DEFINITION OF A NEW UO 2 F 2 DENSITY LAW FOR LOW- MODERATED SOLUTIONS (H/U < 20) AND CONSEQUENCES ON CRITICALITY SAFETY

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1 DEFINITION OF A NEW UO 2 F 2 DENSITY LAW FOR LOW- MODERATED SOLUTIONS ( < 20) AND CONSEQUENCES ON CRITICALITY SAFETY N. Leclaire, S. Evo, I.R.S.N., France Introdction In criticality stdies, the blk density of fissile media being generally nknown, density laws are needed to accrately determine the water content associated with the fissile media. They are applicable only on a determined range. Otside this range, the assessment of concentration vales can be erroneos. Moreover, they do the link between two inpt parameters, the fissile nclide density and the moderation ratio throgh the blk density calclation. 1. UO 2 F 2 «Johnson & Kras» law First of all, it shold be noticed that for ranim concentrations higher than 1157 g/l, UO 2 F 2 mixtres in water look like an inhomogeneos mixtre. Therefore, density measrements are difficlt to realise beyond that concentration. The so-called UO 2 F 2 Johnson & Kras law [1] sed previosly in the standard rote of the CRISTAL criticality safety package [7] was bilt sing measrements for moderation ratios () higher than 18.4 (corresponding to C(U) < 1157 g/l). Below that vale, a polynomial interpolation was done, sing the UO 2 F 2 crystal blk density as interpolation point. However, in spite of conservatism margins on the ranim oxifloride crystal blk density, the Johnson & Kras law was finally not conservative over the whole concentration range and particlarly for moderation ratios prior to It was shown that the so-called Barber law [4] was more conservative with regard to criticality in that concentration range. 2. Presentation of Barber density law The inhomogeneos aspect of UO 2 F 2 mixtres with a high ranim density is de to the presence of hydrates componds sch as UO 2 F H 2 O and UO 2 F 2-2 H 2 O. Many stdies have been devoted to these hydrates. Despite many efforts on these isses, some qestions abot the chemical and physical properties remain. In sch conditions, the knowledge of the ranim density for mixtres with low ratios is qite a challenge. X-ray characterization of hydrates was performed as soon as in s [9]. The strctre (mesh parameters and nmber of nit cells per mesh) is provided allowing deriving the densities of hydrates. More recently, an internal correspondence by E.J. Barber [2] gives the densities of hydrates (UO 2 F 2 + linked water) for 4. A perfect similarity with docment [9] is highlighted. Althogh it is not well established, it seems that the origin of the measrement is the same. These densities are mltiplied, in the same docment [2], by moleclar weight of ranim moleclar weight of UO F 2 2 x H O 2 to obtain the ranim densities. Other experimental ranim densities are reported by the Portsmoth diffsion plant in docment [4]. These densities are indicated as being derived from Barber docment [2]. In docments [4], [5] and [6], the relationships for ranim density as a fnction of ratio for UO 2 F 2 componds are stdied. Althogh E.J. Barber is not the athor of any of these docments, one of the relationships is attribted to E.J. Barber. It will be called the Barber law, which is defined as follows: For < 4, a linear regression of the ranim density against ( ), For 4, an additive volme relationship. It is to be noticed that Portsmoth plant sed UO 2 F 2 and UO 2 F 2-2 H 2 O densities (appearing in bold in Table 1) to bild a linear regression between these two vales (respectively ρ = 4.96 g/cm 3 and 3.68 g/cm 3 ). However, the comparison of the vales reported in docments

