Reaction-Distillation Process with External Recycling

The simplest flow-sheet for the reaction Al o A2 is the RD column sequence with an external recycling loop shown in Fig. 5.l. The system as a whole is fed with pure Al. According to the assumed relative volatility of the two components a > l, the reaction product A2 is enriched in the column distillate product whereas the bottom product contains non-converted reactant Al, which is recycled back to the reactor (continuous stirred tank reactor, CSTR, or plug flow tube reactor, PFTR). The process has two important operational variables: the recycling ratio p = B/F, that is the ratio of recycling flow B to feed flow rate F, and the reflux ratio of the distillation column R = L/D. At steady-state conditions, D = F since the total number of moles is assumed to be constant for the reaction Al o A2. As principal design variables, the Damkohler number,

which characterizes the size of the reactor, and the number of theoretical stages N of the distillation column are considered. The relations between the operational and design variables are governed by the steady-state mass balances for the reactor and the column

In (5.6), a CSTR is considered as reactor, and therefore the reaction rate r* is calculated at the reactor outlet concentration, vR. At infinite reflux ratio, R = œ, the distillate (xD) and bottom concentrations (xB) are related to each other by the Fenske equation [2]

with Nmin as minimum number of theoretical column stages; (5.6)-(5.8) are used to determine the three unknown mole fractions xR, xB, and xD.

As the first step of conceptual process design, the distillation column is considered at infinite reflux ratio, R = », with an infinite number of stages, N = ». Under these perfect separation conditions, the distillation column will yield a bottom product that contains pure A2: vB = 0. Then the distillate mole fraction vD only depends on the size of the reactor (Da), the recycling ratio (<p), and the chemical equilibrium concentration vce. Combining (5.6) and (5.7) yields

Da vD

For a first-order reaction, the distillate mole fraction is given by

In Fig. 5.4, the distillate quality is plotted versus the Damkohler number at different recycling ratios for fixed thermodynamic parameters K = 2 and a = 1.5. As expected, by increasing the recycling flow rate the product quality is improved. At infinite Damkohler number, one obtains a maximum attainable composition level = (1 + ^)vce. Obviously, there is a critical recycling ratio, <pcrit, that has to be attained in order to reach a specified product quality vD

In an analogous manner, at <p = there is a critical Damkohler number, Dacrit, (minimum reactor size) that has to be realized in order to attain a specified product quality xD. This is given by

Fig. 5.4. Mole fraction of product A2 against Damkohler number at different recycling ratios for configuration in Fig. 5.1 (CSTR or PFTR as reactor)

Fig. 5.4. Mole fraction of product A2 against Damkohler number at different recycling ratios for configuration in Fig. 5.1 (CSTR or PFTR as reactor)

Damkohler Number Different Order

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