Dissolution behavior of irradiated mixed oxide fuel with short stroke shearing for fast reactor reprocessing

Abstract

An efficient dissolution process was established for future reprocessing in which mixed-oxide (MOX) fuels with high plutonium contents and dissolver solution with high heavy-metal (HM) concentrations (more than 500 g dm⁻³) will be treated. This dissolution process involves short stroke shearing of fuels (∼10 mm in length). The dissolution kinetics of irradiated MOX fuels and the effects of the Pu content, HM concentration, and fuel form on the dissolution rate were investigated. Irradiated fuel was found to dissolve as 10²–10³ times fast as non-irradiated fuel, but the rate decreased with increasing Pu content. Kinetic analysis based on the fragmentation model, which considers the penetration and diffusion of nitric acid through fuel matrices prior to chemical reaction, indicated that the dissolution rate of irradiated fuel was affected not only by the volume ratio of liquid to solid (L/S ratio) but also by the exposed surface area per unit mole of nitric acid (A/m ratio). The penetration rate of nitric acid is expected to be decreased at high HM concentrations by a reduction in the L/S ratio, but enhanced by shearing the fuel pieces with short strokes and thus enlarging the A/m ratio.

Keywords:

• reprocessing
• dissolution
• mixed oxide fuel
• short-stroke sheared pieces
• Pu content
• heavy-metal concentration
• fuel form
• surface-area model
• fragmentation model

1. Introduction

In the conventional head-end process of a light water reactor (LWR) reprocessing plant, spent fuels are sheared to 20–50 mm in length and dissolved in nitric acid solution in which the heavy-metal (HM, U + Pu) concentration ranges from 100 to 300 g dm⁻³. Future reprocessing plants will treat spent mixed-oxide (MOX) fuels with high Pu content (mass ratio of Pu to heavy metal in fuel), as a larger amount of MOX fuel will be used in the LWR than at present and research on the fast reactor (FR) fuel cycle will progress. The dissolution rate of MOX fuel is depressed upon increasing the Pu content [1]. On the other hand, a modified PUREX process has been suggested for FR fuel reprocessing, which includes a crystallization process for rough uranium recovery prior to the simplified extraction process [2]. For the required uranium recovery to be achieved in the crystallization process, the dissolver solution has to be prepared with a high HM concentration of more than 500 g dm⁻³ [2]. Under such conditions, fuel dissolution will be substantially slower because the highly concentrated condition requires a larger amount of fuel to be treated and a smaller volume of nitric acid. The most effective countermeasure against this problem is the pulverization of fuel pellets to enhance the effective surface area of the fuel in contact with the nitric acid [3]. Such mechanical pretreatment of fuels, however, requires additional equipment in the reprocessing plant, such as a grinder mill. An alternative to pulverization for enhancing the effective surface area of the fuel pieces is to vary the form of the sheared fuel pieces, i.e., to obtain fuel pieces sheared with short strokes. In a previous study on shearing system design for FR reprocessing, it had been confirmed that highly pulverized fuel could be achieved easily by shearing the simulated fuel pins with a length of 10 mm [4]. However, the impacts of the Pu content and concentration on the dissolution rate of irradiated MOX fuel have not yet been clarified quantitatively.

The objective of this study is to show the applicability of fuel pieces sheared with short strokes to the dissolution process under highly concentrated conditions. Because the dissolution kinetics of irradiated MOX fuels is very complicated, there is still a lack of knowledge of the reaction mechanism and the rate-determining factors and their formulation. We especially focus on rate-determining factors such as the Pu contents, HM concentration, and fuel form, from the point of view of their effects on the chemical reaction or mass transfer. Hence, at the beginning of this paper, we will summarize the current knowledge on the dissolution kinetics models developed for irradiated MOX fuel. The results of dissolution tests using irradiated MOX fuels under highly concentrated conditions are presented, and the kinetics of U, Pu, and fission-product (FP) nuclides are discussed. Second, the effect of the Pu content on the dissolution rate is investigated, because the proportion of refractory PuO₂ is expected to have a huge impact. Then, the dominant factors considered to affect the dissolution rate under highly concentrated conditions are discussed, taking into account the penetration of nitric acid through the fuel matrices and the chemical reaction at the fuel surface.

2. Two different dissolution models

The dissolution reaction of MOX fuel in nitric acid is expected to consist of a chemical reaction between UO₂ or PuO₂ and nitric acid on the solid surface, and the mass transport phenomena of reactants such as nitric acid or products such as UO₂ ²⁺ and Pu⁴⁺. The dissolution kinetics have been developed using two different approaches. Each model has a particular interpretation of the access path of nitric acid to the fuel and of the reacting zone in the fuel matrix. The first model considers the homogeneous chemical reaction only on the solid surface (so-called “surface-area model”), and the other considers the penetration and diffusion of nitric acid to the fuel surface and through the fuel matrices (so-called “fragmentation model”). In this section, we summarize these two different models, but it should be noted that we never compare their technical superiorities. These models should be applied in accordance with the evaluations of the effects of rate-affecting factors. For example, since the Pu content in MOX fuel is expected to affect only the chemical reaction on the solid surface, we can use the surface-area model. When the effects of HM concentration and fuel form are discussed, we can simply evaluate these factors by using the fragmentation model, as described later.

