I
EMERSON H. tEE and GEORGE D. OLIVER Plastics Division, Monsanto Chemical
Co., Texas
City, Tex.
Calculating Homogeneous Reaction Rates and Orders in a Flowing Gas Reactor Thermal Decomposition of Ethylbenzene Here is a method for calculating specific reaction rates in flow reactors where the temperature varies in the reaction chamber. It is much more rapid than trial and error methods of searching for specific rate data which will agree with experimentally measured conversion rates
IN
INDUSTRIAL ivork the experimenter often needs a ready method of calculating reaction rates and orders from laboratory flow-reactor data. However, the usual flowing gas reactor has an appreciable gradient of temperatures within the reaction chamber, which prevents immediate calculation of specific thermal reaction rates. If a preheater is used, the amount of gas which reacts in the preheater must be measured or estimated. Incremental conversions along the reactor tube may be measured by a manifold of sampling taps, if inherent sampling errors can be eliminated ( 3 ) . Hougen and Watson have shown that trial values of activation energies may be used to obtain specific reaction rates which yield the same values as the measured conversion rates when integrated over the temperature profile of the reactor ( 2 ) . T h e procedure described here is a direct and rapid method of calculating specific reaction rates and orders using flow reactor data. This is done by operating the reactor in the differential range (conversions N 1 to 2%), using an inert diluent, and measuring total conversion rates and temperature profiles in the reactor under actual operating conditions. If the data are sufficiently accurate, activation energy and frequency factor may also be obtained by plotting calculated results in the form of the Arrhenius equation and measuring the slope and intercept of the plotted line. I n using such a method there are a number of severe limitations in obtaining reaction rates from gases flowing through a n empty hot tube. First there is an inherent radial temperature gradient within the tube which introduces error into the measured gas temperature. T h e measurement of temperature of a hot flowing gas is subject to radiation and other errors in any case. When flow is laminar, which applies to the examples given, backstreaming may also occur and affect experimental results. As a result,
turbulent flow is desirable if experimentally possible. Another significant source of error arises from working in the differential conversion range, which increases analytical problems because of the low concentrations of the products. However, if these problems are overcome, calculations for specific reaction rates are easily done and easily verified by summation or integration. T h e procedure was applied to the thermal decomposition of ethylbenzene, considering only the primary products of the reaction, styrene. benzene, and toluene. The reaction orders with respect to ethylbenzene were determined by varying its concentration in the feed gas. This method of calculation should be generally useful for other systems. Calculation of reaction orders by the method given may be rather restricted because of the requirement of a fixed temperature profile under different conditions of flow.
Experimental Ethylbenzene (99.770) was metered and fed in the vapor phase with steam into an empty 20-mm. outside diameter quartz reactor at 1 atm. pressure. Mole fractions of ethylbenzene in the feed were 0.043, 0.073, and 0.140. The reactor contained a coaxial 6-mm. outside diameter quartz thermocouple well; thermocouples in the well indicated temperatures within 5' C. of those of a bare thermocouple, protected by a cylindrical radiation shield, in the gas stream. The reactor was covered with a inch stainless steel shell and heated by a 24-inch conventional type tube furnace. Temperature at any point was maintained at better than f0.5' C. by a controller connected to a thermocouple outside the steel shell. The temperature profile of the reactor was measured during experiments by a traveling thermocouple within the quartz well. The condensed organic product was
separated from the water phase and analyzed for styrene, benzene, and toluene. Concentrations of product in the organic layer were 0.1 to 1% styrene and 0.01 to 0.5(z benzene and toluene. Styrene was determined by titration ( 7 ) and benzene and toluene by gas chromatography, I t was sufficiently accurate to use weight of the organic product as weight of ethylbenzene fed. Over-all conversion rai:es were thus calculated by multiplying mass flow rate of ethylbenzene by weight fraction of any product in the organic 1ay-er. Results
