On the Estimation of Kinetic Rate Constants SIR:Values for the pyrolytic dehydrogenation of benzene from Hougen and Watson (1945) were used by Tanner (1972) as well as previously by Seinfeld and Gavalas (1970) to illustrate the application of their proposed techniques for the estimation of kinetic rate constants. It is implied that these values are representative of real experimental data as contrasted with simulated data. However, analysis of these values suggests that they are also manufactured. The deviations do not have the magnitude or the erratic variation characteristic of real measurements with continuous tubular reactors. A careful reading of Hougen and Watson (1945) and of the original source of these values (Murphy, el al., 1938) confirms the suspicion that they were manufactured, probably by reading from smooth curves through unpublished experimental data. Hence, the methods of Tanner (1972) and Seinfeld and
Gavalas (1970) have not really been applied to experimental kinetic data. Unfortunately, as noted by White and Churchill (1959), most of the data obtained from continuous tubular reactors do not justify such refined treatment.
SIR:The data of Hougen and Watson were selected for our study more as a vehicle for examining a number of general questions related to estimation of kinetic parameters than strictly to determine the rate constants for that system. I n fact, it was noted in our analysis of that system that the experimental data were suspiciously smooth. For that reason, the data were intentionally corrupted in order to test more realistically the various measurement alternatives. I n principle, nonlinear parameter estimation algorithms can be ap-
plied regardless of the level of error in the data. These techniques are very straightforward to use and, in our opinion, deserve serious consideration whenever parameters must be estimated from data, regardless of the quality of the data. John H . Seinfeld*
SIR: Professor Churchill’s comment on the synthetic character of the benzene pyrolysis data is well taken. His note, however, raises a host of interrelated questions within a broader context. Should, for example, sophisticated optimization techniques be developed when present-day models do not contain the detailed information which one desires to extract? Should, in turn, models be developed to provide such information when the tools for identifying complex models and discriminating between candidate models are either inadequate or cumbersome? If so, then, as Dr. Churchill infers, should these tools be formulated when experimental supporting data may be variously unavailable, difficult to obtain, or fraught with error? What is an acceptable amount of information for the data to contain in order to build this hierarchy of modeling implements for analysis? I n particular, the pyrolysis of benzene example illustrates t,hat a simple polynomial method reveals, without calculation, that kl may be relatively insensitive to errors in the data, while kz is only meaningfully estimated from precise measure ments. Is ICl by itself useful? Is the additional refinement
needed to define kt properly justified by its application? The orthogonal polynomial-Picard iteration technique has, in fact, been shown to be useful for analyzing experimental enzyme kinetic data obtained with a stopped-flow apparatus (Tanner, 1972). It should be neither surprising nor undesirable for one modeling tool to outpace its present ability to be applied or even be realistically tested, especially if we restrict that test to our narrow spectrum of chemical engineering problems. There are many anomalous results, especially in the biological literature, awaiting systematic investigation with our hierarchy of methods.
literature Cited
Hougen, 0. A., Watson, K. M., “Chemical Process Principles,” Vol. 3. Wilev. New York. N. Y.. 1945. Murphy; G. B:, Lamb, G: C., Watson, K. M., Trans. Amer. Inst. Chem. Eng. 34, 429 (1938). Seinfeld, J. H., Gavalas, G. R., A.I.Ch.E. J . 16, 644 (1970). Tanner, R., IND.ENG.CHEM.,FUND.4M. 11, 1 (1972). White, R. R., Churchill, S. W., A.1.Ch.E. J. 5,355 (1959). Stuart W . Churchill University of Pennsylvania Philadelphia, Pa. 19104
George R. Gavalas
Department of Chemical Engineering California Institute of Technology Pasadena, Calif. 91 109
literature Cited
Tanner, R. D., A.I.Ch.E. J . 18,385 (1972). Robert D . Tanner Merck d% Go., Inc. Rahway N . J . 07066 Ind. Eng. Chern. Fundam., Vol. 11, No. 3, 1972
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