In the future, it is probable that the supplier of enrichment services will permit a customer to specify the assay (®*U content) of the tails to which feed is to be stripped so as to minimize the combined cost to the customer of natural UF6 feed and separative work. Figure 12.20 shows qualitatively the effect of tails composition on the contributions to product cost arising from costs for feed and for separative work in stripping and enriching sections. The amount of separative work required in the enriching section is independent of tails composition. But the cost of separative work required in the stripping sections varies from zero when хц/ = Zp (no stripping) to infinity when хц/ = 0. Conversely, the cost of feed varies from infinity when хц/ — zp to a minimum at хц/ = 0, as may be seen from Eq. (12.152). There is therefore an optimum tails assay x0 between Хц/ = 0 and хц> = zp, at which the sum of the cost of separative work and the cost of natural uranium feed is a minimum.

An equation for evaluating the optimum tails composition is derived by substituting explicitly into Eq. (12.152) for the unit cost of product cp the separation potentials фр, фц/, and фр expressed in terms of the corresponding weight fractions xp, хц>, and xp by Eq.

(12.144) :

0 zF Figure 12.20 Effect of tails composi-

Tails composition, xw tion on cost of product.

yp-xw

zp-xw

Optimum tails composition occurs when

When cp from Eq. (12.158) is substituted into Eq. (12.159) and optimum tails composition x0 is substituted for xw, the result is

— УР ZF (Izp — 1) In j~~— і (12.160)

(zp-x o)2 1~zf

This may be simplified to

Figure 12.21 shows the dependence of optimum tails composition on the feed-to-separative work cost ratio.

An interesting interpretation may be given Eq. (12.161). Hie optimum tails composition is

0 12 0.20 0 30 0.40 Figure 12.21 Optimum tails com-

Optimum % U-235 in tails position.

the composition of material from which natural uranium can be produced in an ideal cascade without stripping section for the same cost as natural uranium from an external source. This may be seen by comparing the right side of Eq. (12.161) with the term in brackets of Eq. (12.137) for the total flow rate in the enriching section of an ideal cascade. Further discussion of these equations is given by Hollister and Burlington [H3].