Method for Determining the Rate Constants of Chemical Reaction Stages in an Enclosed Gradientless Reactor
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Method for Determining the Rate Constants of Chemical Reaction Stages in an Enclosed Gradientless Reactor N. I. Kol’tsova,* a Chuvash
State University named after I. N. Ulyanova, Cheboksary, 428015 Russia *e-mail: [email protected]
Received February 12, 2020; revised April 6, 2020; accepted July 27, 2020
Abstract—A method is described for determining the rate constants of the stages of chemical reactions occurring in an enclosed isothermal gradientless reactor based on non-stationary data. The method is based on the description of the relaxation features of various sections of non-stationary experimental dependences of reagent concentrations using continuous smooth curves (time splines) at all experimental points. This approach makes it possible to calculate the concentrations of reagents and the instantaneous rates of their change at any time points with an accuracy not exceeding the error in measuring reagent concentrations. This method was used to determine the rate constants of the stages and the intervals of their possible changes for the reaction of hydroalumination of olefins. The stability of the method was checked by changing the measurement errors of reagent concentrations (noise). Keywords: non-stationary chemical kinetics, enclosed gradientless reactor, stage rate constants, relaxation, time splines, hydroaluminization of olefins, measurement errors, noise DOI: 10.1134/S1070427220100092
One of the topical problems in chemical kinetics is the problem of calculating kinetic constants (inverse problem) for complex multistage reactions from nonstationary experimental data. The main difficulties in solving such a problem are inaccuracies in measuring the concentrations of reagents (noise), ambiguity in the results of solutions (different results of solutions can equally well describe the experimental data) and the problem of stability of the calculation method (small perturbations should not cause sharp deviations in solutions). To overcome these difficulties, as a rule, complex approaches and mathematical optimization methods are used [1–7]. In [8], a method is presented for determining the rate constants of the stages and the intervals of their changes for some classes of catalytic reactions without optimization methods due to the use of various relaxation characteristics (linear and nonlinear relaxation times, non-stationary concentrations). In [9, 10], the rate constants of the stages of adsorption–desorption of carbon dioxide on chromium and gallium oxide catalysts were determined from linear and nonlinear relaxation times under the assumption
that the process proceeds according to three alternative mechanisms (linear, dissociative, and bimolecular), and the most probable dissociative adsorption mechanism. To simplify the method for estimating the rate constants of adsorption–desorption of carbon dioxide on a supported chromium oxide catalyst, an approach was proposed for solving the inverse problem based on the use of experimental values of non-stationary concentrations of car
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