I n d . Eng. Chem. Res. 1987, 26, 1796-1803
1796
larger than the submicropores. Registry No. 02,7782-44-7; COZ, 124-38-9.
Literature Cited Ballal, G. Ph.D. Dissertation, Rice University, Houston, 1985. Ballal, G.; Zygourakis, K. Ind. Eng. Chem. Res. 1987, 26, 911. Bhatia, S. K.; Perlmutter, D. D. AIChE J . 1980, 26, 379. Bhatia, S. K.; Perlmutter, D. D. AIChE J . 1981, 27, 226. Dubinin, M. M. “Porous Structure and Adsorption Properties of Actie Carbons”, In Chemistry and Physics of Carbon;Walker, P. L., Jr., Ed.; Marcel Dekker: New York, 1966; Vol. 2, p 51. Dutta, S.; Wen, C. Y. Ind. Eng. Chem. Process Des. Deu. 1977, 16, 20. Dutta, S.; Wen, C. Y.; Belt, R. J. Ind. Eng. Chem. Process Des. Deu. 1977, 16, 31. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1979; pp 190-200. Gan, H.; Nandi, S. P.; Walker, P. L., Jr. Fuel 1972. 51, 272. Gavalas, G. R. AIChE J . 1980,26, 577. Guerin, H.; Siemieniewska, T.;Grillet, Y.; Francois, M. Carbon 1970, 8, 727. Guerin, H.; Siemieniewska. T.; Grillet. Y.; Francois, M. Carbon 1971, 9, 657.
Hashimoto, K.; Miura, K.; Yoshikawa, F.; Imai, I. Ind. Eng. Chem. Process Des. Deu. 1979, 16, 72. Hippo, E.; Walker, P. L., Jr. Fuel 1975, 54, 245. Jenkins, R. G.; Nandi, S. P.; Walker, P. L., Jr. Fuel 1973, 52, 288. Kamishita, M.; Mahajan, 0. P.; Walker, P. L., Jr. Fuel 1977,56,444. Kelemen, S . R.; Freund, H. Carbon 1985, 23, 723. Lamond, T. G.; Marsh, H. Carbon 1964, 1, 28. Linares-Solano, A.; Mahajan, 0. P.; Walker, P. L., Jr. Fuel 1979,58. 327. Mahajan, 0. P.; Walker, P. L., Jr. Fuel 1979, 58, 333. Mahajan, 0. P. “Adsorption and Pore Structure and Coal-Water Interactions”, In Sample Selection, Aging and Reactivity of Coal; Klein, R., Wellek, R., Eds.; Wiley: New York, 1984. Marsh, H.; Wynne-Jones, W. F. K. Carbon 1964, I , 269. Moudgalya, K. Ph.D. Dissertation, Rice University, Houston, 1985. Moudgalya, K.; Zygourakis, K. Chem. Eng. Commun. 1986,49, 165. Tomita, A.; Mahajan, 0. P.; Walker, P. L., Jr. Fuel 1977, 56, 137. Tseng, H. P.; Edgar, T. F. Fuel 1984, 63, 385. Tseng, H. P.; Edgar, T. F. Fuel 1985, 64, 373. Zygourakis, K.; Arri, L.; Amundson, N. R. Ind. Eng. Chem. Fundam. 1982, 21, 1.
Received for review November 1, 1985 Revised manuscript received J u n e 1, 1987 Accepted J u n e 22, 1987
Kinetics of Simultaneous Absorption of Ethylene and Chlorine into Water and Hydrochloric Acid in an Agitated Vessel with a Flat Gas-Liquid Interface Haruo Hikita, Haruo Ishikawa,* Takashi Okamoto, and Kiyotaka Mogami Department of Chemical Engineering, University of Osaka Prefecture, 804 Mozu- Umemachi 4-cho, Sakai, Osaka 591, Japan
The rate of simultaneous absorption of ethylene and chlorine into water and hydrochloric acid was measured at 288.2,298.2, and 308.2 K by using a baffled agitated vessel operated batchwise. The experimental results were analyzed by using chemical absorption theory based on the Leveque model. The experimental reaction factors supported the reaction mechanism in which ethylene reacts with chlorine to form a charged intermediate, and the resulting intermediate reacts with water to produce ethylene chlorohydrin and also with chloride ions to produce ethylene dichloride. The reaction rate constant of the rate-controlling reaction was determined and correlated by a n empirical equation. Ethylene chlorohydrin is an important intermediate for the synthesis of various organic compounds and is manufactured by absorbing ethylene into chlorine water. A substantial amount of information, therefore, is available on the reaction between chlorine and ethylene. However, much of the information is concerned with yields of ethylene chlorohydrin under specific conditions. Investigations of the kinetics of the reaction between ethylene and chlorine and the kinetics of the absorption of ethylene into aqueous chlorine solutions are rather limited, and the results are contradictory, as will be reviewed below. Two different mechanisms have been suggested for the reaction. Gomberg (1919) postulated first that ethylene reacts with free chlorine in solution to produce ethylene dichloride and also with hypochlorous acid to form ethylene chlorohydrin as CzH, + Clz C1CH2CH,C1 (a) CZH, + HOCl ClCHZCHzOH (b) where HOCl is formed by the hydrolysis of C1, as
-
4
* To whom
correspondence should be addressed.
