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DOI 10.1007/s10512-014-9886-0 Atomic Energy, Vol. 117, No. 1, November, 2014 (Russian Original Vol. 117, No. 1, July, 2014)

ENRICHMENT OF REGENERATED URANIUM WITH SIMULTANEOUS DILUTION OF 232–236U BY RAW AND WASTE URANIUM

A. Yu. Smirnov and G. A. Sulaberidze

UDC 621.039.31

A scheme is proposed for a five-flow (three feed, product and waste flows) gas-centrifuge cascade for enriching regenerated uranium simultaneously diluted by natural raw material and waste uranium. Computational experiments show the advantages of such a cascade in terms of the consumption of natural uranium with respect to the previously proposed multiflow cascades. In contrast to previously proposed cascades for enriching regenerated uranium, this cascade makes it possible to vary the consumption of natural uranium in obtaining products of equivalent quality, which makes it possible to seek and pick the optimal way to enrich the regenerated material in order to obtain VVER fuel.

The inevitability of a two-component structure for nuclear power (reactors based on fast and thermal neutrons) with VVER dominating in the next few decades, a significant production–consumption disbalance for natural uranium, and the strategic orientation of the industry toward transitioning to a closed fuel cycle make it necessary to work out different variants for bringing nuclear materials recovered during the reprocessing of spent fuel into VVER-type reactors now under construction and being designed. One such material is regenerated uranium. Aside from reducing the need for natural uranium, the use of regenerated material will make it possible to reduce appreciably the volume of stored radioactive wastes compared with the open fuel cycle [1, 2]. This material can be used in different ways in the production of nuclear fuel, including obtaining uranium fuel or in mixed fuel (uranium–plutonium) [2–5]. We note that the use of regenerated uranium for the production of VVER fuel is impossible in isolation from a separation-sublimation complex. During the enrichment of regenerated material in gas-centrifuge cascades, difficulties arise mainly due to the presence of 232U and 236U in it [2, 5, 6]. The content of these isotopes in commercial low-enrichment uranium is subject to strict requirements associated with the need to satisfy radiation safety requirements in the fabrication of fuel elements and preserve the neutron-physical characteristics of the fuel. It is difficult to enrich regenerated material directly in an ordinary (three-flow) cascade, used for the enrichment of natural uranium, because when regenerated material is enriched in such a cascade, aside from 235U, lighter components, first and foremost 232U, unavoidably become concentrated in the product flow of such a cascade. Nonetheless, an ordinary cascade can be used to solve this problem by the following methods: 1) enrichment of regenerated material pre-diluted, for example, by natural uranium [7]; 2) production of enriched uranium from regenerated material followed by dilution with natural raw uranium or other diluents, in which case prior to dilution the content of 235U in the enriched regenerated material can be varied from the low- to high-enrichment uranium [8]; and 3) enrichment of natural raw material to 235U content somewhat above the level required for nuclear fuel and mixing of this product with the regenerated raw material [7]. These methods make it possible to enrich regenerated material, but there are drawbacks. For example, the loss of separative work when the products with different 235U content are mixed is a drawback common to all these methods. For method 2, the problems are once again the need to enrich the regenerated material to 235U concentration above 20%, National Nuclear Research University – Moscow Engineering-Physics Institute (NIYaU MIFI), Moscow. Translated from Atomnaya Énergiya, Vol. 117, No. 1, pp. 36–42, July, 2014. Original article submitted April 3, 2014.

