Published: December 14, 2011 r2011 American Chemical Society 1131 dx.doi.org/10.1021/ie201087h | Ind. Eng. Chem. Res. 2012, 51, 1131–1142 ARTICLE pubs.acs.org/IECR Influence of the Experimental Errors and Their Propagation on the Accuracy of Identified Kinetics Parameters: Oxygen and Temperature Effects on Ascorbic Acid Oxidation during Storage Caroline P  enicaud, † Philippe Bohuon, ‡ St  ephane Peyron, † Nathalie Gontard, † and Val  erie Guillard* ,† † UMR 1208 IATE Agropolymers Engineering and Emerging Technologies, Universit  e Montpellier 2, CIRAD, INRA, Montpellier SupAgro, CC 023 Place Eug ene Bataillon F-34095 Montpellier Cedex 5, France ‡ UMR Qualisud, Food Process Engineering Research Unit, Montpellier SupAgro, CIRAD, Universit  e Montpellier 2, 1101 avenue Agropolis, CS 24501, F-34093 Montpellier Cedex 5, France ABSTRACT: The oxidation of ascorbic acid was chosen as a case study to investigate the effect of experimental errors and their propagation on the identification of the parameters of a kinetics law involving both ascorbic acid and oxygen content, on a typical food storage temperature range (833 °C) and under conditions representing anaerobic storage (0% O 2 ) to storage under air (21% O 2 ). A nonlinear method was used to identify kinetic parameters, both by incremental identifications of intermediate parameters and by direct identification of relevant parameters. Confidence intervals on all these identified parameters were evaluated using Monte Carlo simulations. The propagation error during the incremental stages of parameters identification induced a high uncertainty on the values obtained, thus a direct identification was preferred. The accuracy of the identified parameters was also shown to be strongly dependent on the experimental procedure carried out to obtain experimental data, but the time required to perform an ideal procedure is unrealizable. A methodology based on Monte Carlo simulations was proposed to optimize a priori the experimental procedure and data treatment to improve the characterization of such a kinetics law. 1. INTRODUCTION The determination of kinetics parameters is crucial to inves- tigate chemical reactions. Such determinations are based on a comparison between the experimental data and the mathematical models (kinetic laws) that represent the reaction. The resulting values of the reaction rate constant are dependent on the accuracy of the experimental data, the pertinence of the structure of the mathematical model chosen, and the identification proce- dure employed. The experimental values necessarily go with errors, resulting in uncertainties on the identified reaction rate constants. The identification procedure can also introduce un- certainty on identified values of constant rates. Although these statements are generally taken into account in chemistry, 14 they are rarely considered in food science and the influence of the experimental and numerical errors on the accuracy of the identified parameters is scarcely evaluated. Moreover, the choice of the mathematical model to be used can be controversial. 5,6 In the case of ascorbic acid oxidation, the reaction is generally recognized to follow a first-order kinetics law, with respect to ascorbic acid, 7 which assumes that the oxygen content in the medium does not impact the kinetics rate. This is surprising if we consider that some of the authors using this kinetics law simultaneously observed that the rate of oxidation was depen- dent on oxygen’s availability. 810 On the other hand, a few authors considered the reaction rate as a first-order kinetics, with respect only to oxygen, considering that the ascorbic acid content in the medium does not affect the reaction rate constant. 1113 Despite the wide number of investigations carried out on ascor- bic acid oxidation, only three studies have pointed out a joined effect of ascorbic acid and oxygen contents in food, which is the case that seems the most likely. Singh et al. 14 studied the kinetics of ascorbic acid oxidation in an infant formula during storage at 7.2 °C. Below the oxygen content limit of 8.71 mg L 1 in the product, the reaction rate was assumed to follow a second-order kinetics (order one with respect to ascorbic acid and order one with respect to oxygen). Eison-Perchonok and Downes 15 also described the kinetics of ascorbic acid oxidation in a buffered model system by a second-order kinetics (order one with respect to ascorbic acid and order one with respect to oxygen) on the temperature range of 3355 °C. Patkai et al. 16 analyzed the decrease of vitamin C content of model solutions simulating real citrus juices, on the temperature range of 80100 °C. The rate of vitamin C consumption was considered to be first order, with respect to vitamin C, and the kinetics constant rate was expressed as a polynomial equation involving the initial oxygen content, the temperature, and the duration of heat treatment. In these previous studies, the typical law used for modeling the reaction rate constant of ascorbic acid degradation is r = k[AA] α [O 2 ] d β , where k is the reaction rate constant and α and β are the orders of the reaction, with respect to ascorbic acid and oxygen, respec- tively. Three input parameters are required for modeling ascorbic acid oxidation, according to this law: k, α, and β. They are deduced from experimental measurements and are consequently not true values but rather values going with uncertainties that must be taken into account in a prediction step. In practice, that means that model input variables and parameters can be repre- sented by probabilistic distributions due to observed variability. Received: May 20, 2011 Accepted: December 14, 2011 Revised: December 8, 2011