I
PAUL W. TIDWELL
A Case History.
Plastics Division, Monsanto Chemical Co., Texas City, Tex.
..
Chemical Process Improvement Response Surface Methods
by
Response surface experimentation is an efficient method of doing chemical research without the inadequacies of other empirical techniques, and can lead to a better definition of the experimental variables of the system
-
Conclusions drawn from this laboratory research
,Responses of the two systems were adequately mapped ,The system by a new definition had been simplified .Catalyst 2 was shown to be better than catalyst 1 through economic evaluation ,The efficiency of the experimental approach is clearly illustrated
improvement has clearly been demonstrated by the work of Box and Wilson ( 4 ) . Their work and the work of others (7-3,5-72) have resulted in increased use of these experimental methods for these purposes, which is apparent in the chemical literature of the past few years. This example shows how response surface methods were used for solving a process improvement problem. While this problem was part of a process development project, the concept is applicable to the improvement of a large scale industrial processes. Because of company security requirements, the feedstocks, products, and others, must remain unnamed, and data are coded. At the time of this study, Monsanto was interested in and had done some research on a process for making D. D could economically be made by the following reaction
+ B + C-D
catalyst
A
-8/C-
A/B+CFLOW RATE-
THE utility of response surface methods in chemical process development and
Figure 1. Relative effects of the variables on yield are perimental by the classical technique ex-
-I- B + C + other products
For the early research work, catalyst 1 had been used, and while its performance was satisfactory, catalyst 2 possessed certain features which made it potentially superior to catalyst 1. T h e actual performance of catalyst 2 was not known. As catalysts often perform differently a t identical conditions, the response surfaces of both catalysts were needed so the economic evaluation for each catalyst could be made a t its most favorable conditions.
tI 510
INDUSTRIAL AND ENGINEERING
CHEMISTRY
S T A T I S T I C S IN CHEMICAL PROCESSES Table
I.
The Experimental Plan and Results of the First Designed Experiment Response Variables Independent Variables % D XI XZ X8 % Yield in product
Run No. 1
-1 +1
-1 +1
+1
-1 -1 -1
-1
68.8
15.79 12.03 11.91 12.37
5 6
-1
-1
+1
7
-1 +l
61.3 61.0 16.6 66.5
15.77 11.92 11.58 12.27
8.9 67.0 62.4 45.1 66.8 66.5 64.6 65.5
11.26 10.96 13.68 12.68 14.02 13.80 13.70 13.71
2 3 4
-1
-1 $1
+I
8
17.8
+I
-1 +l +1
+1
+I
0
9 10 11 12
-2.0 $2.0 0 0
13 14 15 16
0 0 0 0
0 0
0 0 -2.4 +2.4
0
0
0
0
17 18
0
0
0
0
0
0
XI
= log (BJC)
0
0
0 -1.65 f1.65
- Ci.
x2
1% [ A I @
Ki
+ C)l - c2.
-
x3
Source
T h e constants K1, K2, K3, CI,CZ, and C3 (Table I) were chosen so that the center of the experimental work was at the “optimum conditions” found in the earlier work, and the ranges were within safety and operability limitations consistent with the system.
Table II. Coefficients for the Yield Model Experiment 1 Biz = -4.589 Bo = 64.436 Baa = 0.236 B I = 13.500 Biz = 12.750 Bz = -7.776 Bl3 = -0.075 B3 = -0.273 B23 = -0.300 Bii -6.929
Analysis of Variance for the Yield Experimental Results of First Designed Experiment SS d.f. MS
L:Y2 Bo Terms Linear
61,095.9300 54,659.2006
18 1
3,730.3660
3
2916.0000
BTI/BR B ~ B ;B~ ~ , B38/BZ%,Bii, BO \Biz
2nd order
1243.4553
Fa,s = 97.46“
1.4499 1026.7632 \ 273.7904 2,604.2969
6
102.0665 101.4965
5
12. 7583b 20.2993
0.5700
3
0.1990
1300.5000 0.0450 0.7200)
Residual Lack of fit Experimental error
8
434.0495 F6,8~34.02~
Significance of 0.1% level. Earlier experimental work established the experimental error variance to be this order of magnitude.
Table IV. i=1
-
K3
Table 111.