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1063-4258/14/11701-0044 ©2014 Springer Science+Business Media New York

Fig. 1. Diagram of a five-flow cascade (three feed and two outgoing flows).

the impossibility of securing the required reduction of the 232U concentration in the low-enrichment uranium obtained, and 232,234,236 U contamination of the separation equipment [7]. It has been proposed that, aside from ordinary cascades, dual cascades, each one having a different configuration, be used to obtain low-enrichment uranium using regenerated material [9–11]. The general principle of operation of such cascades is two-step enrichment of regenerated uranium: a mixture is separated into two fractions (‘light’ and ‘heavy’) followed by separation of one fraction in the second cascade, which makes it possible to separate undesirable components from the main product, enriched 235U. Other methods of enriching regenerated material are also known. These are based on the use of multiflow cascades with, for example, two feed flows (regenerated and natural uranium) and in some cases an additional product flow [12, 13]. In such a cascade, in parallel with the production of the main product (low-enrichment uranium), a product with low (relative to the initial mixture) content of 232,234,236U is produced in the product at the end of the cascade. The advantages of using such cascades with respect to the indicated methods are minimum losses of separative work upon feeding the additional feed flow and extraction of additional product. But, an appreciable reduction of the 232,234,236U content in the low-enrichment uranium is attained, first and foremost, by diluting the regenerated material with the natural raw material inside the cascade, which results in a savings of natural uranium of no more than 10–15% [7]. An obvious way to increase the savings of natural uranium in multiflow cascades used for the enrichment of regenerated material is to use as the diluent, for example, a mixture of waste uranium. However, because the 235U content in this material is lower than in the natural mixture, the use of waste uranium as a diluent in a cascade with two feed flows makes it possible to increase the expenditure of separative work on obtaining commercial low-enrichment uranium. In the present work, it is shown that regenerated uranium can be enriched in a five-flow gas-centrifuge cascade with three feed flows (regenerated material, waste, and natural uranium). A combination of two diluents (waste and natural uranium) in such a cascade makes it possible to vary the consumption of uranium raw material and the expenditures of separative work so as to optimize the specific expenditure in obtaining commercial-quality low-enrichment uranium. Computational experiments confirmed the appreciable advantages of the proposed cascade in terms of the consumption of natural uranium over the previously proposed multiflow cascade. A quasi-ideal cascade, used for analysis of the physical laws of mass transfer of the components in such setups and for determining their optimal parameters, is investigated [12, 14, 15]. Development of a Mathematical Model of a Cascade with Three Feed Flows. We shall examine a cascade with three feed flows (Fig. 1). The cascade has two outgoing flows: the product flow P and the waste flow W with concentrations CiP, CiW, i =⎯⎯⎯ 1, m, where i is the number of the component of the mixture being separated, and m is the total number of components. The concentration of the components is expressed as a mass fraction. The feed flows are the flows of the waste F1, natural F2 and regenerated F3 uranium with the concentration of the components CiF1, CiF2, CiF3. The cascade consists of N steps, connected by a symmetric-counterflow method and enumerated from waste to product [12]. The flows F1, F2, and F3 are delivered to the steps with the numbers ƒ1, ƒ2, and ƒ3, respectively, which are chosen so as to minimize mixing with different 235U concentration. 45

In the stationary operating regime of the cascade in the absence of losses of the working matter, the following balance equations for matter and each component separately are valid at the steps: F1 + F2 + F3 – P – W = 0; F

F2

F1Ci 1 + F2 Ci

F3

+ F3Ci

− PCiP − WCiW = 0, i = 1, m.

(1)

The balance equations for the unit connecting the flows in front of an arbitrary step with number s (s ≠ ƒ1, ƒ2, ƒ3) of the cascade operating in the stationary regime have the form [12]: Ls = Ls′ −1 + Ls′′+1; L s C i , s = L s′ − 1C i′, s − 1 + L s′′+ 1C i′′, s + 1, i = 1, m ,

(2)

where Lt, L′t, L″t (t = s – 1, s, s + 1) are the feed, product, and waste flows at the corresponding steps; Ci,t, Ci,t′ , Ci,t″ are the concentration of the ith component in the flow Lt, L′t , L″t . The partial flows of the components Gi,s, G′i,s, Gi,s″ for the sth step and the cutoffs of the partial flows ϕi(s) are determined from the relations Gi , s = Ls Ci , s ; ϕ i ( s) =

Gi′, s Gi , s

Gi′, s = Ls′Ci′, s ;

;

1 − ϕ i ( s) =

Gi′′, s Gi , s

Gi′′, s = Ls′′Ci′′, s ; , i = 1, m.

