Menez, G. D.. M.S. Thesis in Chemical Engineering, University of California, Santa Barbara, 1972. Nysing, R. A. T. A.. Krarners, H.. Eur. Symp. Chem. Eng., 1st (1957). Perry, R. H., Chilton, C. H., Kirkpatrick, S. D., Ed., "Perry's Chemical Engineers' Handbook," 4th ed, pp 14-41, McGraw-Hili, New York, N. Y., 1963.
Reichardt, H., Z.Angew. Math. Mech. 31,208 (1951). Roberts, D., Danckwerts, P.V., Chem. Eng. Sci. 17, 961 (1962). VivianJ. E., King, C. J.,A.I.Ch.E. J. 10,220 (1964).
Receivedfor review April 16, 1973 Accepted September 7 , 1973
Steady-State Multiplicity and Control of the Chlorination of Liquid n-Decane in an Adiabatic Continuously Stirred Tank Reactor James S. Y. Ding, Shanmuk Sharma, and Dan Luss* Chemical Engineering Department, University of Houston, Houston, Texas 77004
This paper reports the results of an experimental study of the chlorination of liquid n-decane in an adiabatic stirred tank reactor. Under certain operating conditions, two stable steady states with widely different levels of conversion, selectivity, and temperature were obtained, and the start-up procedure determined which one was attained. The experiments revealed a significant influence of a small amount of impurities on the behavior of the reactor and the possible existence of multiple steady states. A feedback control, which manipulated the decane feed rate, was used to operate close to an unstable steady state. The resulting flow averaged selectivity was higher than that corresponding to a stable steady state with the same conversion level. The control scheme was reliable, safe, and easy to implement.
Introduction A large number of industrially important reactions such as chlorination, nitration, sulfonation, and alkylation are carried out in a two-phase CSTR (continuously stirred tank reactor). In these reactors a large number of coupled physical and chemical rate processes occur simultaneously, and at present it is practically impossible to develop a complete, rigorous, quantitative prediction of all these mutually interacting rate processes. Moreover, various studies indicate that important physical parameters, such as hold-up and interfacial area, may vary with position in the tank. Thus, it is customary to design and control these two-phase reactors using limiting simplified models, since there is no justification for using sophisticated, complex models whose predictive accuracy exceeds that of the experimental data or correlations on which they are based. It is well known that when a chemical reaction is carried out in a CSTR, multiple steady states may occur under certain conditions. The first theoretical analysis of this phenomenon was presented by Liljenroth (1918) while a quantitative treatment of oscillatory behavior of chemically reacting systems was presented by Bonhoeffer (1948a, b; 1949a, b, c). Bilous and Amundson (1955) presented the first modem stability analysis of a CSTR with a single exothermic reaction, and Westerterp (1962) generalized the treatment to the case of two reactions. Schmitz and Amundson (1963a, b, c, d) discussed several aspects of the stability of two-phase CSTR for certain limiting models and demonstrated that the behavior of the system is far more complex than that of a homogeneous CSTR. Experimental studies' by Furusawa, et al. (1969), and Vejtasa and Schmitz (1970) have demonstrated the existence of multiple steady states for a homogeneous single-phase reaction in a CSTR. Experimental demonstration of oscillatory behavior of CSTR was presented by Bush (1969) and Hancock and Kenney (1972). 76
Ind. Eng. Chem., Fundam., Vol. 13, No. 1, 1974
