Single-stream multistage operation

Consider a two-stage reactor system in which the first stage behaves like a single CSTR (Fig. 6.19a Herbert, 1964 Malek and Fend, 1966 Ricica and Necinova, 1967). The second stage may be treated in much the same way as the first, but the equations will be more complicated, since x and s enter the second stage. The balance equations for x and s are 

Solving this equation for 2 after substituting Equ. 6.6 gives a quadratic equation 

For the first stage, with Xq,c the straight line represented by Equ. 6.63 with the slope F/V = is drawn. The intercept of the line with the kinetic 

In the same way, additional curves can be drawn for N = 2,3... (Equ. 6.63), each with the starting concentration of the previous reactor in the series. The slope of the straight line represents the value of D for each case. When F is a constant for the whole system, the volume of each stage of the cascade may be optimized. 

In developing a process with a continuous cascade of stirred vessels, it should be remembered that the productivity (in terms of product per unit volume per unit time) is not optimized. Rather, the conversion (in terms of substrate utilization) is maximized. To clarify this, Fig. 6.20 (similar to Fig. 6.1a) is the diagram of a two-stage process (Herbert, 1964). One sees here that the productivity of the two-stage CSTR (Pr = D X2) is less than D x, but the use of substrate ( 2) is more complete than with a single stage CSTR (si). 

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Figure 6.19. Different types of multistage CSTR operation (a) single-stream multistage system, (b) multistream multistage system, (c) multistage with recycle.

The domain of the search for an improved separation process was defined by certain criteria (a) isotopic fractionation should be achieved by means of a two-phase, chemical exchange reaction which was amenable to countercurrent operation in a multistage contactor at ambient temperature and pressure (b) the single-stage isotopic fractionation factor for the reaction should be appreciably larger than that for the distillation of Me20 BF3 (c) the molecular species in each process stream should be thermally refluxable—i,e, convertible from one species to the other by the addition or removal of heat alone (d) process materials should be more stable with respect to irreversible decomposition than those used in the (CH3)20 process and (e) the chemical form of the product should permit a ready, quantitative conversion of the separated isotopes to the elemental state. 

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