2 2 [4] and [2] is pzzling, since they are qite different, except for = 0. At first, it was believed that a safety margin had been applied on vales reported in [2]. In fact, the X-ray crystal hydrate density (forth colmn of Table 1) has been interpreted as being the density of UO 2 F 2 (withot linked molecle of water), which appears to be wrong. Indeed, the X-ray crystal densities [2] are moleclar weight of ranim mltiplied by to obtain the ranim densities. This ratio is eqal to moleclar weight of UO F (sixth colmn of Table 1), which confirms the assmption. As a conseqence, the vales in [4] are not retained. At last, concerning UO 2 F 2 crystal blk density, the density based on X-ray characterization [8], giving the mesh parameters, is also provided in Table 1. This vale is consistent with those provided by E.J. Barber. Table 1. Comparison of ranim concentrations Uranim density (Johnson, & Kras) g/cm 3 Uranim density [4] g/cm 3 X-ray crystal hydrate density [2] and [9] g/cm 3 Uranim density [2] g/cm 3 X ray Ratio hydrate density [2] Uranim density [4] Hydrate formla *, 6.407*, 4.92, 4.93**, 6.44* 4.95, , 1.30, 1.31 UO 2 F 2 3 (α) UO 2 F H 2 O (α) 3 (β) UO 2 F H 2 O (β) * UO 2 F 0.9 (OH) 1.1 -H 2 O UO 2 F H 2 O UO 2 F 2-2 H 2 O (γ) * These vales are not reported in docment [9] ** Calclated vale sing mesh parameters [8] 3. Constrction of a new UO 2 F 2 density law The main considerations that proceed to the constrction of a revised density law mainly deals with the fact that the approach shold be based on a physical approach spported by experimental measrements and that the constrction process shold be conservative with regard to the choice of the experimental points and their mathematical treatment. 3.1 Chemical considerations The bibliographical review done by I.R.S.N. allowed identifying three steps dring the hydration of UO 2 F 2 : as long as 4, UO 2 F 2 is a mixtre of hydrates of UO 2 F 2 - x H 2 O, when the moderation ratio increases, the first drop of liqid appear; the hydrate of UO 2 F 2-2 H 2 O dissolves in a satrated soltion of UO 2 F 2 - H 2 O till the solbility limit of UO 2 F 2 (C(U) = 1157 g/l), over this vale, the soltion is homogeneos. These considerations are based on the Ph-D works condcted by F. Morato [3] indicating the presence of two main stable phases dring hydration of UO 2 F 2 : the β phase UO 2 F H 2 O and the γ phase UO 2 F 2-2 H 2 O. According to the athor, hydrates of higher water content cold be formed bt were more or less qickly transformed into UO 2 F H 2 O throgh UO 2 F 2-2 H 2 O. The crystalline strctre was partially provided. X-ray measrements enabled to identify the natre of mesh and the mesh parameters. However the nmber of chemical nits per mesh in the crystal was lacking, which did not allow determining the blk density of UO 2 F 2-2 H 2 O. 3.2 Constrction of the law A density law based on measred X-ray densities was bilt.

3 3 For a moderation ratio comprised between 0 and 4, different phases have been identified. A volme addition law was considered for componds whose composition is comprised between two phases. Different phases were identified by X-ray measrements, the two more stable being UO 2 F H 2 O and UO 2 F 2-2 H 2 O. For the first one, there are two phases: α and β. The α phase density cold not be determined on the basis of the crystallographic strctre. On the contrary, the β phase density cold be determined sing the mesh parameters. Moreover, another hydrate was identified for = 3.2. This hydrate has not been identified in [3]. Despite the lack of confidence in this vale, it is considered in the constrction of the density law, for safety reasons, as it leads to higher vales than UO 2 F H 2 O hydrate. As a conseqence, the two following phases were retained: UO 2 F H 2 O and UO 2 F 2-2 H 2 O. The retained nmerical vales of UO 2 F 2 hydrates densities are those fond in British [9] and American archives [2] (see Table 1). As a checking, It can be noticed that these measrements are coherent with the densities calclated sing the anion volmes in docment [9], which wold be comprised, for instance, between 4.34 and 5.02 g/cm 3 for UO 2 F 2-2 H 2 O compared to the measred vale of 4.76 g/cm 3. For UO 2 F 2 crystal, the retained vale of ranim density is eqal to 4.93 g/cm 3 since no jstification is given for E.J. Barber UO 2 F 2 density vales (mean vale 4.95 g/cm 3 ). Nevertheless, these vales are consistent. Three experimental points corresponding to three crystal strctres are retained to bild the law: = 0 (UO 2 F 2 crystal), = 3.2 (UO 2 F H 2 O hydrate) and = 4 (UO 2 F 2-2 H 2 O hydrate) (see Fig. 1 and Fig. 2). Different portions of the generic additive volme law are based on the formla given below. They correspond to volme additive laws between different hydrates (see Table 2). The relationship associating the density with the moderation ratio is the following: C(U) = ρ (hyd. 2) + (ρ (hyd.1) - ρ (hyd. 2)) A) in g/cm 3 where A = H U ρ (hyd. 2) ( ρ (hyd. 2) ρ (hyd.1)) 2 n(hyd.2) ρ (hyd. 2) + 2 n(hyd.1) ρ (hyd. 1) ρ (hyd.): ranim density of hydrate H 2 n(hyd.2) U n(hyd.): nmber of molecle of water per molecle of hydrate. Table 2. Uranim densities of hydrates Hydrate 1 Hydrate 2 ρ (hydrate 1) g/cm 3 ρ (hydrate 2) n(hydrate 1) n(hydrate 2) g/cm UO 2 F 2 UO 2 F H 2 O UO 2 F H 2 O UO 2 F 2-2 H 2 O UO 2 F 2-2 H 2 O Satrated soltion For a moderation ratio higher than 18.4, the density law is connected to the former Johnson & Kras law. It shold be noticed that UO 2 F 2 blk density is set eqal to 6.37 g/cm 3. It corresponds to the crystal density X-ray measrement vale. This vale is qite lower than the one retained for the Johnson & Kras density law (6.77 g/cm 3 ). It is de to the fact that the Johnson & Kras UO 2 F 2 blk density vale had been intentionally overestimated in order to make a conservative

