Kinetics of Nitrate Hydrogenation in Water on Alumina and Niobia Supported Palladium-Copper Catalysts

Abstract

The kinetics of nitrate hydrogenation in water over niobia- and alumina-supported Pd-Cu catalysts were examined. A Langmuir-Hinshelwood kinetic model fitted concentration data, providing consistent kinetic and thermodynamic parameters. The kinetic model assumed a bimolecular surface reaction as the rate-determining step, with two types of sites. Pd-Cu/gamma-Al2O3 was active and selective under the reaction conditions. However, Pd-Cu/Nb2O5 deactivated during time on stream, and a deactivation function was added to the kinetic model to best fit the experimental data.

Glycerol acetylation considering competing dimerization

“…For deeper understanding of the underlying mathematics of the maximum likelihood method and its applications in kinetic models, the reader is referred to seminal previous applications of this method. [22][23][24] 4 RESULTS AND DISCUSSION Figure 1 shows liquid phase formation of MAG, DAG, TAG, and DGTA for Amberlyst-15, and Figure 2 for Amberlyst-70, using fits for reference model A and model B, containing the parallel dimerization reaction. Table 1 shows the values of the apparent kinetic constants.…”

“…Nonlinear regression was done using the maximum likelihood methodology through an algorithm specifically written for that purpose with the software Scilab and was also cross‐checked with Polymath (student version) for least squares nonlinear regression. For deeper understanding of the underlying mathematics of the maximum likelihood method and its applications in kinetic models, the reader is referred to seminal previous applications of this method …”

Modeling of Hydrogenation of Nitrate in Water on Pd–Sn/Al2O3 Catalyst: Estimation of Microkinetic Parameters and Transport Phenomena Properties

“…Despite the good adherence to experimental data and low variance achieved, considerably large variations in the fitted parameters set tended to have little impact in the objective function, as in other works devoted to kinetics parameters regression. 38,39 This apparent paradox can be explained by the peculiar topology of the likelihood function when dealing with kinetic models, which seems to exhibit a large flat region around its minimum (which leads to low parameter sensitivity and large parameter variances and covariances) but at relatively low values of the likelihood function itself (which leads to low model fundamental variance). Of course, this jeopardizes establishing the set of the most relevant parameters to the complete model and decreases the reliability of each one but also guarantees the fluctuations in the fitted parameters (which could be caused by experimental errors, for instance) will have little effect on the predictive capabilities of the model.…”