Theory Of Isotope Separation Research Articles

Peculiar properties of transient processes in cascades with additional product flow

One of the important stages in the campaign for separation of multicomponent isotopic mixtures is bringing the separation cascade to a stationary mode of operation. This process, depending on the applied separation method, can be characterized by a relatively long time with associated consumption of the working substance and operating costs. Therefore, the search for the values of the control parameters of the cascade at which it is possible to reduce the transient process time is practically a significant problem in the theory of isotope separation in cascades. One of the current trends in the modern theory of cascades is the study of physical laws of stationary mass transfer in cascades with additional outgoing flows. Such cascades can find application for solving a number of urgent problems, in particular, obtaining relatively high concentrations of isotopes with intermediate masses. At the same time, the laws of unsteady mass transfer in such cascades remain poorly understood. The paper analyses the key patterns of transient processes in a square cascade with an additional product flow. The interconnections between the time of bringing such a cascade to the stationary mode and the external conditions under which the process of separation of the mixture occurs are revealed.

Optimization of cascades with variable overall separation factors by various efficiency criteria

Construction and operation of separation facilities require considerable investments. That is why the special attention in the theory of isotope separation in cascades is paid to their optimization. The installation allowing obtaining the required quantity of a commercial isotope product by a minimum unit cost it is customary to call as the optimum cascade. However, the use of such the criterion in theoretical calculations is inconvenient, in view of the fact that the cost coefficients are generally inaccessible and can vary depending on external factors. Therefore, theoretically the minimum possible number of separation unit or elements, for instance, gas centrifuges, is often used as the optimization criterion, since its value directly indicates the unit costs. In addition, such criteria as the minimum of the total cascade separation capacity or the minimum of the deviation sums of the maximum possible separation capabilities are also applied in the optimization calculation. In this connection for the case of the cascade with a variable from stage to stage overall separation factor of a centrifuge, the parameters of the cascades optimized by means of various optimization criteria may differ largely. In this paper, we compare the parameters of cascades with the same external conditions, which are optimized by the above criteria. As the criterion to compare all cascades under investigation is chosen the minimum number of separation elements in the installation. The chosen approach allows us to estimate the deviation in the number of gas centrifuge in a case of optimization of a separation plant by different efficiency criteria.

Theory of isotope separation by displacement chromatography

Theoretical aspects of isotope separation are discussed for the steady-state and intermediate (non-steady-state) stages of the displacement chromatography of two isotopes. It is shown that the steady-state solution can be used even for the non-steady state to some extent. The theory could provide a basis for a feasibility study of an isotope separation process.

Theory of Isotope Separation by Electrochemical Parametric Pumping

Abstract Electrochemical parametric pumping is a novel separation process in which cycles of reversible electrochemical processes on high surface area electrodes are conducted in synchronization with cycles of solution flow through the separating column. In the present work, isotope separation by electrochemical parametric pumping is studied theoretically. The proposed model is based on the similarity between the parametric pumping and the countercurrent processes and on the division of the separating column to “cells” when dispersion processes are neglected. Steady-state isotopic concentration gradients are calculated and process optimization is performed with respect to system parameters such as the fraction of the isotopes bound to the electrode, the solution displacement volume, and the fraction of the isotopes withdrawn as product. The model may also be applicable to other types of parametric pumping.

The Theory of Isotope Separation, especially regarding a Relation between the Multiplication of Elementary Process and the Kineties of Column Operation

Efforts to place separation of isotopes, especially by chromatography or column operation, on a theoretical basis are reviewed. Emphasis is placed on fundamental principles and concepts rather than on details of experimental investigations. Theoretical studies fall into two main lines of approach. The first line of approach is characterized by the application of the ion-exchange or extraction theory to isotope separation; historically this approach as a consequence of the fact that the ion-exchange chromatography was applied to practically the isotope separation of elements. The second line of approach is represented by the chemical exchange method which has hitherto been used in two-phase separation. This approach is applied to interprete the experimental results which were obtained on the uranium isotope separation by the reverse frontal technique and on the lithium isotope separation by the band-elution technique. The relation between the two lines of approach is systematized.