For a quasi-ideal cascade, Eqs. (2) can be rewritten in the form [12, 14]: Gi′, s −1 +

g +1 1 Gi′, s +1 − i Gi′, s = 0, i = 1, m , gi gi

(3)

where gi = ϕi /(1 – ϕi) are the ratios of the partial flows of the ith component in the total flows L′s, L″s leaving the sth step. The solution of the finite-difference equation (3) can be represented in the form [14]: Gi′(s) = Ai gis + Bi.

(4)

To find the constants Ai and Bi, we use the boundary conditions: Gi′,0 = Gi′, N +1 = 0; Gi′(1) = giWCiW ,

Gi′( N ) = PCiP ; i = 1, m ,

(5)

as well as the balance equations at the entry into the step with numbers ƒ1, ƒ2, ƒ3: Gi′,l −1 +

g +1 1 F Gi′,l +1 + Fl Ci l − i Gi′,l = 0, i = 1, m , l = 1, 3. gi gi

(6)

Substituting the solution of (4) into conditions (5) and (6) and using the equations of balance for the components of the external flows (1), we obtain expressions for calculating the quantities Gi′(s) on all sections of the cascade. Next, relations 46

can be obtained between the concentrations of the components of the separable mixture in the in-, outgoing flows and these flows and the length of the sections of the cascade (the sections between the entry or exit of the external flows):

W = F3

m

⎧⎪

m

T1, j + T2 , j + T3, j

P = F3



;

(7)

CiP =

F3 T1,i + T2 ,i + T3,i ; P 1 − gi− N −1

(8)



∑ ⎨⎪⎩ X j ⎨⎩T1, j + T2 , j (1 − Y j ) + C Fj ⎡⎢⎣1 − g −j f 3

j =1

CiW =

F3 W

1 − g −j N −1

j =1

3

⎪ − f ⎞ ⎤⎫⎫ ⎛ −f − ⎜ g j 1 − g j 3 ⎟Y j ⎥⎬⎬ ⎠ ⎦⎭⎭ ⎝

⎫ ⎪⎧ ⎧ F ⎡ −f − f ⎞ ⎤⎫⎪ ⎛ −f ⎨ Xi ⎨T1,i + T2 ,i (1 − Yi ) + Ci 3 ⎢1 − gi 3 − ⎜⎝ gi 1 − gi 3 ⎟⎠ Yi ⎥ ⎬ ⎬ ⎪⎩ ⎩ ⎣ ⎦⎭⎭

where ⎞ ⎛ −f Xi = ⎜ gi 1 − gi− N −1⎟ ; ⎠ ⎝

Yi =

1 − gi− N −1

− f1

gi

− gi− N −1

(

)⎤⎥⎦ ;

(

)⎤⎥⎦ ,

⎡⎛ − f1 ⎞ − N −1 ⎢⎣⎜⎝ 1 − g j ⎟⎠ 1 − g j ⎡⎛ − f1 ⎞ − N −1 ⎢⎣⎜⎝ 1 − gi ⎟⎠ 1 − gi

(9)

(10)

;

F ⎛ F ⎛ F ⎛ −f ⎞ −f ⎞ −f ⎞ T1,i = ( F1 / F3 )Ci 1 ⎜ 1 − gi 1 ⎟ ; T2 ,i = ( F2 / F3 )Ci 2 ⎜ 1 − gi 2 ⎟ ; T3,i = Ci 3 ⎜ 1 − gi 3 ⎟ (i = 1, m ). ⎠ ⎝ ⎠ ⎝ ⎠ ⎝

The total flow of the cascade being studied can be expressed as N

m

∑ Ls = ∑ ⎡⎣⎢WC Wj ν1, j + PC Pj ν2 , j − F2C Fj ν3, j − F4C Fj ν4 , j ⎤⎦⎥ , 2

s =1

4

(11)

j =1

where f

ν1, j =

g j1 − 1 (ln g j )

