ETHYLATION OF BENZENE A Statistical Study V . M . H . G O V I N D A R A O , P. K. D E S H P A N D E , A N D N . R. KULOOR Department of Chemical Engineering, Indian Institute of Science, Bangalore 12, India
A central composite rotatable experimental design was constructed for a statistical study of the ethylation of benzene in the liquid phase, with aluminum chloride catalyst, in an agitated tank system. The conversion of benzene and ethylene and the yield of monoethyl- and diethylbenzene are characterized by the response surface technique. In the experimental range studied, agitation rate has no significant effect. Catalyst concentration, rate of ethylene flow, and temperature are the influential factors. The response surfaces may b e adequately approximated b y planes.
ethylation of benzene in the liquid phase, in the presence
tion to decreasing the complexity of the chemical reaction, eliminates the need for the induction period.
composite rotatable design experiment. Monoethylbenzene, the first ethylation product of benzene, is the raw material for the production of styrene. The ethylation is carried out commercially either in the liquid phase with acid catalysts like aluminum chloride, or in the vapor phase a t elevated temperatures and pressures with silica-alumina or phosphoric acid-based catalysts. T h e liquid-phase process is the most widely employed. Since the discovery of this Friedel-Crafts type reaction in 1879, a number of investigations have been conducted. No detailed analysis of the process has, however, been reported in the literature, perhaps because of the highly complex nature of the reaction system. With aromatic hydrocarbons, aluminum chloride forms complexes which are active catalysts for the alkylation reactions. The extremely complex nature of these compounds is not yet well understood (Patinkin and Friedman, 1964). They are capable of activating simultaneously a wide variety of other reactions that include isomerization, polymerization, disproportionation, carbon skeleton-rearrangement, /3-cleavage. and hydride transfer. The degree of participation of the various reactions depends on operating conditions. No analytical treatment can, therefore, be developed as yet, to represent reliably the aluminum chloride-catalyzed ethylation of benzene. Empirical methods, like the response surface technique, must be used. The response surface technique is particularly effective because of the relatively large number of variables involved. The present work reports a preliminary study to evaluate the effect of six process variables on liquid-phase ethylation and to characterize the conversions and yields by regression surfaces (response surfaces) on the six variables. Such regressions are useful in the design of reactors. The use of statistical tools in this work should be a significant contribution to the study of the reaction.
Experimental Design. T h e six variables-reaction time, temperature, agitator speed, catalyst concentration, rate of gas flow, and initial quantity of benzene-may be identified as the six primary factors influencing the ethylation reaction. Because nonlinear trends of a t least some of these variables are likely to be predominant, we construct a secondorder design, like the central composite rotatable design, for the experiment. The number of experimental units required in this layout is 80: 64 corresponding to the 26 factorial design, 12 a t + Z levels of each of the six factors, and a t least four center replicates. This number of experiments is considered very large for a preliminary study of the reaction undertaken in the present work, particularly because it requires a long time to determine the composition of the product from each experiment (the spinning band semimicro fractionation method was used). Hoivever, since the third and higher order interactions are not likely to be significant, we may reduce the experimental effort by confounding any three four-factor interactions-that is, by using a quarter replicate of the 26 factorial experiment. This reduces the total number of experiments of the design to 32. I n a quarter replicate, any factorial effect (other than the defining contrasts) has three aliases-that is, any effect is confused with three other effects. The reduction of the size of the experiment may, therefore, lead to misinterpretations. Hence, we shoulcl select a quarter replicate by careful consideration of the alias pattern. Selection of Quarter Replicate. T o seek a n effective design for 26 factorial