QUASI-INVARIANTS OF CHEMICAL REACTIONS IN DISTRIBUTED SYSTEMS WITH DIFFUSION

Abstract

For reactions occurring in distributed systems with longitudinal and radial diffusion, the relations between the concentrations of reagents and temperature remaining practically constant in time and space (space-time kinetic quasi-invariants) are found. A method for determining such quasi-invariants for chemical reactions occurring in the mixing reactor taking into account the diffusion of reagents and temperature changes in the longitudinal and radial directions has been developed and tested. The quasi-invariants found relate nonequilibrium concentrations of diffusing reagents and temperatures measured in two or more experiments with different initial conditions (multi-experiments), and practically do not change throughout the reaction both in length and in radius of the reactor. Analytical expressions for quasi-invariants are obtained, allowing a priori to estimate the corresponding constants (initial values). It is shown that the number of basic quasi-invariants is determined by the number of reagents. The application of the method is illustrated by the reaction of isomerization A=B in a non-isothermal system with diffusion of reagents. Found for this reaction quasiinvariant based on three-dimensional (surface) matched with three-dimensional variations of concentrations and temperature given the diffusivity in the course of the reaction. It is shown that quasi-invariants change in a smaller spatial range than their corresponding concentrations and temperatures in different experiments, i.e. remain practically constant in time and space. Visually, quasi-invariants are four-dimensional structures, three-dimensional projections of which are similar to "recumbent" waves, pillows, lenses, etc. Elaborated method for determining quasi-invariants of chemical reactions in systems with diffusion develops D.A. Frank-Kamenetsky's macrokinetic methods for approximate study of temporal and spatial characteristics of distributed dynamic systems. The obtained results can be used to solve inverse problems and optimize the operation modes of chemical mixing reactors with longitudinal and radial diffusion of reagents and temperature changes.