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

Abstract

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 , , ,

New approach to optimize Q-cascades

“…The only requirement is that the values of concentrations in the outgoing flows from the cascade should be specified properly (Sulaberidze et al, 2006). For instance, one should not specify the concentrations in the product and waste flows both to be higher than in the feed.…”

On the problems of reusing reprocessed uranium by enrichment in schemes based on ordinary cascades

“…This cascade has 3 external flows: 1) Feed -mixture input to be separated into the cascade; 2) Product --the flow enriched in 235 U; 3) Waste -the flow depleted in 235 U. In the general case, such a cascade does not allow enrichment of reprocessed uranium with a simultaneous correction of its isotopic composition -the concentrations of even-numbered uranium isotopes [10]. An exception may be compositions with a relatively low initial content of even isotopes, which does not fit for modern light-water reactors.…”