in a quarter replicate, we choose (Davies, 1956) as the defining contrasts two four-factor interactions that have two factors in common. Their generalized interaction, the third defining contrast, is another four-factor interaction. Among the six factors there are 15 possible combinations of such four-factor defining contrasts. I n such a quarter replicate design, the aliases of the main effects are interactions of only three or more factors. However, some of the aliases of the two-factor interactions are themselves two-factor interactions. This is a drawback in the use of the quarter replicates. If the interactions of three and more factors are negligible, these quarter replicate schemes furnish estimates of the six main effects, seven sets of the two-factor interactions, plus two alias sets that contain only the three-factor interactions. We
HE
Tof aluminum chloride catalyst, was studied in a central
Experimental
Apparatus and Procedure. The apparatus mainly consists of a semiflow reactor where ethylene is bubbled through a n agitated reaction mixture of benzene and catalyst. Govindarao et ~ l (1966) . describe the experimental setup, procedure, and other details. The aluminum chloride catalyst is in powdered form, and in such concentrations that its complex with benzene forms only a homogeneous phase with the liquid benzene. This, in addi-
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may use these two sets of the three-factor interactions for estimating a pooled error variance. I t was difficult to select one from the 15 possible sets of defining contrasts. The method of selection adopted here considers the associated pattern of aliases among the seven sets of the two-factor interactions. Since the aluminum chloride catalyst is chemically very active, we may expect the catalyst concentration factor to have strong interactions with the other factors. Kinetic considerations indicate that the interaction between the time of reaction and the temperature is most likely to be significant (Davies, 1956). We therefore select a set of definingcontrasts that gives the alias pattern wherein the time-temperature interaction is not confused with any two-factor interaction of the catalyst concentration. Such defining contrast sets are six in number. There is no further criterion for choosing any particular one from these six. Therefore, the set X 1 X 2 X 3 X 5 - X l X 4 X 5 X 6 - X 2 x ~ 4 X 6 is chosen a t random. This defining contrast set may be used to split the original 26 factorial experiment into four blocks. The best of these four quarter replicates is the principal block (Davies, 1956)-that is, the confounded block containing the treatment combination where all the factors are a t their lower levels. The complete design can now be constructed as in Table I. I t consists of 16 experimental units of the quarter replicate,
Table 1.
Design No. 1 2
3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22
23 24 25 26 27 28 29 30 31 32
$1 $1
XlXZX4 XiXaXc XZX4X6
-1 -1 +1
x3x4x5
XlXZ~S
Results and Discussion
The 32 experiments at the corresponding factor levels were conducted in a random sequence. The four responses Conversion of ethylene, X, Conversion of benzene, X, Yield of monoethylbenzene, Yield of diethylbenzene, Y, were computed from the data.
-1 -1
XaX5Xs
Center
0 -2 +2 0 0 0 0 0 0 0 0 0 0 0 0 0
aXl,l Dll,Xl
ax2,1 %XZ
aX8,l
ff1,xa aXb1 %X4
ax5,1
a1,xs ffX691
aliX6
Center Center Center
Ethylene flow rate, g. moles/hr. Initial quantity of benzene, g. moles
Code Name x1 X2
xa x4
xs XK
Unit 15 10 150
+I
-1
-1 +l -1
$1
-1 +l -1 +1 -1
2: +1
fl
XiXaX6 xZXSx6
Variable Reaction time, min. Temperature, C. Agitator speed, r.p.m. Aluminum chloride concn., weight
-1 0 0
+:,0
0 -2 +2 0 0 0 0 0 0 0 0 0
0 0 0 -2 +2 0 0 0 0 0 0 0 0
0 0
Y,
Table I11 lists the results.
$1 $1
+l
fl
-1 -1 -1 -1
0 0 0 0 0
0 0 -2 $2 0 0 0 0 0
0 0
0
-1 -1 +I
+I
-1 -1 +1 $1 0 0 0 0 0 0 0 0 0 -2 +2 0 0 0 0 0
-1 -1
-1
-1 +1 +l +1 +1
0 0 0 0 0 0 0 0 0 0 0 -2 +2 0 0 0
Levels of Input Variables -2
15 30 600
0.06 0.0545 0.255
-
574
where y is the response, b are the regression coefficients, and x are the levels of the factors.
Locating levels of Independent Variables in Experiments of Central Composite Rotatable Design for Ethylation of Benzene Treatment Com6ination x1 x2 Xa XI x.5 XK -1 -1 -1 -1 -1 -1 (1) +1 -1 -1 XzXa -1 -1 +1 XIXS +l -1 -1 -1 -1 +1 XiXzXaXs +I +I $1 -1 +I -1 x4x6 -1 -1 -1 +1 -1 +1 +l +l -1 XzXax~X6 -1 $1 +1 xlx4x5X6 +1 -1 -1 $1 +1 fl x1xZx3x4x&yK $1 +I $1 +1 +I +1
Table II.
