Multiple Stationary States in Continuous Stirred Tank Reactors

MULTIPLE STATIONARY STATES IN CONTINUOUS STIRRED TANK REACTORS 

Multiple steady-state behavior is a classic chemical engineering phenomenon in the analysis of nonisothermal continuous-stirred tank reactors. Inlet temperatures and flow rates of the reactive and cooling fluids represent key design parameters that determine the number of operating points allowed when coupled heat and mass transfer are addressed, and the chemical reaction is exothermic. One steady-state operating point is most common in CSTRs, and two steady states occur most infrequently. Three stationary states are also possible, and their analysis is most interesting because two of them are stable whereas the other operating point is unstable. 

Nonisothermal operation of a liquid-phase CSTR with reversible exothermic nth-order chemical kinetics is the focus of this chapter. The reactor is well insulated from the surroundings, except for heat exchange across the cooling coil. The reaction scheme is 

Coupled mass and thermal energy balances are required to analyze the nonisother-mal response of a well-mixed continuous-stirred tank reactor. These balances can be obtained by employing a macroscopic control volume that includes the entire contents of the CSTR, or by integrating plug-flow balances for a differential reactor under the assumption that temperature and concentrations are not a function of spatial coordinates in the macroscopic CSTR. The macroscopic approach is used for the mass balance, and the differential approach is employed for the thermal energy balance. At high-mass-transfer Peclet numbers, the steady-state macroscopic mass balance on reactant A with axial convection and one chemical reaction, and units of moles per time, is 

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