Many important two-phase organic substitution reactions proceed through a consecutive mechanism, and often a high selectivity of the desired intermediate product is attained only at low conversion levels, while a rather poor selectivity is obtained at high conversion levels. Hence, it is important to operate a t conditions which offer a reasonable compromise between selectivity and activity, and this often requires operation close to an unstable steady state by use of some control scheme whose practical feasibility, reliability, and ease of implementation depend on the time constants of the system. In control literature it has been proposed to stabilize an unstable steady state by use of forced cyclic motion and this idea has been applied by Fjeld (1971) for stabilizing an unstable steady state of CSTR in which a single exothermic reaction occurred. The main practical difficulty of applying his scheme is that it requires an exact dynamic model and knowledge of all the associated parameters. In industry, operation around unstable steady states is attained by feedback control schemes which do not require an exact knowledge of the dynamic response of the system. Iscol (1970) presented an excellent example of how fluid catalytic crackers (FCC) are kept close to an unstable equilibrium point by continuous compensatory set point adjustments. Similarly, Knorr and O'Driscoll 1970) proposed to control the conversion of styrene in a CSTR by regulating the rate of monomer feed. This type of control seems to be rather promising for a two-phase CSTR in which several consecutive reactions occur. However, an important question is which variable(s) need to be measured and which input stream(s) should be regulated. This work reports an experimental study of the steadystate multiplicity, stability, and control of an adiabatic two-phase CSTR used for the chlorination of n-decane. The aims of the study were to demonstrate the possible existence of multiple steady states with different tempera-
VENT
WATER OUT
Figure 1. Schematic diagram of the experimental apparatus: 1, automatic pressure regulator; 2, dryer; 3, rotameter; 4, manometer; 5 , liquid trap; 6, thermocouple; 7, condenser; 8, scrubber; 9, liquid seal; 10, storage bottle
with chlorine on atom j. Using the standard pseudosteady-state and long-chain assumptions it can be shown that the rate of every reaction is proportional to the concentration of the corresponding hydrocarbon and the dissolved chlorine. The various chlorination rate constants are very sensitive tp temperature variations and the activity energy is about 30,000 cal/mole. The heat of reaction of liquid decane and chlorine to form primary or secondary monochlorodecane is 24,100 and 26,750 cal/mole a t 25"C, respectively. The heat of reaction of monochlorodecane is about the same. This combination of high activation energy and heat of reaction is responsible for the possible occurrence of multiple steady states. The instantaneous selectivity of any isomer (ratio between monochloride formed to decane converted) is governed by the equation
1-1
0 SEALING
FLUID CbP
@
THERMOCCUPE
@
GAS CUTLET
@ RUBBER
SPLIT
@ALUMINUM
@ RUBBER
@U
RING
FLANGE / TEFLON GASKET
V LIGHT
WELL
@ LIQUID
OUTLET
@SAMPLE
PORT
@
Integration yields the concentration of any monochlorodecane isomer as a function of the unconverted decane
PORl
1-1
( j = 1, 2, ,5)
BAFFLES
0 LlOUlD FLAT
@ @
GAS OISPERSER
GAS
The ratio between the various rate constants is a rather weak function of temperature. Thus, while eq 2 was derived for isothermal conditions, it can serve as a reasonable approximation for adiabatic conditions. Kinetic considerations discussed elsewhere (Golikeri and Luss, 1974) enable estimation of the ratio between the various rate constants from knowledge of p , the relative reactivity of secondary to primary hydrogen. Values of p for various chlorination reactions are reported by Bratolyubov (1961) and are rather insensitive to changes in the temperature.
INLET
@
PADDLE AGITATOR
INLET
Figure 2. Chlorination reactor
tures, conversions, and selectivities under the same operating conditions, to obtain qualitative and quantitative information concerning the key phenomena which affect the reactor so that rational design and control models can be developed, and to explore the possibility of a feedback control close to an unstable steady state by manipulation of the flow rate of the liquid reactant. It is well known that most industrial feeds contain small amounts of impurities and an additional objective of this investigation was to check their effect on the qualitative behavior of the system.