2.1. Surface-area model

If we assume that the chemical reaction occurs homogeneously on the surface of the sheared fuel pieces, the dissolved amount at time t can be described by:

where W ₀, φ , r(t), S ₀, and F(φ) are the initial amount of fuel (mol), the dissolved ratio (–), the instantaneous dissolution rate (mol cm⁻² min⁻¹), the initial geometrical surface area of the cross section of sheared fuel pieces (cm²), and the transitional function of the surface area (–), respectively. Nemoto et al. [5] reported that the instantaneous dissolution rate and transitional function of the surface area of irradiated MOX fuel (sheared with 30 mm in length) were described as:

where k, [H⁺], y, R, T, and E are the rate constant (arbitrary unit), the proton concentration (mol dm⁻³), the reaction order related to [H⁺], gas constant (J mol⁻¹ K⁻¹), the absolute temperature (K), and the apparent activation energy (J mol⁻¹), respectively. Under conditions where the Pu content is equal to 30%, these parameters were determined experimentaly as k = 9600 g cm⁻² min⁻¹ (mol dm⁻³)^−1.74, y = 1.74, and E = 11 kcal mol⁻¹ [5]. Due to Equation (3), the surface area contacted with nitric acid is expected to keep almost constant until when the φ reaches to approximately 60% and then to drop rapidly. This trend is thought to be due to the low powderization ratio of the fuel through the shearing process (same procedure as used in this study, see section 3.1.).

2.2. Fragmentation model

Hodgson [6] proposed the fuel dissolution model via the fragmentation of solid material by the penetration and diffusion of nitric acid through fuel matrices. In this model, the dissolution process follows the exposure of unexposed fuel surfaces by nitric acid and the dissolution of the exposed part of the fuel. The dissolution rate of the fuel is assumed to be proportional to the mass of fuel exposed to nitric acid.

W _d, W _e, and λ are the weight of fuel dissolved in the solution, the weight of fuel exposed to nitric acid, and a formula constant that corresponds to the reciprocal of the dissolution rate constant, respectively. The penetration rate of nitric acid into the fuel matrices is described as a function of the dissolution rate of fuel and the mass ratio of the unexposed to exposed fuel:

W _u is the weight of undissolved fuel, and f is a non-dimensional number representing the ease of penetration and diffusion of nitric acid into the fuel matrices. The mass balance through the dissolution process, that is, the summation of W _d, W _e, and W _u is constant, leading to the following equation:

As seen from Equations (4)–(6), the dissolution rate of fuel can be described by two parameters: 1/λ, which represents the dissolution rate of the exposed part of the fuel, and the f value, which represents the penetration and diffusion of nitric acid through the dissolver solution and fuel matrices. The value of 1/λ is expected to vary with acidity, temperature, Pu content, and other rate-affecting parameters. Sano et al. [3] surveyed the dissolution behaviors of irradiated MOX fuels under several different dissolution conditions, and they noted that 1/λ can be expressed as follows:

where B and n are the average burn-up of fuel and the Pu content, respectively. On the other hand, the f value is expected to depend on the form of the dissolver cell, the agitation, the volume ratio of solution to fuel pieces, the effective surface area, and other physical configurations. In a strict sense, due to the evolution of cracks and pores, the f value is considered as a variable through the dissolution progress. However, the macroscopic shape of sheared fuel pieces is expected not to change drastically. In order to simplify the model description in this study, we considered the f value as a constant value which can vary only with experimental configuration.

3. Experimental

3.1. Materials

The MOX fuels used in this study had been irradiated in the Mk-I, Mk-II, and Mk-III cores of the experimental fast reactor “JOYO” of the Japan Atomic Energy Agency. In this study, in order to prepare the surface geometry of the sheared pieces as uniform as possible, a single fuel pin was sheared using a shear blade. The cross section of fuel was observed to have a smooth surface, being kept roughly circular in shape. The ratio of powdered fuel after the shearing were estimated to be less than 10 wt%, and only sheared pieces of fuel were used for the dissolution tests. It should be noted that, in commercial reprocessing plants, fuel assemblies are sheared, and their surface of cross sections are expected to be coarser than that obtained in this study. Furthermore, the powdered ratio would be higher than that from single-pin shearing. In such conditions, the dissolution rate would be larger in commercial plants than those obtained in this study.

Fuel pins from the Mk-II and Mk-III cores were sheared with 10-mm length. The Pu content after irradiation, assembly average burn-up, and cooling time of these fuels are 27.4%, 54,700 MWD/t, and 8000 days, respectively, for the Mk-II fuel, and 22.4%, 53,300 MWD/t, and 1000 days, respectively, for the Mk-III fuel. A fuel pin from the Mk-I core was sheared with 20-mm length and used for the dissolution test, which aimed at obtaining the data on dissolution rate of fuel pieces with intermediate length between 10 mm and 30 mm. The Pu content after irradiation, assembly average burn-up, and cooling time of the Mk-I fuel are 15.8%, 40,100 MWD/t, and 8400 days, respectively.