Specific Reaction Rates. Total conversions in the reactor at different peak temperatures are shown in Figures 1 and 2. These temperatures are an average of the three thermocouple readings at the positions shown in Figure 3. Temperature profiles at various peak temperatures were similar and nearly parallel, as shown. The specific reaction rates, gram-moles per second per cubic centimeter of reactor space, were calculated as follows : Using line 1 in Figure 3 as an example, it was divided at the vertical line AB and the two parts moved horizontally until they superimposed as closely as possible on line 2. The gap left in line 1 represented the volume of reactor space, at the peak temperature of line 2, which contributed to the increase in total measured conversion rate in going from temperature conditions of line 1 to those of line 2. This neglects the lack of fit of these lines at the extremes, which is justified because of the relatively low temperatures at the extremes and the exponential dependence of conversion rate on temperature. Values of specific reaction rates were calculated as shown by Table I . Calculated data were plotted as log conversion rate 2's. 117 ,and a straight line was fitted through the points giving the smoothed data in the last column. VOL. 51, NO. 1 1
NOVEMBER 1959
135 1
c
SI
TEMP, “ L 600
6:;
5%
I
I
-STYRENE
.__ _. BENZENE
1 106
.-
‘IOI I06
112
I10
114
116
116
120
I22
-0
124
106
I08
I10
112
116
114
IO3/ T
I6
I20
122
24
IP/T
Figure 1 . Measured conversion rates of ethylbenzene to styrene and benzene as a function of peak reactor temperature and ethylbenzene concentration
,
Eo
g-. 0
Figure 2. Measured conversion rates of ethylbenzene to toluene as a function of peak reactor temperature and ethylbenzene concentration MFEB = mole fraction of ethylbenzene in feed
,
2
,
THERMOCOUPLE LOCATIONS
4
6 B 10 12 14 16 DlSTbNCE INTO REACTOR, IN
, I
18
20
Figure 3. Temperature profiles of reactor under reaction conditions Thermocouple locations shown were used to obtain on average peak temperature
MFEB = mole fraction of ethylbenzene in feed
Ra = kiClV
Because of the scatter of the points, there is some uncertainty about the slope and intercept of these lines. However, these are easily checked by using the smoothed data in a summation of conversions over small volume increments of the reactor tube, and comparing the summations with total measured conversions. Summation of conversions in each 1-inch section of the reactor at a maximum temperature of 600” C. gave the following: For benzene and toluene, respectively, the total of summed conversions were 16.9 X 10-8 and 4.2 X 10-8 mole per second; the respectively measured total conversions were 14.0 X 10-8 and 4 . 3 X 10-8 mole per second. Conversion rates to styrene are not shown as conversion to this product on the walls of the reactor as well as in the gas phase was indicated, as explained below. Reaction Orders. Because ethylbenzene in the feed stream was relatively dilute, changes in its concentration caused only small changes in temperature profile of the reactor. Therefore, assuming a constant temperature profile for a fixed stream flow and various ethylbenzene concentrations. measured conversion rates, RA and RB a t concentrations A and B, were
+ kyC‘‘‘V
-I-
+ . . . + kiCTV R B = klCgV + k2C;V -Ik,C;V+ . . + kiC,”I’ kaC,”V
(1) (2)
,
where V = a small constant unit of reactor volume, C, CB = concentrations of ethylbenzene, essentially constant, m = reaction order, and k l , k? . , . = specific rate constants at temperatures in each V. Then
23 “4
F)
Figure 4. Apparent reaction order m, with respect to ethylbenzene, is determined using Equation 5 MFLB = mole fraction of ethylbenzene
Taking logarithms, log RA/I?B = m log C.i/Cs
(4)
and m = (log Ra
- log RB)/(log Ca
log C a ) (5)
Using Equation 5, a plot of log conversion rate t‘s. log concentration (or mole fraction) for a given temperature yields the reaction order as the slope of the line (Figure 4 ) . An alternate method would be to calculate specific reaction rates for each
ethylbenzene concentration as given above and use these in Equation 5. Conversion to styrene was about first order with respect to ethylbenzene a t lower temperatures and approached zero order at higher temperatures, as shown by the converging lines in Figure 1. This indicated conversion to styrene on the walls of the reactor as well as in the gas phase ( 4 ) . Because reaction order for conversion to benzene and toluene were constant in the temperature range used, a single reaction path in the gas phase may be assumed for these products. Acknowledgment
Table 1.
Values of Specific Reaction Rates
Mole/Sec
tmax.
(See.)
Mole/ (Sec.)a
x
x
Mole/
A
Mole/ Ser.
A Reactor
105
VOL, CC.
e.) 108
(CC.)
Product
Line
oc.
1031~
x
Benzene
1 2 3 4 5 6
575 581 587 594 600 607
1.179 1.171 1.163 1.153 1.145 1.136
4.30 6.00 7.70 13.30 18.50 27.5
1.70 1.70 5.60 5.20 9.00
11.5 12.5 13.5 16.0 14.5
0.148 0.136 0.415 0.325 0.620
0.146 0.202 0.305 0.425 0.605
1 2 3 4 5 6
575 581 587 594 600 607
1.179 1.171 1.163 1.153 1.145 1.136
1.88 2.35 2.98 4.00 5.30 6.60
0.47 0.63 1.02 1.30 1.30
11.5 12.5 13.5 16.0 14.5
0.041 0,050 0.076 0.081 0.090
0.039 0.052 0.074 0.097 0.132
Toluene
a
108
x
Smoothed data obtained from straight-line plot of log conversion rate us. 1 / T
~~
1 352
INDUSTRIAL AND ENGINEERING CHEMISTRY
105
Thanks are given to E. E. Drott for helpful suggestions and to Nina Hadden and T. E. Boyd for assistance in obtaining experimental data. literature Cited (1) Byme, R. E.: Jr., Johnson, J. B., Anal. Chem. 28, 126 (1956). (2) Hougen, 0. A., Watson, K. M., “Chemical Process Principles. Part 111. Kinetics and Catalysis,” p. 874, Wiley,
New York, 1947. (3) Laidler, K. J., “Chemical Kinetics,” p. 37, McGraw-Hill, New York, 1950. (4) Zbid., p. 154. RECEIVED for review March 9, 1959 ACCEPTED June 29, 1959
