Stages, number

In an ideal continuously stirred tank reaclor (CSTR), the conditions are uniform throughout and the condition of the effluent is the same as the condition in the tank. When a batteiy of such vessels is employed in series, the concentration profile is step-shaped if the abscissa is the total residence time or the stage number. The residence time of individual molecules varies exponentially from zero to infinity, as illustrated in Fig. 7-2>e. 

Figure 13-47 shows the concentration profiles from the final solution. Note the discontinuities at the feed stage and the fact that feed-stage composition differs considerably from feed-stream composition. It can be seen in Fig. 13-47 from the n-C4 and i-C profiles that the separation between the keys improves rapidly with stage number additional stages would be worthwhile. 

Let the order of corrections to the unknowns be according to stage number, which in terms of the corresponding unknowns is... 

The nonequilibrium-model equations for the stage in Fig. 13-56 are as follows in residual form, where i = component (i = 1 to C), j = stage number (j = 1 to N), and V = a stage in another column that supplies an interlink. 

Sn = any side stream from the stage, qn = heat flow into, or removal from, the stage, n = any stage, numbered from the top of the column, z = mol fraction of component i in the feed stream (note, feed may be two-phase),... 

With equimolar overflow equations 11.14 and 11.16 can be written without the subscripts to denote the stage number ... 

The PXRD pattern does not change after the treatment of graphite nitrate with acetic acid (Fig. 1 B), indicating the conservation of Ic and the stage number of the GIC when nitric acid is partially substituted by acetic acid. Note that both initial graphite nitrate and that modified with acetic acid are thermally unstable (see the Table above.)... 

The stage number n( l, 2, 3. ..) stands for the number of individual graphite sheets which separate sheets of guest in the intercalate. A higher stage (n high) therefore means a more dilute intercalate. 

Note that the program is written such that the number of stages in the cascade, Nstage, can be varied as an additional parameter in the simulation. The stage numbers can be plotted versus the final values by choosing [i] as the X-axis. In this way the steady state concentration profiles can be graphed. A part of the program is shown below. 

Refer to stage numbers Refers to absorption tank Refers to feed... 

Stage Number of dosage units tested Complies if... 

Liquid on equilibrium-stage number (from bottom)... 

The primed or unprimed symbols refer to isotope fractions. The single stage separation factor for infinitesimal product removal (yi/zj 0), (rj)0, is given the symbol a . The i s index the stage number. Most often a is close to unity and it is convenient to define the isotope enrichment factor (the single stage enrichment factor), e, between the i th and (i + l) th stage... 

When a lies close to 1 the minimum reflux ratio is large, but since Xj varies with stage number so does [n(i+1)/P]MiN- At the feed point in a 235U plant enriching to 90% 235U, (nf/P)MiN is 29,100, but at the product end of the cascade it approaches zero. 

A practical isotope separation plant can operate at neither minimum reflux (where the separation is zero, but the rate of production is high), nor at minimum number of stages (where the rate of production is zero, but the separation is high). A compromise is required. Since optimum reflux varies with stage number it is customary to employ tapered cascades for isotope separation. This results in marked savings in material hold-up, and in plant size and investment. 

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