T h e program tended to converge and give good answers in very few iterations when the proposed kinetic model adequately represented the chemical system-i.e., the final S was relatively small. However, when the model did not fit the data points well-Le., the final S was relatively large-many more iterations were performed, seemingly in a random fashion. Apparently the shape of the least square surface (six-dimensional in the sample problem) is not so smooth and well defined as in the rapidly converging case. Nomenclature cij
c,
C,
D e
h k,
K, L
M N
= maximum subscript for t, = number of components C, -
P PT
= matrix of partial derivatives = transpose matrix of P = reaction rate for zth reaction
ri
tj
6
X
1
= time‘corresponding tojth set of data points = vector of corrections = a weighting factor
literature Cited
= measured concentration of component C, at time t,.
Initial concentrations, c,~, assumed to be exact (based on weighing of reactants) ~= concentration of component i a t time t j computed from kinetic model = ith reagent or reaction product = a matrix consisting of only the diagonal elements of PTP = vector of concentration errors = t,+1 - tj = rate constant for ith reaction = equilibrium constant for ith reaction = number of reactions considered in system
(1) Fehlberg, Erwin, “Numerically Stable Interpolation Formulas
with Favorable Error Propagation for First and Second Order Differential Equations,” National Aeronautics and Space Administration, Tech. Note D-599 (March 1961). (2) Hamming, R. W., J . h o c . Computing Machinery 6 , 37 (1959). (3) Marquardt, D. W., J . Soc. Ind. Appl. Math. 11,431 (1963). (4) Rosenbrock, H. H., Computer J . 3, 175 (1960). ( 5 ) Van Wazer, J. R., Hofmeister, H. K., Crutchfield, M. M., Groenweghe, L. C. D., White, W. A., J . Am. Chem. SOC.(submitted). RECEIVED for review July 12, 1965 ACCEPTED January 24, 1966
FILM MODEL FOR ETHYLENE DICHLORIDE FORMATION of Two Gases in a Liquid
Absorption and Reaction
S. N. BALASUBRAMANIAN, D. N. R I H A N I , AND
L. K. D O R A I S W A M Y
National Chemical Laboratory, Poona, India The kinetics of ethylene dichloride formation in a stirred tank reactor has been studied.
This system involves
solution of two gases (ethylene and chlorine) and reaction between them in a body of the liquid product (ethylene dichloride). A general reaction model is proposed, based on two important assumptions: The mass transfer coefficient of ethylene is not influenced by the presence of chlorine bubbles, and the film thickness and surface area of ethylene and chlorine at nearly equal velocities are the same. For this system a rate equation has been developed in terms of the mass transfer coefficient for ethylene and Henry’s law constants of the two gases. By correlating the mass transfer coefficient with ethylene velocity and assuming the Henry’s law constants to be independent of concentration, it is shown that the reaction rate can b e expressed as a function of ethylene velocity. This equation represents the experimental data with an average deviation of less than 1%. THYLENE
dichloride (1,2-dichloroethane) is produced by
E the simple addition of ethylene and chlorine: CzH4
+ Clz
-P
CzH4Clz
Two methods are employed industrially for carrying out this reaction: reaction between ethylene and chlorine in a body of ethylene dichloride [EDC] in a stirred tank reactor; and contact of the two gases with a circulating stream of ethylene dichloride in a packed or empty reactor. Other methodse.g., bubbling of gaseous ethylene in liquid chlorine and addition of liquid chlorine and liquid ethylene (4,9)-are of academic interest only. A large volume of process data is available on the first method, including two patents (7, 7) giving details of the process and reactor. The principal criterion for getting the maximum selectivity for ethylene dichloride is the use of low temperatures, preferably below 40’ C., since a t higher temperatures the proportion of higher 184
l&EC FUNDAMENTALS
chlorinated products (mainly trichloroethanes) tends to increase. Useful process data obtained in a stirred reactor in the presence of dissolved catalysts have been reported by Galitzenstein and Woolf (6). Calculations based on reported thermodynamic data (8) show that the reverse reaction is negligible. Several cases of absorption followed by chemical reaction for gas-liquid systems have been analyzed by Sherwood and Pigford (72). In a recent paper, Roper, Hatch, and Pigford ( 7 7 ) have considered the theory of absorption and reaction of two gases in a liquid, and have presented numerical solutions to the nonlinear partial differential equations corresponding to the penetration theory. In the present work, a film model is proposed for this system, with particular reference to the formation of ethylene dichloride by simultaneous absorption and reaction of ethylene and chlorine in liquid ethylene dichloride.
