Multiple steady states in an adiabatic CSTR

Figure 13.7 Range of multiple steady states in an adiabatic CSTR (on an X-T plot).

Steady-State Multiplicity and Stability A simple example of steady-state multiplicity is due to the interaction between kinetics and heat transport in an adiabatic CSTR. For a first-order reaction at steady state, Eq. (19-13) gives... 

The fact that multiple steady states are indeed a real phenomenon has been illustrated by various experimental studies. An example is given by Figure 3.14 in which the experimentally observed and theoretically calculated steady states [4] are shown for a bimolecular reaction between hydrogen peroxide (H2O2) and sodium thiosulfate (Na2S203). The experiments were performed in an adiabatic CSTR. A similar phenomenon has been predicted even for multiple industrially important reactions such as the polymerization of styrene [5]. When designing a CSTR for exothermic reactions, one should always be alert to the possibility of steady-state multiplicity. 

Problem Statement In Chapter 5, a system involving multiple CSTR steady states is shown (the isola example). Multiple steady states often arise in isothermal constructions when the kinetics is nonlinear. Nonlinearity is also often introduced in nonisothermal systems (i.e., in adiabatic systems, for example), and thus multiple steady states appear in these systems as well this is true even with simple kinetics. Consider an adiabatic reaction of the following form (Hildebrandt et al. 1990) ... 

In this chapter, we have seen that multiple steady states can occur when an exotirermic reaction takes place in an ideal CSTR, and when a feed/product heat exchanger is used in conjunction with an adiabatic PFR. We might ask whether this multiplicity is coincidental, or whether there is a link between these two examples. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

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