I
HERBERT GROHSKOPF American Cyanamid Co., New York 20, N. Y.
Statistics in the Chemical Process Industries Present and Future
-
After ten years of growth, three tools have proved most valuble in chemical work
b b b
The factorial experiment Latin and Youden square experiments Central composite experiments
T H E first serious use of experimental statistics in applied chemistry dates to World War 11; the place, Great Britain. I n the past ten years there has been increasing use of statistical methods in the United States chemical industry. Most chemical and petroleum companies now” employ experimental statisticians to provide specialized statistical services in their laboratories and plants. Most laboratories have chemists and engineers who are making increasingly good use of statistical design of experiments. Yet, while experimental statistics is saving industry much time and money, the biggest developments in the application of statistical methods to chemical problems lies ahead. How will this development shape up, who will participate in it, who will benefit from it? T o answer these questions, let us consider what the use of statistics means now, and how advances in chemical technology will soon force the development of new statistical methods.
Development and Uses of Statistics to Date
Statistics has had a strong positive influence on experimental efficiency in the chemical industry. T o understand this, it is necessary to look beyond the mechanics of experimental design, to the effects that experimental statistics has on the process of defining the experimental problem. Designs provide well-organized plans of action to explore and measure chemical systems with many operating variables, and many measures of chemical system performance. Chemical systems are not simple; they are difficult to measure and to understand. And while the wrong formulation of some experimental problems is inevitable,
Plans for Experimenting and Problems They Help Solve Variables That Can Some Uses of Experimental Plan Be Evaluated These Plans Factorial (6) Qualitative, quantitative, and Screening of variables and of mixed treatments Estimation of main effects and of interactions Latin squares Differences between individuals To estimate quality or efficiency Youden squares (6) Batches of individuals, free of position and time effects in process of Samples Formulations making such estimates Treatments (Interactions are mingled with Cultures differences between test equipments, positions, and time of tests) Central composite Usually quantitative and scalar For efficient mapping of chemical system performance (3,5) throughout variable ranges of greatest interest
the incidence of experimental failure can be reduced. The statement of the problem; the questions raised in adapting a n experimental plan to solution of the problem; the listing of the variables to be checked out, varied, controlled, and measured-all these help define and clarify experimental objectives. Although investment in planning time is small compared with days, weeks, and months of experimental work, it can increase the productivity of experimental programs many times. Increased experimental productivity comes from clearer definition of the experimental problem, and from the use of simple tools, such as the factorial experiment. The engineer can work wonders screening process variables with the help of simple statistical plans. H e can do this even though the process effects he must define are small compared with batchto-batch or shift-to-shift variability. The use of factorials, Youden and
Latin squares, and central composite experiments permits the measurement of the effects of variables free of the pull of other variables. Using these designs, comparisons are made with the least possible effort, and each experiment contributes information on the effect of all the variables in the design. To make good use of this science, chemists and engineers need formal instruction and seasoned guidance, preferably by other chemists and engineers. To build a nucleus of statistical skills to do the training job is difficult. One method is to retain the best possible statistician and to assign him to work with a selected group of chemists and engineers. The statistician trains his coworkers in the principles of experimental design, and works with them solving their problems. Another plan is to send selected chemists and engineers to graduate training, such as offered by the Institute of Statistics at North Carolina State ColVOL. 52, NO. 6
JUNE 1960
497
lege. A number of companies have sent men to participate in this two-year program. The University of Wisconsin is now offering a similar, but more chemically oriented program under the direction of Dr. G. E. P. Box. With a few such exceptions, the schools have been of little help. I n the chemical industry few take the time and trouble to study the logical structure and the flow of chemical process development work. Even the simplest chemical systems are difficult to understand. To the experimenter in other fields, the chemist’s problems in measurement appear forbidding. Often lack of suitable chemical analytic methods prevents quantitative process understanding. If people within the process industries give little thought to the structure of development problems, such inquiry is even further removed from the awareness of statistical research workers in universities. To date this has almost precluded the working out of a common ground between the chemical and chemical engineering disciplines on the one hand, and the mathematical and statistical disciplines on the other. T o become productive in chemical work, the experimental statistician should have undergraduate training and experience in physics, chemistry, or in chemical engineering. Following this he must become familiar with problems in chemical research and development by intensive work with chemists and engineers. The acute and chronic scarcity of people bvith good training in engineering applications of statistics is a problem of economic importance. Less than 20% of the population is suitable for training in chemistry and in engineering. Men with top potentials make up a much smaller fraction of the total. This very small fraction of the population provides the staffs for researches which cost industry hundreds of millions of dollars each year. I t makes up the total inventive resources of both the chemical and the petroleum industries. Managers of industrial development and research, and leaders of chemical and engineering education must see that better statistical course work for chemists and engineers is developed and made available a t the undergraduate and graduate levels, as well as in industry. Finally, statistical departments have the problem of establishing specialized programs to train experimental statisticians with strong roots in the physical sciences. I n addition to the usual statistical training, such men should be given solid grounding in operational mathematics, and in the mathematical statement of engineering problems. Such men are needed to innovate and to build in a field just beginning to grow. In the last ten years G. E. P. Box has made outstanding contributions in statistical methods to solve chemical process