Reaction Model
where
Chlorine and ethylene dissolve separately in the ethylene dichloride, and reaction occurs in the liquid. It is assumed that the reaction can be regarded as instantaneous. As shown below, since the solubility of chlorine is about seven times that of ethylene and their diffusivities are about equal, it can be assumed that the reaction takes place close to the surface of the ethylene bubble, and that the bulk of the solution contains a uniform concentration of free chlorine. T h e film-model representation of the situation is shown in Figure 1. Ethylene dissolves and diffuses through the liquid film to meet chlorine diffusing in the opposite direction. T h e reaction zone (or plane) moves away from the gas-liquid interface, and within a very short time reaches an equilibrium position (shown by plane RR' in the model). CA* and CBo represent the equilibrium concentration of ethylene and the bulk concentration of chlorine. respectively, in the liquid. As the reaction is extremely fast, these concentrations fall to zero a t the reaction surface, and ethylene dichloride formed as a result of the reaction diffuses (not shotzn in the diagram) to the main body of the liquid. The following equations can be written for the rates of transfer of A and B , on the assumption that the concentrations of both the components a t the reaction surface are zero.
XL = XA
+
XB
Also, for the dissolution of gaseous chlorine into ethylene dichloride,
on the assumption that film thickness and surface area are the same for chlorine and ethylene bubbles. This assumption, though not of general applicability, should hold good in the present case, since the velocities of the two gases are usually kept equal (occasionally the velocity of ethylene is about 57, higher). Combining Equations 3 and 4,
or
(5) Reaction rate? R, is normally measured as gram moles reacting per unit volume per unit time. Equation 1 can be written in terms of R, if a term. a, for the interfacial area per unit volume can be introduced. Thus,
R = kA'CA*
(6)
where The negative sign for
Llh merely denotes that the diffusion of
B occurs in a direction opposite to that of A . I n the present reaction, normally 1 mole of ethylene is used for every mole of chlorine, and occasionally 2 to 5% excess ethylene is maintained. It is therefore reasonable to assume that 1 mole each of chlorine and ethylene diffuse to the reaction zone a t its equilibrium position. Thus from Equations 1 and 2, on the basis of equimolal diffusion
The area term in this case refers to phase A and may be based on the holdup of this phase. However, since the dispersed phase holdup bears a certain ratio to the total holdup in the reactor, both R and a can be conveniently expressed in terms of this total holdup, V. Combining Equations 5 and 6, applying Henry's law (C* = p,"), and simplifying.
(3)
(7)
If bubbles of chlorine and ethylene d o not coalesce, it is logical to assume that
LIQUID FILM
I PA
=PB =
since the two gases enter separately and the bubbles may be considered to be pure ethylene and chlorine. Thus Equation 7 may be simplified to give
1
DB 1
HA
DA HB
Equation 8 expresses the reaction rate in terms of the diffusivities and Henry's law constants of the two gases and a mass transfer coefficient. Experimental
The experiments to determine the controlling mechanism in this reaction were carried out in a stirred reactor shown diagrammatically in Figure 2.
-
XA
?XL-
Figure 1 .