0888-5885/87/2626-1796$01.50/0
Clz + H 2 0 + HOCl
+ H+ + C1-
(C)
Later, Shilov (1949) proposed a different mechanism in which the reaction proceeds via an intermediate complex of ethylene and chlorine as shown in the reaction scheme C2H4
+ Cl,
-
C2H4-.Cl2 yliquid-phase complex)
C2H4.-Cl2+ H 2 0
-
(d)
ClCH2CHz0H+ H+ + C1- (e)
Akehata and Johnson (1965) carried out experiments on the absorption of ethylene into aqueous chlorine solutions in an agitated vessel with a flat gas-liquid interface and made a quantitative analysis by using chemical absorption theory based on the film model. This was the first investigation in which the kinetics of the absorption of ethylene into aqueous chlorine solutions was analyzed by using chemical absorption theory. They determined the rate constant of reaction b by comparing the experimental reaction factors, measured by using nonacidified chlorine solutions, with theoretical predictions based on the Gomberg mechanism. However, their experimental results did not necessarily support the Gomberg mechanism. According to the Gomberg mechanism, the reaction factor 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1797 is expected to be smaller when C2H, is absorbed into acidified chlorine solutions than when nonacidified solutions are used as absorbing liquids, due to lower HOC1 concentration in the former case. Their experimental reaction factors obtained by using acidified chlorine solutions, however, were much larger than those obtained by using nonacidified chlorine solutions, and furthermore, these values were higher than those predicted for absorption accompanied by an instantaneous chemical reaction. Dun and Wood (1966, 1967) measured the rate of absorption of ethylene into aqueous chlorine solutions using a wetted-wall column. They also analyzed the absorption rates, obtained by using acidified chlorine solutions, with absorption theory based on the penetration model and determined the second-order rate constant of reaction d. However, they did not analyze theoretically the reaction factors for absorption of CzH4into nonacidified chlorine solutions and gave only a qualitative explanation for the difference in the reaction factors measured by using acidified and nonacidified aqueous solutions as absorbing liquids. Recently, a new enzymatic process for epoxidation of alkenes via halohydrin has been proposed (Neidleman, 1980). If this process is successfully industrialized, the old processes for producing chlorohydrin as an intermediate may be replaced by this process. However, the improvement of the old processes is important, and it is still worthwhile to clarify the mechanism and the kinetics of the reaction between ethylene and chlorine in aqueous solutions. In the present work, experiments on the simultaneous absorption of ethylene and chlorine gases into water and hydrochloric acid have been performed at various temperatures by using a similar baffled agitated vessel with a flat gas-liquid interface to that used by Hikita et al. (1969, 1975, 1980), and the results of absorption rate have been analyzed by using chemical absorption theory based on the Leveque model (Leveque, 1928; Hikita et al., 1973a, 1975), in order to clarify the mechanism and the kinetics of the reaction between ethylene and chlorine in aqueous solutions.
Theory Chemical Reaction Mechanism. Of the two reaction mechanisms proposed by Gomberg (1919) and Shilov (1949), the latter is considered to be more plausible. Therefore, we used a mechanism similar to that of Shilov for analyzing the experimental absorption rates. Though Shilov postulated an intermediate complex of ethylene and chlorine, we assume a different liquid-phase intermediate which is formed by the reaction C2H4 t Cl2
-
CH2-CH2
t CI-
(f)
\CI+’
1
Intermediate 1, which was first assumed by Roberts and Kimball (1937), reacts with water to produce ethylenechlorohydrin and hydrogen ions and also with C1- to produce ethylene dichloride CH2-CH2 \CI+’ CH2-CH2
t Hfl
-
t CI-
ClCH2CH2OH
+
CICH2CH2CI
H’
(0)
(h)
‘CI+’
In addition to the reactions f-h, the hydrolysis of ClZ given by reaction c occurs also as a side reaction in aqueous solutions. However, the hydrolysis of Clz can be neglected
when hdyrochloric acid of sufficiently high concentration is used as an absorbing liquid. Chemical Absorption Mechanism. As postulated by past investigators, we assume that reaction f is first-order with respect to both concentrations of C2H4and C1, and is the rate-controlling reaction of the three reactions, reactions f-h, while taking into consideration the hydrolysis of C1, in nonacidified solutions. Then, the differential equations describing the diffusion of C2H4,Cl,, HOCI, and H+(Cl-) in the solution, based on the Leveque model, can be written as ux (aA/ay) = DAL ax
(a2A/ax2)-
AB
(1)
( a B / a y ) = DBL (a2B/aX2)- k f A B - kJ3 + k,‘EF2 (2)
+ kJ3 - k,‘EF2 (3) ( d F / a y ) = DFL (d2F/dx2)+ kJ3 - k,’EF* + &AB ax ( d E / d y ) = DEL (a2E/ax2)
ax
(4) where A, B, E , and F express the concentrations of C2H4, Clz, HOC1, and H+(Cl-), respectively. The a in eq 4 expresses the ratio of the production rate of ethylene chlorohydrin to the total production rates of ethylene chlorohydrin and ethylene dichloride and is defined by k,H 1 1 where G and H stand for the concentration of C1- and 1, respectively. The boundary conditions are given by y=O, x>O; A=O, B=Bo, (6) F = Fo E = Eo, y IO,
x = 0; = 0,
A = Ai, B = Bi, aF/ax = o
(7)
x =
A = 0, F = Fo
(8)
m/ax yI0,
m;
E =Eo,
B = Bo,
Equations 1-5 are nonlinear partial differential equations and cannot be solved analyticslly. Therefore, they must be solved numerically to obtain the reaction factors PA and PB by the finite difference method similar to those used by Brian et al. (1961) and Hikita et al. (197313). Here the reaction factors PA and PB for CzH4and Cl,, respectively, are defined as PA
PB
=
NA/kLA*Ai
= NB/kLB*(Bi - BO)
(9)
(10)
When hydrochloric acid is used as an absorbing liquid, the hydrolysis of C1, can be neglected as mentioned above. In this case, the above problem is reduced to that of simultaneous absorption of two gases A and B accompanied by a reaction, A + B products. This problem was first solved numerically by Roper et al. (1962), who obtained a solution for the reaction factors based on the penetration model. However, the range of variables covered in their numerical calculations was limited. Later, many approximate theoretical solutions for the reaction factors based on the film model were reported (Teramoto et al., 1971; Ramachandran and Sharma, 1971; Chaudhari and Doraiswamy, 1974; Juvekar, 1974; Hikita et al., 1977). Among them, the approximate solution derived by Hikita et al. (1977)was shown by comparison with the numerical results to be the most accurate. Therefore, we derived an approximate solution for the reaction factor PA based on the
-
1798 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 Ds/Dn=l 38 DE/DA=I44, Dc/Da=310
4
Bo=E3=0
’1
1001 I
1
g .ld2
I
Acidified soin
F0=200mol/m3
==lo,
Non-acidified S o h kc=16 S I , k f . 2 5 2 mSmoIs K.394~10‘ moi’/m6 A.013 mol/m3 B = I 3 mol/m3 kh/ kg 3 4x10 ”/mol
--
’
/
2
4
IO
2
4
loo
Y Figure 1. Reaction factors for simultaneous absorption of C2H4and C1, into water and hydrochloric acid. Leveque model solution.
