Optimum reference temperature for reparameterization of the Arrhenius equation. Part 2: Problems involving multiple reparameterizations

Existence of high parameter correlations is one of the major problems during parameter estimation. This is particularly true when the mathematical model presents one or more kinetic constants that depend on temperature, as defined by the Arrhenius equation. In a recent work, Schwaab and Pinto [2007. Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: problems involving one kinetic constant. Chemical Engineering Science 62, 2750–2764] showed that an optimum reference temperature can be defined for reparameterization of the Arrhenius equation and elimination of parameter correlation, when the model contains a single kinetic constant. However, when the model contains more than one kinetic constant, the number of parameter correlations is larger than the number of reference temperatures that can be defined; consequently, it becomes impossible to eliminate all the parameter correlations simultaneously. For this reason, in this work different norms are defined for the parameter correlation matrix and are used to allow for minimization of the parameter correlations through manipulation of reference temperatures. Three parameter estimation problems are used to illustrate the use of the proposed two-step parameter estimation procedure and to show that the minimization of parameter correlations and relative errors are indeed possible through proper manipulation of reference temperatures in problems involving multiple model parameters.