-x&
I
I
It%-+ Idealized representation of film model
The reactor consisted essentially of a stirred glass vessel of about 350-ml. effective capacity provided with a jacket con' to 4' C. The two nected to a condenser cooled by water at 2 gases \vere introduced into the reactor through separate sintered disks, as shown in the figure. Extreme care was taken VOL. 5
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to maintain anhydrous conditions within the reactor in order to avoid the formation of &P’-dichlorodiethyl ether. One part by weight of water corresponds to 8 parts of the ether, thus leading to a wasteful consumption of chlorine and ethylene. Agitation was accomplished by a vaned disk stirrer made of Monel, and its design \+as generally in accordance with the specifications of Cooper et al. (2) Ethylene dichloride escaping \I. ith the unreacted gases was returned to the reactor through a condenser, and the exit gases were analyzed for ethylene and chlorine. Product EDC formed in the reactor was continuously withdrawn through a side outlet, the position of this outlet determining the liquid holdup in the reactor. Reaction rate R could thus be directly determined. The temperature in the reactor was maintained a t any desired level by using a n appropriate liquid in the jacket. Although the exothermic heat of this reaction is high, about 136 kcal. per gram mole, the reactor could be maintained a t strictly isothermal conditions by effective stirring within the reactor and the use of a condensing vapor in the jacket. Normally, unless the temperature is low. the tendency for the formation of higher chlorinated compounds increases. To ensure maximum selectivity for EDC in this investigation, the bulk of the experimental work was carried out with diethyl ether as the jacket fluid.
1
Results end Discussion
Effect of Agitation. The eddy diffusivity in the fluid bulk can be increased to a near-constant value by increased agitation, thus increasing the mass transfer and leading to an equivalent film which should now be independent of agitation. I t is desirable to eliminate the effect of agitation, so that the equations developed earlier can be applied to the experimental results without an agitation parameter. Figure 3 represents the effect of stirrer speed on conversion a t three different gas rates. Below about 230 r.p.m. the effect of agitation is recognizable for all the three rates, while above it there is practically no effect. The stirrer speed was therefore maintained a t 400 in all the runs used for testing the equation. Incorporation of Estimated Values of D and H. The diffusivities of the two gases ( D Aand DB) in ethylene dichloride were calculated from Wilke and Chang’s equation (73) as recommended by Reid and Sherwood (70), and the values estimated a t 32’ C. are: DA =
$- =
!-so+ Figure 2.
All other details of stirrer according to (2) Dimensions in mm. 1. Stirrer seal 2. Condensers 3. Gas inlets, 10 mm. 4. Sintered disk distributors, 15 mm. 5. Vaned disk agitator, 24.4 mm. 6. Jacket 7. Stirrer rod, 6-mm. Monel 8. Overflow 9. Baffle
DB = 2.92 X 10-5 sq. cm./sec.
The diffusivities being equal, Equation 8 can be further simplified to give
dependent of concentration. written as
R = 1.2
Equation 9 can be verified, if Henry’s law constants, H A and H B , are known. As these were not available, they were determined experimentally by measuring the solubilities of the gases in ethylene dichloride by a standard method using a n apparatus similar to the type employed in gas analysis. The results were reproducible to within 1.1’%. The values obtained are: H A
2.5
Experimental assembly
= 3.27
x
Equation 9 may therefore be kAl
(10 )
Estimation and Correlation of Mass Transfer Coefficient. The mass transfer coefficient, kA’, was determined by saturating liquid ethylene dichloride with chlorine, bubbling ethylene a t a predetermined rqte through this liquid (with diethyl ether as jacket fluid), and determining the concentration of chlorine in the reactor holdup as a function of time. The mass transfer coefficient was calculated from Equation 3, which applies for the dissolution of ethylene alone. This equation can be written as
X IO4 atm. cc./gram mole
HB = 0.477 X lo4 atm. cc./gram mole The solubilities were also determined by confining the gases a t a constant pressure over ethylene dichloride under agitation in the reactor used for kinetic studies and chemically estimating the equilibrium concentrations. The average values of H A and HB determined from these measurements agreed with the above values to within 6%. Since the concentrations involved are low and their ranges are small, H A and H B should be in186
l&EC FUNDAMENTALS
which enables direct estimation of kA’. A plot of the rate us. C,” gives a straight line, confirming the validity of Equation 11. The values of kA’ thus calculated are plotted in Figure 4 as a function of ethylene velocity. Gas XJelocity in this investigation is defined in terms of the free cross-sectional area of the reactor. The straight line of Figure 4 can be correlated by the equation
Table I.
