Parametric Estimation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 317

effort if one need to write the integrator routine as well. However, if one takes the inte-
grator routine developed here in this paper, the general approach becomes easier to apply
than the traditional integral and differential methods.

7.9. SUMMARY

In this chapter, the basic regression approaches have been discussed. Regression model is
a mathematical equation intended to be applied to describe a given set of experimental or
observed data. To perform parametric analysis, one must first understand the error and error
structure of the data. One should not cater to a linear regression model just because straight
lines are easy to deal with and visually pleasing. More fundamental regression models do
however bring complexity into the parametric estimation. In particular, one common type
of regression mode: differential regression model is discussed in detail and an example
has used for further discussions. In the Physical Chemistry and Reaction Engineering litera-
ture, the integral methods and the differential methods have been standardized for solving
the differential regression model problems. Irrespective of the error structure in data, it
had been a common practice to transform the regression models into linear ones. The integral
method is marked by its trial-and-error nature and the differential method generally shows
higher degrees of uncertainty. Discussions with these two frequently used methods espe-
cially for computer illiterates are made with the real batch kinetic estimation problem. The
basis for not trusting the kinetic parameters obtained using these two methods is the igno-
rance of the error structure of data during regression. To this end, a viable approach to para-
metric estimation for the differential regression model problem is preferred. However, one
does need to use computer to carry out the analysis. The viable method is combining a general
numerical integrator such as ODExLIMS and the utilization of the solver program in Excel .
As such, the trial-and-error nature and the tedious calculations of the traditional (precom-
puter age) methods can be eliminated. Above all, the parameters estimated directly reflect
the quality of the data series and thus can be trusted over those obtained from the traditional
methods.

Further Reading

Adamson, A.W., 1986. A Textbook of Physical Chemistry (3rd ed.). Orlando: Academic Press College Division.
Alberty, R.A., Silbery, R.J., 1992. Physical Chemistry . Wiley: New York, NY. p. 635.
Butt, J.B., 1999. Reaction Kinetics and Reactor Design (2nd ed.). New York: Marcel Dekker, Inc.
Chapra, S.C., Canale, R.P., 1998. Numerical Methods for Engineers (3rd ed.). Toronto: McGraw-Hill.
Fogler, H.S., 1999. Elements of Chemical Reaction Engineering (3rd ed.). Upper Saddle River, New Jersey: Prentice Hall.
Hairer, E., Nørsett, S.P., Wanner, G. 1987. Solving Ordinary Differential Equations: 2 Stiff and Differential-algebraic
Problems . New York: Springer-Verlag.
Hellin, M., Jungers, J.C., 1957. Bull. Soc. Chim. France , 386

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Hinshelwood, C.N., Hutchison, W.K., 1926. A Comparison between Unimolecular and Bimolecular Gaseous
Reactions. The Thermal Decomposition of Gaseous Acetaldehyde. Proc. R. Soc. Lond. A, 111: 380 e 385.
Kremenic, G., Nieto, J.M.L., Weller, S.W., Tascon, J.M.D., Tejuca, L.G. 1987. Selective oxidation of propene on
a molybdenum-prasedodymium-bismuth catalyst. Ind. Eng. Chem. Res. , 26(7), 1419 e 1424

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Levenspiel, O., 1999. Chemical Reaction Engineering (3rd ed.). Toronto: John Wiley & Sons.
Rodriguez, Tijero. 1989. Can. J. Chem. Eng. , 67(6), 963 e 968

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