Second-order reactions multiple steady states

We took the 4- sign on the square root term for second-order kinetics because the other root would give a negative concentration, which is physically unreasonable. This is true for any reaction with nth-order kinetics in an isothermal reactor There is only one real root of the isothermal CSTR mass-balance polynomial in the physically reasonable range of compositions. We will later find solutions of similar equations where multiple roots are found in physically possible compositions. These are true multiple steady states that have important consequences, especially for stirred reactors. However, for the nth-order reaction in an isothermal CSTR there is only one physically significant root (0 < Ca < Cao) to the CSTR equation for a given T. ... 

Some specific aspects in the modeling of gas-liquid continuous-stirred tank reactors are considered. The influence of volatility of the liquid reactant on the enhancement of gas absorption is analyzed for irreversible second-order reactions. The impact of liquid evaporation on the behavior of a nonadiabatic gas-liquid CSTR where steady-state multiplicity occurs is also examined. 

The occurrence of steady-state multiplicity in gas-liquid CSTRs has been demonstrated in experimental (9) and theoretical investigations (cf., 10). The irreversible second-order reaction system, in particular, has been treated extensively in several theoretical studies (10-15). These studies are however based on neglecting energy and material losses which result from evaporation of the liquid. 

This problem concerns multiple steady states for the second-order reversible liquid-phase reaction. [Old exam problem]... 

Figure 13.23 Multiple steady states of two-reactants, second-order reaction in isothermal CSTR-Separator-Recycle system...

Fig. 6 Second-order reaction in CSTR/Separator/Recycle a) Control structure relying on selfregulation b) bifurcation diagram showing multiple steady-states...

This set of equations gives the possibility to calculate the dynamic behavior of a CSTR and, what is more important, the characteristics of the steady state. In contrast to free radical polymerization where multiple steady states and even oscillating regimes can exist owing to the second-order chain termination reaction and the gel effect [54], Eqs. (3.22) and (3.23) have only one stationary solution. Hereinafter, steady-state parameters of the MWD are discussed. 

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