Multicomponent Isotope Mixtures Research Articles

Method of Calculating and Optimizing Multiflow Cascades for Separating Multicomponent Isotopic Mixtures

Method of Calculating and Optimizing Multiflow Cascades for Separating Multicomponent Isotopic Mixtures

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.

Separative Cascade Shape Effect on the Isotopic Mixture Concentration in Cascade Holdup

Numerical studies are performed of the separation of a model multi-component isotopic mixture in a three-stream cascade. The particulars of isotope accumulation as a function of cascade shape (length, stage distribution of interstage flow) are examined. The regularities of the effect of the cascade shape on the component concentration in the cascade holdup are determined. An enriched isotopic mixture can be obtained by accumulation and partial removal of the process gas from the stages where the target component concentration is highest.

Classification of model cascades for separation of multicomponent isotope mixtures

ABSTRACT As far as we know, it is the first attempt to build the classification of the currently existing models of molecular-selective mass transfer in cascades for isotope separation in the stationary mode of their operation. In papers devoted to this subject, such cascades are often called as “model” ones. It is shown that for the case of symmetric separation any of such a “model” cascade can be represented as a special case of a cascade with constant separation factors. There are established interrelationships of the “model” cascades, both with each other and with the symmetrical countercurrent cascades feasible in practice.

Mathematical Modeling of Nonstationary Separation Processes in a Cascade of Gas Centrifuges for Separation of Tungsten Isotopes

We have developed and program-realized a mathematical model of nonstationary separation processes proceeding in cascades of gas centrifuges for separation of multicomponent isotope mixtures. With the help of this model we have calculated the parameters of nonstationary separation processes proceeding in the cascades of gas centrifuges for tungsten isotope separation. It has been shown that the model adequately describes the nonstationary processes in the cascade and is suitable for calculating their parameters during separation of multicomponent isotope mixtures.

Modeling of nonstationary processes during separation of multicomponent isotope mixtures

ABSTRACTThe article presents a mathematical model for calculation of nonstationary hydraulic and separation processes in a gas centrifuge (GC) cascade for separation of multicomponent isotope mixtures. The model has been applied to calculate the parameters of nonstationary processes in a GC cascade for separation of krypton, germanium and tungsten isotopes. As a result, the specifics of the excess holdup distribution along the cascade stages has been identified, and variations of the isotope concentrations in a nonstationary process have been revealed. The data obtained show that the proposed mathematical model is able to adequately describe nonstationary hydraulic processes in GC cascades for separation of multicomponent isotope mixtures.Highlights:Mathematical model of cascade for separation of multicomponent isotope mixture has been developed.The model verification has been done.The isotope transient regularities into cascade during nonstationary processes has been identified.

Mathematical Model of Nonstationary Separation Processes Proceeding in the Cascade of Gas Centrifuges in the Process of Separation of Multicomponent Isotope Mixtures

We have developed and realized on software a mathematical model of the nonstationary separation processes proceeding in the cascades of gas centrifuges in the process of separation of multicomponent isotope mixtures. With the use of this model the parameters of the separation process of germanium isotopes have been calculated. It has been shown that the model adequately describes the nonstationary processes in the cascade and is suitable for calculating their parameters in the process of separation of multicomponent isotope mixtures.

Applicability of Separation Potentials to Determining the Parameters of Cascade Efficiency in Enrichment of Ternary Mixtures

The separation potentials suggested by various researchers for separating multicomponent isotopic mixtures are considered. An estimation of their applicability to determining the parameters of the efficiency of enrichment of a ternary mixture in a cascade with an optimum scheme of connection of stages made up of elements with three takeoffs is carried out. The separation potential most precisely characterizing the separative power and other efficiency parameters of stages and cascade schemes has been selected based on the results of the estimation made.

Mathematical model of nonstationary hydraulic processes in gas centrifuge cascade for separation of multicomponent isotope mixtures

This article presents results of development of the mathematical model of nonstationary separation processes occurring in gas centrifuge cascades for separation of multicomponent isotope mixtures. This model was used for the calculation parameters of gas centrifuge cascade for separation of germanium isotopes. Comparison of obtained values with results of other authors revealed that developed mathematical model is adequate to describe nonstationary separation processes in gas centrifuge cascades for separation of multicomponent isotope mixtures.

Mathematical Modeling of Non-Stationary Hydraulic Process Occurring in the Gas Centrifuge Cascade During the Separation of Multicomponent Isotope Mixtures

This article presents results of development of the mathematical model of nonstationary separation processes occurring in gas centrifuge cascades for separation of multicomponent isotope mixtures. This model was used for the calculation parameters of gas centrifuge cascade for separation of germanium isotopes. Comparison of obtained values with results of other authors revealed that developed mathematical model is adequate to describe nonstationary separation processes in gas centrifuge cascades for separation of multicomponent isotope mixtures.