498
problems. As a statistician Dr. Box has been most fruitful because he was first a practicing chemist, and because he has maintained continuous contact with a broad range of chemical research and development problems. Box maintains that the experimental process is iterative in nature: That knowledge of physical and chemical systems increases by repeated statement of the problem and testing of hypotheses. There is an appropriate experimental strategy for each stage in this iterative process (4). While others have studied methods of problem solving as a problem in logic (7), Box has added to their contributions by adapting the statistical tools and numerical methods needed to provide a simple, readily understandable method for the quantitative description of chemical processes. Surface fitting, and the central composite design are still the high points of Box’s contributions to chemical engineering practice and to the chemical industry (3, 5). In another and familiar vein, Dr. W. J. Youden has encouraged and stimulated chemists and engineers in the practical use of statistics by extensive personal contacts and through his widely AND ENGIread column in INDUSTRIAL NEERING CHEMISTRY. Dr. Youden has made many original contributions to experimental design and measurement. Mew Statistical Tools With advances in chemical technology new statistical tools are needed. The first stage in the development of statistical methods has about run its course. While the development of standard statistical designs will now slow down, the profitable application of these designs will continue to grow. The theory of standard statistical designs has been well worked over. Certainly, the problems which must now be solved in an advancing chemical technology are not obvious. They will be solved by work pointed in new directions. To understand how the need for new statistical research is related to current technical problems, consider the present state of chemical and engineering practice. I n the past 15 years physics and electronics have shot ahead at a great pace. The process of catching up is just beginning, and chemical engineering technology is now at the threshold of great new growth and development. As is often the case in periods of farreaching technical change, there is some difference of opinion, and even a widespread lack of opinion, as to what must be done to advance chemical engineering technology. The big steps that must now be taken are development of more advanced skills in : 0
INDUSTRIAL AND ENGINEERING CHEMISTRY
Definition of mechanisms of chemical reactions
Estimation of reaction rates in systems with many concurrent reactions Reduction of physical facts to mathematical statements to make possible mathematical analysis and description of chemical process operation Computer simulation of chemical reaction systems to help evaluate alternate reactor, purification, and recycle designs Design of reaction systems which selectively favor product formation and which hold back by-product formation The potentials of these developments are immense. They will enable engineers to custom-design chemical reaction systems for greatly improved efficiency, and for lower fixed investments per annual ton of capacity. Leaders in chemical engineering education have started training future chemical engineering science: a plan of study with heavy emphasis on applied mathematics, physics, and physical chemistry ( 9 ) . While this promises to provide industry with well-trained. mathematically able engineering scientists, industry itself must take far-reaching steps to employ them profitably. To develop and to apply the new engineering science, industry must organize process analysis teams of chemists, chemical engineers, mathematicians, statisticians, control engineers, and numerical analysts. Only by cutting across the bounds of traditional disciplines is there hope of shortening the years of learning, development, and fumbling which inevitably lie ahead in establishing the new technology. At best, the cost of this development will be large. ib‘ithout free interplay of specialized skills, the cost will be larger, both in time and money, than it need be. Development managers in the chemical and petroleum industries must take the time to define this problem, to set broad objectives, and to organize programs which will assure participation in the engineering advances which will distinguish the next ten years. Each day that passes without definition of the problems in developing a more effective chemical engineering technology brings waste of one sort or another. Nowhere is this more apparent than in the fumbling and the pressures of keeping u p that are confusing the processing industries’ first experiences with automatic process control. Automatic computer control is a development which logically lies beyond better process understanding, and beyond better methods for chemical reactor design. In this brush with another rapidly advancing technology, the chemical and petroleum industries’ need for quantitative process understanding becomes quite apparent. Meanwhile elaborate computer control systems are being designed to operate
STATISTICS IN CHEMICAL PROCESSES and control processes by naive criteria of process performance : Best performance curves, fit visually from scatter charts of existing plant data, have been used as Process metals for computer control k Processes are controlled on the wrong
variables, making manual intervention necessary k Most of the system’s work is done in a way that offers little assurance that two of the controlled variables may not be fighting each other Too many constants are estimated from too few measurements, taken a t two few points
An experimental program w a s p r o p o s e d at American Cyanamid to t e s t the validity of a kinetic model for a chemical r e a c t i o n system. The tests were run in a four-stage c a s c a d e of c o n t i n u o u s s t i r r e d tank reactors. Independent variables in this experiment were: Temperature Concentration Average r e s i d e n c e t i m e
The g e n e r a l expression for the nth s t i r r e d tank in a c a s c a d e of cont i n u o u s r e a c t o r s is: Cn
- F-Fn 1 C n - 1 ~
. . .)e
= k (asbe..