Leveque model by applying the approximation method of Hikita et al. (1977) as
PA = ay + 0.474715/(7-y)’
(77 I2.4)
(lla)
m
PA = 1 + Cbj(7y)” J=1
(77 5 2.4)
(1lb)
where bl, bz, ..., b, are the numerical constants given in the previous papers (Hikita et al., 1973b, 1975). The dimensionless parameters 7 and y are defined as
DAL ‘ I 3 Ai
DAL ‘ I 3 Ai .=[l-S[(,)
(z)-L((g) 1
(E)-
+ 3Bi 4 ] ] 1 i (12) z
and y = (kfBiDAL)”z/kLA*
(13)
The reaction factor PB is given by
Figure 1 shows a comparison of the reaction factors, P A and OB,calculated for the case in which CzH4 and C1, are absorbed simultaneously into the hydrochloric acid with those for the case in which the two gases are absorbed into water. The conditions required for the calculation were given in the figure. As can be seen in the figure, the reaction factor PAfor CzH4in which the absorbing liquid was water is a little less than that for C2H, in which the absorbing liquid was hydrochloric acid. On the contrary, the reaction factor OB for C1, in which water is used as the absorbing liquid is much larger than that for C1, where hydrochloric acid is used as the absorbing liquid, because the rate of the absorption of Cl, when the absorbing liquid is water is accelerated by the C1, hydrolysis reaction. The rate constant hf of reaction f can be determined by comparing the experimental values of PAor PBwith the theoretical lines. Experimental Section Apparatus and Procedure. Figure 2 shows schematically the experimental apparatus for experiments of simultaneous absorption of C2H, and C1, into water or
Figure 2. Schematic diagram of experimental apparatus: (1) Nz cylinder, (2) Clz (diluted with N,) cylinder, (3) C,H, cylinder, (4-6) gas flow meter, (7) agitated vessel for absorption experiment, (8,9) constant-speed motor, (10) sampling pipet, (11) agitated vessel for experiment on gas-phase reaction, (12) constant-speed motor, (13) liquid feed tank, (14) storage tank, (15) air bath, (C) cock, (GC) gas chfomatograph, (V) valve.
hydrochloric acid. The main parts of the apparatus were kept at a constant temperature of 288.2,298.2, or 308.2 K. Absorption vessel 7 was similar to that used in our previous work (Hikita et al., 1975, 1980). The liquid stirrer was driven at a constant speed of 1.67 or 2.33 s-l, and the stirring speed of the gas-phase stirrer was 10 s-l. The absorbing liquids were water and hydrochloric acids with concentrations of about 0.1 and 1.0 kmol/m3. The gas phase consisted of a mixture of ethylene and chlorine of partial pressures pa = 2.55-22.0 kPa and pB = 0.679-3.89 kPa, and the rest being nitrogen, though the gas flowing out of the absorption vessel contained some vapor of the products. The total gas flow rate ranged from 1.7 X to 3.0 X m3/s. Absorption experiments were carried out in a batch operation with respect to the liquid and in continuous operation with respect to the gas. Pure CzH, and N, and C1,-Nz mixed gas (Clz content: 4.8%) from pressure cylinders 3, 1, and 2, respectively, metered individually, were introduced into the vessel and exhausted continuously from the vessel, while stirring with the gas stirrer. After the air in the vessel was completely replaced by a mixed gas of a given composition, the absorbing liquid of a fixed volume (1.51 X m3) was introduced into the vessel from the bottom and then the stirring of the liquid phase was started. About 10 min later, two liquid samples of about 1.2 x m3 each were taken by sampling pipet 10 from the bottom of the vessel. Absorption experiments continued usually from 960 to 1200 s, and at the end of each experiment, another two liquid samples were taken. The rate of absorption of CzH, was determined by the increase in the total concentration of the reaction products, ethylene chlorohydrin and ethylene dichloride, in the liquid phase and that of ClZwas from the increase in the concentration of the reaction products and the remaining effective chlorine in the liquid phase. However, the gas samples taken at the exit of the absorption vessel contained some ethylene chloride and ethylene chlorohydrin which were produced in the gas phase in the vessel and/or desorbed from the liquid phase. Therefore, the amounts of C,H, and C1, thus determined were corrected for the amounts of the products desorbed from or absorbed into the liquid phase. To determine the amount of the products desorbed from or absorbed into the liquid phase, experiments on the gas-phase reaction were also performed by using another reactor. Reactor 11 was a continuous stirred tank reactor of which the inner diameter and height were 123 and 77
