Ind. Eng. Chem. Res. 1987,26, 1536-1540
1536
Chem. Eng. Sci. 1985a, 40(1), 59-74. Holt, B. R.; Morari, M. “Design of Resilient Processing Plants V. The Effect of Deadtime on Dynamic Resilience”, Chem. Eng. Sci. 1985b, 40(7), 1229-1237. Huang, H.; Stephanopoulos, G. “Adaptive Design of Model-Based Controllers”, Presented at the American Control Conference, Boston, 1985. Kantor, J. C.; Andres, R. P. “The Analysis and Design of Smith Predictors Using Singular Nyquist Arrays”, Int. J. Control 1980, 30(4), 655-664. Meyer, C.; Seborg, D. E.; Wood, R. K. “A Comparison of the Smith Predictor and Conventional Feedback Control”, Chem. Eng. Sei. 1976, 31 775-778. Meyer, C.; Seborg, D. E.; Wood, R. K. “An Experimental Application of Time Delay Compensation Techniques to Distillation Column Control”, Znd. Eng. Chem. Process Des. Dev. 1978,17(1), 62-67. Meyer, C. B. G.; Wood, R. K.; Seborg, D. E. “Experimental Evaluation of Analytical and Smith Predictors for Distillation Column Control”, AIChE J. 1979, 25(1), 24-32. Moore, C. F.; Smith, C. L.; Murrill, P. W. “Improved Algorithm for Direct Digital Control”, Znstrum. Control Syst. 1970, 43, 70. Ogunnaike, B. A,; Ray, W. H. “Multivariable Controller Design for Linear Systems Having Multiple Time Delays”, AIChE J. 1979, 25(6), 1043-1057.
Pavlechko, P. D.; Wellons, M. C.; Edgar, T. F. “Multivariable Adaptive Control with the Generalized Analytical Predictor”, Presented at the AIChE Meeting, Miami Beach, 1986. Smith, 0. J. M. “Closer Control of Loops with Dead Time”, Chem. Eng. Prog. 1957, 53, 217. Watanabe, K.; Ishiyama, Y.; Ito, M. “Modified Smith Predictor Control for Multivariable Systems with Delays and Unmeasurable Step Disturbances”, Znt. J. Control 1983, 37(5), 959-973. Wellons, M. C. “A Generalized Analytical Predictor for Process Control”, Masters Thesis, University of Texas, Austin, May 1985. Wellons, M. C.; Edgar, T. F. “A Generalized Analytical Predictor for Process Control”, Proceedings of the American Control Conference, 1985, p 637. Wong, K. P.; Seborg, D. E. “A Theoretical Analysis of Smith and Analytical Predictors”, AZChE J. 1986, 32(10), 1597-1605. Wood, R. K.; Berry, M. W. ”Terminal Composition Control of a Binary Distillation Column”, Chem. Eng. Sci. 1973,28, 1707-1717. Zafiriou, E.; Morari, M. “Digital Controllers for SISO Systems-A Review and a New Algorithm”, Znt. J. Control 1985, 42(4), 855-876. Received for review March 14, 1986 Revised manuscript received May 18, 1987 Accepted May 24, 1987
Kinetics of the Hydrobromination of 10-Undecenoic Acid Suhas P. Bhagwat,? D. H. S. Ramkumar, Raghunathan S. Tirukkoyilur, and Arvind P. Kudchadker* Department of Chemical Engineering, Indian Institute of Technology, Bombay 400 076, India
The kinetics of the reaction between 10-undecenoic acid and hydrogen bromide solution in toluene initiated by benzoyl peroxide was studied in a batch reactor in the temperature range 0-30 O C . The effects of temperature, initiator concentration, and initial mole ratio of HBr to 10-undecenoic acid on the yield of ll-bromoundecanoic acid and reaction rates were experimentally investigated. This reaction was found to exhibit “limiting conversion” behavior in the range of variables studied. A plausible explanation in the form of a mechanistic scheme for the overall reaction is provided. On the basis of the kinetic results, a free-radical chain reaction mechanism for the formation of 11bromoundecanoic acid from hydrogen bromide and 10-undecenoic acid has been postulated. Hydrobromination of 10-undecenoic acid (10-UA) to 11-bromoundecanoicacid (11-BUA)is one of the important steps in the manufacture of nylon-11 from m t o r oil, which is a renewable agricultural resource. Nylon 11 possesses superior mechanical characteristics and also better physical as well as chemical properties than nylon 6 and nylon 66 for specific applications (Aelion, 1956). Hydrobromination of 10-undecenoic acid can be represented as CH2=CH(CH2)&OOH 10-UA
+ HBr
peroxide
Br(CHJloCOOH (1) 11-BUA
In the presence of a peroxide, the terminal addition of hydrogen bromide takes place by anti-Markovnikov’srule (Kharasch and Mayo, 1933). The aim of this work is to present our experimental investigations on the kinetics of this hydrobromination reaction. This reaction was carried out in the past by various investigators (Walker and Lumsden, 1901; Smith, 1935; Urshibara and Takebayashi, 1938; Jones, 1947; Societe Organico, 1957; Adamek and Scheiber, 1959) using different experimental conditions. Presently at Larsen and Toubro Ltd., Bombay 400 072, India.
