Thermal characteristics of packed reactors

There are several aspects of thermal sensitivity and instability which are important to consider in relation to reactor design. When an exothermic catalytic reaction occurs in a non-isothermal reactor, for example, a small change in coolant temperature may, under certain circumstances, produce undesirable hotspots or regions of high temperature within the reactor. Similarly, it is of central importance to determine whether or not there is likely to be any set of operating conditions which may cause thermal instability in the sense that the reaction may either become extinguished or continue at a higher temperature level as a result of fluctuations in the feed condition. We will briefly examine these problems. 

To illustrate the problem of thermal sensitivity we will analyse the simple one-dimensional model of the countercurrent cooled packed tubular reactor described earlier and illustrated in Fig. 3.25. We have already seen that the mass and heat balance equations for the system may be written  

Substituting equation 3.105 into the heat balance equation 3.95 for the reactor  

The temperature of the non-reacting heating fluid at the reactor inlet is T0 and at the exit Tcl so the difference, say AT, is 

Since the numerical values of TL and YL are dependent on the heat exchanging capacity (as shown by equation 3.106), the quantity on the right-hand side of equation 3.110 may be displayed as a function of the inlet temperature to the bed, T0, with T as a parameter. The three bell-shaped curves in Fig. 3.30 are for different values of T and each represents the locus of values given by the right-hand side of this equation. The left-hand side of the equation may be represented by a straight line of unit slope through the point (rCi, 0). The points at which the line intersects the curve represent solutions to equation 3.110. However, we seek only a stable solution which coincides with a high yield. Such a solution would be represented by 

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