Stage Separation Factor Research Articles

Improvement of the Mathematical Simulation Model for a Multicomponent Separating Cascade

This Note reports remarkable improvements in the previously reported mathematical model for multi-component separating cascades, which are applicable to the cases where the interstage flows and the stage separation factors are input variables for the calculations. The number of the independent variables is greatly decreased for much more efficient iterative calculations by the multidimensional Newton-Raphson method. Particularly, if the stage separation factors are independent of concentrations of the up and down streams, the improved model presents great decreases both in the computation time needed at each iterative step and in the number of total iterations. Several numerical experiments made for a five-component system of N2-O2-41 Ar-85Kr-133Xe, which are separated by using the porous membrane method, indicate that the total computation time is shortened by almost two orders of magnitude if the improved model is used.

Mathematical Simulation Procedure of Multicomponent Separating Cascade

A simulation procedure of multicomponent separating cascades is developed. This procedure is applicable and effective in such cases that the cut of mixture of each stage is prescribed and required to be independent of concentration, and the stage separation factors are given as input variables and very large. It can deal with cascades which have multiple feeds and sidestreams. The stage separation factors are allowed to be given as functions of compositions of down streams and up streams. The exact solutions are found out treating all the basic equations simultaneously by use of multi-dimensional Newton-Raphson method. As an application of this procedure to actual cascade calculations, a computer simulation study is carried out for hydrogen isotope separation system by porous membrane method which consists of two cascades and two catalytic equilibrators. It is proved that the Newton-Raphson iterative calculation proceeds stably under the assumed input and output conditions, and the porous membrane method ...

Mathematical simulation procedure of multicomponent separating cascade. Application to analysis of hydrogen isotope separation system by porous membrane method.

A simulation procedure of multicomponent separating cascades is developed. This procedure is applicable and effective in such cases that the cut of mixture of each stage is prescribed and required to be independent of concentration, and the stage separation factors are given as input variables and very large. It can deal with cascades which have multiple feeds and sidestreams. The stage separation factors are allowed to be given as functions of compositions of down streams and up streams. The exact solutions are found out treating all the basic equations simultaneously by use of multi-dimensional Newton-Raphson method. As an application of this procedure to actual cascade calculations, a computer simulation study is carried out for hydrogen isotope separation system by porous membrane method which consists of two cascades and two catalytic equilibrators. It is proved that the Newton-Raphson iterative calculation proceeds stably under the assumed input and output conditions, and the porous membrane method ...

On the Composite Nature of the Extent of Separation

Abstract The fundamental expression for Rony's extent of separation in a 2-component system has been reexamined for any separation stage with respect to its relation with the traditional stage separation factor for a wide variety of separation processes. It has been shown that for a single entry or double entry rate governed barrier separation stage, the extent of separation is a composite index consisting of a stage capacity factor proportional to the barrier area and a stage enrichment factor (α − 1) or (β1 1). The latter-need not be close to zero. For a reverse osmosis and a gaseous diffusion stage, the extent of separation has been expressed in terms commonly used for these processes. The composite nature of the extent of separation has been also determined for batch dialysis, batch thermal diffusion, as well as for a single equilibrium stage, and related to known features of these separation processes in terms of stage capacity and stage enrichment.

Taperization of Step Cascade for Uranium Enrichment by Gaseous Diffussion Process

Abstract An analysis of the effect of flow (or pressure) tapering on the productivity of step cascades, with account taken of the relations existing between the interstage flow rates, pressure levels and stage separation factors, revealed that productivity and separative work could increase by about 4% in a typical 3-size gaseous diffusion plant. A considerable gain could be expected by applying the tapering to sections comprising about 30 stages, into which each step would be divided. Further, an examination is made of the extent of reduction that can be expected of the mixing loss through flow tapering.

Taperization of Step Cascade for Uranium Enrichment by Gaseous Diffusion Process

An analysis of the effect of flow (or pressure) tapering on the productivity of step cascades, with account taken of the relations existing between the interstage flow rates, pressure levels and stage separation factors, revealed that productivity and separative work could increase by about 4% in a typical 3-size gaseous diffusion plant. A consider-able gain could be expected by applying the tapering to sections comprising about 30 stages, into which each step would be divided. Further, an examination is made of the extent of reduction that can be expected of the mixing loss through flow tapering.

Separation of calcium isotopes with macrocyclic polyether calcium complexes

Enrichment of the heavy isotopes of calcium by means of the chemical exchange reaction 40 Ca 2+( aq)+ 44 CaL 2+(org) 40 CaL 2+(org) where L represents a macrocyclic polyether was investigated. The single stage separation factor for isotopes differing by one mass unit was 1·0010 ± 0·0002 (95% C.I.) using the polyether dicyclohexyl 18-crown-6. A liquid-liquid chemical exchange system utilizing this reaction is considered technically feasible for separation of calcium isotopes.

