The phenomenon of conservatively perturbed-equilibrium (CPE) in multi-route catalytic reactions was studied in the plug-flow reactor (PFR). The following multi-route mechanisms were chosen for studying, i.e., the two-route mechanism with the single common intermediate, the three-route mechanism with some common steps, and the two-route mechanism with the single common step and two common intermediates. All mentioned mechanisms exhibit the CPE-phenomenon. At given rate coefficients, the mechanism with the single common intermediate showed the greater CPE-effect than the mechanism with the common steps. A special computer experiment was performed in which the kinetic characteristics of non-catalytic and catalytic reactions have been compared. In this experiment, both non-catalytic and catalytic reactions have the same overall-reactions with the given equilibrium constant. It was shown that the absolute values of extreme concentrations at the CPE-point are almost the same. In this case, it is possible to estimate the concentrations at the CPE-values for complex reactions based on similar characteristics of the corresponding simple ones.

Finding the optimal mode is a conceptual problem. The most important indicator that reflects the perfection of a chemical reactor is the intensity of the process in it. The phenomenon of conservatively perturbed-equilibrium (CPE) in the conditions of different types of reactors (in acyclic and cyclic systems) was studied: the ideal displacement reactor ("steady-state plug flow reactor, PFR") and the ideal mixing reactor ("steady-state continuous stirred tank reactor, CSTR"). For the acyclic reaction, the time of extremum onset was less in CSTR by ≈2.1%, but the concentration of substance B in the extremum in PFR was greater by ≈17.2% than in CSTR. For the cyclic reaction, the time of extremum onset was less in CSTR by ≈5.6%, but the concentration of substance B in the extremum in PFR was greater by ≈11.6% than in CSTR. For the acyclic and cyclic reaction in PFR, the time of occurrence of the extremum of the cyclic reaction was lower by ≈44.2% than in the acyclic, but the concentration of substance B in the extremum of the acyclic reaction was greater by ≈24.8% than in the cyclic reaction. For the acyclic and cyclic reaction in CSTR, the time of occurrence of the extremum of the cyclic reaction was lower by ≈46.2% than in the acyclic, but the concentration of substance B in the extremum in the acyclic reaction was greater by ≈18.9% than in the cyclic reaction. The cyclic system showed a shorter time for the onset of the extremum, but the acyclic reaction system showed a higher concentration of substance B at the extremum in PFR and CSTR. Although the time of extremum onset was the lowest in CSTR in the cyclic system, the concentration of substance B in the extremum was highest in the PFR in the acyclic system. Therefore (from our systems and reactors) the acyclic system in PFR shows the best characteristics. The extremum in transient modes is always observed for acyclic and cyclic complex reactions in both reactors, both in PFR and in CSTR. The phenomenon of conservatively perturbed-equilibrium is manifested in both PFR and CSTR. With the same rate constants, the acyclic system in PFR is characterized by higher values of "over equilibrium" conversion than the acyclic system in CSTR. Similarly, with the same rate constants, the cyclic system in PFR is characterized by higher values of "over equilibrium" conversion than the cyclic system in CSTR. The time of extremum onset is less in CSTR. This is true for acyclic and cyclic systems. The greater the difference between the initial concentrations of the two substances, the greater the "over equilibrium" concentration of the third substance, the initial concentration of which was equilibrium. At our values of kinetic parameters, the sensitivity of the time of occurrence of the extremum of the same reaction in different reactors (PFR and CSTR) is small (up to ≈5.6%), and at different reactions (acyclic and cyclic), but in one type of reactor (PFR or CSTR) - significant, reaching ≈46.2%.

The effect of over-equilibrium, i. e., the effect at which the concentration of some substance is higher than the corresponding equilibrium value, is demonstrated for two types of ideal chemical reactors, continuously stirred tank reactor (CSTR) and plug-flow reactor (PFR), respectively, under conditions of conservatively perturbed-equilibrium (CPE). Two types of complex chemical mechanisms are analyzed, acyclic and cyclic ones. Using numerical experiments and the same residence times, it is shown that for the steady-state PFR this effect is more pronounced that for the steady-state CSTR, and it is true both for acyclic and cyclic reactions. In the studied mechanisms, cyclic and acyclic, the initial concentration of some substance is taken as the equilibrium one, and two other concentrations are the nonequilibrium ones. The greater the difference between the two initially nonequilibrium concentrations, the greater the concentration of the third substance, which was taken initially as the equilibrium one. At the specific values of kinetic parameters considered here, the sensitivity of the occurrence time of the B-concentration extremum for the different reactors (PFR and CSTR) at the fixed mechanism is small, but for the different mechanisms (acyclic and cyclic) at the fixed reactor is significant.

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.