The Decane Chlorination Reaction The chlorination of decane proceeds by a free radical chain mechanism with initiation by thermal or photochemical dissociation of the dissolved chlorine. The overall reaction network can be presented by reaction I, where j-CIOH1lCl denotes a monochlorodecane isomer ,
p
l-C,,H,,CI
(2)
h:
I
Experimental Apparatus and Procedure The apparatus (Figure 1) consisted of a chlorination unit and a gas disposal section. The decane, chlorine and nitrogen were -fed to the reactor by Il4-h. diameter stainless steel tubing and metered with glass Brooks Shorate 150 rotameters. The jacketed stirred reactor (Figure 2) was built of amber tinted Pyrex glass and had a 400 ml operating volume when no agitation was used. Mixing was provided by a three-blade flat paddle agitator whose speed could be varied from 200 to 600 rpm. Two sets of three glass baffles were used to improve the mixing. The jacket was insulated by an asbestos layer and maintained under vacuum to minimize heat losses. The gas was dispersed into the liquid phase by passage through a porous glass plate fritted onto the bottom of the reactor. The exit gases were cooled by a condenser connected to the top of the reactor so that any condensate would drip back into the redichlorides
)
I
(I)
Ind. Eng. Chem., Fundam., Vol. 13,No. 1, 1974
77
30 d i f f e r e n t
higher
possible
chlorides
isomers
Figure 3. Typical gas-liquid chromatograph actor. The gas disposal section consisted of a spray packed absorption column, through which aqueous NaOH solution was circulated by a rotary pump. The column kept the reactor at nearly atmospheric pressure and also absorbed any unreacted chlorine which accumulated in the liquid product storage bottle. The temperatures inside the reactor were measured by a pair of chromel-alumel thermocouples with monel sleeves and recorded by a two-pen Honeywell Electronik 194 recorder. Liquid samples from the reactor were withdrawn through the sample port by a syringe and transferred quickly to prechilled sample bottles, from which remaining absorbed chlorine was stripped by air. The samples were analyzed by a Hewlett Packard Model 700 laboratory chromatograph using a 10-ft column of 5% FFAP dispersed on 80-100 mesh Chromsorb W. The column distinguished between the n-decane, primary, and secondary monochlorides but did not distinguish between the higher chlorides. A typical chromatograph is shown in Figure 3. This separation was sufficient for our work. Before the start of any experiment, air, which is known to inhibit chlorination reaction, was purged from the system by a stream of nitrogen. The reactor was then filled with decane and a stream of chlorine replaced the nitrogen. During the continuous flow experiments, it was assumed that a steady state was attained when the temperature of the reactor did not change for at least two residence times. Several preliminary experiments indicated that under these conditions the concentration in the system attains a steady state. In the experiments three different lots of n-decane manufactured by Phillips Petroleum Co. were used. The composition of each lot (classified by a number in brackets) was determined by passing a sample through a 500-ft stainless steel capillary column and analyzing the various compounds by a mass spectrograph. n-Decane (1) was found to be 99.9% pure and the two major contaminants were several isomers of n-decene and an aromatic compound. Due to the difficulty in separating the decane from the decene the lot may be only 99.5% pure. n-Decane (2) was found to be 97.0% pure and the major contaminants were 3-methylheptane, 4-methyloctane, benzene, n-C11, n-Clz, and a small amount of normal paraffins C13-C18. n-Decane (3) was found to be 99.3% pure and the major contaminant was branched undecane. The analysis indicates the existence of some additional trace impurities whose nature could not be determined. Lot n-decane (Id), which was used in several experiments, was almost 100% pure and contained a small trace of aromatic impurity. It was prepared by washing n-decane (1) several times with 78
Ind. Eng. Chem., Fundam., Vol. 13,No. 1, 1974