MATHEMATICAL MODEL OF NON-STATIONARY HYDRAULIC PROCESSES IN GAS CENTRIFUGE CASCADE FOR SEPARATION OF MULTICOMPONENT ISOTOPE MIXTURES

It is known that the optimal modes of gas centrifuge (GC) cascades are violated occurring the non-stationary hydraulic processes for a separation of multicomponent isotope mixtures. The perturbation arise and lead to violations of operating specifications and intolerable overloads equipment. The non-stationary hydraulic processes affect the cascade efficiency and the quality of the product. The GC cascades for the separation of multicomponent isotope mixtures have insignificant gas content, and, as a consequence, low inertia. It leads to increased influence of non-stationary processes on the cascade efficiency. In this regard, an important urgent task is the comprehensive investigation and modeling of these processes. We solved this problem by creating mathematical model and software for it. The separation stage of the GC cascade is presented in the form of four dedicated object (a feed manifold, GC, a heavy fraction manifold and a light fraction manifold). The calculation of non-stationary hydraulic amounts to replacing the first order differential equations by difference equations of the implicit Euler scheme [1] and the decision obtained by non-linear algebraic equations. The calculation is iteratively performed; the pressures and flow are determined in all objects at each time step, satisfying the equation of material balance in the cascade. These values must satisfy the balance of substances in the GC cascade. The developed mathematical model was tested for isotope separation of Si, Xe, Ni, W. The deviation of the calculated and actual values was 7.5%. As a result, this mathematical model is universal for calculation of hydraulic parameters of GC cascades for separation of multicomponent isotope mixtures by using different working substances.

Influence of 236U on the Efficacy of Recycling Regenerated Uranium in VVER Fuel

This scientifi c and technical communication examines the physical mechanisms of the change in the isotopic composition of regenerated uranium recycled in VVER-1000 and -1200 fuels. Modeling of the Multiple Recycling of Regenerated Uranium. An approach based on matched modeling of the neutron-physical processes occurring during the irradiation of fuel in a reactor and molecular-selective mass transfer in separative cascades of gas centrifuges for the enrichment of uranium is used to investigate the mechanisms. The approach is very similar to that used in [1, 2]. Aside from the asymptotic case, where multiple recycling of regenerated uranium with dilution of natural uranium is accomplished without restrictions on the U content in low-enriched uranium, scenarios in the presence of such restrictions are analyzed. The following recycling sequence is considered [3]. The fuel in the initial load with prescribed enrichment of U fabricated from natural uranium is irradiated in the reactor core, allowed to decay for 10 yr, and reprocessed. Natural uranium is the second feed stream of the cascade, making it possible to dilute the regenerated uranium and lower the content of U in the product. The fuel obtained in this manner is once again irradiated, after which it is allowed to decay and then reprocessed. Next, the cycle is repeated. In all, fi ve successive recycles of the regenerated uranium are considered. Multiple recycling of regenerated uranium by burnup to 48 MW·days/kg with different restrictions on the U content in low-enrichment uranium was analyzed fi rst. Three cases were considered. The U concentration did not exceed 2·10 wt.% in the fi rst case and 5·10 wt.% in the second; there were no restrictions on the U concentration in the third. The effect of U was compensated by additional enrichment with U and reactivity compensation factor 0.29 [3, 4]. The restriction on the U concentration in low-enrichment uranium at the level 0.1% was examined separately; compensation of the parasitic absorption of neutrons by this isotope is not required below this level. The burnup considered in the present work corresponds to the maximum unfavorable situation from the standpoint of the content of U and U in the regenerated uranium. For example, burnup 48 MW·days/kg with 4% enrichment is reached only in individual fuel assemblies. The average burnup with such enrichment equals 43 MW·days/kg. A model of a quasi-ideal cascade, widely used in the theory of separation of multicomponent isotopic mixtures, is used for numerical modeling of the enrichment of regenerated uranium in a cascade with two feed streams (natural uranium and regenerated uranium) [5]. This model is used as a replacement for an ideal cascade, often used in the evaluation of the parameters of cascades for enrichment of natural uranium, because regenerated uranium, in contrast to natural uranium, cannot be regarded as a binary mixture, since it contains, aside from U, a fourth component – U, U, U, or U [6]. The neutron physical processes were calculated by the Monte Carlo method using the MCNP5 code (USA).

