In nonisothermal reactors

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

There are many interesting problems in which complex chemistry in nonisothermal reactors interact to produce complex and important behavior. As examples, the autocatalytic reaction, A — B, r = kC/ Cg, in a nonisothermal reactor can lead to some quite complicated properties, and polymerization and combustion processes in nonisothermal reactors must be considered very carefully in designing these reactors. These are the subjects of Chapters 10 and 11. 

In the following analysis, both the solid and gas phases are assumed to move in countercurrent plug flow so that both concentrations (and temperature in nonisothermal reactors) vary with axial position. The material balance with boundary condition for the gas phase reactant is... 

COUPLED HEAT/MASS TRANSFER IN NONISOTHERMAL REACTORS... 

Figure 14.13 Distribution of concentration and temperature in nonisothermal reactors.

Mears [68] derived criteria for negligible axial mass and heat transfer effects in nonisothermal reactors with uniform wall temperature (so that the rate deviates <5% from the one observed from a plug-flow model), extending the results from Young and Finlayson [139]. In terms of the bed length to particle diameter ratio, it writes as... 

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