Least squares criteria for the kinetic evaluation of thermoanalytical experiments. Examples from a char reactivity study

Abstract

The mathematical modeling of the chemical processes is a crucial problem of the thermal analysis. Simple models with few parameters seldom can describe the real complexity of the phenomena arising during the heating of the various substances. In the case of more complex models the determination of the parameters and the validation of the model require the evaluation of carefully designed experimental series. The one-by-one evaluation of the experiments is a mathematically ill-defined problem at a larger number of unknown parameters. The non-statistical experimental errors of the thermal analysis hinder the determination of a single parameter set by the simultaneous least squares evaluation of the experiments. This paper discusses several evaluation techniques for the handling of the non-statistical errors during the least squares evaluation of experimental series. The methods are illustrated by the evaluation of oxidative thermogravimetric experiments of a lignite and a coal char.