Reducing Activation Energies

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Consider the case in which the forward and backward activation energies are both reduced to 3000 cal/mol, which is an order of magnitude smaller than used in the base case. The rate constants at 366 K are kept the same as in the base case (0.008 and 0.004 kmol s_1 kmol"1 for the forward and backward reactions, respectively) by changing the preexponential factors. These changes impact the reactive distillation column in two ways. First, the reactions are not quite as temperature sensitive as in the previous case. Second, the heat of reaction is 0, as opposed to the previous case where 10,000 cal of energy are released for every mole of reactant converted.

Base Case with Low Activation Energies. Figure 18.9a shows that, with the conventional feed arrangement, the profiles for the temperature, composition, and fraction of total conversion are qualitatively similar to those of the higher activation example (Fig. 18.5a). However, the profile of the backward reaction rate is smaller. The energy consumption is higher in the present example compared to one with a higher activation energy (0.0393 vs. 0.0320 kmol/s). The reason for this is that energy is no longer released from the reactions, and the effect of direct heat integration disappears. The optimization calculations show that the optimal feed trays becomes NF,A = 11 and NF,B = 15, and this results in a 10.7% energy savings when compared to the conventional feed arrangement (see

Figure 18.9 Profiles of temperature, composition, fraction of total conversion, and reaction rate constants in reactive zone for base case with low activation energy using (a) conventional feed arrangement (NF,A = 8 and NFB = 18) and (b) optimal feed arrangement (NF,A = 11 and Nf,B = 15) with 11% energy savings.

Figure 18.9 Profiles of temperature, composition, fraction of total conversion, and reaction rate constants in reactive zone for base case with low activation energy using (a) conventional feed arrangement (NF,A = 8 and NFB = 18) and (b) optimal feed arrangement (NF,A = 11 and Nf,B = 15) with 11% energy savings.

Table 18.3). Figure 18.9b demonstrates that, similar to the example of high activation energy, these two fresh feedstreams are separated by four trays. However, unlike the previous case, the relative position moves up slightly. This seems reasonable because we have a less temperature-sensitive reaction, and the effect of the temperature profile is not as important as in the previous example. This indicates that the composition profile is much more important in this example. The fraction of total conversion on the reactive trays clearly indicates a nonmonotonic profile throughout the reactive zone, compared to the high activation energy case (Fig. 18.9b vs. 18.5b). The temperature insensitivity is also illustrated in the profile of the rate constants where the ratio of the maximum over the minimum rate constants is 1.3 in this case, while the high activation energy example gives a value of 22! In terms of energy savings via feed tray optimization, both cases show quite similar results (10.9% vs. 10.7% as shown in Tables 18.2 and 18.3, respectively).

Changing Relative Volatilities of Reactants. Similar to the previous example, we first explore the case of difficult separation between the two reactants. The relative volatilities are aC = 6, aA = 3, aB = 2, and aD = 1. Optimization calculations show that the optimal feed trays are NFA = 13 and NF,B = 15, and a 19.1% energy savings (from 0.0482 to 0.0390 kmol/s) can be achieved by the feed rearrangement (Table 18.3). It is

TABLE 18.3 Effects of Feed Locations on Design for Systems with Different Relative Volatilities"

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