Analytical calculation of the content of uranium isotopes in a cascade with two feed flows, two product flows, and one waste flow

Abstract

The problem of estimating the 232,234,236 U content in the product flows of an optimal cascade is examined. Relations are found for studying the characteristics of the concentration variations along the cascade for various ratios of the feed flows. It is shown that an effective procedure is to obtain from the intermediate product of the cascade a diluent for high-enrichment uranium.The technical characteristics of low-enrichment uranium produced in separation cascades for nuclear power must meet the ASTM C996-04 standard specifications. This imposes stringent constraints on the content of uranium isotopes 232 U, 234 U, and 236 U and requires that their concentrations in the product cascade flows be determined beforehand.A general theory of quasi-ideal cascades and R cascades which makes it possible to estimate the content of various isotopes during multicomponent separation in an ordinary (three-flow) cascade has been constructed in [1]. This theory was elaborated in [2-4] for the case of an additional flow and low relative concentration. However, the theoretical relations have only limited applications because the indicated cascades differ from the optimal cascades used in practice.When the 232,234,236 U content is much less than that of the target isotope 235 U and the separation effects at each step are small, the optimal cascade is identical to the ideal cascade with respect to 235 U and 238 U [5].A novel approach to obtaining an analytical solution of the system of differential equations for the separation of a multicomponent mixture in a cascade which is ideal with respect to the two main components was developed in this approximation [6]. This approach can be extended to any number of components and any number of external flows. A general method and algorithm for calculating the separation of uranium isotopes that makes it possible to obtain simple evaluation formulas have been proposed on the basis of this approach. Specifically, an analytical method of finding a solution for an ordinary cascade with three external flows on the basis of the method of [6] was presented in [7].The present paper examines the problem of obtaining an analytical estimate of the concentration of uranium isotopes in a more complex cascade used in practice -two feed flows, two product flows, and one waste flow. The salient features of the variation of the 234 U concentration for different ratios of the external flows are examined. It is shown that an effective procedure is to obtain obtaining from the intermediate product of the cascade a diluent for high-enrichment uranium.Formulation of the Problem. We shall study a cascade with two product flows, two feed flows, and one waste flow (Fig. 1). Its external parameters are the flows in the first (main) and second (intermediate) product flows P 1 and P 2 , the first and second feed flows F 1 and F 2 , and the waste flow W as well as the corresponding isotopic concentrations -C i P 1 , C i P 2 , C i F 1 ,The index i denotes the number of the isotope. We shall use it to denote the las...

Determination of the Content of Admixed Components in an Optimal Multistream Cascade

“…This imposes strict limits on the content of the impurity isotopes 232,234,236 U and requires that it be determined beforehand in the product streams of cascades. For this analytical relations have been proposed for determining the 232,234,236 U concentration in uranium cascades with different numbers of streams [2][3][4]. A method of determining the content of the components in the streams of an ordinary three-stream cascade in the case of an arbitrary mixture with two main components is described in [5].…”

“…Similarly, writing R n = C n /(1 -C n ) we fi nd K (n) = -R n d for C m = C m P with C = C P . The constants of integration K(2) , K(3) , ..., K (n-1) are determined from the continuity of the change in the concentration C m on the boundaries of the neighboring sections. We shall denote the function of concentration of the target component by…”

Analytical evaluations of the isotope content of weakly enriched regenerated uranium in optimal multiflow cascades

“…Relations for different cases of optimization of cascades for 235 U production were obtained in [2][3][4]. These relations make it possible to find analytical estimates of the content of the isotopes 232,234,236 U provided that their concentration is much lower than that of 235 U.…”