The vapor compositions are determined by using a constant relative volatility model. Since both reactions are equimolar, vT1 = vT,2 = 0. Eliminating L from (6.1) and (6. 2), we get

The Damkohler number [7], Da = Hk{ ref/P, is the ratio of a characteristic liquid residence time (H/P) to the characteristic reaction time (1/kf_ ref), where, kf_ ref is the rate constant for the reference reaction. 0 = V/P, is the fraction of liquid feed that is vaporized. Using these parameters in (6.3), we get rk (x)

The difference between the liquid composition vectors x and x0 is given in terms of a separation vector (x — y) and a reaction vector Y^2 = 1 Vk(x). Given a value for P, a choice of 0 sets all of the flows and Da determines the reactor volume. The yield of the desired product B and the conversion of A is found from the combined streams L and —, and the overall outlet composition vector is given by ((1 - 0)x + 0y). The selectivity to B is simply the ratio of yield of B to conversion of A.

Conversion of A Fig. 6.2 Effect of separation on the attainable region for A ^ B ^ C

We use first order reaction rate models for both reactions, where the rates are given as r1 = kf, 1xA and r2 = kf, 1xA - kf, 2xB. We choose 0 = V/F = 0.8, and a liquid feed of pure A to the two-phase CSTR. Assuming that the rate constant for both reactions is identical, kf1 = kf 2 = kf ref, the conversion of A, the yield and selectivity to B are determined from the overall composition vector after specifying a value for Da and solving (6.4). The conversion increases monotonically with Da since the characteristic residence time increases for a given characteristic reaction time. Fig. 6.2 shows the yield of B against the conversion of A for the two-phase CSTR. The hatched area is the attainable region for single-phase reactors (CSTR, PFR). The figure shows that using a CSTR with vapor removal gives a larger region of feasible compositions than for single-phase reactors. Fig. 6.3 shows the selectivity to B against the conversion of A.

Good improvement in selectivity is possible by using a two-phase CSTR over a conventional reactor. Since the desired product, B is the lightest boiling component in the mixture, vaporization improves yield and selectivity to B. It is therefore logical to string together a series of CSTRs where the liquid and vapor streams move in a counter-current fashion (Fig. 6.4).

The resulting reactive-separation device greatly increases the feasible region, and dramatically improves the selectivity to B, Figs 6.5 and 6.6.

Fig. 6.3 Selectivity to B against conversion of A for a two-phase CSTR and for the boundary of the attainable region

Conversion of A

Fig. 6.3 Selectivity to B against conversion of A for a two-phase CSTR and for the boundary of the attainable region

Fig. 6.4 Schematic of a counter-current cascade of two-phase CSTR's

Fig. 6.4 Schematic of a counter-current cascade of two-phase CSTR's

Conversion of A

Fig. 6.5 Feasible region (hatched region) for reactions-in-series in a counter-current reactive separator

A comparison of the selectivity of B corresponding to the boundary of the feasible region and that for a single phase PFR is shown in Fig. 6.6. The selectivity to B is high even at higher conversions by using a counter-current reactive separator. This approach provides an estimate of the raw material savings by using simultaneous reaction-separation in a counter-current device, and therefore the economic incentive for implementing such a configuration. For a 95 % selectivity, the single phase reactor network can be operated at a maximum conversion of about 10%, however, to achieve the same selectivity, the reactor network consisting of a counter-current cascade can be operated at about 40 % conversion. In plants with recycling (typically continuous processes) higher conversions significantly reduce the recycle flows and also the flow rates entering the separation system of a process. Batch plants without recycle are normally operated near the maximum yield. In this example, the maximum yield for a single phase reactor is about 35 % at a conversion of about 60%, giving a selectivity of about 58%. A separative reactor in a counter-current device significantly improves all these quantities simultaneously, giving a maximum yield of about 65 % at a conversion of about 90 %, with a selectivity of about 72 %. Therefore, significant savings in raw materials, and significant decrease in waste by-products can be expected by using counter-current reactive separators to carry out the reactions. Such a configuration can also be expected to increase the conversion in equilibrium limited reactions.

The logical next step in device development is to consider a RD column. The feasible products from such a device are estimated using the approach described next.

current reactive separator over conventional reactors C fl 11 f iî; i q 11 <■ I i.

current reactive separator over conventional reactors C fl 11 f iî; i q 11 <■ I i.

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