Ethylene Rate, Cc./Min. 100 150 200 250 300 500 600 800 200 500 600
Chlorine Rate, Cc./Min. 100 150 200 250 300 500 600 800 150 400 550
Experimental and Calculated Rates
Exptl. 5.150 7.041 8.533 9,200 11.166 15.875 19.500 21.100 8.160 15.500 18.210
.-a 1
R P M
Figure 3.
R X IO3, G. Mole/Cc./Hr. Exptl. Using Eq. 13 0.618 0.625 0.845 0.850 1.024 1.025 1.104 1.185 1.340 1.360 1.905 1.885 2.340 2.330 2.530 2.550 0.980 1.025 1.860 1.885 2.180 2.330
k A ' , fir.-'
Cm./Hr . 196.1 294.2 392,2 490.3 588.3 980.5 1176.6 1568.8 392.2 980.5 1176.6
C ~ A ,
Effect of stirrer speed on reaction
An exponent of "3 was also found by Cooper et al. (2) for the air oxidation of aqueous sodium sulfite. Combining Equations 10 and 12,
R
= 1.92
x
10-5
UgA*/3
I
(13)
Equation 13 was verified by carrying out experiments with different rates of ethylene and chlorine a t 32' C. (using ether as the jacket fluid), and determining the reaction rate by measuring the quantity of liquid ethylene dichloride produced per unit time (Table I). Equation 13 represents the experimental data with a n average deviation of less than 1%. The closeness of this fit is remarkable, particularly as the deviation is small even for cases where the two gases are not used in strictly molal ratios; even with about 10% excess of ethylene the reaction rate is predicted by Equation 13 to within 3%. Effect of Temperature. The reaction is assumed to be very rapid. Therefore the effect of temperature is not expected to be as pronounced as where chemical reaction offers the controlling resistance. Experiments were therefore carried out a t a second temperature, with acetone as jacket fluid, corresponding to a reaction temperature 56 ' C., by saturating ethylene dichloride with chlorine and bubbling gaseous ethylene through it under conditions where agitational effects were absent. This series of experiments was similar to that organized for determining the mass transfer coefficient. Figure 5 shows a plot of the concentration of chlorine in ethylene dichloride as a function of time for 32' and 56' C. The effect is not as pronounced (qualitatively) as might be expected for chemical reaction-controlling, for which the effect of temperature would be exponential. This might therefore be considered to support the model which postulates that absorption offers the principal resistance in this case.
