Page 42 - Radiochemistry and nuclear chemistry

Nuclei, Isotopes and Isotope Separation 31

2.8.1. Multistage processes
Figure 2.8 shows a flow scheme for an isotopic fractionation process (or isotope
enrichment process) based on an c~-value near 1. Each stage consists of a number of cells
coupled in parallel; in the Figure only one cell is shown for each separation stage, but in
order to obtain a high product flow, the number of cells are usually high at the feed point
and then decrease towards the product and waste stream ends. Each cell contains a physical
arrangement, which leads to an isotope fractionation. Thus the atomic fraction for a
particular isotope is different in the two outgoing streams from a cell; in the product stream
the isotope is enriched (atomic fraction x'), while in the waste stream it is depleted (atomic
fraction x"). The separation factor tx is defined as the quotient between the isotopic ratios
of the product and waste streams for a single step, thus ((2.2) and (2.3)):

= ~'/~" = Ix'/(1 -x')]/[x"/(1 -x")] (2.47)

In most cases tx has a value close to unity; et - 1 is commonly called enrichment factor.
Since separation factors in general are small, it is necessary to use a multistage process
to obtain a product with a high enrichment. The number of stages determines the degree
of the enrichment of the product, while the number and size of cells in each stage determine
the amount of product. This amount (P moles of composition Xp) is related to the amount
of feexl (F moles of composition XF) and the amount of waste (W moles of composition Xw)
by the equations

F = P + W and F x F = P xp + Wx w (2.48)

From these equations we obtain

F = P (Xp-Xw)/(x F-x w) and W = P (xp--XF)l(x F-xw) (2.49)

The number of stages required to separate feed into product and waste of specified
composition is a minimum at total reflux, when P = 0. For this condition M. R. Fenske
has derived a relation, which can be divided into one part for the enrichment:

Np In ~ = In[xp(1--XF)l{xF(1--xp)}] (2.50)

and one for the stripping part of the cascade:

N w In a = ln[XF(1--Xw)/{Xw(1--XF) }] (2.51)

Np and N w are the minimum number of enrichment and stripping stages, respectively. In
isotope separations a is often very close to one; In ot can then be replaced by (et - 1). In
practice some product flow is desired, the fraction withdrawn at the enrichment stage being
known as "the cut" P/F. The number of stages required to produce the composition xp then
increases. The most economic, and thus also the most common, type of cascade for
processes with near unity a is the so-called ideal cascade. In this there is no mixing of
streams of unequal concentrations, thus x' n_ 1 --X"n+ 1 ill Fig. 2.8. Although the number of