%
supplemented with 13 units at levels =k2 of the six factors, and four center replicates-32 experimental units in all. Table I1 gives the actual and coded levels, and the defined units of the six factors under study. The limitations of the equipment and the expected complexities of the reaction influenced the selection of the levels for each factor. The alias pattern, for the selected fractional replicate, is given in the first two columns of Table IV. The aliases of any effect are obtained by multiplying the defining contrasts by the effect. The form of the response function, that is characterized by the experimental design, is:
l & E C PROCESS D E S I G N A N D DEVELOPMENT
0.48
0.1126 1.670
-1 30 40 750
0.54 0.1671 1.925
Levels 0
45 50 900 0.60 0.2216 2.180
+I 60 60 1050 0.66 0.2761 2.455
+2
75 70 1200 0.72 0.3306 2.690
Table Ill. Conversions and Yields from Central Composite Rotatable Design Experiment on Benzene Ethylation
Exp t (Ue,ign)
.YO.
Ethjlene Concersion (‘YB), F‘o
1
89 943
2 3 4 5 6 7
98 272 21 518 56 130 80 036 87 154 80,868 70.749 88 249 89 593 64 277 90 724 61 598 45 884 83 253 19 997 80 989 100 000 50 091 14 687 75 640 78 714 83 041 11 962 87 108 88 590 71 827 80 423 87 728 82 072 79 286 84 GO5
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Benzene Conzerszon (‘Ye), 7c 3 519 3 830 2 914 7 165 2 495 2 681 8.307 7.262 6.697 6.791 4,250 5,997 3.783 2.856 4,341 1.127 5.695 2.438 5.830 0.950 5.277 5,558 5,836 0.906 6.010 3.213 7.408 7.278 5.051 5.758 5.598 6.008
MonoethylDtethjlbenzene benzene Yield ( Y u ) , Yield ( Y D ) , Moles/ Moles/ 700 M o l e s 100 M o l e s Ethjlene Ethqlene Fed Fed 80 629 87 356 19 012 43 526 73 095 77 386 65,482 57.195 73,980 74.915 53,895 76.013 54.470 41.721 69,627 19,678 68.173 91.600 41.567 10.193 62.571 66.849 69.803 11.769 70.297 78.799 58.757 65,327 75.670 68.714 67.318 72,727
4 657 5 456 1 250 6 302 3 471 4 884 7,692 6.777 7.934 7.339 5.191 7.356 3,564 2.082 6,813 0.159 6.408 4.233 4.262 2.246 6.534 5.933 6.619 0,096 8.406 4.896 6,534 7,548 6.029 6.679 5.983 5,939
Analysis of Factorial Portion of Design. T h e data from the quarter replicate of the 26 factorial experiment are analyzed by Yate’s technique (Davies, 1956 ; Johnson and Leone, 1964). Table I V gives the average effects and the mean squares calculated by this method for the four responses. \$‘e can simply look a t the mean squares and note which
Table IV.
