The phenomenon of conservative-perturbed equilibrium in conditions different reactors

Abstract

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%.

Conservatively Perturbed Equilibrium (CPE)—Phenomenon as a Tool for Intensifying the Catalytic Process: The Case of Methane Reforming Processes

“…where L CPE is the length at which the extremum of the chosen component is reached and L eq is the reactor length at which the molar flow rate of this component is located within the vicinity of its equilibrium value (±2.5%) Corresponding results for different cases are shown in Table 4. The majority of previous studies of the CPE phenomenon were performed using only linear models for better analytical understanding [2,3,5,6]. This study, on the contrary, uses non-linear real-world kinetic models.…”

“…This is an important feature of the CPE regime, which can be used for intensifying catalytic processes. In many calculations [5,6], it is shown that in some domain, the magnitude of this extremum is proportional to the perturbation of initial concentration, i.e., CPE is the unavoidable and controlled phenomenon.…”

“…The CPE phenomenon can be illustrated by the simple example from [2,3]. The kinetic mass action law model relates to the linear two-step mechanism (consecutive first-order reactions) [5,6]:…”