Applying constraints on model-based methods: Estimation of rate constants in a second order consecutive reaction

This paper describes estimation of reaction rate constants and pure ultraviolet/visible (UV–vis) spectra of the component involved in a second order consecutive reaction between Ortho-Amino benzoeic acid (o-ABA) and Diazoniom ions (DIAZO), with one intermediate. In the described system, o-ABA was not absorbing in the visible region of interest and thus, closure rank deficiency problem did not exist. Concentration profiles were determined by solving differential equations of the corresponding kinetic model. In that sense, three types of model-based procedures were applied to estimate the rate constants of the kinetic system, according to Levenberg/Marquardt (NGL/M) algorithm. Original data-based, Score-based and concentration-based objective functions were included in these nonlinear fitting procedures. Results showed that when there is error in initial concentrations, accuracy of estimated rate constants strongly depends on the type of applied objective function in fitting procedure. Moreover, flexibility in application of different constraints and optimization of the initial concentrations estimation during the fitting procedure were investigated. Results showed a considerable decrease in ambiguity of obtained parameters by applying appropriate constraints and adjustable initial concentrations of reagents.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► In this study two rate constants of a second order consecutive reaction were estimated. ► Two types of model based techniques were used to estimate the rate constants of reaction. ► It was shown that different rate constants were obtained when different methods were applied. ► It was shown that proper constraints can reduce the range of acceptable results.