Consecutive reactions, batch reactor intermediate

At a fixed temperature, a single, reversible reaction has no interior optimum with respect to reaction time. If the inlet product concentration is less than the equilibrium concentration, a very large flow reactor or a very long batch reaction is best since it will give a close approach to equilibrium. If the inlet product concentration is above the equilibrium concentration, no reaction is desired so the optimal time is zero. In contrast, there will always be an interior optimum with respect to reaction time at a fixed temperature when an intermediate product in a set of consecutive reactions is desired. (Ignore the trivial exception where the feed concentration of the desired product is already so high that any reaction would lower it.) For the normal case of bin i , a very small reactor forms no B and a very large reactor destroys whatever B is formed. Thus, there will be an interior optimum with respect to reaction time. 

For the consecutive reactions A => B => C, a higher yield of intermediate B is obtained in batch reactors or PFRs than in CSTRs. 

For the situation in which each of the series reactions is irreversible and obeys a first-order rate law, eqnations (5.3.4), (5.3.6), (5.3.9), and (5.3.10) describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For consecutive reactions in which all of the reactions do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time at which the concentration of a particular intermediate passes through a maximum. If interested in designing a continuous-flow process for producing this species, the chemical engineer must make appropriate allowance for the flow conditions that will prevail within the reactor. That disparities in reactor configurations can bring about wide variations in desired product yields for series reactions is evident from the examples considered in Illustrations 9.2 and 9.3. 

Fig. 1.25. Reaction in series—batch or tubular plug-flow reactor. Concentration Cr of intermediate product P for consecutive first order reactions, A -> P -> Q...

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