R
Y
1 Y
X
1 X
R E ?
1
à
ln
1
1 à
?
Y X
X(1 X)
BASIC SEPARATION THEORY
DOE-HDBK-1015/1-93
Appendix A
CH-01
Rev. 0
Page A-4
The actual separation achieved by a stage is expressed in terms of the mol fraction of the
light component and for the purpose of this discussion is designated by the capital letter
R. It can be defined as follows: if Y is the concentration of light component in the
enriched stream leaving a converter and X is its concentration in the depleted stream
leaving the same converter, then
.
This definition is similar to that of the separation factor, but, as shown in Figure A-1, the
value of R is based on the overall separation of a stage while that of the separation factor
is based on the performance of the barrier alone. The relation between the two is given
by the following equation.
E is a correction factor called the mixing efficiency. It can be explained as follows:
since the light component passes through the barrier more rapidly than the heavy
component, the layer of gas at the surface on the high pressure side of the barrier
becomes more depleted in the light component than the bulk of the gas on the high
pressure side. Thus, there is a concentration gradient perpendicular to the surface of the
barrier which results in a decrease in separation. In the particular process of separation
of uranium isotopes, the value of R in the preceding equation differs very little from unity
(R = 1.003) and is somewhat inconvenient for use in calculations. By subtracting 1 from
each side of the equation, equating the symbol ? (psi) to R - 1, and by making a slight
approximation, the equation becomes
.
This equation is used frequently in the plant in making separation tests.