\
0011
I
I
I
I
0,010
l
o 001-
O 003
'
1
I
I
I
VOL. 5
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187
Discussion
Product analysis showed that 2 to 5% of the chlorine was converted to higher chlorinated products. This does not affect the proposed equations, since the percentage of higher chlorinated compounds may be considered to be negligible, and according to the reaction model product composition will affect the reaction rate only in so far as it influences the diffusivities of the gases in the liquid product, and this effect may also be considered negligible. I t is appropriate to analyze the evidence in support of the theory as well as the assumptions made in the development of the model. The values of the mass transfer coefficient for ethylene, kA’, were calculated from Equation 3, and the same constant was used in the derivation of Equation 13, which represents the experimental data with a n average error of about 1%. Although apparently the form of Equation 13 does not suggest any bearing on the model, yet the value of the constant in this equation is determined on the basis of the model, as brought out in Equations 8 through 13. Therefore, even if this equation might appear to be a simple empirical correlation between the rate and the velocity of ethylene, it is a fair conclusion that it provides adequate support to the proposed model. Basic Assumptions. f i A = -2VB. Considering the fact that 1 mole of ethylene reacts with every mole of chlorine and only a slight excess of ethylene is used, if a t all, this assumption appears to be reasonable. The film thickness and surface area of both the chlorine and ethylene bubbles are assumed to be the same. This assumption is also justified where the velocities of the two gases are the same, as in the present instance. I t is assumed that the same kA’ applies to the ethylene bubbles whether only ethylene is bubbled through the liquid or both chlorine and ethylene are bubbled through it. This would imply that there is no interference from the chlorine bubbles on the mass transfer coefficient of ethylene. This assumption is open to question, but the kA’ values calculated when ethylene alone is bubbling in the liquid fit the data accurately where both ethylene and chlorine are bubbling simultaneously. pa has been assumed to be equal to P A . As the two gases are introduced separately, this assumption seems logical. Nevertheless the possibility of some degree of mixing between the two gases cannot be ruled out, leading to slight deviations from this assumption. There is no direct evidence in support of the assumption that ethylene and chlorine bubbles do not coalesce.
188
l&EC FUNDAMENTALS
Conclusions
The validity of the proposed model is borne out by experimental evidence. Nevertheless more experimental work is required both on this system and on similar systems to test this model more extensively. A system which might be chosen is the reaction leading to the formation of thiodiglycol by bubbling ethylene oxide and hydrogen sulfide in a medium of the product. Nomenclature a = interfacial area per unit volume, sq. cm./cc. Co = concentration in liquid bulk, gram moles/cc.
c* =
:
eauilibrium concentration. m-am moles/cc. I
”
D = diffusion coefficient, sq. cm./sec. H = Henry’s law constant, PIC*, atm. cc./gram-mole k
k’ =
It’
=
P
=
R =
v =
u, XL
= =
1
gram moles- gram moles hr. sq. cm. cc. mass transfer coefficient, l / h r . moles diffusing per unit area per unit time, gram moles/ sq. cm./hr. partial pressure, atm. reaction rate, gram rnoles/cc.,/hr. holdup in reactor, cc. gas velocity, cm./hr. thickness of total liquid film, cm.
= mass transfer coefficient,
SUBSCRIPTS A = ethylene B = chlorine References (1) Banerjee, S. C., Doraiswamy, L. K., Pai, M. U., Phatak, S. L.,
Indian Patent 66,836 (1959). (2) Cooper, C. M., Fernstram, G. A., Muller, S. A., 2nd. Eng. Chem. 36, 504 (1944). (3) Curme, G. O., Jr., Chem. Met. Eng. 25, 99 1921). (4) Curme, G. O., Jr., U. S. Patent 1,315,54511919) (5) Electric Furnace Products, Ltd., Norwegian Patent 31,349 (1920). (6) Galitzenstein, E., Woolf, C. C., J . Soc. Chern. Znd. 69, 289 (1950). (7) Hammond, J. A. S., U. S. Patent 2,393,367 (1946). (8) Kobe, K. A,, Harison, R. H., Petrol. Refiner 30, No. 8, 119 (1951). (9) Marks, E. C. R., Brit. Patent 136,489 (1919). (10). Reid, R. C., Sherwood, T. K., “Properties of Gases and Liquids,” McGraw-Hill, New York, 1958. (11) Roper, G. H., Hatch, T. F., Jr., Pigford, R. L., IND.END. CHEM.FUNDAMENTALS 1, 144 (1962). (12) Sherwood, T. K., Pigford, R. L., “Absorption and Extraction,’’ McGraw-Hill, New York, 1952. (13) Wilke, C. R., Chang, P., A.1.Ch.E. J . 1, 264 (1955). RECEIVED for review April 23, 1965 ACCEPTED October 12, 1965 National Chemical Laboratory Communication 694.