factors stand out. To make a formal analysis of variance, however, we require an estimate of the error variance. The error variance estimated from the four center replicates is likely to be lower than that encountered in other regions of the experiment. This variance is pooled with the mean squares of the two three-factor interactions (calculated in Yate’s analysis) to obtain a relatively better (“improved”) estimate of the error. These pooled error estimates (up2)are also listed in Table IV. HALF-SORMAL PLOT. The half-normal plot (Figure 1) is a graph of the empirical cumulative distribution of the orthogonal contrasts from the factorial experiment, drawn on half-normal probability paper (Daniel, 1959). The effects are arranged in the order of the estimated absolute magnitude, as in Table V, then plotted on half-normal probability paper, where the ordinate is the ascending order number (rank), and the abscissa is the value of the effects. The equation
r = (2n/100)(P - 50)
+
l/2,
r = 1, 2, . . ., n
(2)
where n is the number of points, equal to 15 in the present experiment, defines the conversion from the ordinary cumulative probability, P, of the normal distribution, to the cumulative ordered rank, r . In the plot, the factors x4, xg x1
X5
x4
For For For For
conversion of ethylene conversion of benzene yield of monoethylbenzene yield of diethylbenzene
show up strongly (Table IV). This simply indicates that these effects are larger than would be expected of the greatest values out of the 15 mutually independent half-normal variables for each response. Individual significance has still to be judged by the analysis of variance of the mean squares of the individual effects (Johnson and Leone, 1964). ANALYSIS OF VARIANCE. The critical F-ratio, for one and five degrees of freedom, is listed for 1, 5, and 10% significance levels a t the bottom of Table IV. Mean squares greater than, or equal to, F X up2 are significant a t the a% level. I n the analysis of variance it is considered that the interactions of three and more factors are not appreciable.
Average Effects and Mean Squares from Factorial Experiment in Quarter Replicate
Aliases
Ethylene Conversion Av. Mean eject square 613.39 518.92 11.21 7.90 61.96 105.55 467.10 915.30 696.96 457.40 53.02 231.20 729.00 299.00 364.70
re*(degrees of freedom = 3 ) np2 (degrees of freedom = 5 ) F5, (1,5) X up2
5.97 160.00 1057.0
Benzene Conversion Au. Mean effect square 2.19 0.75 0.26 0.17 0.42 0.29 1.09 1.87 1.22 -1.42 -0.15 0.07 -1.14 -1.04 0.70
19.22 2.25 0.27 0.12 0.70 0.34 4.74 13.96 5.92 8.13 0.10 0.02 5.19 4.32 1.96
Monoethylbenzene Yield Av. Mean effect square -13.42 8.36 - 1.35 - 1.55 2.65 4.92 -19.89 16.99 11.22 -15.12 3.50 6.31 -11.09 - 6.33 8.19
0.043 1.08 7.14
720.60 279.70 7.30 9.61 28.16 96.94 582.11 155.00 503.36 914.87 49.07 159.46 492.27 160.47 268.49
5.76 111.72 738.34
Diethylbenzene Yield Av. Mean effect square 0.52 1.51 -0.16 0.07 0.64 0.11 0.37 2.45 1.49 -1.98 0.15 0.64 -1.52 -1.16 0.68
1.08 9.17 0.10 0.02 1.65 0.05 0.55 23.92 8.89 15.72 0.10 1.66 9.24 5.34 1.84
0.126 1.94 12.82
F l s ( l , 5 ) = 4.06; F6%(l,5)= 6.61; FlO7,(1,5)= 16.30
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Table V.
Ranking Effects for a Half-Normal Plot
Ethylene Conoersion Effect Rank
Effect Measured
Benzene Conuersion Effect Rank
10 9 1 15 14 7 2 4 11 5 13 6 8 3 12
2.19 0.75 0.17 1.87 1.09 1.04 0.26 0.42 1.22 0.29 1.42 0.07 0.70 0.15 1.14
Monoethylbenzene Yield Effect Rank
15 8 3 14 10 9 4 6 12 5 13 1 7 2 11
13.42 8.36 1.55 16.99 19.89 6.33 1.35 2.65 11.22 4.92 15.12 6.31 8.19 3.50 11.09
Diethylbenzene Yield Effect Rank
12 9 2 14 15 7 1 3 11 5 13 6 8 4 10
0.52 1.51 0.07 2.45 0.37 1.16 0.16 0.64 1.49 0.11 1.98 0.64 0.68 0.15 1.52
6 12 1 15 5 10 4 7 11 2 14 8 9 3 13
( 6) Conversion of benzene
(Xd
/
14
5
1 0
I
5
0
1s
10
20
V
I
I
1
I
0.5
1.0
1.5
2.0
2.5
24
2.5
Absolute value of the average effect ~
-
15
/
(c)
Yi eld of monoethylbenzene (YM) 14 r.