+
+
-
64.6 13.90 65.1 14.08 = Flow rate C3
Kz
T h e earlier experimental work had been done empirically, as a satisfactory kinetic model did not exist. These results are shown in Figure 1. T h e earlier workers chose to define the system as two weight ratios, and the total flow (Figure 1). From these data one might conclude that the yield would be maximized at any given flow rate by operating a t a unique set of ratios A / ( B C) and B / C . (The yield was based on C, as it was the most expensive of the feed components.) Using the above definition of the system an experimental plan was formulated, and the plan and results are given in Table I. The logarithmic scaling of the two ratios was used. The data were fitted to the model :
*
62.1 61.3
Fitting the yield data to the model shown by the method of least squares yielded the constants given in Table I1 and analysis of regression in Table 111. T h e results are shown as response contours; the effects of A / ( B C) and B/C at a constant flow rate on yield and D-in-the-product are shown in Figure 2. T h e analysis of regression clearly shows the highly significant interaction between the two ratios, a fact that was undetected by the classical(one variable at - a - time) experimental approach. Further, the results clearly show the absence of a maximum in yield, and that increasing yield reduces the concentration of the desired product in the product stream. The highly significant interaction between the ratios suggested an alternate definition of the system, and this possibility was investigated. Ratios of
The Experimental Plan and Results of the Second Designed Experiment
Run
No. 1 2 3 4
5 6
7 8
-1 +1 -1
+I -1 +l
-1 +I
-1 -1
-1
+I +I
-1
-1 -1 +1
+I
+I
+l
-1 -1
+1
+I
52.7 75.3 61.9 76.4
13.91 15.52 16.70 17.35
61.4 82.2 63.4 72.8
14.66 15.93 16.33 17.01
44.5 80.2 65.7 69.0
14.02 16.44 14.21 17.25 16.39 16.71 16.32 16.47 16.61
9 10 11 12
-1.65 +1.65 0 0
0 0 -1.65 +1.65
13 14 15 16
0
0 0 0
-2 +2 0
17
0
0 0
60.4 74.7 71.1 70.9
0
74.0
0 0 0
0 0 0
0
0
VOL. 52,
NO. 6
JUNE 1960
51 1
.o
- 2.0
-1.0
0.0
+1.0
+ 2.0
XI
XI Figure 2. Effects of XI (log 6/C) and Xz (log A/B significant interaction between the two ratios
+ C) on yield and 70 D in the product stream of
experiment 1 show
Left. Yield Right. % D in product stream
-1.0
t1.0
0.0
XI Figure 3. Effects of XI ( 6 / A ) andXz (C/B) on yield and conclusion
-1.0 %
0.0
+ 1.0
XI
D in the product stream for experiment 2 support an earlier
Left. Yield Right. 70D in product stream
B / A were found to be approximately a linear function of the significant canonical variable, which indicated that the system could be simplified if this and another ratio were used in place of the two ratios used in the study. For the evaluation or catalyst 2, the system was defined with the ratios of B / A and C/B, and the total flow rate. T h e experimental plan and results are given in Table IV. As in the above example, the runs were made in random order. The contours for yield and % D-in-the-product at a constant flow rate for catalyst 2 are shown in Figure 3. T h e analysis of regression showed that the equation adequately described the data. T h e data and Figure 3 51 2
support a n earlier conclusion that the new definition of the system simplified its representation. Acknowledgment
T h e author would like to acknowledge the cooperation and assistance of John MacPherson in preparing this article. literature Cited (1) Box, G. E. P., Biometrics 10, 16-60
(1954). (2) Box, G. E. P., Biomefrika 39, 49-57 (1952). (3) Box, G. E. P., Hunter, J. S., Ann. Math. Statistics28, 195-241 (1957). (4) Box, G. E. P., Wilson, K. B., J . Roy. Statistical Sod. 13, Ser. B, 1 -45 (1751).
INDUSTRIAL AND ENGINEERING CHEMISTRY
( 5 ) Box, G. E. P., Youle, P. V., Biometrics 11, 287-323 (1955). (6) Bradley, R. A., Znd. Qual. Control 15,16-20 (July 1758). (7) Davies, 0. L., “Design and Analysis of Industrial Experiments,” Hafner, New York, N. Y.,1956. (8) DeBaun, R. M., Biometrics 12, 20-22 (1956). (9) Hunter, J. S., Znd. Qual. Control 15, 16-24 (December 1958). (10) Zbid., 16,7-15 (January 1957). (11) Zbid., 16, 6-14 (February 1959). (12) ,Hunter, J. S., Trans. N . Y. Acad. Scz. 17,124-32 (1754). RECEIVED for review September 15, 1957 ACCEPTED April 8, 1960 Division of Industrial and Engineering Chemistry, 136th Meeting, ACS, Atlantic City, N. J., September 1757.