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1799 Table I. Experimental temp, NL, PA, run K s-l kPa 1 298.2 3.33 2.64 2 298.2 1.67 2.58 3 298.2 3.33 5.96 4 298.2 1.67 5.97 5 298.2 3.33 2.65 6 298.2 1.67 2.66 7 298.2 3.33 5.96 8 298.2 1.67 5.97 9 288.2 3.33 2.66 10 288.2 1.67 2.65 11 288.2 3.33 6.05 12 288.2 1.67 6.09 13 308.2 3.33 2.53 14 308.2 1.67 2.54 15 308.2 3.33 5.77 16 308.2 1.67 5.76 17 298.2 3.33 2.64 18 298.2 1.67 2.65 19 298.2 3.33 5.93 20 298.2 1.67 5.92 2 1 298.2 3.33 4.77 22 298.2 1.67 4.77 23 298.2 3.33 10.0 24 298.2 1.67 10.0 25 298.2 3.33 7.14 26 298.2 1.67 7.11 27 298.2 3.33 22.0 28 298.2 1.67 22.0
Conditions and Results PB, PECH,PEDC, &,a,, kPa kPa kPa mol/m3 1.69 0.03 0.19 0.219 1.64 0.03 0.19 0.164 0.09 0.43 0.284 3.75 3.78 0.09 0.43 0.187 1.70 0.03 0.19 0.223 1.71 0.03 0.19 0.194 3.74 0.09 0.43 0.455 0.09 0.43 0.280 3.77 1.72 0.01 0.18 0.200 1.72 0.01 0.18 0.0851 3.83 0.03 0.38 0.318 3.89 0.03 0.38 0.256 1.60 0.07 0.25 0.140 1.60 0.07 0.25 0.0962 3.54 0.12 0.55 0.279 3.54 0.12 0.55 0.156 1.55 0.03 0.19 0.0078 1.63 0.03 0.19 0.0024 3.61 0.09 0.43 0.0201 3.66 0.09 0.43 0.0113 1.22 0.06 0.22 0.0044 1.24 0.06 0.22 0.0029 3.12 0.09 0.61 0.0740 3.33 0.09 0.61 0.0118 0.679 0.08 0.26 0.0038 0.709 0.08 0.26 0.0020 2.42 0.09 0.75 0.0210 2.50 0.09 0.75 0.0073
FQ,, mol/m3 0.00739 0.00740 0.0109 0.00739 0.00009 0.00008 0.00019 0.00056 0.00546 0.00232 0.00866 0.00694 0.00679 0.00490 0.0136 0.00745 1.19 0.715 1.28 0.828 0.764 0.542 1.24 0.494 0.537 0.393 0.329 0.157
mm, respectively, and its volume was the same as that of the gas phase in the agitated vessel used in the absorption experiments. The stirrer was the same as that used in the absorption experiments and was placed at the center in the vessel. In these experiments, N2from pressure cylinder 1was passed through the gas phase of the agitated vessel used for the absorption experiments and then mixed with Clz and C2H, just before the inlet of the vessel. Water content was considered to be almost the same as that of the case of the absorption experiment. Gas samples were taken at the inlet and the exit of the vessels and analyzed by a gas chromatograph with FID and TCD as detectors. The liquid-phase products, ethylene chlorohydrin and ethylene dichloride, were determined also by a gas chromatograph. The effective chlorine concentration, which is defined as the sum of the concentrations of Cl, and HOC1 in solutions, was determined iodometrically; a known amount of the liquid sample was added into an aqueous KI solution of 0.4 mol/m3, and the concentration of the liberated I2 was determined by measuring the optical density at wavelength 289 nm with a spectrophotometer. The hydrochloric acid was determined by titration with a standard Na2C03solution using methyl orange as an indicator. The experimental conditions are given in Table I.
Results of the Absorption Experiments The correction of the absorption rate due to absorption of the gas-phase products into the liquid phase or desorption of the liquid-phase products into the gas phase was 12.7% at most and was usually less than a few percent. It was expected that there was some transfer resistance of C2H4and Cl, in the gas phase. This gas-phase resistance to mass transfer was estimated by using the gas- and the liquid-phase mass-transfer coefficients which were calculated from the empirical equations (Hikita et al., 1969, 1975) and was found to be negligible (less than 2%) compared to the overall resistance for CzH4 or C1, under the experimental conditions studied.
mol/m3 101.0 101.0 102.0 101.0 1010.0 1000.0 1020.0 999.0 101.0 102.0 102.0 102.0 103.0 100.0 102.0 103.0 1.61 1.14 2.49 2.37 1.58 1.44 4.83 3.07 1.67 1.41 4.98 4.27
Ai, Bi, lo6 NA, lo6 NB, mol/m3 mol/m3 mol/(m3 s) mol/(m3 s) 0.120 1.13 5.66 7.75 0.117 1.10 6.36 7.44 24.7 28.0 0.270 2.50 2.52 22.5 24.6 0.270 1.14 6.02 7.71 0.111 1.14 0.112 5.53 6.73 23.1 27.0 2.49 0.250 21.8 24.0 2.51 0.250 1.63 6.42 8.51 0.152 6.60 7.12 1.63 0.151 3.62 0.345 20.3 23.2 19.4 21.9 3.67 0.347 0.798 0.0980 5.65 7.43 6.49 7.69 0.798 0.0984 23.7 26.5 1.76 0.223 1.76 23.7 25.1 0.223 0.121 1.05 6.05 16.0 0.121 1.09 6.32 13.1 0.271 2.41 22.6 34.4 0.270 2.44 22.4 30.3 0.218 0.812 8.89 16.8 0.218 0.826 12.2 17.5 0.458 2.09 34.0 45.1 0.464 2.22 34.8 39.8 0.326 0.454 8.67 14.0 0.325 0.474 9.94 13.8 1.00 1.62 64.2 66.9 1.01 1.67 56.6 57.8
PA
OB
30.0 56.1 58.3 86.0 36.2 53.4 61.6 94.3 35.8 60.2 49.9 77.0 29.0 53.6 53.4 86.4 31.6 53.6 52.8 85.2 25.8 57.5 46.9 77.0 16.8 31.4 40.5 57.7
4.35 6.54 6.44 8.73 4.51 6.21 7.15 9.44 4.08 5.15 4.82 7.16 4.55 7.21 7.22 10.3 7.85 9.93 7.34 10.3 10.5 17.6 11.4 14.9 15.9 24.2 21.3 28.8
ECH yield 0.850 0.914 0.665 0.713 0.775 0.830 0.788 0.722 0.855 0.815 0.653 0.681 0.778 0.960 0.917 0.873 0.841 0.872 0.630 0.788 0.850 0.890 0.768 0.799 0.887 0.932 0.847 0.865
All the experimental results of the rates of absorption of CzH4and Cl,, NA and NB,respectively, are also shown in Table I.
