Calibration of a kinetic model for wet air oxidation (WAO) of substituted phenols: Influence of experimental data on model prediction and practical identifiability

Abstract

Calibration of kinetic models of wet air oxidation (WAO) is usually performed through minimisation algorithms with respect to total organic carbon (TOC) experimental data. However, the reliability of the estimated value of the kinetic parameters is frequently not reported. Moreover, the influence of data quantity/quality in the kinetic parameters identifiability is not properly assessed. The objective of this study is to compare the calibration goodness of a proposed kinetic model when using one set of data (total effluent TOC [TOC eff ]) or two sets of independent experimental measurements (total effluent TOC [TOC eff ] and residual TOC of target pollutant [TOC [A] ]). The systematic comparison was made using identifiability analysis with contour plots of both objective functions and the confidence intervals were calculated through the Fisher information matrix (FIM). The experimental data used in this study comes from a previous one, where WAO was investigated as a suitable precursor for the biological treatment of industrial wastewater containing high concentrations of o -cresol or 2-chlorophenol [M.E. Suárez-Ojeda, J. Carrera, I.S. Metcalfe, J. Font, Wet air oxidation (WAO) as a precursor to biological treatment of substituted phenols: refractory nature of the WAO intermediates, Chem. Eng. J. 144 (2008) 205–212.]. The results show that the model correctly fitted the experimental [TOC eff ] in all cases with less than 6% as averaged relative deviation, either using one set of data ([TOC eff ]) or two sets of independent experimental measures ([TOC eff ] and [TOC [A] ]) in the objective function. However, when using only [TOC eff ], the model was not capable of fitting the proportion between [TOC [A] ] and intermediates TOC. The obtained E ACT for the calibration made with [TOC eff ] and [TOC [A] ] were 71 ± 20 kJ mol −1 ( R 2 = 0.92) and 47 ± 9 kJ mol −1 ( R 2 = 0.96) for o -cresol and 2-chlorophenol, respectively. However, when using just [TOC eff ], the obtained E ACT values were not in the range of the values reported in the literature and had smaller regression coefficients. Moreover, the calibration with just [TOC eff ] presented a high correlation between the obtained rate constants, whereas the calibration with [TOC eff ] and [TOC [A] ] was statistically more reliable. As example, the D-criterion values are three to six times larger for the calibration made with ([TOC eff ] and [TOC [A] ] than for the calibration made only with [TOC eff ], in the framework of OED/PE criteria, this is related to minimisation of the geometric mean of the identification errors.