2



− ( f 2 − f1 )

ν3, j =

− N − 1+ f 3

f1 ; ln g j

gj

(ln g j )

2

ν2 , j =

−1

gj

− N − 1+ f 2

+ gj

(ln g j )

ν4 , j =

gj

−3

2

− ( f3 − f2 )

f − f1 ; + 2 ln g j

− N − 1+ f1

+ gj

− ( f 3 − f1 )

+ gj

(ln g j )

−2

2

+

− N − 1 + f1 ; ln g j

+

f 3 − f1 . ln g j

We shall examine the particular case of a quasi-ideal cascade – an R-cascade, or a cascade with no mixing occurring in the cascade units of the relative concentration of the chosen pair of reference components with the numbers n and k. The relation of the relative concentration of the reference components in the external flows and the lengths of the corresponding sections of the cascade can be represented in the form [12]: f

gn1 =

Rnk , F

1

Rnk ,W

;

f − f1

gn 2

=

Rnk , F

2

Rnk , F

1

;

f − f2

gn 3

=

Rnk , F

3

Rnk , F

2

;

N − f 3 +1

gn

=

Rnk , P Rnk , F

,

(12)

3

where Rnk,W, Rnk,P, Rnk,F1, Rnk,F2, Rnk,F3 are the relative concentrations of the components with the numbers n and k in the corresponding flows of the cascade. 47

Fig. 2. Relative change in the flow of natural uranium flow in a cascade with three feed flows compared with an ordinary cascade with a different ratio of the naturaland waste-uranium flows; δF = F2/F0·100%, where F0 is the natural uranium flow in the base variant of a cascade.

We note that for molecular-kinetic methods of separation the relations for calculating the quantities gi of all components of the separable mixture can be represented in the form [12]: M k − Mi

gi = q0

M * − Mi

gn−1 = q0

,

i ≠ k , n,

where M* = (Mk + Mn)/2; q0 is the relative separation factor per unit difference of the mass numbers. Simplified expressions for calculating the external parameters of an R-cascade with three flows can be obtained by substituting relations (12) into Eqs. (7)–(11). Analysis of Eqs. (7)–(11) shows that for prescribed M *, q0 and concentrations of the components in the external feed flows of the cascade for the five-flow R-cascade under study we have (2m + 6) variables (CiP2, CiW2, F2 /F3, F1 /F3, ƒ1, ƒ2, ƒ3, N) which appear in 2m independent equations (8) and (10). Six parameters must be given in order to close the system of equations obtained. It is of interest from the practical standpoint to determine the parameters of the cascade with a prescribed concentration of the target component in the external flows. Then the quality of the commercial product obtained is determined uniquely, which makes it possible to compare the effectiveness of different methods of producing equivalent isotopic materials. For particular formulations of the separation problem, aside from the concentration of the target isotope in the external flows of the cascade, other parameters of the cascade can also be given. The remaining characteristics of the separation setup can be calculated on the basis of the criteria adopted for its operating efficiency. For the cascade considered here, this problem can be formulated as follows: 1) CnP, CnW (n is the number of the target component), F2 /F3, F1/F3 are given; 2) ƒ1, ƒ4 are variable parameters; 3) CiP, CiW (i ≠ n), W/F3, P/F3, and all internal parameters of the cascade are to be determined. The problem posed was solved numerically. In addition, the variable quantities were given approximately at each iteration step, after which all parameters of the cascade were calculated. The iteration procedure was stopped when the required accuracy of the discrepancies between the computed and prescribed free parameters was reached. The system of equations for the discrepancies was solved by Newton’s method [16]. Results and Discussion. As an example, we shall examine the enrichment of regenerated uranium with the following component concentrations (%): 232U 2.98·10–7, 233U 5.81·10–7, 234U 1.91·10–2, 235U 0.9, and 236U 0.57. This composition corresponds to VVER-1000 spent fuel. The initial fuel was prepared from the natural raw materials [17]. 48

Fig. 3. Relative change in the total flow for a cascade with three feed flows compared with the corresponding value for an ordinary cascade with a different ratio of the naturaland waste-uranium flows; δ(ΣL) is the ratio of the total flow for a cascade with three feed flows to the total flow in the base variant of a cascade.

