Appendix ADOE-HDBK-1015/1-93BASIC SEPARATION THEORYRev. 0CH-01Page A-7To choose this feed point, therefore, it must be possible to calculate the concentration ofUF in the process gas at any point in the cascade. These calculations can be made by2356knowing two things: first, the concentration of U F in the process gas at several points in2356the cascade (determined by laboratory and instrument analysis); and second, the increase in theconcentration of U F accomplished by each stage. This is called the stage enrichment and2356should 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 the2356cascade, 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 F2356with the remainder being UF . Consequently, a far greater amount of the feed flows2386downward in the cascade and is removed as tails than is removed at the top of the cascade asU F or product. For this reason, as we progress upward in the cascade from the feed point,2356the total flow through the converters becomes progressively smaller. It follows, therefore, thatin 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 maybe achieved by the use of many identical units. For this reason, the cascade is composed ofa series of sections, each of which contains a large number of identical stages. The change inequipment size is accomplished in a step-wise manner by varying the equipment size of eachso-called section.CircuitBalancesOf 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 byinstrumentation. Since the cascade is made up of sections each of which contains a largenumber of identical stages and since the stage is the smallest separating unit of a cascade, thesecalculations 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 calculationsmade from those pressures and temperatures ordinarily measured by instrumentation in thecascade, and from experimental data obtained from test loop studies.For illustration purposes, the pressures, temperatures, and flows in a typical X-31 stage whichare taken by instrumentation, plus those to be calculated, are shown in Figure A-3. It isobvious that the cost to install instruments in every stage to measure all of the values indicatedwould be prohibitive.
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