## Changing Relative Volatilities of Products

Now we consider the cases in which the relative volatilities between the two products and their adjacent reactants are different from the base case value of 2. Two cases are explored: one is when light product C is easier to separate from light reactant A (i.e., aC/ aA = 4), and the other is when the relative volatility between heavy reactant B and heavy product D (i.e., aB/aD = 4) is larger than the base case value of 2.

In the first case, we have aC = 16, aA = 4, aB = 2, and aD = 1. With the conventional feed arrangement, the energy consumption (0.0285 kmol/s) is 10.9% less than the base case because of the large relative volatility between C and A. The optimization calculations show that the optimum feed trays become NF A = 12 and NF B = 14 (Fig. 18.7b). Compared to the conventional feed arrangement, this corresponds to a 46.8% energy savings (from 0.0285 to 0.0152kmol/s)! This is a very significant energy savings by very simple means (feed rearrangement).

Two observations can be made immediately. First, the two feeds are quite close to each other and the feed locations move to the upper section of the reactive zone. Second, the fraction of total conversion is distributed relatively uniformly throughout the reactive zone (at least compared to other cases) as shown in Figure 18.7b. This implies that none of the reactive trays are underutilized, and this is achieved because of the interplay between the composition and temperature distributions (e.g., showing temperature increases whenever necessary). An almost monotonic composition distribution in D is also seen; a significantly smaller amount of product C is also observed in the upper reactive zone, which allows for higher reactant concentration. All of these factors result in a much smaller vapor rate compared to the conventional feed arrangement.

The second example is just the opposite. We have an easy separation between the heavy reactant and the heavy product. In this case, the relative volatilities are aC = 16,

Figure 18.7 Profiles of temperature, composition, fraction of total conversion, and reaction rate constants in the reactive zone for aC/aA/aB/aD = 16/4/2/1 system with (a) conventional feed arrangement (NF,A = 6 and NFB = 16) and (b) optimal feed arrangement (NF,A = 12 and Nf,B = 14) with 46.8% energy savings.

Figure 18.7 Profiles of temperature, composition, fraction of total conversion, and reaction rate constants in the reactive zone for aC/aA/aB/aD = 16/4/2/1 system with (a) conventional feed arrangement (NF,A = 6 and NFB = 16) and (b) optimal feed arrangement (NF,A = 12 and Nf,B = 14) with 46.8% energy savings.

Figure 18.8 Profiles of temperature, composition, fraction of total conversion, and reaction rate constants in reactive zone for aC/aA/aB/aD = 16/8/4/1 system with (a) conventional feed arrangement (NFA = 7 and NFB = 17) and (b) optimal feed arrangement (NFA = 8 and NF,B = 10) with 15.6% energy savings.

Figure 18.8 Profiles of temperature, composition, fraction of total conversion, and reaction rate constants in reactive zone for aC/aA/aB/aD = 16/8/4/1 system with (a) conventional feed arrangement (NFA = 7 and NFB = 17) and (b) optimal feed arrangement (NFA = 8 and NF,B = 10) with 15.6% energy savings.

aA = 8 , aB = 4 , and aD = 1. For the conventional feed arrangement, the energy consumption (0.0281 kmol/s) is only 87.8% of the base case. The concentration of D is smaller toward the lower reactive zone compared to the other two cases (cf. Figs. 18.5a and 18.8a), and this allows a higher reactant concentration in the same section. The optimization calculations show that the optimum feed trays are NF,A = 8 and Nf,b = 10 (Fig. 18.8b), which corresponds to a 15.6% energy savings (from 0.0281 to 0.0237 kmol/s) over the conventional feed arrangement (Table 18.2). Note also that these two feeds are quite close to each other and they are located in the lower section of the reactive zone, as can be seen in Figure 18.8b. In addition to an almost monotonic composition distribution in D, there is also a high concentration of B throughout the reactive zone in Figure 18.8b, and this improves the effectiveness of the reactive trays. This is allowed because B can be separated easily from heavy product D. However, unlike in the previous case, the decreasing trend of the temperature toward the upper reactive zone leads to a monotonically decreasing fraction of total conversion in the same direction (Fig. 18.8b). The underutilized reactive trays in the upper reactive zone explain why the margin of improvement is not quite as significant as in the previous case.

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