The following parameters were given in the calculations: the 235U concentration was 4% in the product (neglecting the additional enrichment for purposes of compensating the effect of 236U) and 0.1% in the waste; the reactivity compensation factor was 0.29 [2]. The 232U concentration in the waste was limited by 2·10–7%. The natural and waste uranium with 235 U content 0.25% were considered as diluents. In the calculation of the parameters of the cascade, the ratio of the waste and natural uranium flows with constant flow of the regenerated material were varied. An R-cascade with no mixing in the units of the cascade with respect to the 235U and 238U concentrations was examined. An ordinary R-cascade for enriching natural uranium with the same 235U concentration obtained in the product and waste was chosen as the base variant for comparison. The objectives of the computational experiments were to determine the consumption of natural uranium and the total flow of the cascade referred to unit product, while varying the ratio between the natural and waste uranium. It should be noted that in the case of separation of multicomponent mixtures it is difficult to introduce into the analysis a quantity that is completely analogous to the concept of separative work used for the separation of a binary mixture of uranium. For this reason, the total flow of the cascade as the quantity that actually determines the number of separative elements in the cascade and, therefore, the specific expenditures on the production of enriched uranium was used as the analog [9]. Analysis of Figs. 2 and 3 shows that the use of the proposed scheme for enriching the regenerated material makes it possible to reduce the consumption of the natural raw material for its dilution. The quite rapid change in the quantities being considered for the values of the parameter F2/F1 ranging from 0 to 2 attests that the specific expenditures on obtaining commercial low-enrichment uranium can have an optimum with the corresponding ratio between the natural and waste uranium. For F2/F1 > 2, the parameters considered here start to move asymptotically toward the values corresponding to a cascade with two feed flows (natural and regenerated uranium). We note also that for almost zero consumption of natural uranium the total flow with respect to the base variant of the cascade increased approximately 2.2-fold. Nonetheless, the proposed scheme of the cascade makes it possible to bring into the production of nuclear fuel both regenerated uranium and the accumulated waste uranium, which is an important advantage of this scheme. The factors indicated above could make it possible to reduce the expenditures on the VVER fuel cycle on account of an appreciable reduction in the demand for natural uranium and the dynamics of the accumulation of waste uranium, in view of its repeated use, as well as a reduction in the volume of uranium to be buried. Conclusion. The scheme proposed for a cascade for enriching regenerated uranium using natural and waste uranium simultaneously as diluents of the isotopes 232,234,236U has noticeable advantages over a cascade with two feed flows for enriching regenerated material. In addition, the cascade makes it possible to obtain product in which the 232U concentration 49

does not exceed the admissible index 2·10–7%. At the same time, the proposed cascade makes it possible to effectively bring waste uranium into the production of low-enrichment uranium. A final conclusion concerning the expediency of using this cascade in practice can be made after economic calculations taking account together both the increase in the total flow in such a cascade as well as the advantage in the consumption of natural uranium and the reduction in the amounts of waste disposal and storage of waste uranium. This work was performed as part of the Russian-Chinese Project on New Approach to Optimizing a Separation Cascade with Large Enrichments at Steps Using the Dependences of the Total Separation Factor of a Step on Its Working Parameters with financial support provided by the Russian Fundation for Basic Research (Project No. 13-08-91156-GFEN_a) and the State Foundation for the Natural Sciences of China (Project No. 11311120046). We wish to express our gratitude to A. A. Orlov for initiating the research on the use of waste uranium for diluting regenerated uranium during its enrichment in a multiflow cascade.

REFERENCES 1. 2.