dilute KMn04 followed by several washes with concentrated until no further coloration appeared on further additions of acid. This decane was then distilled over PZOJ under a nitrogen atmosphere and the middle distillate was collected and redistilled ove; dry sodium under a dry nitrogen atmosphere. The chlorine (>99.5 vol 9'0) supplied by the Matheson Co. and the nitrogen (>99.95 vol %) manufactured by Union Carbide were dried by,passing over a drierite column before entering the reactor with an inlet pressure of 0.50 psig. The experiments were not carried out under strict adiabatic conditions due to the inevitable heat losses from the reactor. At high temperatures an appreciable part of these losses is due to the evaporation of the organic phase (boiling points of n-decane and 1-chlorodecane are 174.2"C and 225.8"C, respectively, while the average for the secondary monochlorodecane isomers is 209.8"C). The vortex of the liquid in the reactor was affected by changes in the position of the stirrer. Hence, in order to guarantee a constant liquid holdup, the position of the stirrer and its speed were controlled carefully during each run. The values of the holdup reported here are based on measurements at room temperature and pure decane. However, correlations indicate that the holdup at higher temperatures of a mixture containing various chlorinated products should not deviate significantly from the value reported here. The changes in the physical properties of the reaction mixture usually required a decrease in the power to the stirrer and a slight increase in the chlorine inlet pressure as the operation was shifted to higher temperature and conversion conditions. In all the experiments, unless otherwise specified, the temperature of the feed was 75°F. The inlet chlorine pressure was 0.5 psig and the pressure in the reactor was 0-4 cm of HzO. The flow rate of chlorine was 2.4 f 0.05 ft3/hr at 75°F and 1 atm pressure. The stirrer speed was 425 rpm and the decane holdup 344 cm3. Experimental Results a n d Discussion Preliminary Semibatch Experiment. Semibatch experiments in which a continuous chlorine feed was bubbled through a fixed amount of decane were carried out in order to compare the behavior of the four decane lots and to examine the phenomena which affect this reacting system. The experiments (Figures 4 and 5) revealed a marked difference between the temperature and concentration histories of the four lots and demonstrate that a small amount of impurity may change the qualitative behavior of the system. The high activity of n-decane (1) is most probably due to the catalytic action of the olefinic impurity. Evidently, the rapid addition reaction of the olefins liberates sufficient energy to dissociate molecular chlorine into free radicals and hence activates the substitution reaction. The distilled n-decane ( I d ) most probably represents the behavior of pure decane. The initial rapid jump of its temperature and conversion is apparently due to the presence of a very small impurity. The reduced activity of the other samples must be attributed to the presence of some chain inhibitors. A qualitative test for the presence of peroxides (liberation of iodine from KI-HCl solution) proved negative. The inhibiting effect in n-decane (3) was so strong that the batch did not ignite even after 6 hr when 34% of the decane had already been converted. The selectivity of the four decane samples (Figure 6) was essentially the same in spite of the large difference in reactivities. For the sake of clarity, Figure 6 contains only a fraction of the experimental data. The dashed curves in
I75
/"e ag I a,
4 25
20
60
40 T I M E Cminl
so
P-P-
-
n - D E C A N E (Id)
n n
RES,DENC€
LlQJlb
Figure 4. Temperature histories of the four n-decane lots during batch experiments
A
o 72
ff3/hr
I
1 . 1
0
2 4 fI3/hr
a
TIME
Cmln3
Figure 7. Steady-state temperatures as a function of the residence time for n-decane (1)for two chlorine flow rates
~
- DECANE ( 2 1
- DECANE ( 3 ) ,
0
20
0
40 TIME
60
80
Cminl
Figure 5 . The conversion of the four $-decane lots during batch experiments LIQUID
__-
AESIDEYCE
Iminl
Figure 8. Steady-state conversions and selectivities as a function of residence time for n-decane (1)for two chlorine flow rates
-DECANE (Id) 40, e n-DECANE ( I i 0 .-DECANE ( 2 1
% :
I 0L
I
40
20 L aui3 CONVERSION
TIME
OF DECANE
[mole
60
RESIDENCE T I M E cmlnl
%I
Figure 6. The selectivity as a function of n-decane conversion for the four lots during batch experiments that figure represent the predictions of eq 2 assuming p = 2.25, which is the value reported by Van de Vusse (1966) for chlorination at 100°C. The curves adequately fit the data up to 60% conversion. Visual observations revealed the existence of many small chlorine bubbles during the initial reaction period. However, during the rapid temperature rise, which occurred for all samples except n-decane (3), there was a rapid increase in the size of the bubbles and about a 30% expansion in the volume of the two-phase mixture. After a few minutes, the mixture returned to its original volume, but the size of the bubbles remained large. The rapid expansion is probably due to the sudden release of the rather insoluble hydrogen chloride as well as stripping of the dissolved chlorine due to reduced solubility a t increased temperatures.
