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

Abstract

When choosing a cascade scheme for separating regenerated uranium, it is best to evaluate the content of isotopes in the product flows first. The cascades can be optimized for enrichment by the main isotope 235 U as well as impurities 232,234,236 U. Analytical evaluations are difficult to obtain because of the presence of feed and product flows in the cascades. The approximate calculations of cascades operating to enrich natural uranium are based on analytical solutions of a system of differential equations which approximately describes the change of the concentration of the isotopes [1]. Relations for different cases of optimization of cascades for 235 U production were obtained in [2‐4]. 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. The present article examines the solutions of the system of differential equations for the case of weakly-enriched regenerated uranium, when the 232,234,236 U concentration is much higher than for the separation of natural uranium. The computational model of a cascade in the form of a collection of sections on each of which the feed point location can also be the product location is proposed. The present model makes it possible to obtain analytical estimates for the concentration of isotopes when optimizing the cascade for any selected uranium isotope and arbitrary number of feed and product flows. Formulation of the Problem. The computational model of a cascade consisting of an arbitrary number n of sections is presented in Fig. 1. Each section is characterized by a prescribed concentration of the chosen target isotope and possesses feed and product flows at the right-hand end. It is assumed that the feed flows are introduced into the cascade without mixing with respect to the target isotope. The feed and product flows in an individual section which are not present in the cascade under study are set equal to zero in the calculation. Let W denote the waste flow of the cascade, F 1 , F 2 , ..., F n the feed flows, and as P 1 , P 2 , ..., P n the product flows. Let the concentration of the target isotope of the waste be C W ; C 1 , ..., C n the concentrations at the right-hand ends of the sections; the waste concentration for the evaluated uranium isotope in the waste flows C m W ; C m F1 , C m F2 , ..., C m Fn , in the feed flows; and C m P1 , C m P2 , ..., C m P n in the product flows. These parameters of the cascade are external and are related by the balance equations