4 4 interpolation with the experimental points (at > 20). In fact, it appeared not to be sfficient (see Fig. 2). 5.5 "BARBER" law 5 M easrements (X-ray) Revised law C(U) in g/cm Johnson&Kras Anion pper bond Anion lower bond Figre 1. Comparison between experimental measrement vales and density laws 6 5 " BARBER" law Revised law Johnson&Kras C(U) in g/cm Figre 2. Revised law comparison with «Johnson & Kras» and Barber density laws

5 5 4. Minimm critical vales calclations The introdction of a revised density law and the evalation of conseqences on criticality safety is one of the main concerns of I.R.S.N. To evalate the impact of this choice, criticality standard vales are calclated and presented hereafter. In a first step, minimm critical vales (targeted k eff = 1) were calclated for three geometries and for two ranim enrichments (93.5% and 5%) sing the APOLLO2-S n deterministic code from the CRISTAL V1 package [7] with the revised law and the Johnson & Kras density law. These vales were compared one to another. The dimensions discrepancies are reported in Fig (CP revised /CP J&K )-1 % Mass (kg) % Cylinder % Slab % Mass (kg) - 5% Cylinder - 5% Slab - 5% Figre 3. Critical parameters (CP: dimensions or mass) discrepancies between revised law and «Johnson & Kras» law Another good means to compare density laws is to se critical standard configrations and rn calclations sing atom densities issed either from one density law or from another. In fact, for the same critical dimension (determined with the atom densities of Johnson & Kras density law), the calclations are rern sing atom densities calclated by the revised density law. The k eff discrepancy given by the S n calclations are representative of the impact of the laws in terms of criticality. Some of the reslts are reported in Table 3. Table 3. K eff discrepancies for three geometries corresponding to critical dimensions Revised law k eff at moderation optimm Geometry k eff (Revised) k eff («Johnson & Kras») % Sphere Cylinder Slab 5% 235 U 93.5% 235 U Moderation optimm ( = 12) = Moderation optimm (=40) =

6 6 For low enriched ranim, the mass optimm is obtained at 30 and the geometry optimm at 12, whatever the geometry. It follows that, at the geometry optimm: the revised law leads to k eff higher by 1% from the one determined sing Johnson & Kras density law, for a moderation ratio of 4, the discrepancy is far greater and varies from 2.8 to 4.0% depending on the geometry. For high-enriched ranim, the mass optimm is obtained at > 100 and the geometry optimm at 40, whatever the geometry. It follows that, at geometry optimm: the revised law leads to the same reslts as the Johnson & Kras law at geometry and mass optimm, for a moderation ratio of 4, the discrepancy is far greater and varies from 2.6 to 5.2% depending on the geometry. The former reslts are confirmed by the plot of the material bckling verss the moderation ratio for the revised law and Johnson & Kras law (see Fig. 4a and 4b). For low-enriched ranim, the moderation optimm is reached for comprised between 10 and 16 whereas, for highenriched ranim the moderation optimm is obtained for arond 40 where there is no difference between the different laws. Moreover, the material bckling profiles for revised and Johnson & Kras density laws seem to be very similar for low-enriched ranim. On the contrary, for high-enriched ranim, a secondary maximm appears at = 4 for revised law involving UO 2 F 2-2 H 2 O hydrate. Under specific interaction conditions, the moderation optimm can eventally be shifted to that vale. In that case, the discrepancy between the ranim densities given by both laws is maximized. Given that the revised law is based on a theoretical approach based on measred density of UO 2 F 2-2 H 2 O, an exact assessment of atom densities is done for For that reason and also for a prpose of conservatism in the safety approach, the selection of the revised density law is recommended B 2 m (cm -2 ) Revised law, 5% 235U Johnson & Kras, 5% 235U Figre 4.a. Low-enriched ranim - B 2 m verss moderation ratio for revised and «Johnson & Kras» density laws

