Limiting enrichment of intermediate isotopes in the output material at the ends of a cascade

Minenko, V.P.

doi:10.1007/bf01261857

Cited by 22 publications

(4 citation statements)

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“…For a given value fA½0,1 and the index number m A N C , the concentrations of the jth component in the product and waste flows satisfy conditions (Minenko, 1972;Zeng and Ying, 2000) …”

Section: Q-cascade Optimization With the Effective Fraction Specifiedmentioning

confidence: 99%

Use of the Q-cascade in calculation and optimization of multi-isotope separation

Zeng¹,

Jiang²,

Borisevich³

et al. 2011

Chemical Engineering Science

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“…For a given value fA½0,1 and the index number m A N C , the concentrations of the jth component in the product and waste flows satisfy conditions (Minenko, 1972;Zeng and Ying, 2000) …”

Section: Q-cascade Optimization With the Effective Fraction Specifiedmentioning

confidence: 99%

Use of the Q-cascade in calculation and optimization of multi-isotope separation

Zeng¹,

Jiang²,

Borisevich³

et al. 2011

Chemical Engineering Science

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“…The production of isotopes of more than twenty chemical elements is possible using cascades of gas centrifuges [1]. To make the production more efficient, it is important to optimize the separation process, including transient processes [9,10] and separation of non-typical for this method isotopes such as carbon isotopes [11].…”

Section: Introductionmentioning

confidence: 99%

Comparison of the efficiency of square cascades with an additional product flow and double cascades to concentrate intermediate isotopes

Azizov

Smirnov

Sulaberidze

2022

J. Phys.: Conf. Ser.

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Original techniques were proposed for calculating and optimizing double cascades (DC) built of square cascades and a square cascade with an additional product flow (SCAP). Both cascade schemes (DC and SCAP) were tested in solving a task of simultaneous enrichment of three components of a model mixture to a pre-defined level. A comparison of the DC and SCAP efficiency was made according to the minimum of total cascade flow. The results have shown that the double cascade is more efficient in terms of the chosen criterion.

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“…(1) In the second case, the limit ƒ → ∞, expression (8) for determining the concentration of the target component in the product form becomes [8] (12) and in the limit ƒ → 0 expression (10) becomes (13) The ratio of the logarithms of the parameters g i and g n in expression (13) will be greater or equal to 1: ln g i /lng n ≥ 1 (i = 1, 2, ..., n). It follows from formulas (8) Thus, expressions (8)-(14) with possible values of the length of the product and waste parts of a quasi-ideal cascade make it possible to construct curves which limit the region of existence of the solution of system of equations (1)-(4) (Fig.…”

mentioning

confidence: 99%

“…3). We note that the change of the curve, describing the upper limit on C nP with fixed C nW , which are calculated using formulas (8) and (9), does not depend on the separation coefficient per unit difference of the mass numbers q 0 and is determined only by the initial composition of the mixture of components.…”

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confidence: 99%

Special features of the enrichment of components with intermediate mass in a quasi-ideal cascade

et al. 2006

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An approximate approach is described, making it possible to estimate without solving nonlinear equations describing the mass transfer of a multicomponent mixture in a quasi-ideal cascade, the maximum concentration of the intermediate target component which can be obtained in the product flux from the cascade. Asymptotic formulas are obtained for the range of existence of the solutions of the system of equations which relates the external and internal parameters of the cascade. The approach developed is illustrated by examples of a process of separation of a natural mixture of krypton isotopes in a quasi-ideal cascade for admissible concentrations of the target intermediate component in the product and waste flows.The theory of quasi-ideal cascades -symmetric counterflow cascades with relative separation coefficient at the steps substantially different from 1 is described in [1][2][3]. The separation coefficient of the partial flows in such cascades is constant. A particular case of a quasi-ideal cascade is a R cascade. In such a cascade, at the entrances into its steps the flows of the mixture to be separated are combined with the same relative concentration of the vapor of the chosen components [3][4][5][6][7].When a m-component mixture is separated, the parameters of the quasi-ideal cascade are the feed flow F, the product flow P, and the waste flow W, and the corresponding concentrations C iF , C iP , and C iW (i = 1, m), the total separation of the steps q ik and the coefficient of separation of the steps with respect to the enriched (light) α ik and depleted (heavy) β ik fractions (i =  1, m), which are constants and are independent of the number of the steps. In addition, the parameters of the problem are the total number N of steps in the cascade, the number f of the step at whose entrance the feed flows enter, and the number k of the component (called the reference component), relative to which the separation coefficients q ik , α ik , and β ik are calculated.For molecular-kinetic methods of separation of isotopes (gas diffusion, gas centrifuge, and thermal and mass diffusion), the total separation coefficient q ik of a step can be represented in the form [3][4][5][6][7] where q 0 is the separation coefficient per unit difference of the mass numbers, and M k and M i are, respectively, the mass number of the kth and the ith component.Since the concepts of "product" and "waste" in separating multicomponent mixtures are conditional, for definiteness we shall assume that the product is obtained at the end of the cascade, where the lightest component of the mixture being separated is concentrated, and the waste is obtained at the opposite end. We shall enumerate the steps of a quasi-ideal cascade in increasing order from the waste (heavy, s = 1) to the product (light, s = N), and the mixture components in order of their increasing mass number. q q i m ik M M k i = = − 0 1 , , ,

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Limiting enrichment of intermediate isotopes in the output material at the ends of a cascade

Cited by 22 publications

References 1 publication

Use of the Q-cascade in calculation and optimization of multi-isotope separation

Use of the Q-cascade in calculation and optimization of multi-isotope separation

Comparison of the efficiency of square cascades with an additional product flow and double cascades to concentrate intermediate isotopes

Special features of the enrichment of components with intermediate mass in a quasi-ideal cascade

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