Figure 9. Steady-state temperatures as a function of residence time for n-decane (2). The stirrer speed was 545 rpm and the liquid holdup was 246 cm3. Chlorine feed rate was 2.4 ft3/hr
Continuous Flow Experiments Experiments in a CSTR using n-decane (1) and two different gas flow rates (Figures 7 and 8) exhibited the existence of a unique stable steady state over a wide range of residence times. Figure 8 shows that the selectivity, defined as the ratio of monochlorodecane to the amount of converted decane, depends on the gas flow rate when reported as a function of the liquid residence time. However, when the selectivity is measured as a function of the conversion of decane it is found to be essentially independent of the chlorine flow rate except at low conversions, where its determination is accompanied with a relatively high experimental error. In all these experiments the degree of chlorine utilization was very high and the increase Ind.
Eng. C k m . , Fundam., Vol. 13, No. 1, 1974 79
'
7-
2 loo k sol-
A Y
# m-
2
E
s U
$
I
601 1 1 401
I
oLu
206
I-
IO
0
20 LIQUID
W LL I
30
A
-
.
50
40
RESIDENCE
L
TIME
60
70
2
50
0
Figure 10. Steady-state conversion and selectivity as a function of residence time for n-decane (2). The stirrer speed was 545 rpm and the liquid holdup 246 cm3 Chlorine feed rate was 2.4 ft3/hr
150
100
LIOUID
Cmnl
RESIDENCE TIME
Cminl
Figure 12. Steady-state conversion and selectivity as a function of liquid residence time for n-decane (3). Chlorine feed rate was 2.4 ft3/hr
t
LIQUID
RESIDENCE
TIME
Cminl
Figure 11. Steady-state temperature as a function of liquid residence time for n-decane (3). Chlorination feed rate was 2.4 ft3/hr
of temperature and conversion with either gas flow rate or liquid residence time is due to the increase in the ratio of the C12-CloH22 molar feed ratio. Experiments with n-decane (2) and a 2.4 ft3/hr chlorine feed rate (Figures 9 and 10) revealed the existence of two stable steady states, with rather different levels of temperature, conversion, and selectivity, for any liquid residence time in the range 8.6-18.3 min. Under these operating conditions the start-up procedure determined which specific steady state was attained. The conversion of the low temperature steady states was low, but their selectivity was very high. On the other hand, the conversion of the high-temperature steady states was high, but their selectivity decreased rapidly with increase in the conversion. The high-temperature steady states were obtained by operating in a batch mode until the temperature increased and then switching to a continuous feed of decane. 'The low-temperature steady states were attained by starting up with a continuous feed. Once a steady state was reached, additional steady states on the same branch were attained by slow variations in the feed rate. In several experiments the low-temperature steady states were ignited by irradiation of the reacting mixture for about 1 min by a small ultraviolet lamp, which was housed in a glass well inside the reactor. Several experimental runs in which the continuous decane feed was started at various temperatures and conversion levels were used to explore the possible existence of more than two stable steady-state branches. However, in all the experiment,s the reactor shifted to either one of the two stable steady states. Experiments with n-decane (3) (Figures 11 and 12) demonstrated the existence of two stable steady states for 80
Ind. Eng. Chem., Fundam., Vol. 13, No. 1. 1974
r
O L - -
0
I L-
--L
- - I
20
IO
LIOUID
R E S DENCE
I
30
40
-2
50
TIME I m n l