Influence of Stage Separation Factor on Squared-Off Cascades

Influence of Stage Separation Factor on Squared-Off Cascades

Influence of Stage Separation Factor on Squared-Off Cascades

An example of optimization problem for the design of squared-off cascades to be incorporated in uranium enrichment plants utilizing gaseous diffusion is solved from an economic point of view, whereby minimization is obtained of the plant annual expenditure expressed in terms of simple cost functions. The equi-step squared-off cascade is studied. The salient features of such a cascade are illustrated by a comparison of the cascade performance between one aimed at minimum plant annual expenditure and one aimed at minimum total flow rate. For the first-mentioned form of optimized cascade, the influence of the stage separation factor on plant economics is studied. The discussion covers the determination of optimum waste assay, and the exponential relationship between the enrichment coefficient and plant economics. The economic considerations affecting the stage separation factor are summarized in sensitivity curves relating this factor to changes in various economic indicators.

534. ガス拡散法における流れ様式の効果

In the process of uranium enrichment by gaseous diffusion, the scale of operation of the plant (e.g. barrier area, power consumption) is highly dependent on the single stage separation factor. The effect of the flow pattern on the separation factor is worth thorough investigation, because it may contribute to reducing the plant size by half.In this paper the flow patterns of perfect mixing and cross-flow are analyzed exhaustively. The results should serve in estimating quantitatively any intermediate flow pattern between these two extreme cases.Various flow patterns were realized by connecting in series 1-10 pieces of barrier made of sintered nickel, and extremely good separation effect was obtained with cross-flow, as verified by experiments in isotope separation made on nitrogen gas. The applicability of the present analysis to the estimation of intermediate flow patterns has also been demonstrated. Cases of counter-current flow and parallel flow can be dealt with similarly to cross-flow.

Solvent extraction of technetium and molybdenum by tetraalkylammonium iodides

Solvent extraction of technetium and molybdenum using quaternary ammonium iodides in benzene and chloroform was carried out from neutral and alkaline media. The influence of the anomalous activity coefficients of the extractants on the solvent dependency has been examined. The separation of Tc from Mo with good single stage separation factors is reported.

Thermal diffusion of salt solutions in single‐stage cells and in continuous horizontal columns: The system copper sulfate‐cobalt sulfate‐water

AbstractThe application of thermal diffusion to the separation of a pair of salts in aqueous solution was investigated. Experiments were conducted with the system copper sulfate‐cobalt sulfate‐water with both static, single‐stage cells and continuous, countercurrent flow contactors (or columns) of the horizontal Jury‐Von Halle type which utilizes flow through a porous membrane. Design equations for the continuous columns were developed, based on an idealized representation of the combined hydrodynamic and diffusion problem. Data from the single‐stage experiments were used in conjunction with these equations to predict stage separation factors and transfer unit heights. These mass transfer parameters were measured under various operating conditions on continuous units of two different sizes.The effects of size and operating conditions on the separation factor and transfer unit height were successfully predicted by use of the design equations. The accurate calculation of these quantities directly from single‐stage separation data was less successful, owing to the highly idealized nature of the mathematical model employed.

Nitrogen Isotope Exchange between Liquid N2O3 and NO at Low Temperature and Elevated Pressure

The single stage separation factor, a, for nitrogen isotope exchange between liquid N2O3—N2O4-mixtures and their vapor has been measured at temperatures ranging from — 76°C to room temperature and pressures between 1 atm. and 7.4 atm. At —76°C and 1 atm., α = 1.061 ± 0.003; at —23°C and 1 atm., α=1.034 ± 0.002; at +23°C and 2.1 atm., α=1.017 ± 0.002; at +23°C and 7.4 atm., α=1.030 ± 0.002. The results are compared with values, calculated from spectroscopic data for N2O3, N2O4, NO and NO2. The value of α = 1.030 found at room temperature and 7.4 atm. pressure enhances the usefulness of the N2O3—NO-system for separating the nitrogen isotopes, since it eliminates the need of refrigeration.

Lithium Isotope Separation on Complex Formation I. Equilibrium Study

Lithium isotope separation on molecular complex formation has been studied in lithium chloride- 1, 4-dioxane systems. The complex shows an absorption maximum at 270 mμ, and the molar ratio LiCl/dioxane in the complex has been found to be 1:1. The isotope ratio has been determined by a mass spectrometer using a surface ionization ion source. The results show that Li is enriched in the complex and the single stage separation factor is 1.026 in equilibrium at 100 °C. The separation of lithium isotopes seems to occur during the isotope exchange reaction between LiCl-dioxane complex and uncomplexed LiCl.

Separation of stable isotopes by chemical and ion-exchange methods

Methods of separating stable isotopes by the use of various types of molecular compounds. The use of molecular compounds for separating isotopes of boron, sulphur and oxygen. Isotopic exchange reactions in the electric discharges. Calculation of single stage separation factors for exchange reactions. Potentialities of the isotope separation process using ion exchange. The use of ion exchange for separating lithium isotopes. Combination of ion chromatography with electromigration of ion. Synthetic zeolites (molecular sieves) used as ion exchangers. Principles and applications of the continuous countercurrent ion exchange method.

