BASIC SEPARATION THEORY
To choose this feed point, therefore, it must be possible to calculate the concentration of
F in the process gas at any point in the cascade. These calculations can be made by
knowing two things: first, the concentration of U F in the process gas at several points in
the cascade (determined by laboratory and instrument analysis); and second, the increase in the
concentration of U F accomplished by each stage. This is called the stage enrichment and
should not be confused with the separation accomplished by a stage previously discussed.
Therefore, by knowing the stage enrichment and the U F concentration at some point in the
cascade, it is possible to determine the concentration at other points.
The feed material ordinarily charged into a plant contains a very small percentage of U F
with the remainder being U
F . Consequently, a far greater amount of the feed flows
downward in the cascade and is removed as tails than is removed at the top of the cascade as
U F or product. For this reason, as we progress upward in the cascade from the feed point,
the total flow through the converters becomes progressively smaller. It follows, therefore, that
in the ideal design each stage would be different in size from the adjacent stages. However,
since the cost of construction of a production cascade is of great importance, a lower cost may
be achieved by the use of many identical units. For this reason, the cascade is composed of
a series of sections, each of which contains a large number of identical stages. The change in
equipment size is accomplished in a step-wise manner by varying the equipment size of each
Of major importance in a production cascade is the ability to calculate pressures, temperatures,
and flows of the process gas which cannot be practically or economically measured by
instrumentation. Since the cascade is made up of sections each of which contains a large
number of identical stages and since the stage is the smallest separating unit of a cascade, these
calculations are made on a stage basis. This system of calculating temperatures, pressures,
and flows is commonly referred to as a circuit balance and consists of a series of calculations
made from those pressures and temperatures ordinarily measured by instrumentation in the
cascade, and from experimental data obtained from test loop studies.
For illustration purposes, the pressures, temperatures, and flows in a typical X-31 stage which
are taken by instrumentation, plus those to be calculated, are shown in Figure A-3. It is
obvious that the cost to install instruments in every stage to measure all of the values indicated
would be prohibitive.