Estimation of parameters in differential equations of reaction kinetics in a solid based on thermogravimetric data

On the accuracy and precision of estimation of the activation energy of non-isothermal decomposition of a solid

“…Since the experimental data were designed to separate the information on activation energy from that on f(c0, the two criteria were in good agreement; it can be shown, however, that for a single experimental run, a complex model may best fit the data while having an unreasonable activation energy value [4].…”

“…Similar methods, but involving intergration of the rate squation, can be used to determine the activation energy from integral (i.e. conversion vs. time) data [4]. In both cases, to estimate the activation energy it is necessary to assume a functional form f(~) for the reaction mechanism, which is an additional source of error in estimation.…”

“…Since Eq. (5) is non-linear with respect to the activation energy, the weighted non-linear regression technique described in [4] was used to find the optimum activation energy estimates.…”

“…However, in the elaboration of these methods some assumptions were made that are difficult to fulfil in real experiments, e.g. linear temperature rise.Nowadays the advance in numerical, computer-oriented methods, such as the non-linear least squares, maximum likelihood, quasi-linearization and others [3][4][5], allows one to overcome the computational problems of identification. Effective optimization procedures are capable of handling models of any complexity.…”

Determination of the kinetic parameters of the multi-stage thermal decomposition of solids under non-isothermal conditions by the non-linear estimation approach

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The activation energy of decomposition of alurniniurn hydroxide vs. weight loss was estimated from thermogravirnetric data collected over a wide range of heating rates, without resorting to the model of the reaction mechanism.These activation energy values were subsequently used to distinguish individual dehydration stages and to determine the best models of the reaction kinetics for these stages.Finally, the overall decomposition model was formulated, and its parameters were determined by the non-linear estimation approach.Owing to the development of numerical, computer-based identification method, derivation of a model for the multi-stage thermal decomposition of a solid has become a greatly simplified task [1 ]. However, a suitable procedure for processing of experimental data to obtain the most information possible on the individual decomposition stages remains of significance.

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