Experimental errors in kinetic tests and its influence on the precision of estimated parameters. Part I—Analysis of first-order reactions

The proper characterization of the experimental errors is essential for the correct evaluation of estimated model parameters, model fit and model predictions based on kinetic rate expressions. However, it is common to ignore the influence of experimental errors during kinetic studies due to difficulties to characterize how experimental errors depend on the reaction conditions. The behavior of experimental error depends on the specific features of the experimental system; however, in many cases the main sources of experimental errors are the unavoidable oscillations of the input variables. This work analyzes how the experimental errors affect kinetic studies based on catalytic tests when oscillations of the input variables are the main sources of uncertainties. The first part of this work assumes that the reaction rate can be described accurately as a first-order reaction in a PFR. Analytical expressions are derived for the variance of the reactant conversion in distinct scenarios and are used to analyze the quality of the obtained parameter estimates. It is shown here that the conversion variances can be described as functions of the measured conversion values, normally presenting a point of maximum for conversion values in the range of 0.6 < X < 1.0 when observed experimental fluctuations are controlled by the fluctuations of the input variables. Constant conversion variances should be expected only when fluctuations are controlled by analytical conversion measurements. As a consequence, optimum parameter estimation may be performed either with differential or integral methods, depending on the behavior of the conversion variances.