The common method of carrying out this reaction is to pass dry HBr gas through a solution of 10-undecenoic acid in a suitable solvent. However, in the present investigation, a solution of HBr in toluene was used and the integral method of analysis of batch reactor data was carried out. Toluene was chosen as the solvent, as the solubility of HBr gas is higher in toluene than in other reported solvents (Obrien and Bobaleck, 1940). Benzoyl peroxide was used as initiator in the reaction studied in the temperature range 0-30 “C.
Experimental Section Materials. 10-Undecenoicacid (Jayant Oil Mills, India) was found to be 98.5% pure, as determined by its iodine value, 135. The maximum concentration of hydrogen bromide in toluene (Sontara Organic Industries, India) was 0.4-0.42 kmol/m3. Additional solution of HBr in toluene was prepared by evolving out HBr gas from its solution in acetic acid and dissolving it in AR-grade toluene. Benzoyl peroxide (Robert-Johnson, India) and all other reagents used in the analysis were of analytical reagent grade. Experimental Setup. Experiments were carried out in a stirred batch reactor made of stainless steel (Bhagwat, 1982). Temperatures in the range of 0-30 “C were main-
0888-588518712626-1536$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1537 Table I. Limiting Conversion Data under Various Experimental Conditions run
temp, K
7 8 9 11 14 15 16 17 18 19 20 21 22 23 24 26 27 28 29 30 31 32 33 34 35
303.15 303.15 303.15 303.15 283.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 293.15 293.15 293.15 283.15 283.15 283.15 283.15 273.15 273.15 273.15
CTn, kmol/m3 5.95 x 10-3 5.95 x 10-3 5.95 x 10-3 0.011 0.018 0.018 0.018 0.018 0.018 0.018 0.012 5.95 x 10-3 2.93 x 10-3 8.92 x 10-3 0.023 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018
CR,, kmol/m3 M = C a n / C ~ n 0.215 0.215 0.213 0.215 0.250 0.333 0.243 0.213 0.224 0.215 0.215 0.286 0.213 0.215 0.212 0.176 0.166 0.215 0.179 9.325 0.250 0.148 0.329 0.358 0.187
1.55 1.53 1.56 1.67 1.81 0.95 1.21 1.39 1.50 1.53 1.71 1.44 1.61 1.46 1.49 0.98 1.25 1.45 1.42 1.37 1.06 1.38 1.06 1.06 1.06
XR,
k,"
0.600 0.630 0.640 0.680 0.785 0.560 0.578 0.619 0.620 0.640 0.690 0.540 0.649 0.649 0.642 0.535 0.595 0.703 0.715 0.800 0.700 0.682 0.769 0.739 0.678
0.103 0.083 0.088 0.035 0.049 0.122 0.124 0.136 0.150 0.139 0.116 0.141 0.109 0.111 0.145 0.069 0.071 0.077 0.045 0.052 0.049 0.044 0.033 0.037 0.027
kn 2.377 2.194 2.351 0.721 0.872 1.901 1.931 2.290 2.171 2.181 2.268 2.220 4.114 2.732 2.132 1.749 1.634 1.637 1.244 1.181 1.500 1.361 1.069 0.946 1.013
ko at 30 "C = 2.256
ko at 20 "C = 1.672
ko at 10 "C = 1.321
ko at 0 "C = 1.009
kd values in the present study are considerably higher as compared to the data reported in the literature (Bartlett and Nozaki, 1946). This may be attributed to the fast decomposition of benzoyl peroxide on the walls of the reactor.
