ,4dd enough volatile solvent so that the temperature can be controlled by refluxing solvent. Usually 10% is
. 180
UNSTlRREO
STIRRED
CYLINDER
VESSEL
Editor's Note. The curves of Figure 4 may be used as a guide for other reaction conditions by using transformations covered in a 5-page mimeographed discussion. This may be obtained at no cost by addressing the authors at the Hercules Research Center, Hercules Powder Co., Wilmington, Del.
&
' K.
160
0
Figure 5. The exothermic rise i s similar for stirred vessel and cylindrical solid
-ATc
= 19.5'C.
CAT,
=
19.0°C.
Activation energy, 23,000 CUI. per mole Critical ambient temperature, 123' C.
I
60
80
I
I
I
IO0
120
I 110
0
A M B I E N T T E M P E R A T U R E . OC. VOL. 51, NO. 4
APRIL 1959
493
enough, if good means for return of the refluxing solvent and mixing with the batch are provided. This method can also be used with pressure and vacuum, but is then somewhat a t the mercy of the controls. 4. Consider operation with a large A T if the time available for reaction is long enough (greater than 2 hours). T h e controls should be responsive enough to catch a n incipient runaway reaction by providing adequate cooling. I t is usually best to provide separate pathways for heating and cooling. Cooling should be by the pathway of loivest time lag, such as an internal coil. 5. Design coil reactors to remove the heat of reaction with a small A T . Several parallel coils are often necessary, to avoid excessive pressure drop while securing enough area. If sectionalized coils are used with increasing diameter to allo\r for exhaustion of reagent as the reaction proceeds, the system has to be hot before starting up.
can be detonated. These mixtures also give trouble with ordinary exothermic reactions. Summary
Strongly exothermic reactions Mill run aicay if the temperature rises more than 10’ to 20‘ C. above the ambient temperature a5 a result of reaction. Trouble may he prevented by the use of enough heat-transfer area to prevent such a rise, or by auxiliary cooling by a refluxing liquid or by additional cooling surface that may be controlled by reliable and responsive instrumentation. An ample factor of safety is desirable in any case, as mischance that allows the temperature to rise only 10’ C. above the control point will require twice the original cooling effect to bring the reaction under control. Nomenclature
Storage
= heat generation proportionality
1 Storage vessels should be filled with cold material. I t usually takes a long time for a dangerous condition to build u p in storage, so that temperature-warning devices should give ample time for corrective measures. Warning of incipient fire in storage of dry materials is a difficult problem, as there is little chance of predicting where the trouble will start. One difficulty is illustrated by Figure 6. If the initiallv cold material is exposed to a surface temperature only slightly above critical, the exothermic peak Mill develop some\vhere near the middle (Figure 6 , A ) . If there is a sudden exposure to temperatures considerably above the critical. the exothermic peak will develop near the walls, while the center is still cold (Figure 6.B). Normal weather changes may throw the surface temperature of a large batch of sensitive material over the critical point, so that fire is initiated there rather than at the center. Detonations
Some salient factors should be kept in mind. A detonation is defined as an explosive wave traversing a body of the material, with a definite front ahead of which the temperature is low. Contrasted to this, an exothermic reaction builds u p uniformly through a large part or all of its volume, until the vessel ruptures or the mixture spews over the surroundings. If a material undergoing an exothermic temperature rise can detonate, it will sometimes do so. Almost any material with a potential exothermic rise of more than 1000° C. can be detonated. However, a detonation wave may be very difficult to set off, as in the case of nitromethane or ammonium nitrate. Gas detonations are usually easy to initiate. Solids may be very sensitive or very insensitive. Liquids
494
Figure 6. Schematic course of temperature profiles of solid exothermic reaction mixture suddenly exposed to temperature A.
Slightly above critical 6. Far above critical
have a very favorable characteristic; experience indicates that concentrations of less than 50y0 in a n inert solvent cannot be detonated. I n chemical practice, detonations can be avoided if gases are kept out of the explosive range of composition and dangerous liquids and solids are kept in solution. T h e safest plan is to use plenty of high-boiling diluent. -4ddition of 10% by volume of dibutyl phthalate or joycsodium hydroxide will, for example, prevent peroxide explosions in the distillation of ethyl ether. Liquid mixtures containing nitric acid, oxides of nitrogen, or perchloric acid in the explosive range of composition should be avoided. If solids or oily liquids of unknown composition separate from mixtures containing free oxygen, hydrogen peroxide, halogens, acetylene, nitric acid; nitric oxides, chromates, permanganates, or heavy metals, the greatest caution should be exercised. For example, copper acetylide is sometimes produced when mixtures of chlorinated solvents are handled hot in the presence of copper equipment. Mixtures of finely poivdered active metals, such as sodium, magnesium, and aluminum, with chlorinated solvents and with some oxygenated compounds
INDUSTRIAL AND ENGINEERING CHEMISTRY
B
=
E
= =
Q Q’
factor in Figures 1 and 2, cal./mole- hr. heat transfer proportionality factor in Figures 1 and 2, cal.: mole-hr. O C. activation energy, cal.! mole heat produced by chemical retion, cal./mole heat transferred, cal.,’mole molal gas constant, cal.;mole
R
= =
S
= heat-transfer surface, sq. cm.
7’
= temperature of reacting mixture,
O
K.
C. or O K. To = ambient or wall temperature, C. or O K. T , = critical ambient temperature, C. or K. T D = temperature increase required to double reaction rate, O C. or O
K.
A T , = T - T,, C. or OK. t = time, hours I’ = volume of reactor, cc. Literature Cited (1) &is, R., Amundson, N. R., Chem. Eng. Sci.7,121, 132, 148 (1958). (2) Beutler, J. A., Chem. Eng. Progr. 50,
569 (1954). (3) Bilous, O., Amundson, N. R., A.Z.Ch.E. Journal 1 , 5 1 3 (1955); 2,117 (1956). 14) ChambrC. P. L.. Grossman. L. M.. ‘4ppl. Sci. Risearch A5, 245 (1955). ( 5 ) Frank-Kamenetskii, D. A , , “Diffusion ~
and Heat Exchange in Chemical KinetPrinceton University Press. Princeton, h-.J., 1955. (6) Gee, R. E., Linton, W. H., hfaier, R. E.. Raines, J. W., Chem. Eng. Progr. 50,497 (1954). ( - ) Heerden, C . van, IIVD.ENG. CHEM. 45, 1242 (1953). ( 8 ) Semenov, Nikolai, “Chemical Kinetics and Chain Reactions,” Oxford University Press, London, 1935. (9) Thomas, P. H., Trans. Faraday Soc. 54, 60 (1958). ics,” pp. 236-66,
RECEIVED for review September 3, 1958 ACCEPTED December 22, 1958 Delaware Science Symposium, Newark, Del., February 15, 1958.