a
E
Yield of diethylbenzene (YD)
13 12
=I 11
=r . 109 a 8 2 7
"X
$
2 1
0
0
I
I
I
I
5
la
16
20
0.5
1.0
Absolute value of the average effect Figure 1 . 576
Half-normal plot for data of factorial experiment
I & E C PROCESS D E S I G N A N D DEVELOPMENT
1.5
Main Effects. T h e main effects in the order of decreasing magnitude of the mean squares for each of the responses are: Conversion of ethylene Conversion of benzene Yield of monoethylbenzene Yield of diethylbenzene where
x4*, x1*,
x5*3
x1,
2 2 , x6,
,r3
X4*$ x 5 , 26, 2 2 , *3
x 5 * , x4*, x1, x2, 2 6 , ?(3 x4*, x 2 , x61 x1, X5, x8
* indicates significant effect a t the 57, level.
For all four responses, the effect of agitator speed (x3) is very insignificant. This suggests that the diffusional phenomena are negligible in the region under study. I n further experimental work on the system this variable may be disregarded. The effect of the catalyst concentration (x4) is very significant for all the responses. This is to be expected from the strongly chemical nature of the aluminum chloride catalyst. The positive sign of the effect shows that an increase in the level of the catalyst concentration results in an increase in all the responses. LVhile the reaction time (XI) is the other significant factor affecting the conversion of benzene, the rate of ethylene flow is significant for the conversion of ethylene and yield of monoethylbenzene. The conversion of benzene increases with increase in the reaction time. The rate of ethylene flow also has a favorable, though not significant, effect on this response. Negative values of the effect of ethylene flow rate on the conversion of ethylene and the yield of monoethylbenzene suggest that an increase in this factor reduces the two responses. At higher rates of ethylene flow, larger quantities of ethylene may pass unreacted and, therefore, ethylene conversion decreases. Increase in reaction time (XI) has a similar effect on these two responses. All variables, except the initial quantity of benzene, favor the yield of diethylbenzene. This is to be expected, because increase in reaction time, temperature, catalyst concentration, and ethylene flow rate leads to severe alkylation where the polyalkylation reactions will be predominant. Temperature factor (XZ) has no significant effect. Two-Factor Interactions. Each of the two-factor interactions is confused with one or more of the other two-factor interactions. The seven sets of the two-factor interactions estimated are: xlx2 - x ; x j ; X1x3 - XZXg; x2x3 - X1xg - x4x6; X1X4 h'gx6; X2X4 - .Y3X6; X3X4 - X2X& and X4X5 - Xlx& The two-factor interactions can be separated from each other only by conducting a t least one more block of the quarter replicate experiments, However, we may conclude from chemical considerations that the two-factor interactions likely to be significant are those between the catalyst concentration and the other variables. For all four responses, the only two-factor interaction found significant is that between the temperature and catalyst concentration ( ~ 2 x 4 ) . This is confused with the interaction between the agitator speed and the initial quantity of benzene (x3x6), which is unlikely to be appreciable. The interaction between reaction time and catalyst concentration (x1x4), though not significant, has the next highest mean square. Its alias is the interaction between the rate of ethylene flow and the initial quantity of benzene (xbX6). The reaction time and temperature interaction are expected to be appreciable from kinetic considerations, but the results (Table IV) show no significance for this effect. The postive effect of x 4 , combined with its negative interaction with X Z , shows that the increase in yields and conversions with the catalyst concentration is greater a t lower temperatures. Since temperature also has a positive effect, lower catalyst concentrations and higher temperatures would also be favorable, The first alternative is, however, preferable.
-
Response Surfaces. Equation 1 is the general form of the expectation that the experiment estimates. I n the experiment, the levels chosen for the supplementary points along the axes do not provide orthogonality of the complete design. Even in such cases, the estimates of the first-order effects and their interactions are still orthogonal to each other and to the remaining estimates (Davies, 1956). Hence, coefficients bi of Equation l may be obtained individually as the sum of the products of the observed response, y, and the elements of the appropriate independent variable, divided by the sum of the squares of the elements of the independent variable-that is, by the equation
Similarly, coefficients b i j are obtained from the equation:
b,* =
C YnXinXjn ; Cn X i n X j n
i