tained within f 2 "C. Due to HBr, some amount of corrosion was found to occur inside the stainless steel reactor. The reactor had to be thoroughly cleaned before it could be used for the next run. The conversion of 10-UA was studied by determining the concentrations of both HBr and 10-UA independently, and the agreement between these two routes was found to be within our experimental uncertainties. Analysis. Samples were withdrawn from the reactor at regular intervals of time and were analyzed for 10-UA and HBr. A known part of a sample was added to a flask containing diethanolamine, and the iodine value of 10-UA in that part was found by Wij's method (Indian Standards, 1964). The other part of the sample was simultaneously added to a flask containing standard silver nitrate solution, and a standard sodium chloride solution was then added. The unreacted sodium chloride was analyzed by Mohr's titration (Shapiro and Gunevich, 1972) in order to determine HBr concentration in the sample. The error in our analytical procedure is estimated to be a maximum of *3%. Other experimental details are given in the supplementary material (see paragraph at the end of this article regarding supplementary material).
observed even at very large times of reaction. It appears, therefore, that an appropriate description of the observed maximum conversion under a given set of experimental conditions would be to denote it as "the limiting conversion" in the overall process. Table I lists the limiting conversions obtained at a variety of operating conditions. An explanation of the observance of the limiting conversion may be obtained by a detailed study of the overall reaction mechanism. Benzoyl peroxide is known to act as a free-radical initiator especially in the homopolymerization of several vinyl monomers: CH,=CHX where X is a substituent such as H, CH,COO, etc. The reactant B of the present study can also be considered as CH,=CHY where Y stands for (CH,),COOH. It is wellknown that reactions initiated by substances such as benzoyl peroxide and other free-radical-generating species exhibit low limiting conversions although the equilibrium conversions of the reactant are much higher. The kinetic origin of this phenomenon arises from the fact that the overall rate equation of the main reaction may be written as r = (concn of reactants of the main reaction) X (rate of generation of free radicals through the decomposition of benzoyl peroxide)'I2
Results and Discussion The reactor was operated under conditions of "good mixing", and this was ensured by maintaining agitation levels at ca. 700 rpm (any increased agitation beyond this level did not make any material change to the concentrations). Limiting Conversions in the Hydrobromination. A very interesting observation made in the present study relates to the virtual stoppage (or ceasing) of the overall hydrobromination reaction at conversions of the limiting reagent (10-undecenoic acid) far removed from the thermodynamic equilibrium conversions. An estimate of the equilibrium constant at 298.15 K was made, and it was found to be 96.7, corresponding to a &Go (298.15 K) of -11.4 kJ/mol. It is also useful to remark that Kharasch and Mayo (1933) have observed that this reaction is essentially irreversible although near 100% completion is not
r = f(CA, Cg, CR, etc.)Riliz The occurrence of limiting conversions in the hydrobromination of undecenoic acid may be attributed in a similar fashion to the existence of a rate equation which contains the term Rill2 as a product. Since, BZzOz= 2C6H&00'[-rI = Ri = kdCI] (3) the reaction rate for the hydrobromination must be of the form r = f ( c A 7 c B 7 CR)(kdCI)'i2 (4) In order to correlate the experimental information on hand, the integral method of analysis of the data was employed by using two different forms of f(CA, CB, CR) in eq 4, and these are presented below. Considering that 11BUA is the sole product of reaction according to A + B
1538 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
r o P
0 8-
0 10 6-
0.71
o -- Colculoled Expermenial
t o 5 XB 0 4-
- - Calculated o
Y
0
l
l
20
40
l
60
l
80
l
l
f
IC0
120
140
l
l
I80
160
l
200
l
220
Experimental
l
240
Lu-d-2-
Time,min
0
Figure 1. Plot of XB vs. t for run 14.
= R, we have cases I and 11. Case I. Assuming f(CA, CB, CR) = kCACB, one finds r = koCACBCI1/’
10
20
40
30
Time,min
50
60
Figure 2. Plot of XB vs. t for run 17.
1
0.6
In a constant-volume batch isothermal reactor, CI = CIOeXp(-kdt) A mass balance on B leads to l n ( M(1 M --XXB) B )=k’[l--exp(-?)]
-
P
(5)
where
--
Calculated
2
k’ = ( M - 1)CBoCIo1/2-ko kd
Data on limiting conversion XB at t = m may be u ed to evaluate k’from ( 5 ) . By rearranging eq 5, we get
”
10
20 30 Time, min
40
50
60
--.c
Figure 3. Plot of XB vs. t for run 21.
