Exothermic reaction in adiabatic CSTR

We have seen in earlier chapters that kinetic systems with two independent concentrations can show additional complexities of dynamic behaviour beyond those of one-variable systems. Of particular interest are undamped oscillations. The cubic autocatalysis with the additional decay step 

We should first recall the stationary-state behaviour for this case. If the reaction rate constant for the catalyst decay step is large compared with that for the autocatalytic step, so that k2 iV, the system can only ever have one stationary state. This state corresponds to no net conversion of A to B, so ass = 1. For slower decay rates, k2 Vs non-zero stationary states exist over a range of residence times t 9 ires t+s in the form of an isola. The extents of conversion along the branches of the isola are given by 

It will be convenient to identify the three possible stationary states with subscripts 1, 2, and 3 in order of increasing extent of conversion, as shown in Table 8.1 where the group T = (1 4- K2Tres)2/Tres. 

Stationary-state concentrations and extents of reaction for cubic autocataly- 

The route to determining the local stability of a given stationary state begins with the Jacobian matrix for this system  

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