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Conservatively perturbed equilibrium phenomenon in multi-route catalytic systems

Increasing the intensity of a complex catalytic reaction is an obvious task of chemical technology, and one of the important problems is obtaining the over-equilibrium kinetic characteristics (rate, concentration, yield, selectivity) in the transient non-steady-state regime. 
As known, for a closed system or an open system of infinite length, the chemical equilibrium is the final state of the chemical reaction, simple or complex. 
The fundamental properties of the equilibrium composition are its uniqueness and stability. For the closed chemical system, it means that at fixed amounts of chemical elements and at the given temperature, the system reaches the same chemical composition starting from any initial state, and the equilibrium chemical composition is unique and stable. 
The calculation of the equilibrium composition has become the basis for solving many problems of chemical and biochemical engineering. Such calculations are made based on a list of reactions with known equilibrium constants, or using a list of components with known chemical potentials and minimizing the Gibbs energy of chemical system. In this phenomenon, some initial concentrations of components are replaced by corresponding equilibrium concentrations. The temperature of the system and the total amount of any given chemical element in the system are assumed to be constant. 
In this paper, the phenomenon of conservatively perturbed-equilibrium (CPE) in multi-route complex catalytic reactions was studied. 
The computational phenomenon of the CPE is carried out as follows: 
 
The values of equilibrium concentrations of all components are determined. 
Some components are selected so that their initial concentrations differ from the equilibrium concentrations. 
At least one component is selected so that its initial concentration is equal to the equilibrium value. 
Perturbations referred above (see item 2) shall comply with all conservation laws of chemical elements which are applicable to this reaction system. 
The evolution of all concentrations is observed when they tend to the final chemical equilibrium. 
 
The following multi-route catalytic mechanisms have been studied: 
 
the two-route mechanism with the single common intermediate; 
the multi-route mechanisms with common steps. 
 
The kinetic model of plug-flow reactor (PFR) was chosen. The phenomenon of CPE was demonstrated for all indicated mechanisms. At given rate constants, the mechanism with a single common intermediate exhibited a CPE‑effect which is more pronounced than for the mechanism with common steps. In comparing the kinetic characteristics of non-catalytic and catalytic reactions, a special computer experiment shows that the absolute values of extreme concentrations at the CPE-point are almost the same. It was assumed that non-catalytic and catalytic reaction have the same the overall reaction with same equilibrium constants. 
This fact makes it possible to estimate the CPE value of the concentrations of complex catalytic reactions based on similar characteristics of the corresponding simple reactions.