Figure 13. Steady-state temperature as a function of liquid residence time for n-decane (3) using an equimolar Clz-ClgH22 feed rate residence times larger than 25 min. Batch experiments with this decane indicated that a low temperature steady state would exist even for a residence time of 6 hr. Thus, we did not explore the exact residence time a t which ignition would occur. However, it was established that with this decane two stable steady states exist over a wide range of residence times. Several experiments with different start-up conditions were carried out to explore the existence of additional steady-state branches, but none were found. A branch of unstable steady states separates the branches of the stable states. The initial temperature at which the transition between a shift to a high- or lowtemperature steady state occurs approximates the unstable steady state, and these values are described by the dotted curve in Figure 11. The heating to the initial temperature was carried out by ultraviolet radiation which promoted a rapid reaction. Fortunately, the reactor's response when no light was radiated was rather slow. Hence, after some skill was acquired in the experimental technique, the intermediate steady state could be determined rather rapidly. It should be pointed out that the above technique can yield only approximate values, since the response of the reactor depends not only on the initial temperature but also on the initial composition of all the reacting species and we had no information about the exact composition of the unstable steady state. A comparison of the experiments with the three decane lots indicates that a small amount of impurities had a sig-
Y
u
W IY
c 2
a
K W
a
zc "z
1
A
: 2oL i ' Y
t
8
01
%
1
CONVERSI ON
0 % SELECTIVITY
2
0
t 1
' A IO LIOUIO
20
'
RESIDENCE
' 30
'
' 40
TIME Crninl
Figure 14. Steady-state conversion and selectivity as a function of liquid residence time for n-decane (3) using an equimolar ClzCloHzz feed rate
nificant effect on the quantitative as well as the qualitative behavior of the reactor and on the possible existence of steady-state multiplicity. Thus, the presence of impurities has important implications on the required start up and operation policies and any failure to account for it may lead to severe pitfalls. In all the previously reported experiments, the chlorine feed rate was maintained constant and independent of the decane feed rate. In practice it is common to maintain a certain prescribed ratio between the gas and liquid reactants feed rates. Figures 13 and 14 describe experiments in which the chlorine to decane molar feed ratio was always unity. The results exhibit essentially the same qualitative features as the fixed gas feed rate experiments (Figures 11 and 12). The liquid residence time at which extinction occurs for the equal molar feed case was 10 min as compared with 25 min for the fixed chlorine feed rate. The reason for this difference is that in the latter case the molar chlorine to decane feed rate ratio increases monotonically with the liquid residence time and its value at extinction is only 0.68. For all the high-temperature steady states the chlorine utilization was very high. Thus, for the fixed molar feed ratio experiments the conversion and selectivity of the high-temperature steady states were rather insensitive to changes in the liquid residence time. However, for the fixed chlorine feed experiments, the increase in the liquid residence time and the accompanying increase in the molar chlorine to decane feed rate ratio caused an increase in conversion and a decrease in selectivity.