Analysis and Discussion Prediction of Physical Properties. In order to analyze the experimental results, it is necessary to know the values of physical properties such as A,, D A L , etc. When water is used as an absorbing liquid, near the interface in the liquid, there exists an aqueous solution containing ethylene chlorohydrin, ethylene dichloride, H+ + C1-, and HOC1. However, since their concentrations are very low, the solubility and the diffusivity of CzH4and C1, in water can be taken as A,, Bi, DAL,and DBL, respectively. On the other hand, when hydrochloric acid is used as an absorbing liquid, the hydrolysis of C1, will be almost completely negligible. Furthermore, the concentration of hydrochloric acid near the interface will be almost constant and equal to the bulk concentration. Therefore, the solubility and the diffusivity of C2H4and C1, in the hydrochloric acid, the concentration being equal to the bulk one, were used for Ai, Bi, DAL, and DBL, respectively. The solubility (Ai) of C2H4 in hydrochloric acid was calculated from log (Ai/Ai,) = -k,l
(15)
where Ai, is the solubility in water, and k , is the salting out parameter expressed as the sum of the contributions owing to the positive (H+) and negative (C1-) ions present and the dissolved gas (van Krevelen and Hoftijzer, 1948): k , = i,
+ i- + i,
(16)
The value of i+ and i- for H+ and C1-, respectively, were taken from the data of van Krevelen and Hoftijzer, and the value of i, for CzH4 at 298.2 K determined by Onda et al. (1970) was used irrespective of the temperature studied. The value of Ai, was calculated from the partial pressure of C2H, in the gas phase by use of the Henry’s law constant (Morrison and Billett, 1948).
1800 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 400
400 Acidified s o h
1
I
'
Acidified s o h
IOC
42 1
Q/,:,B,j
IO
2
Figure 3. Reaction factors for simultaneous absorption of C2H4and C1, into 0.1 kmol/m3 hydrochloric acid a t 298.2 K. (BJAJav= 9.33.
Y Figure 4. Reaction factors for simultaneous absorption of C,H, and C1, into 1.0 kmol/m3 hydrochloric acid a t 298.2 K. (BJAJav= 10.0.
The solubility (B,) of Clz in hydrochloric acid was estimated by a method analogous to that for the solubility of C2H4. The values of i, for Clz at various temperatures were taken rom those of Hikita et al. (1973a). The values of the Henry's law constant for Clz at various temperatures were determined by using the data of the solubility of Clz measured at pB = 0.667-4.00 kPa by Adams and Edmonds (1937). The liquid-phase diffusivities of CzH4 and Clz in hydrochloric acid were estimated from the following equation proposed by Ratcliff and Holdcroft (1963): DAL -
10 0 A 0052 I 1 0 A 0088 12 O A 0070
- DBL -=
1 - KF (17) DEW where DAL and DBL are diffusivities in the solutions, DAW and DBware those in water, and K is the constant which is determined by the dependence of the viscosity on the concentration of the electrolyte solution. The diffusivity of CzH4in water, DAW, was predicted from the value of 1.08 X m2/s obtained at 298.2 K (Unver and Himmelblau, 1964),by correcting for temperature and viscosity of water, according to the well-known Stokes-Einstein relation. The diffusivity of Clz in water, DBw,was predicted from the value of 1.48 X low9m2/s obtained at 298.2 K (Peaceman, 1951) by correcting for temperature and viscosity. For the K value, 5.94 x m3/mol determined by Hikita et al. (1975) was used. The ratios of the diffusivities of Clz, HOC1, and HC1 to C2H4,DBL/DAL, D a / D a , and Dm/DAL, respectively, were assumed to be equal to those at finite dilution or in water and to be constant irrespective of temperature. The diffusivities (Dm and Dn) of HOC1 and HC1 in water at 298.2 K were taken from the literature as 1.54 X lo4 (Peaceman, 1951) and 3.32 X lo4 mz/s Danckwerts, 19701, respectively. Therefore, the values of DEL/DAL,and &IDAL were 1.38, 1.44, and 3.10, respectively. The liquid-phase mass-transfer coefficients, kLA* and kLB*, were calculated from the empirical equation obtained by Hikita and Ishikawa (1969). The gas-phase masstransfer coefficients, k~~ and kgB, were also calculated from the empirical equation (Hikita et al., 1975). The equilibrium constants K (=k,/k,') of reaction c a t various temperatures were obtained from the data of Connick and Chia (1959). The reaction rate constants (k,) of the forward reaction of reaction c a t various temperatures were taken from the data of Brian et al. (1966). DAw
Analysis of Experimental Data The experimental reaction factors for CzH4 and C1, were calculated from the measured values of the absorption
100 200
4
Y
13
parameter
2
,
1
IO
2
4
BO/B
100 200
Y Figure 5. Reaction factors for simultaneous absorption of C2H, and C1, into 0.1 kmol/m3 hydrochloric acid a t 288.2 K. (BJAl)av= 10.6. Acidified s o h 1L 0 A 0121
16
21
IO
a A 0089
,
1
2
"
0
4
,
,
I
100 200
Y Figure 6. Reaction factors for simultaneous absorption of C2H4 and C1, into 0.1 kmol/m3 hydrochloric acid at 308.2 K. (BJAJav= 8.03.
