On a Criterion Efficiency for Multi-Isotope Mixtures Separation

Wood, Houston G.; Borisevich, V. D.; Sulaberidze, G. A.

doi:10.1081/ss-100100654

Cited by 16 publications

(11 citation statements)

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“…However, to do this, another equation is needed since M * becomes yet another parameter. To find this equation, results developed in Houston G. Wood's (et al) research are utilized (Wood, et al 1999). Equation 28 in this reference is presented here as Equation 17.…”

Section: Multi-component Enrichmentmentioning

confidence: 99%

Advanced Fuel Cycle Economic Tools, Algorithms, and Methodologies

Shropshire¹

2009

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Section: Multi-component Enrichmentmentioning

confidence: 99%

Advanced Fuel Cycle Economic Tools, Algorithms, and Methodologies

Shropshire¹

2009

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“…The expression for the multicomponent value function differs from the variants proposed earlier [6][7][8][9]. The value of the mixture, according to (6), is determined by the sum of the terms, each depending just on the concentration of one component, whose number is equal to the number of the components of the mixture.…”

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“…Whereas the fi rst axiom is beyond question, since it is only the concentration of the end product that is of interest in the process of separation of the mixture and the expenditure on the separation process must refl ect the change in this precisely concentration under the conditions of constancy of the remaining thermodynamic parameters, the second axiom is not as indisputable as this. Generalizations of formula (1) to multicomponent mixtures were repeatedly proposed [6][7][8][9], but such generalization on the basis of direct calculation of the elementary molecular-kinetic separation model was not attempted.…”

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Multicomponent separation potential. Elementary kinetic theory

Aleksandrov

Gadelshin

2013

J Eng Phys Thermophy

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Studying the multicomponent separation potential is a topical problem that is expediently solved from fi rst principles, i.e., on the basis of the molecular-kinetic model of a separation process without ties to a concrete cascade. This seems correct, since the theory of multicomponent separating cascades is quite complicated and is in the process of development.The cost of the energy expended on separating a mixture of isotopes, i.e., on changing the concentration of the required isotope in the mixture, is the main item of expenditure of the separation production. The minimum energy expended in the "ideal" process of separation of isotopes is called "separative work." This notion is of special importance in separation theory, since it enables one to compare various methods of isotope separation and to evaluate the expenditure on obtaining a certain concentration of the isotope from the raw material with a prescribed concentration of the components. The separative work ΔU depends just on the initial and fi nal state of the mixture and, for a mixture of two components, is defi ned as ( ) ( ) ( ) ( )This work is directly proportional to the product of the number of moles M j of the separated mixture and to the change in a certain function V(C j ) called the separation potential [1] and dependent on the concentration of the mixture C j . By analogy with the thermodynamic potential, the separation potential V(C) is a dimensionless quantity refl ecting the minimum energy that is necessary for changing the concentration of one mole of the mixture regardless of a concrete separation process [2,3]. The separation potential is also called the "value function," since the product MV(C) refl ects the "cost" of the number of moles M of the mixture with concentration C. The issue of the physical nature of the separation potential and of the method of derivation of an expression for it is still controversial. The classical expression for the separation potential [4], derived by Dirac and Peierls for a binary mixture of isotopes (uranium-235 and uranium-238) on the basis of Dirac′s axioms in the approximation of a small change in the concentration of the mixture, is of the form ( ) ( )

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“…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.…”

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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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On a Criterion Efficiency for Multi-Isotope Mixtures Separation

Cited by 16 publications

References 16 publications

Advanced Fuel Cycle Economic Tools, Algorithms, and Methodologies

Advanced Fuel Cycle Economic Tools, Algorithms, and Methodologies

Multicomponent separation potential. Elementary kinetic theory

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

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