Control by Feed Rate Cycling The experiments indicate that in order to obtain a reasonable compromise between activity and selectivity, it is most desirable to operate close to extinction. This situation is typical of many industrial applications where operation close to the point of instability or even close to or around a naturally unstable steady state yields .optimal results. Operation around an unstable steady state can be carried out by use of a feedback control. The choice of the states of the system that should be controlled and the operating variables that should be manipulated is the key to the design of a safe, reliable, and sound control scheme. It was decided to explore the possibility of feedback control close to an unstable steady state by manipulating thy decane flow rate manually as the temperature changed between prescribed limits. The temperature was used as the control variable since it could be measured continuously with negligible time delay. This control
In IY W
z
8 ar
-
33Ji
0 N
30
h
u-
s
9
\
0
P,
26 0
\
'Q
TIME
IO
20
, 30
[Mln]
, 40
Figure 15. Transient temperature, conversion, and monochlorodecane yield during controlled cyclic operation using n-decane (3) and a 2.4 ft3/hr chlorine feed rate
43
I
115
120
125
TEMPERATURE,
J
130 [
'CI
Figure 16. Limit cycle obtained during controlled cyclic operation with n-decane (3) and 2.4 ft3/hr chlorine feed rate
scheme was based on the knowledge that when the decane flow rate exceeds the value corresponding to extinction, the reactor always shifts toward the unique low-temperature steady state and the temperature decreases. On the other hand, when the liquid flow rate decreases below that corresponding to extinction, then if the initial temperature exceeds that of the intermediate unstable steady state, the reactor shifts to the high-temperature steady state and the temperature increases.' When the temperature of the reactor exceeds only slightly that of the unstable steady state, the shift to the high-temperature steady state may not occur with some special liquid-phase compositions. Thus, in order to increase the reliability of the control policy, the switch in flow rates was made when the temperature was about 17°C above that of the unstable steady state. The temperature, decane conversion, and yield of monochlordecane histories, which are described in Figure 15, were obtained by use of the above control policy. The reactor converged quickly to a stable cyclic mode of operation. Each cycle consisted of 7 and 6.6 min operation with the high and low flow rates, respectively. The flow rate averaged residence time was 27.5 min while the flow averaged conversion and selectivity were 47.4 and 6370, respectively, and the flow averaged temperature was 123°C. The flow averaged selectivity of this stable feedback controlled periodic operation around an unstable steady state exceeds that which can be attained by any Ind. Eng. Chern., Fundarn., Vol. 13, No. 1, 1974
81
stable steady state with the same conversion. A description of the temperature as a function of conversion during one of the cycles is shown in Figure 16. It should be noted that theoretical considerations do not guarantee a priori that the reactor, which is characterized by a large number of dependent variables, will shift toward a stable limit cycle. Due to the nonlinear nature of the system the time averaged flow rate usually differs from the average of the two limiting flow rates. The switching frequency depends in general on the width of the temperature control band and the two limiting flow rates. Selection of the control band and the two limiting flow rates determines the time averaged flow rate. In practice the averaged flow rate is a specified value. Thus, the selection of the flow rates and the control band, which yields a prescribed time averaged flow rate, requires either on-line tuning or iterative use of numerical or analog simulations. Several experiments indicated that the above feedback control was very reliable, safe, and easy to implement, due to the slow response of the reactor. The results of numerical simulations as well as of other control policies which are being experimented with at present will be reported elsewhere. The describing function method (Gelb and VanDer Velde, 1968; Holtzman, 1970) can be used for checking whether the feedback control will result in a stable oscillatory operation and for determining its frequency and amplitude ratio. The main deficiency of this approach is that it fails in certain cases (Holtzman, 1970), is restricted to the region in which the linearized dynamic model of the system is valid, and is rather cumbersome to apply to a system with many dependent variables. Moreover, this technique requires an accurate linearized model and exact knowledge of all the parameters which appear in it. Unfortunately, this information is rarely available and the design of