3. 4. 5. 6. 7. 8. 9. 10.

11.

12. 13. 14. 15.

50

B. V. Nikipelov and V. B. Nikipelov, “Fates of regenerated uranium,” Byull. At. Ener., No. 9, 34–43 (2002). A. Yu. Smirnov, G. A. Sulaberidze, P. N. Alekseev, et al., “Evolution of the isotopic composition of regenerated uranium during multiple recycling in light-water reactors with makeup by natural uranium,” Vopr. At. Nauki Tekhn. Ser. Fiz. Yad. Reakt., No. 4, 70–80 (2010). J. Coleman and T. Knight, “Evaluation of multiple, self-recycling of reprocessed uranium in LWR,” Nucl. Eng. Design, 240, 1028–1032 (2010). A. M. Pavlovichev, V. I. Pavlov, Yu. M. Semchenkov, et al., “Neutron-physical characteristics of a VVER-1000 core with 100% load of fuel consisting of regenerated uranium and plutonium,” At. Énerg., 101, No. 6, 407–413 (2006). V. N. Proselkov, S. S. Aleshin, S. G. Popov, et al., “Analysis of the possibility of using fuel based on regenerated uranium in VVER-1000,” At. Énerg., 95, No. 6, 422–428 (2003). L. V. Matveev and E. M. Tsenter, Uranium-232 and Its Effect on the Radiation Conditions in the Nuclear Fuel Cycle, Energoizdat, Moscow (1985). A. Yu. Smirnov, G. A. Sulaberidze, V. A. Nevinitsa, et al., “Cascade schemes in studying the regularities in the variation of the isotopic composition of repeatedly regenerated uranium,” Yad. Fiz. Inzhinir., 3, No.5, 396–403 (2012). A. A. Vlasov, V. V. Vodolazskikh, V. I. Mazin, et al., RF Patent No. 2236053, “Method of isotopic recovery of regenerated uranium,” Byull. Izobret. Polezn. Modeli, No. 25, 562 (2004). V. A. Palkin, “Purification of regenerated uranium in cascades with 235U enrichment to 5%,” At. Énerg., 115, No. 1, 28–33 (2013). V. N. Prusakov, A. A. Sazykin, L. Yu. Sosnin, et al., “Adjustment of the isotopic composition of regenerated uranium with respect to 232U by the centrifugal method with the introduction of a carrier gas,” At. Énerg., 105, No. 3, 150–156 (2008). G. A. Sulaberidze, V. D. Borisevich, and Tsi-an-sin Se, “On some separation problems of bringing regenerated uranium into the fuel cycle,” in: 9th All-Russ. Sci. Conf. Physicochemical Processes in the Selection of Atoms and Molecules, Zvenigorod (2004), pp. 78–85. G. A. Sulaberidze, V. D. Borisevich, and Tsi-an-sin Se, “Quasi-ideal cascades with an additional flow for separation of multicomponent isotopic mixtures,” Teor. Osn. Khim. Tekhnol., 40, No. 1, 7–16 (2006). V. A. Palkin, “Separation of uranium isotopes in a cascade with intermediate product,” Persp. Mater., No. 8, 11–14 (2010). A. A. Sazykin, “Thermodynamic approach to the separation of isotopes,” in: Isotopes: Properties, Production, Applications, V. Yu. Baranov (ed.), IzdAt, Moscow (2000), pp. 72–108. T. Song, Z. Shi, and V. D. Borisevich, “Comparative study of the model and optimum cascades for multicomponent isotope separation,” Sep. Sci. Technol., 45, 2113–2118 (2010).

16. 17.

N. N. Kalitkin, Numerical Methods, Nauka, Moscow (1978). V. A. Palkin, A. Yu. Smirnov, and G. A. Sulaberidze, “Design-analytical research of a refinement of the recycled uranium from 236U isotope by use of the Q-cascade,” in: Proc. SPLG-2010, St. Petersburg, Russia, June 13–18, 2010, pp. 142–149.

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