.
= (Ae-E’RT)(asbt.. .)e
(1)
where,
F7Z
= c o n c e n t r a t i o n of product in the nth tank = volumetric flow rate in l i t e r s per minute from the l a s t
k
= the r e a c t i o n rate c o n s t a n t
U6
= order
bt
=
e
=
A
=
C-E/RT
=
G n
tank
of product formation reaction with r e s p e c t to concentration of raw material order of p r o d u c t f o r m a t i o n r e a c t i o n with r e s p e c t to c o n c e n t r a t i o n of an intermediate r e s i d e n c e time in minutes f r e q u e n c y factor in the A r r h e n i u s equation energy of activation
T h e n t r a n s f o r m i n g logarithmically:
The t r a n s f o r m e d variables: l/T, In 8, and the l o g a r i t h m s of the c o n c e n t r a t i o n driving forces, s u c h a s a and b, were selected a s independent v a r i a b l e s in a 23 factorial experiment. Two c e n t e r p o i n t s were added. T h u s , ten e x p e r i m e n t s were run, and c o n c e n t r a t i o n s into and out of the four process stages were m e a s u r e d . In all, 40 sets of concentrations were m e a s u r e d . From t h e s e data f r e q u e n c y factors and activation e n e r g i e s for six reactions were estimated. The r e s u l t i n g rate equations are being u s e d in computer simulation of the p r e s e n t plant, and for evaluation of i m p r o v e d r e a c t o r designs. T h i s method for defining the kinetic model of a reaction s y s t e m is b a s e d on the u s e of simple a l g e b r a i c equations. Problems of s a m p l i n g in time, a s in the s t u d y of a batch reaction, and u s e of nonlinear estimation are avoided. In t h i s s t u d y the energy of activation of the p r o d u c t i s smaller than that of one of the b y - p r o d u c t s , and larger than that of tw‘o other by-products. T h i s m a k e s it possible that, by u s i n g m e t h o d s of calculus of variations, solution f o r the best time-temperature profile for a plug flow reactor may be worked out (77).
The effective handling of problems such as these will provide the major subjects for statistical research and development in the years ahead. Even simple statistical methods can help a great deal in solving the control problems listed above. Beyond this, researches are needed in the design of experiments for chemical rate studies, in making confidence statements about estimated rate constants (Z), in studying process dynamics, estimating transfer functions ( I ) , working out methods for studying the dynamics of processes with several inputs and several outputs, all of which may, or may not be correlated with each other (70). These are major objectives, and many years of statistical research will be needed to make work on these problems more tractable. I n 1956 chemists and engineers were at the frontiers of statistical practice when they first ventured experiments based on central composite designs. Today the pioneers are working on the more difficult problem of nonlinear estimation. Meantime interesting process studies are being carried out with the help of a good blend of chemical, engineering, and statistical skills. The process study (left) carried out by chemists and statistically trained chemical engineers in American Cyanamid Co. is a case in point.
Refer en ces (1) Blackman, R. B., Tukey, J. W., “The Measurement of Power Spectra,” Dover Publications, New York, 1958. (2) Box, G. E. P., Coutie, M. A,, Proc. Inst. Elec. Engrs. 103,Pt. B , 1 (1956). (3) Box, G. E. P., Hunter, J. S., Ann. Math. Stat. 28, l(1957). (4)Box, G. E. P., “Integration of Techniques in Process Development,” 11th Ann. Convention,ASQC, p. 687, Detroit, Mich., May 1957. (5) Box, G . E. P., Wilson, K. B., J . Royul Statistical Sac. 13, Ser. B, 1 (1951). (6) Cochran, W. G., Cox, G. M., “Experimental Designs,” 2nd Ed., Wiley, New York, 1957. ( 7 ) Cohen, M. R., Nagel, E., “An Introduction to Logic and Scientific Method,” Harcourt Brace, New York, 1934. (8) Davies, 0. L. (Editor), “The Design and Analysis of Industrial Experiments,” Oliver and Boyd, London, 1956. (9) Elgin, J. C., Chem. Eng. Prop. 52, 1 , 85 (1956). (10) Goodman, N. R., “On the Joint Estimation of the Spectra, Cospectrum, and Quadrature Spectrum of a TwoDimensional Gaussian Process,” Scientific Paper No. 10, Engineering Statistics Laboratory, New York University, 1957 (Ph.D. thesis, Princeton Univ.). (11) Katz, S., “Best Temperature Profiles in Plug Flow Reactors: Methods of Calculus of Varjations,” Ann. N . Y. Acad. Sci. (1960), in press.
RECEIVED for review September 30, 1959 ACCEPTED March 30, 1960
Division of Industrial and Engineering Chemistry, 136th Meeting, ACS, Atlantic City, N. J., September 1959. VOL. 52, NO. 6
JUNE 1960
499