the control scheme usually has to be based on a simplified lumped dynamic model. This approach is usually successful ,but may lead to pitfalls when the dynamic response is very sensitive to the details of the mathematical model or to the value of its parameters. Concluding Remarks The experimental study demonstrates that under certain operating conditions two stable steady states with widely different levels of temperature, conversion, and selectivity exist during the chlorination of decane in a CSTR. The fact that the behavior of the reactor and the possible existence of multiple steady states were strongly dependent on the presence of a small amount of impurities has important practical implications. While there is no hope of an exact a priori prediction of the effect of unidentified impurities, their possible effects have to be accounted for during the design, since contaminants are always present in industrial feeds. Vejtasa and Schmitz (1970) have described a simple technique for predicting the behavior of an adiabatic CSTR, in which a single homogeneous exothermic reaction occurs, from the temperature history of a single batch experiment. It would be of much value to extend this technique for a gas-liquid CSTR in which multiple competing exothermic reactions occur. However, there are two difficulties which prevent a direct application. First, when
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several competing reactions occur, the product distribution in an adiabatic CSTR and an adiabatic batch reactor are in general different when the temperature in both reactors is the same. Moreover, for organic reactions the exact heat of the reaction depends on the isomer which is being formed. Secondly, strict adiabatic operation is not feasible in gas-liquid reactors due to the inherent heat losses caused by the flowing gas and the evaporation of the liquid. It seems that the only solution is use of a batch experiment for determination of the key kinetic and physical parameters to be used in a model of the CSTR. This is by no means a simple task due to the large number of interacting physical and chemical rate processes and the fact that the controlling rate processes do often change with the temperature. This point will be discussed in detail in a forthcoming publication. The experiments demonstrate the advantages of controlling the reactor close to the unstable steady state. The relatively slow response of the reactor makes the implementation and on-line tuning of the controller a rather easy task. Fortunately, the dynamic response of many chemical reactors is rather slow and a design and tuning of a controller, which will keep the reactor close to a n unstable steady state, should not be too difficult. In this study the feedback control scheme was based on manipulation of the liquid reactant flow rate. Other control policies are obviously possible, and there is a definite need for experimental and theoretical studies on the merits and disadvantages of each control scheme. Acknowledgments A preliminary investigation of this system has been carried out by Paul P. Buntin and Stephen W. Johnston as a senior students' project. We are most thankful to Drs. D. W. Nooner and S. C. Welch for help in the analysis and purification of the decane and to Dr. J. E. Bailey for helpful discussions. Literature Cited Bilous, O., Amundson, N. R.,A./.C.h.E. J. 1,513 (1955). Bonhoeffer, K. F., Z. Nekfrochem. 51, 24 (1948a). Bonhoeffer, K . F., 2. Eiektrochem. 51, 29 (1948b). Bonhoeffer, K. F., Z. Elektrochem. 52, 60 (1949a). Bonboeffer, K. F., Z. Eiektrochem. 52, 67 (1949b). Bonhoeffer, K. F., Z. Elekfrochem. 52, 149 ( 1 9 4 9 ~ ) . Bratolyubov, A. S., Russ. Chem. Rev. 30,602 (f961). Bush, S.F., Proc. Roy. SOC.,Ser. A 309, 1 (1969). Fjeld, M., Ph.D. Thesis, University of Trondheim, Norway, 1971. Furusawa, T., Nishimura, H., Mlyauchi, T., J. Chem. Eng. Jap. 2, 95 (1969). Gelb, A . , VanDer Velde, W. E., "Multiple Input Describing Functions," McGraw-Hill, New York, N. Y., 1968. Golikeri, S.V., Luss, D., Chem. Eng. Sci. in press (1974). Hancock, M. D., Kenney, C. N., Chem. React. Eng., Int. Symp., 2nd (1972). Holtzman, J. M., "Nonlinear System Theory," Prentice-Hail. New York, N. Y.. 1970. iscol, L., Proc.-JointAuto. Conf. Conf. 602 (1970). Knorr, R. S., O'Driscoll, K. F., J. Appl. Polym. Sci. 14, 2683 (1970). Liljenroth, F. G., Chem. Met. Eng. 19, 287 (1918). Schrnitz, R. A . , Arnundson, N. R., Chem. Eng. Sci. 18, 265 (1963a). Schrnitz, R. A., Arnundson, N. R., Chem. Eng. Sci. 18,391 (1963b). Schmitz, R. A., Arnundson, N. R., Chem. Eng. Sci. 18,415 ( 1 9 6 3 ~ ) . Schrnitz, R. A., Arnundson, N. R., Chem. Eng. Sci. 18,447 (19636). Van de Vusse, J., Chem. Eng. Sci. 21, 631 (1966). Vejtasa, S. A., Schmitz, R. A.,A./.C.h.E. J. 16,410 (1970). Westerterp, K. R . , Chem. Eng. Sci. 17, 423 (1962).
Receiuedfor review March 5, 1973 Accepted August 16, 1973
