Tails separation factor

This relation between the heads and tails separation factors and the stage separation factor is the key property of an ideal cascade. 

In the ideal cascade discussed up to this point, each stage receives as feed two streams of the same composition, a tails stream from the stage next higher in the cascade and a heads stream from the stage next lower in the cascade. In such a cascade the heads separation factor /, tails separation factor 7, and overall separation factor a are related by... 

Design example. The foregoing equations will be applied to the two>up, one-down ideal cascade considered by Oiander [01] having three stripping stages (tig = 3), seven total stages ( = 7), and a tails separation factor (7) of 1.3027. Values of r, s, and t then are... 

A gas centrifuge 300 cm long and 40 cm in diameter is to be run at 300 K and 500 m/s peripheral speed. It is fed at the midplane with UFs at a rate of 0.03 g UFe/s. The longitudinally uniform heavy-stream flow rate is 0.20 g UF /s. Heads and tails flow rates are set so that there is no mixing loss at the point of feed injection. Find the heads separation factor, tails separation factor, and separative capacity. Note /], I3 and /(/ i/a) are given in Table... 

Similarly, the tails separation factor between feed stream 2 and the heavy fraction is... 

Figure G1.4.4 Resolution Rs = 2AfR/(lVbi + Wb2) at different separations. (A) sufficient separation, Rs = 1 (B) baseline separation, Rs = 1.5. C, D, and E have the same separation factor, but show problems cause by overloading the column. (C) Good resolution (D) some peak broadening and tailing (E) excessive tailing causing peak overlap.

The sensory data are inconsistent and coelution is suspected. If the solutions given above fail, then the problem may be difficult to resolve because the contamination may be occurring from an odorant that is present in such small quantities that it is only detectable by GC-O. Possible causes the separation factor a is too small, tailing of peaks is occurring, both enantiomers have the same odor, or one enantiomer is odorless. Interaction of coeluting odors may vary with small variations in the concentrations of any of the odorants the note of an odorant can vary with concentration. 

Chromatographic Separation. With respect to chromatographic techniques, specificity can be demonstrated by a sufficient separation of the substances present. For the assay, appropriate separation means an adequate resolution between the peak of interest and other peaks (e.g., impurities, placebo or matrix components), which need not to be separated from each other. In contrast, universal procedures for the determination of impurities require a sufficient separation of all relevant impurity peaks. The required resolution is strongly dependent on the difference in the size of the corresponding peaks as well as on their elution order. Therefore, if separation factors are determined, the typical concentration levels or the specification limits (as worst case) of the impurities should be maintained. Resolution factors can be calculated according to EP [Eq. (3)] and USP [Eq. (4)] at half height and at the baseline, respectively. However, this is only sensible for baseline-separated peaks. The USP approach is less sensitive toward tailing, but more complex to determine. 

The simplest form of an HPLC SST involves comparison of the chromatogram with a standard one, allowing comparison of the peak shape and the peak width baseline resolution. Additional parameters that can be experimentally calculated to provide quantitative SST report include the number of theoretical plates, separation factor, resolution, tailing or peak asymmetry factor, accuracy, and precision (RSD of six measurements). Resolution may also be combined with a selectivity test to check the resolution of the analytes from components present in the sample matrix. If matrix components interfere with a method, a matrix blank may be included in the SST. Peak shape and asymmetry, or tailing factor, can... 

The degree of separation achieved by a single stage is known as the stage separation factor, or simply the separation factor a. This is defined as the weight, mole, or atom ratio in the heads stream divided by the corresponding ratio in the tails. For a two-component mixture. 

If the separation factor for the system is known and the variation of the reflux ratio is specified as a function of stage number in the cascade, the number of ideal stages required to separate feed into product and tails of specified composition can be calculated. For example, starting with the known tails composition xn, the heads composition from stage 1,, is... 

The minimum number of stages increases as the overall separation increases and as the separation factor approaches unity. Because both these conditions hold in a typical isotope separation plant, the minimum number of stages is often very large. For example, in a gaseous diffusion plant (a = 1.00429) making product containing 90 percent and tails 0.3 percent. 

This result is of great importance for isotope separation plants. It states that the total flow in the plant is the product of two factors, the first a function only of the heads separation factor p, and the second a function only of the flow rates and composition of feed, product, and tails. 

The cascade receives feed of fraction Zp at flow rate F and produces an upper product of fraction yp at flow rate P, a lower product of fraction yg at flow rate Q, and tails of fraction Xw at flow rate W. For this two-up, one-down cascade, p = 2, q = I, the heads separation factor /3 is... 

Figure 12.27 represents one stage of an ideal, close-separation, one-up, one-down cascade whose feed flows at rate 2M and contains Zj fraction U, Zg fraction U, and Zg = 1 — Zs — z fraction At the cut of used in such a cascade, heads flows at rate M and contains fraction and>>6 Stage tails flows at rateAf and containsXg fraction andxg Stage separation factors are defined as... 

It is proposed that B be concentrated by the gaseous diffusion process applied to BFs and "BF3. The plant is to be designed as an ideal cascade and is to separate feed containing 19 percent °B into product containing 90 percent and tails containing 8 percent. The stage-separation factor is 1.0074. 

It is also convenient to define head-to-feed or tail-to-feed separation factors, jS and y. 

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