Optimal experimental design for estimating the kinetic parameters of processes described by the first-order Arrhenius model under linearly increasing temperature profiles

Abstract

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 1ae 2 , 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.

Estimation of Kinetic Parameters for Nonisothermal Food Processes

“…Those who used nonisothermal data to estimate kinetic parameters include others (1989a, 1989b), Nunes and others (1991), Nasri and others (1993), Cunha and Oliveira (2000), and Claeys and others (2001a). These studies assumed a zero-or first-order model and the Arrhenius temperature relationship.…”

“…Nonisothermal methods have the advantage of reduced experimental effort, because the parameters can be estimated from 1 experiment where temperature is varied over the range of interest, and samples are taken at various times. Parameters are estimated from a dynamic environment closer to commercial processing conditions, and thermal lag problems are overcome (Cunha and Oliveira 2000). However, nonisothermal methods require assuming a priori a temperature function, such as the Arrhenius relationship.…”

Optimal design of dynamic experiments for improved estimation of kinetic parameters of thermal degradation

“…In these works, it was shown that from dynamic experiments, or from selected sampling times, more pertinent information can be extracted than from the classical static experiments with uniform sampling schemes. Similarly, Cunha and Oliveira (2000) and Brandão et al (2001) proposed the use of linear temperature profiles and non-equidistant sampling times so as to improve precision on the estimation of the Arrhenius type model parameters. It should be noted that these studies considered simple kinetic models stated as ordinary differential equations (ODEs).…”

Optimal designs for constant‐heating‐rate differential scanning calorimetry experiments for polymerization kinetics:nth‐order kinetics

“…[6][7][8] In this article, our interest is designing constant-heating-rate DSC experiments for the nth-order kinetic model, that is, Figure 3. When designing an experiment, we explicitly mean the specification of the level(s) and independent factor(s) that will be used when the experiment is being conducted; that is, we do not mean the experimental procedure or equipment design.…”