Vapour pressure of isotopic solids by a steady flow method: Argon between 72 °K and triple point

A steady state flow method was devised to measure the single stage separation factor in the solid-vapour equilibrium. The method was applied to the36A-40A solid system and found to work satisfactorily. The logarithm of the separation factor was found to depend linearly from 1/T2 within the experimental errors, ranging from 0.0104 at 72 °K to 0.0072 at triple point. This linear dependence is in agreement with the current theories of small quantum effects on thermodynamic systems. Using Bigeleisen’s formulation of the theory and taking into account anharmonic effects, the value of the mean square frequency of the lattice harmonic vibrations in solid argon is derived; this value agrees satisfactorily with specific heat measurements. The difference in triple point temperatures of40A and36A is derived from the measurements and found to be 0.0435 °K.

The Enrichment of Lithium Isotopes by Ion Exchange Chromatography. III. The Influence of the Nature of the Solution Phase on the Separation Factor

Single stage separation factors for Li6 and Li7 were determined in ion exchange systems containing various other cations and anions in the solution and resin phases. Dehydration of the lithium species in the resin phase may be the major contribution to the change in the isotopic separation factor. The hydrating tendency of the co-ions in the resin phase is directly related to the magnitude of the separation factor. Finally, the effect of coordination of the lithium species with EDTA also is discussed.

Separation of Boron Isotopes. IV. The Methyl Sulfide-BF3 System

The exchange of boron between BF3 (gas) and the dimethyl sulfide-BF3 complex (liq.) was studied from —20°C to +26°C. The single stage separation factor changed from 1.056 to 1.031 over this temperature range with B10 concentrating in the liquid phase. Vapor pressures of dimethyl sulfide and of various mixtures of BF3 and dimethyl sulfide were determined. ΔH for the reaction BF3 (gas)+Me2S (liq.)→BF3·Me2S (liq.) was estimated to be —10.1 kcal/mole over the above temperature range. The melting point of the 1:1 complex was —19.6°C.

Vapour pressure of isotopic liquids

In order to extend previous studies of vapcr pressure of isotopic liquids in a wider temperature range, a new cryostat was butlt. The single stage separation factor alpha of the isotopic pairs Ar/sup 36/- Ar/sup 40/ and Ne/sup 20/- Ne/sup 22/ was measured up to a vapor pressure of 12 atmospheres using natural isotopic mixtures. The logarithum of the vapor pressure ratio of the pure isotopes was derived from a and found to be linearly dependent on I/T: In (p36)/p40) = 1.31(1/T)-8.95 x l0/sup -3/ for argon from 83 to 120 tained K, and in (p20/p22) = 2.510(1/-T)--5.673 x 10/sup -2/ for neon from 25 to 40 tained K. A brief discussion of the results is given. (auth) 1962l The effects of various developers on the transverse dimensions of ion tracks of He, C, N, O, Ne, and Ar in ionographic emulsions G-5, C-2, and L-4 were studied. The discrimination of heavy-ion tracks by their transverse dimension is dependent on this effect which is very great for ordinary developers (amidol, II) 19). A development regulation by measurement of the width of alpha tracks is proposed. The difficulty of using a simple correction factor which accounts for the effects of developmentmore » is pointed out. (tr-auth)« less

Enrichment of Nitrogen-15 by Chemical Exchange of NO with Liquid N2O3

The characteristics of the two-phase exchange system: N214O3(liq)+N15O(gas)⇄N14N15 O3(liq)+N14O(gas) have been studied in laboratory exchange columns to evaluate its usefulness for concentrating nitrogen-15. The effective single stage separation factor α has been determined both by direct equilibration of liquid and gas phases, and by measuring the over-all separation in an exchange column as a function of the rate of product with-drawal. The factor α varies from 1.035±0.005 at —14°C to 1.016±0.004 at +14°C. The system is complicated by the presence of additional oxides of nitrogen in both phases, and it is not yet possible to evaluate the contributions of each of the individual molecular species to the effective separation factor. The over-all separations achieved at total reflux in a 40-stage bubble plate column corresponded to a maximum plate efficiency of ∼60% at an interstage flow of ∼50 mM N/min cm2. Similarly, the separations obtained in a 95-cm column packed with stainless steel wire helices corresponded to stage heights of 1.1 and 1.2 cm for interstage flows of 23 and 31 mM N/min cm2, respectively. A comparison of the present system with the nitric acid-nitric oxide exchange system indicates that approximately equal volumes of column would be required for the same isotope separation task in spite of a considerably lower α for the N2O3 system. This is due to the higher rate of exchange as evidenced by lower stage height. The favorable stage height for this process makes it possible to prepare highly concentrated nitrogen-15 in shorter columns than those used for the nitric acid exchange.