rates N A and N Bby using the values of A,, B,, DA,DB,ku*, and kLB predicted above. Figures 3-6 show the experimental results of the reaction factor obtained with hydrochloric acid as the absorbing liquid, in which the hydrolysis of Clz can be neglected. In these figures, the experimental reaction factors are plotted against the dimensionless parameters y and compared with the theoretical lines, which were calculated from eq 11-14 and are shown by solid lines. The theoretical lines for PA coincide with each other under the experimental conditions in each figure. On the other hand, the theoretical lines for PB are sensitive to the change in the value of Bo/Bi,and so the two lines for the largest and the smallest B,/B,
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1801 Non-acidified sdn
g c
4[
29*2K
1
I
32
' O
I
I 34
1
33
-i
f
4
35
10~1 cK"1 ~
Figure 7. Arrhenius plot of rate constant for reaction between C2H4 and C12.
4L Parameter A ,
2IO
I8 0 A 0121 1 0 0 1 1 9 O A 0.271 20 0 A 0 271
1 2982K
,/4
100 200
4
Y
Figure 9. Reaction factors for simultaneous absorption of C2H4and C1, into water a t 298.2 K. (Bi/AJaV = 4.21.
1
d
2
400
1
Non-acidified s o h
1
4L Parameter A
210
2
4
100 200
Y Figure 8. Reaction factors for simultaneous absorption of C2H, and C12 into water a t 298.2 K. (B,/AJaV= 8.91.
values are shown in each figure. The values of kf required for calculating y were so determined that the experimental values of P A for the four runs agreed well with the theoretical lines. Therefore, it is quite natural that the experimental and the theoretical PA values agree well with each other. However, as can be seen in the figures, the agreement between the experimental values of PB and the theoretical lines is also satisfactory, while the values of y required to plot the experimental results of PB were identical with those used for plotting the experimental values of PA. The values of k , determined a t 298.2 K were constant at 252 and 269 m3/(mol s) for the hydrochloric acids with concentrations of 0.1 and 1.0 kmol/m3, respectively. The values of kf obtained at 288.2 and 308.2 K were 123 and 434 m3/(mol s), respectively. Figure 7 shows the Arrhenius plot of the experimental results of the rate constant (kf) of reaction f. The activation energy was found to be 46.0 kJ/(mol K), being independent of the ionic strength of the absorbing liquids. Thus, the experimental kf values were correlated by using the empirical equation In kf = 24.108 - 5540/T (18) Next, we analyze the experimental results obtained by using water as an absorbing liquid, in which the hydrolysis of Clz should be taken into consideration. Figures 8-10 show the comparison between the experimental and the theoretical values of P A and ,&. The theoretical values of PA and ,&were obtained by solving eq 1-10 numerically. The theoretical lines are drawn in the figures as solid lines. The constant value of 252 m3/(mol s) calculated from eq 18 was used as the kf value. The individual values of k , and kh could not be evaluated in the present work, but the ratio kh/ k , could be estimated by using the experimental results of the yield of ethylene chlorohydrin obtained for the cases where hydrochloric acid was used as an absorbing liquid. In these cases, the concentration profiles of hydrochloric acid were flat in all the area from the gas-liquid
.'L Parameter A ,
2
IO
2
100 200
4
Y Figure 10. Reaction factors for simultaneous absorption of C2H4 and Clz into water at 298.2 K. (B,/AJav= 1.43 and 1.64.
interface to the liquid bulk, and therefore the a values were independent of the distance x . From the results of runs 1-4 and runs 5-8, the kh/k, values were estimated as 2.7 x (Po= 101 mol/m3) and 0.28 X m3/mol (Po = 1010 mol/m3) at 298.2 K. The large difference between the two values was considered to be due to the difference in the ionic strength. Therefore, the (kh/k,) value at I = 0 was estimated as 3.4 X m3/mol by extrapolating the above results, and this constant value was used to calculate the theoretical reaction factors for the absorption of C2H4 and Clz into water. However, the theoretical reaction factors PA and PB calculated with the value of k h / k , = 3.4 X were in good agreement with those calculated with a constant a value of 1. This was because the actual a values at the interface ranged 0.89-0.98 for runs 17-28, the values being almost equal to 1.0. The figures show that the agreement between the experimental and the theoretical values of PA and PB is satisfactory. As mentioned above, the values of the rate constant kf were determined on the basis of the assumption that the reaction is first-order with respect to both CzH4and C12. However, this has not yet been verified. If we assume that reaction f is an irreversible (m,n)th order reaction, the above determined rate constant is equivalent to the apparent rate constant KF expressed by
KF = (29"-'/(m
+ l)}kfA,m+n-2
(19)
which can be derived from the approximate solution for simultaneous absorpton of two gases (Hikita et al., 1977). The constant KF value was obtained above by using the
1802 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 L"~
,Or
-
/
Acidified soln Non-acidifled soin
,,d
1
i
2
4
10
20
Figure 11. Comparison of reaction factors measured by Dun and Wood for absorption of C2H, into acidified and nonacidified chlorine solutions at 306 2 K with theoretical predictions
experimental reaction factors PAwhich were measured by using hydrochloric acid as an absorbing liquid under the conditions of almost constant y values of 9.33-10.0, while the values of A, differed by 2.3 times. This means that m +- n = 2. When water was used as an absorbing liquid, the reaction factors were measured at various y values. When y > 3, the reaction factors PA are almost independent of the hydrolysis of C1, and coincide with those which are obtainable by using hydrochloric acid as an absorbing liquid. Therefore, the fact that the experimental PAvalues obtained in runs 21-24 where the average q values was 4.2 agreed well with those obtained for the cases of q = 9.33-10.0 suggests that KFis independent of y. This means that 71 = 1 and, therefore, m = 1 and KF = hf. From the results obtained above, it was found that the reaction between C2H, and C12 expressed by reaction f is rate-controlling and second-order, i.e., first order with respect to both C2H, and C1,. Furthermore, the above results show that the experimental reaction factors for both C2H, and C1, obtained by using hydrochloric acid and water as absorbing liquids can be well-described by the above reaction mechanism, and the kinetic constants measured are sufficiently accurate.