Mathematical Modeling of Nonstationary Separation Processes in Gas Centrifuge Cascade for Separation of Multicomponent Isotope Mixtures

Mathematical Modeling of Nonstationary Separation Processes in Gas Centrifuge Cascade for Separation of Multicomponent Isotope Mixtures

Determination of the Content of Admixed Components in an Optimal Multistream Cascade

An analytical determination of the concentration of admixed component in the product and waste streams of a multistream cascade separating a multicomponent isotopic mixture is examined. It is proposed that the solution of the systems of differential equations describing the variation in the concentration of the components of a mixture over the steps assuming the enrichment effects to be small be used. The general approach to obtaining analytical relations for the evaluations is shown for the example of cascades with several feed and product streams. Calculations of uranium cascades are performed, showing good agreement between the analytical determinations and the numerical calculations for the separation of natural and waste depleted uranium hexafluoride obtained from regenerated uranium.

Further optimization of Q-cascades

A model cascade is usually created before constructing a practical isotope separation cascade as the target for approximating a practical cascade. The Q-cascade is a widely used model cascade for continuous profiles in separating multi-component isotope mixtures. The optimization of a Q-cascade with specified concentrations for a target component in the product and waste flows can be conveniently performed by adjusting the mass number (M*) of a virtual component. In previous studies, the M* parameter was treated as identical throughout the entire cascade. This paper proposes further optimization of a Q-cascade by splitting the cascade into segments and allowing each segment to take a different value for M*. An example is presented for separating Cd isotopes; the numerical results demonstrated that segmented Q-cascades achieved better separation performance than traditional Q-cascades.

Comparison of Methods of Enriching Intermediate Components in Cascades with the Same Number of Separative Elements

A method is proposed for concentrating in different output flows in a square cascade with two additional extractions the components of the multicomponent isotopic mixture being separated. The parameters of the proposed cascade, a square cascade with additional extraction, and a cascade with flow expansion at internal steps on condition that the number of separative elements in them is the same are compared for the separation of a mixture of tungsten isotopes. It is shown that the proposed cascade expands the possibilities of previously known methods of concentrating intermediate-mass isotopes, since several target products can be obtained at the same time in the output flows.

Q-cascades for obtaining highly concentrated intermediate components of separated mixtures

A comparative analysis of a Q-cascade with a monotonic flow profile and a Q-cascade with flow expansion in the enrichment part is performed under the condition of equal total flows in both cascades. The given cascade schemes are proposed in order to obtain highly concentrated intermediate (with respect to their mass number) components in the separation of multicomponent isotope mixtures. It is shown that the cascade with expansion provides a higher concentration of the target component in the additional product than the usual cascade with monotonic flow profile. However, the amount of isotope accumulated product per unit feed mixture mass in the Q-cascade with expansion is much lower than in the usual Q-cascade.

Comparison of optimal and model cascades for the separation of multicomponent mixtures at arbitrary stage enrichments

A method in which the model-matched abundance ratio (R) cascade to be designed at given concentrations of the target component in the product and waste streams is optimized using the parameter M*, defined as the half-sum of the values of the mass numbers of the target and reference components, is proposed. The comparison between the overall characteristics of the R cascade optimized using the parameter M* and minimal-total-flow cascade shows that they are close to each other. The conclusion that the parameters of the optimized R cascade for separating multicomponent isotope mixtures are reasonable to use as the initial approximation in determining the optimal parameters of multistage separation cascades with a given concentration of the lightest or heaviest target component in output streams is made

Calculation of a square cascade with losses of the working material in the steps and pipelines during separation of multicomponent isotopic mixtures

A method is proposed for calculating the stationary mass transfer of a multicomponent isotopic mixture in a square cascade with arbitrary enrichment and losses at the separation steps and in the pipelines of the cascade. The method, which is based on successive approximation of the cascade separation factor, makes it possible to reduce computational time substantially compared with the conventional method of quasilinearization.

Quasi-ideal cascades with an additional flow for separation of multicomponent isotope mixtures

The theory of the R-cascade is generalized to a cascade with an additional external flow, which can be either one more feed flow to the cascade or an additional product flow from the separator at arbitrary degrees of enrichment in the stages of the cascade. Calculations are performed for the enrichment of recycled fuel in the R-cascade to a necessary concentration, provided that the effect of the isotope 236U is compensated and the concentration of the isotope 232U is decreased. It is demonstrated that the theory of the R-cascade with an additional product flow from an intermediate section of the cascade with the maximal component concentration and an intermediate mass number can be used to calculate the optimal conditions in simultaneous separation of several enriched isotopes in the cascade.