One can therefore evaluate kd and ko from the slope of the plot of the left-hand side vs. time in eq 6 for each experimental XB - t data. These values are also summarized in Table I, with their average values at each temperature. Case 11. Assuming f(C,, CB, CR) = ko[CACB- (CR/Ke)],
1 0’5
O.jl
where
- - Calculated
0.3
o
[(
( M + 1 + 1 1 ~- ~ ) ( M + 1) +
$)
-4
~]”*
r2 =
2 The estimates of ko are not very different between the two cases, which further lends support to the fact that the overall reaction is essentially irreversible. Hence, the recommended rate equation which satisfactorily describes the observed kinetic course of the reaction is r = koCACBCI1/’ ko = A. exp(-E/RT)
(8) The performance of a batch reactor under a variety of operating conditions can be evaluated by using eq 5. The
0
- Experimental
Y , , , , , , 20 30
-
40
10
Time,min
50
60
Figure 4. Plot of XB vs. t for run 22.
results of these calculations together with the experimental findings for some typical runs are presented in the form of X B vs. t curves shown in Figures 1-4. The effect of temperature on ko has been ascertained by plotting In ko vs. 1 / T (Figure 5) and one finds the Arrhenius equation parameters as A. = 5.3 X lo3 (m3/kmol)1.5.min-1 E = 19.6 kJ/mol kd = 2.53 x io4 exp(-3729.3/T) min-l (9)
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1539
Table Effect Benioyl Peroxide Product 0 ' 9 11.
of
on
Composition
wt%
11-BUA in run 1
2 3 4 5
6
product Cr, kmol/m3 mD of moduct. "C mixture 0.0 32 16 or 4 F 0.0 30 24 or 40" 5.95 x 10-3 48.5 99 2.93 x 10-3 49 100 0.018 49 100 0.023 48 98
Corresponding to the melting point lying between 25.5 "C (the eutectic point) and 35 "C (the mp of the 10-bromo isomer), two possible compositions are obtained (Ashton and Smith, 1934).
Equation 10 for the rate of production of ll-bromoundecanoic acid may be represented by
r~ = ~ O C H B ~ C C H ~ C H Y C I ~ / ~(11) where Figure 5. Arrhenius plot for (a) In ko vs. 1/T (0) and (b) In kd vs. 1/T (X).
Thus, one may conclude that eq 8 and 9 are reasonable descriptions of the kinetics of hydrobromination of 10undecenoic acid in the presence of benzoyl peroxide in the range of the experimental variables studied. Mechanism of the Reaction. In an effort to justify the experimentally observed formal dependence of the rate of reaction on CA,CB,and CI, attempts were made to devise a set of mechanistic steps consistent with eq 8. Several alternative reaction paths were hypothesized involving the production and reaction of free radiql/atomic species such as Br', BrCH2CHY,C&15CO0., CH2CHY,etc., and leading to the formation of 11-bromoundecanoic acid (R). The overall rate equation for the production of R, on the basis of Bodenstein's stationary state hypothesis, was derived for each mechanistic scherfie and compared with eq 8. The scheme of mechanistic steps that is consistent with eq 8 was found to be
lZo =
(
)
2k,2k22kd ' I 2
k5k32
Side Reactions. The above analysis is based on the assumption that 11-BUA is the sole product of hydrobromination reaction. During the present study, the supposition may be considered very good in view of the fact that not more than 2% by weight product mixture consisted of 10-BUA. In separate runs, the product of reaction was crystallized out of the reaction mixture, and the relative proportions of 10-BUA and 11-BUA were ascertained by the determination of the melting point of the mixture. The results of these are summarized in Table 11. It may be seen that the assumption of a single reaction leading to the 11-BUA in the presence of benzoyl peroxide is a satisfactory one. Acknowledgment We thank IIT, Bombay, for financial assistance.
+
C6H5C06 + HBr A
C6H5COOH Br k
+ CH2CHY & BrCH,CHY k3 BrCH2CHY + HBr -% BrCH2CH2Y + Br Br
2Br
wall
R
Br2
k6
A reaction mechanism on similar lines to the present one was proposed for the photobrolaination of ethylene and trans-dichloroethylene (Steacie, 1954). The overall rate equation may be written as
Comparing the terms k4(HBr) and k3, one observes that k3 represents the rate constant of a reaction involving a radical alone, whereas the rate constant k4 is related to a reaction involving a radical and a moledule. Therefore, k4 (usually associated with higher activation energy) can be expected to be much smaller than k3. Under these conditions, one may consider k4(HBr)