Analysis of the Previous Data As mentioned above, the kinetics of absorption of C2H, into acidified and nonacidified chlorine water has been studied by Akehata and Johnson (1965) and Dun and Wood (1966, 1967) using an agitated vessel with a flat gas-liquid interface and a wetted-wall column, respectively. Both experimental results were analyzed based on chemical absorption theory, but the analyses were not complete. Much of the data of Akehata and Johnson were obtained in the regime of absorption accompanied by instantaneous reaction, because of the low values of the liquid-phase mass-transfer coefficient in the absorption vessel used and of the high values of the reaction rate. Therefore, we analyzed only the data of Dun and Wood. When chlorine water is used for absorbing C2H4,C1, in the solution may be desorbed into the gas phase. Therefore, we should take into consideration the desorption of C1, when analyzing the data of Dun and Wood. Hikita et al. (1979) analyzed the problem of gas absorption accompanied by an irreversible second-order reaction with a volatile reactant and showed that the reaction factors for this case are less than those for the case of no desorption of the liquid-phase reactant. Applying the approximate method developed by Hikita et al. (1977, 1979),we derived here an approximate analytical solution of the reaction factor for C,H, absorption based on the penetration model. Figure 11 shows a comparison of the representative data of the reaction factors measured by Dun and Wood (data at 303.2 K given in Tables I and I1 in their paper (1967)) with the theoretical predictions. The theoretical values
of P A were calculated by using the values of physical properties such as Ai, D, DBL,etc., estimated by methods similar to those used in the present work and the value of hf given by eq 18. As shown in the figure, the observed values of PA agree well with the theoretical predictions, though the data were obtained by using the chlorine water both acidified and nonacidified with hydrochloric acid as the absorbing liquid. This result also supports the reaction mechanism considered above and the rate constant of reaction f determined in the present work.
Nomenclature A = concentration of solute gas A (CzH4)in solution, mol/m3 A,, A,," = interfacial concentrations or solubilities of solute gas A in solution and in water, mol/m3 a = velocity gradient of flowing liquid at gas-liquid interface, S-1
B = concentration of solute B (Cl,) in solution, mol/m3 Bo = concentration of reactant B in bulk solution, mol/m3 B, = interfacial concentration or solubility of solute gas B in solution, mol/m3 b, = coefficient in eq l l b Da,Dqw= liquid-phase diffusivities of solute gas A in solution and in water, mz/s DBL,DBw= liquid-phasediffusivities of solute gas B in solution and in water, mz/s DEL,DFL= liquid-phase diffusivities of reaction products E and F, m2/s E , F , G , H = concentrations of reaction products, E (HOCl), F (H+),G (Cl-), and H (l),mol/m3 E,, F, = interfacial concentrations of reaction products E and F, mol/m3 E,, F, = concentrations of reaction products E and F in bulk solution, mol/m3 I = ionic strength of solution, mol/m3 i+, i-, i, = contributions of positive ion, negative ion, and solute gas to salting-out parameters, m3/mol K = equilibrium constant of reaction c, mo12/m6 K F = apparent rate constant of reaction f defined by eq 19, m3/(mol s) h,, k,' = first- and third-order rate constants of forward and backward reactions of reaction c, s-' and m6/(moI2s) k , = second-order rate constant of reaction f, m3/(mol s) h, = first-order rate constant of reaction g, s-* kh = second-order rate constant of reaction h, m3/(mol s) hL* = liquid-phase mass-transfer coefficient, m/s h, = salting-out parameter, m3/mol m = order of reaction with respect to CzH, NA,NB = absorption rates of solute gases A and B, mol/(m2 S)
NL = liquid-phase stirring speed, s-l n = order of reaction with respect to C1, pA,P B = partial pressures of solute gases A and B, Pa = partial pressures of reaction products ethylene chlorohydrin and ethylene dichloride, Pa q = concentration ratio, = B , / A , T = temperature, K x = distance from gas-liquid interface, m y = length along liquid flow path, m
PEcH, PEDC
Greek Symbols = ratio of production rate of ethylene chlorohydrin to the
N
total production rates of ethylene chlorohydrin and ethylene dichloride and defined by eq 5 P4, & = reaction factors defined as eq 9 and 1 0 7 = dimensionless parameter given by eq 13 7 = dimensionless parameter given by eq 12 K = coefficient in eq 17, m3/mol Registry No. 1, 23134-14-7; HCI, 7647-01-0; H20, 7732-18-5; Cl-, 16887-00-6; ethylene, 74-85-1; chlorine, 7782-50-5; ethylene
I n d . Eng. Chem. Res. 1987,26, 1803-1810
chlorohydrin, 107-07-3; ethylene dichloride, 107-06-2.
