Conservation Laws for Chemical Reactions with Arbitrary Kinetics in a Partially Stirred Reactor

• Published in: Russian journal of general chemistry 2022-09, Vol.92 (9), p.1845-1851
• Main Author: Kol’tsov, N. I.
• Format: Article
• Language: English
• Subjects: Analysis; Chemical reaction, Rate of; Chemical reactions; Chemistry; Chemistry and Materials Science; Chemistry/Food Science; Computer networks; Conservation laws; Differential equations; Environmental law; Exact solutions; Invariants; Kinetics; Mathematical models; Nonlinear systems; Plug flow; Rate constants; Reaction kinetics
• ISSN: 1070-3632; 1608-3350
• DOI: 10.1134/S1070363222090262

One of the difficulties encountered in solving direct and inverse chemical kinetics problems is the complexity of studying multidimensional systems of differential equations describing the regularities of reactions carried out under unsteady-state conditions. This difficulty emerging when one deals not only with real reaction systems but also with simple model reactions can be overcome by reducing the dimension of the differential equations systems via using conservation laws, whose finding, especially for nonlinear systems, is a challenging task. It is known that chemical reactions occurring in lumped closed systems are subject to stoichiometric conservation laws characterizing the laws of conservation of the atoms of the reactants, which are fairly easy to detect. This is a more difficult task in the case of distributed systems for which the corresponding chemical processes are described by plug-flow and partially stirred reactor models, which do not have analytical solutions. It is in this connection that a method for finding conservation laws (invariants) for chemical reactions proceeding in an open nonisothermal partially stirred reactor operating in an unsteady mode, with longitudinal diffusion of the reactants and heat convection taken into account, was presented. The invariants found by this method can be used for experimental verification of the mechanisms of chemical reactions, whose detailed kinetic characteristics (kinetic laws, rate constants of individual steps, etc.) are not known. These invariants allow comparing the theoretical characteristics of the supposed mechanism of the reaction with its experimentally observed regularities and providing a more reliable solution to the inverse chemical kinetics problem. The effectiveness of the method was illustrated by examples of specific reactions, for which the conservation laws were found and used for identifying their mechanisms.