Note that (5.11) and (5.12) are only valid for perfect separation of the CSTR effluent, that is for R = and N =

Now, the question arises whether the use of a PFTR will result in a higher productivity of the recycling system than the use of a CSTR. For comparison, the attainable product compositions vP are plotted in Fig. 5.4 for both types of reactor for various Da and p. As expected, at finite recycling ratio p < the application of a PFTR yields higher product content in the distillate than a CSTR. But at infinite recycling ratio, the operational curves of the PFTR and the CSTR coincide, since both reactors are fully backmixed in this situation. Therefore, an infinite external recycling ratio always yields the highest mole fraction of the desired product A2, no matter whether a CSTR or a PFTR is used as reactor. The distillation column ensures that the product concentration in the recycling flux (vB) is minimized, and as a consequence, the reaction rate at p = is higher (r* = 1) than the average reaction rate in a PFTR at p < (r* < 1).

5.2.1.2 Nmin)-Analysis

For conceptual process design it is essential to predict the design variables; these are the size of the reactor (Da) and the minimum number of distillation stages (Nmin), for a specified distillate composition Xe. As before, the column is considered at infinite reflux ratio (R = œ).

In Fig. 5.5, the minimum number of stages required to meet the product specification (here, xd = 0.99) is depicted against the Damkôhler number. At a given p value the number of stages decreases with increasing Damkôhler number. At constant Da number, the necessary number of distillation decreases with increasing recycling ratio. One can also see that the smallest investment plant costs (a linearly

Fig. 5.5. Minimum number of distillation stages versus Damköhler number for specified distillate mole fraction of product A2, = 0.99, for configuration in Fig. 5.1 (CSTR as reactor)

Fig. 5.5. Minimum number of distillation stages versus Damköhler number for specified distillate mole fraction of product A2, = 0.99, for configuration in Fig. 5.1 (CSTR as reactor)

weighted sum of Nmin and Da) will be obtained at infinite recycling ratio. For p < œ, the size of the plant needed to meet the specification will be larger. In conclusion, low costs for plant investment correlate with high operational costs caused by recycling pumping. The operational costs for recycling pumping can be avoided by internalization of the external loop, that is by application of an integrated RD process.

At p = œ and Da = œ, the smallest possible column size is reached (Nmin = Ncrit). The same is true for the Da number, the minimum value of which (Da = Dacrit) is obtained at p = œ, Nmin = œ. According to (5.12), this critical value is Dacrit = xD = 0.99. Also at p < œ, a certain minimum Da number is required to meet the product specification.

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