Optimum reparameterization of power function models

Power function models are frequently used to describe rates of adsorption (as in the common Freundlich model) and chemical reaction (for estimation of reaction orders). When power function models are used to fit available experimental data, correlations among obtained parameter estimates are normally very high, which may cause significant numerical problems during the estimation of the model parameters and lead to misinterpretation of the statistical significance of final results. In this work, a reparameterization technique is presented to allow for reduction of parameter correlations in power function models. Afterwards, the two-step parameter estimation procedure [Schwaab, M., Pinto, J.C., 2007. Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: problems involving one kinetic constant. Chemical Engineering Science 62, 2750–2764; Schwaab, M., Lemos, L.P., Pinto, J.C., 2008b. Optimum reference temperature for reparameterization of the Arrhenius equation. Part 2: problems involving multiple reparameterizations. Chemical Engineering Science 63, 2895–2906.] is used for optimum reparameterization and estimation of uncorrelated model parameters in power function models.