Literature Cited Adams, F. W.; Edmonds, P. G. Ind. Eng. Chem. 1937,29,447. Akehata, T.; Johnson, A. I. Can. J . Chem. Eng. 1965,43,262. Brian, P. L. T.; Hurley, J. F.; Hasseltine, E. H. AIChE J. 1961, 7,226. Brian, P. L. T.; Vivian, J. E.; Piazza, C. Chem. Eng. Sci. 1966, 21, 551. Chaudhari, R. V.; Doraiswamy, L. K. Chem. Eng. Sci. 1974,29,675. Connick, R. E,; Chia, Y. T. J . Am. Chem. SOC.1959,81, 1280. Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: ‘;BW York, 1970; p 142. Dun, P. W.; Wood, T. J . Appl. Chem. (London) 1966, 16, 336. Dun, P. W.; Wood, T. J . Appl. Chem. (London) 1967, 17, 53. Gomberg, M. J. Am. Chem. SOC.1919,41, 1414. Hikita, H.; Asai, S.; Himukashi, Y.; Takatsuka, T. Chem. Eng. J . 1973a, 5, 77. Hikita, H.; Asai, S.; Ishikawa, H. Bull. Uniu. Osaka Pref. 1973b, A22, 57. Hikita, H.; Asai, S.; Ishikawa, H.; Saito, Y. Chem. Eng. Sci. 1975,30, 607. Hikita, H.; Asai, S.; Ishikawa, H. Ind. Eng. Chem. Fundam. 1977,16, 215. Hikita, H.; Asai, S.; Ishikawa, H. Bull. Uniu. Osaka Pref. 1979, A B , 57.
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Hikita, H.; Ishikawa, H. Bull. Uniu. Osaka Pref. 1969, A18, 427. Juvekar, V. A. Chem. Eng. Sci. 1974,29, 1842. Leveque, M. Ann. Mines 1928, 13, 201. Morrison, T. J.; Billett, H. J . Chem. SOC.1948, 2033. Neidleman, S. L. Hydrocarbon Process. 1980, 59(11), 135. Onda, K.; Sada, E.: Kobayashi, T.; Kito, S.: Ito, K. J . Chem. Eng. Jpn. 1970, 3, 137. Peaceman. D. W. Sc. D. Thesis. Massachusetts Institute of Technology, Cambridge, 1951. ’ Ramachandran, P. A.; Sharma, M. M. Trans. Znst. Chem. Eng. 1971, 49, 253. Ratcliff, G. A.; Holdcroft, J. G. Trans. Znst. Chem. Eng. 1963, 41, 315. Roberts, I.; Kimball, G. E. J. Am. Chem. Sac. 1937, 59, 947. Roper, G. H.; Hatch, T. F.; Pigford, R. L. Ind. Eng. Chem. Fundam. 1962, 1, 144. Shilov, E. A. J . Appl. Chem. USSR (Engl. Transl.) 1949, 22, 734. Teramoto, M.; Isoda, T.; Hashimoto, K.; Nagata, S. Kagahu Kogaku 1971, 35, 897. Unver, A. A.; Himmelblau, D. M. J . Chem. Eng. Data 1964,9, 428. Van Krevelen, D. W.; Hoftijzer, P. J. Chem. Ind. Congr., Int. Chin. Znd., 21, 1948, 168.
Received for review February 10, 1986 Accepted June 16, 1987
A Geometric Approach to Steady Flow Reactors: The Attainable Region and Optimization in Concentration Space David Glasser* and Diane Hildebrandt Department of Chemical Engineering, University of the Witwatersrand, Johannesburg, W I T S 2050 South Africa
Cameron Crowe Department of Chemical Engineering, McMaster University, Hamilton L8S 4L7, Canada
This paper examines the following problem: for a given system of reactions with given reaction kinetics, find all possible concentrations t h a t can be achieved by using any system of steady-flow chemical reactors, that is, by using the processes of mixing and reaction only. Only isothermal systems with no volume change on reaction or mixing are examined in this paper. A geometric approach is adopted, and a set of necessary conditions is derived. In particular, the attainable region must be convex with non-zero rate vectors on the boundaries not pointing outward. Using the results, one can construct a region which satisfies the necessary conditions. Furthermore, it is demonstrated that no possible combination of plug-flow, CSTR, or recycle reactors can be used to extend this region. Once this region is known, the solution of concentration optimization problems is shown t o be relatively straightforward. A number of two-dimensional examples are examined. The problem of deciding on the best steady-flow system of chemical reactors given a set of reactions with their kinetics is an old and a difficult one. Horn (1964) showed that if one could find the attainable region for the system, that is, the region in the stochiometric subspace which could be reached by any possible reactor system, then the problem of the optimization was essentially solved. We will examine this point at a later stage. Other authors such as Chitra and Govind (1985) and Paynter and Haskins (1970) have tried simpler approaches. The former asking what series of recycle reactors and the latter asking what value of the axial mixing coefficient as a function of length would give the optimum answer for the chosen objective function. The former authors also give an extensive summary of the previous work done in optimization. A more recent article by Achenie and Biegler (1986) has a general structure consisting of constant dispersion model reactors 0888-5885/87/2626-1803$01.50/0
with sinks and sources and splitting points. The results are optimal for the class of problems consistent with the initial structure chosen and if the optimal reactor system can be described by networks of constant dispersion model reactors. When we use the terminology a steady-flow reactor system, we imply that the system will not support sustained oscillations, that is, that the flows and concentrations throughout the system are at steady-state values. The whole question of chemical oscillations and multiple equilibria has been discussed in a review by Feinberg (1980), and the techniques outlined by him could be used to examine the reaction networks to see if these difficulties are likely to arise in the systems under consideration. Shinnar (1983) and Shinnar and Feng (1985) have looked at a similar problem. They have shown that the requirements of thermodynamics place “bounds on the 1987 American Chemical Society