7 B 2 m (cm -2 ) Revised law, 93.5% 235U Johnson & Kras, 93.5% 235U Figre 4.b. High-enriched ranim - B 2 m verss moderation ratio for revised and «Johnson & Kras» density laws 5. Calclation of a UO 2 F 2 tanks storage The conseqences of the density law choice have been assessed in a specific criticality stdy. This stdy consisted in determining the criticality-safety conditions of a storage of standard cylinder tanks containing ranim oxifloride. High-enriched ranim oxifloride was contained in cylinder tanks interacting with each other in a large room bonded by 60-cm concrete ceiling and walls. The tanks were spaced by almost 4 meters. The storage was assmed to be potentially flooded. As a conseqence, either a mist with a variable density or water layers with variable thicknesses were considered between the tanks to deal with the potential moderation. For high-enriched ranim oxifloride, the geometry optimm for a single tank is obtained at a moderation ratio close to 40. For that moderation ratio, the revised density law leads to the same k eff reslts as the Johnson & Kras density law. However, in case of moderation between the tanks (abnormal conditions), the optimal moderation ratio (eqal to 40 in normal conditions) of the fissile medim contained in the cylinder tanks is shifted to a lower vale and cold reach potentially a vale of 4. For that vale, the k eff reslt significantly differs whether the ser chooses one law or the other. The revised density law leads to a maximm k eff vale 5% higher. Conclsions The ranim oxifloride density law proposed by I.R.S.N. is based on experimental observations relative to the formation of stable hydrates and on theoretical considerations concerning UO 2 F 2 blk density [3]. The physico-chemical reactions occrring in soltion for low moderation ratios have been stdied in [3], [4], [5] and [9]. To smmarize, the density law is bilt as specified: When 4, UO 2 F 2 is a mixtre of UO 2 F 2 -x H 2 O (0 x 2) componds; an additive volme law between two phases is proposed; When , UO 2 F 2 trns into UO 2 F 2-2 H 2 O, in a satrated soltion of UO 2 F 2 -H 2 O; a volme addition law between the two phases is proposed; When > 18.4, UO 2 F 2 -H 2 O is in a homogeneos soltion.

8 8 On specific configrations with high-enriched ranim, at moderation optimm, it was shown that the se of the Johnson & Kras law cold nder-predict the reactivity p to 5% compared to revised law. Moreover, it is to be noted that, contrary to Johnson & Kras density law, which was interpolated between measrement vales and the UO 2 F 2 crystal blk density vale, revised law is based on a theoretical approach based on the volme addition of different phases and on experimental data (blk density of UO 2 F 2-2 H 2 O hydrate). In addition, it has the advantage not to be too over-predictive and then seems reasonably bonding. Nevertheless, the conclsions strongly depend on the measrement of UO 2 F 2-2 H 2 O blk density vale. A slightly higher density vale wold lead to higher ranim concentrations and potentially to different minimm critical vales. As a conseqence, the new density law answers the needs for safety regarding or present knowledge. However, to thoroghly consolidate this revised law, complementary measrements wold be helpfl, particlarly to confirm the ones issed from British X-ray measrements. References 1. S. Johnson & K.A. Kras, Johnson & Kras Density and refractive index of ranyl floride soltions, Jornal of the American chemical Society, Vol. 75 (p. 4594), E.J. Barber, Eqations for estimation of ranim density as a fnction of ratio, Union Carbide Internal Correspondence, May 1982, K/PS-242, 3. F. Morato, Contribtion à l étde de la rédction de l ranim. De UF 6 à UO 2 par pyrohydrolyse et action de dihydrogène, Thèse de Docter de l Université de Montpellier II, 4. W. Tayloe, Jr, Calclating Atomic Nmber Densities for Uranim Componds, POEF-T report (managed by Martin Marietta Energy systems, INC. for the U.S. Department of Energy), Janary 1993, 5. W.C. Jordan, J.C. Trner, Minimm mass of moderator reqired for criticality of homogeneos low-enriched ranim systems, Note DE , O.R.N.L., 6. M. S. Wyatt, "Characterization of an enriched ranyl floride deposit at the former K-25 enrichment plant sing active netron and gamma interrogation techniqes, University of Tennessee, Knoxville, December 1997, 7. J.M. Gomit, P. Cosino, Cheikh Diop, G. Fernandez de Grado, F. Gantenbein, J.P. Groiller, A. Marc, D. Mijin and H. Tobon, CRISTAL V1: criticality package for brnp credit calclations, Proc. ICNC2003, Tokaï, 2003, 8. W.L. Myers, A literatre review on the chemical and physical properties of ranyl floride (UO 2 F 2 ), LA MS, University of Illinois at Urbana Champaign. 9. E.V. Garner, D.H. Peel and J.V. Shennan, The hydrates of ranyl floride, DEG report 352 (CA).