Optimal experimental design for estimating the kinetic parameters of processes described by the ®rst-order Arrhenius model under linearly increasing temperature pro®les

The optimum experimental design for systems following the ®rst-order Arrhenius model under linearly increasing temperature pro®les was studied by determining the sampling conditions that lead to a minimum con®dence region of the model parameters. It was found that experiments should be started at the lowest possible temperature and, for each initial temperature, there is an optimal heating rate. This heating rate is often too high to be feasible, implying that experiments have to be conducted at a lower practicable heating rate. In this situation the experiments should be replicated in order to improve the precision of the estimates. If both the initial temperature and the heating rate are ®xed at their optimal values, the optimal sampling times correspond to fractional concentrations that are irrational numbers (approximately 0.70 and 0.19) whose product is exactly 1=e, as earlier found for the Bigelow model. A case study based on the estimation of the kinetic parameters of the acid hydrolysis of sucrose is also presented.