Zur Kaskadentheorie der Trennung polynärer Isotopengemische

The theory of isotope separation in cascades is extended to polynary mixtures. Conditions for minimum reflux (maximum production) are derived. For square cascades, the general solution of the differential equations is indicated; a special solution is given for the important case of large reflux ratio. The enrichment of middle components in ternary mixtures is discussed, it is shown to be impractical in a single square cascade.

A Theory of Isotope Separation by Two Phase Distribution

同位体の分離にイオン交換を用いる際の理論的考察として,二相間分配による同位体分離の基礎理論を展開し,もっとも大きな分離係数をもつ系を理論的に見いだすことを目的とした。同位体A,Bが第一相で配位子Xと段階的に錯塩を形成し,第二相にAXz,AXz-ρ,AXz+q(zは一定の定数,ρ,qはある特定の整数群)が分配可能であるとすれば,分離係数は,(Kn:同位体交換反応係数,B AKz:AXz(BXz)の二相間の交換反応平衡係数,α:noΣ[AXn],-:第二相を示す)であらわされる。分離係数のうち,変化可能なおもな量として,4-lnSBA-1nBAKzを定義し,第二相に分配可能な種として,1.AXzのみ(4z),2,AXz,AXz-p(Δz,p),3.AXz,AXz+q(Δqz,q),4.AXz,AXz-ρ,AXz+q(Δ)について,Δの価を考察した。zの一定の値については,つねにΔz,ρ>4z,4>z,qの関係の得られることが明らかになった。したがって分離係数の1よりのずれを大きくするためには,第一相のイオン種が任意に第二相に分配する場合,またはあるイオン種のみが第二相に分配する場合よりも,あるイオン種より小さなイオン種,または大きなイオン種が第二相に分配可能な方がよく,実際の系では,気液反応または液一液抽出反応で中性の錯イオンのみを第.湘に分配するよりも,液一イオン交換体系によりある一定の数以上のXを配位したすべてのイオン種が分配した方がより大きい分離係数が得られる。さらに第二相に分配可能な種のうち,AXz以外のイオン種の存在最は第一相では少ないほどよく,したがって理想系は,共通に存在するある一つのイオン種AXzを境に,一つの相には,AXzより小さな錯種,他の相にはAXzより大きな錯種のみが存在する系であることが推論された。

Theory of isotope separation of homo and heteronuclear diatomic molecules by adsorption at low temperatures

The ground-state rotational-vibrational energies, E/sub T/, for diatomic molecules adsorbed on plane surfaces were calculated assuming a Morse potential for the surface-molecule interaction. For the moiecular hydrogens it was found that the trend of E/sub T/ as a function of surface barrier, both in units of 8 e (as Fe/sup 59 /sup 2/I/h/sub 2/, is nearly the same for all isotopes. The correlation diagram for the heteronuclear molecules deviates somewhat from that of the homonuclears, the magnitude of the deviation depending on the shift of the center of mass. (auth)

The Theory of Isotope Separation as Applied to Large-Scale Production of U

The Theory of Isotope Separation as Applied to Large-Scale Production of U

On the Theory of Isotope Separation by Thermal Diffusion

We here develop the theory of the processes in an apparatus with two concentric tubes, such as that used by Brewer and Bramley. In the first section we describe the process of thermal diffusion in general, and review the theoretical information on the subject. In Section II we set up the equations for the convection and diffusion processes, and obtain an expression for the net transport of a single isotope which is valid for arbitrary macroscopic properties of the gas. The assumption that the viscosity and heat conductivity of a gas are proportional to the absolute temperature is usually a good approximation; in this case the expression reduces to a simple form. In Section III we apply the transport equation to questions of separation factor and speed of operation. This is done both for the case of discontinuous operation, in which the approach to equilibrium is allowed to reach a certain stage and then the contents of an end-reservoir are removed, and for the case of operation with a continuous flow of gas through the tube. The advantages of the two methods are compared. In the last section we apply the formulas to a numerical example: the concentration of the ${\mathrm{C}}^{13}$ isotope by the use of methane, in an apparatus of moderate dimensions and power consumption.