3.2. Dissolution test

Dissolution tests were conducted to clarify the impacts of the Pu content in fuel, the HM concentration in the product solution (described as “[HM]_p”, 260–510 g dm⁻³), and the fuel form (length of fuel) on the dissolution rate. The experimental conditions in this study are detailed in Table 1. In the scheme of tests A–D, the effect of air bubbling on the dissolution rate was also investigated, but no clear tendency was observed.

Table 1. Experimental conditions in this study.

Test no.	Fuel type	Pu content (%)	[HM] p (g/dm^3)	Mass of fuel (and HM) (g)	Initial HNO3 volume (dm^3)	Initial [HNO3] (mol dm^−3)
10-mm length
A^a	Mk-III	22.4	390	148 (123)	0.325	8
B^a	Mk-III	22.4	260	87.8 (73)	0.270	8
C	Mk-III	22.4	400	147 (130)	0.325	8
D	Mk-III	22.4	∼280	88.6 (83)	0.270	8
E	Mk-II, III	24.9	∼510	268 (220)	0.360	11
F	Mk-II, III	24.9	280	83.0 (68)	0.240	11
20-mm length
G	Mk-I	15.8	∼270	152 (121)	0.500	8
Note: ^aWithout air bubbling.

Table 2. Experimental data on the composition of sample and product dissolver solutions.

Time (min)	Vol. (dm^3)	Heavy-metals and FP metals (g/dm^3)								Gamma activities (TBq/dm^3)				H^+
		U	Pu	Zr	Mo	Tc	Ru	Rh	Pd	^106Ru	^125Sb	^137Cs	^144Ce	(mol/dm^3)
Test A
40	0.01	44	12	–	–	–	–	–	–	0.033	0.027	0.54	0.35	7.3
70	0.01	230	67	–	–	–	–	–	–	0.23	0.12	1.3	2.2	4.4
100	0.01	300	84	–	–	–	–	–	–	0.33	0.14	2.3	2.6	3.5
150	0.01	310	88	–	–	–	–	–	–	0.34	0.14	2.3	2.8	3.4
P	0.27	300	90	1.7	0.85	0.085	0.13	0.13	0.88	0.37	0.11	1.1	2.7	3.5
Test B
P	0.26	200	60	1.1	0.61	0.13	0.096	0.078	0.56	0.25	0.098	1.2	1.9	4.8
Test C
40	0.01	40	9.2	–	–	–	–	–	–	0.062	0.036	0.55	0.72	7.2
70	0.01	230	75	–	–	–	–	–	–	0.43	0.13	2.0	4.8	4.2
100	0.01	300	95	–	–	–	–	–	–	0.59	0.17	1.3	6.7	3.4
180	0.01	320	100	–	–	–	–	–	–	0.71	0.17	1.3	7.4	3.9
P	0.26	300	100	1.6	–	0.095	0.32	0.19	0.83	0.88	0.17	1.6	7.3	3.8
Test D
P^a	0.43	140	40	0.51	0.44	0.070	0.14	0.077	0.28	0.41	0.078	1.1	3.2	–
Test E
40	0.01	80	26	–	–	–	–	–	–	0.027	0.023	1.0	0.21	9.4
70	0.01	260	90	–	–	–	–	–	–	0.11	0.070	2.5	0.83	6.1
100	0.01	330	120	–	–	–	–	–	–	0.13	0.088	2.8	0.98	5.1
150	0.01	370	140	–	–	–	–	–	–	0.17	0.084	3.1	1.0	4.1
P^b	0.31	350	130	2.7	0.71	–	0.24	0.21	1.6	0.18	0.076	1.0	0.97	2.7
Test F
P	0.23	190	70	1.1	0.69	–	0.15	0.10	0.63	0.12	0.045	1.1	0.54	6.9
Note: P, product solution; –, not measured. ^aVariable amounts of HNO3 was added to the product solution improperly. ^bApproximately 0.2 dm^3 of HNO3 was added to the as-received product solution in order to avoid the crystallization through filtration.

Table 3. The composition of insoluble residues.

Test No.	Mass (g)	Heavy-metals and FP metals (wt%)								Gamma activities (GBq/g)
		U	Pu	Zr	Mo	Tc	Ru	Rh	Pd	^106Ru	^125Sb	^137Cs	^144Ce
A	0.78	–	1.8	<1.6	23	–	27	8.0	9.4	400	4.3	0.38	<0.19
B	0.65	–	2.2	<5.4	19	–	20	6.3	7.6	290	2.8	<0.66	<0.66
E	2.2	4.0	4.3	<1.8	16	4.6	19	5.5	6.4	80	2.5	0.64	<0.21
F	0.77	2.6	2.8	–	–	–	–	–	–	83	1.8	0.35	<0.19
Note: –, not measured.

Figure 1 shows the procedure of sample separations conducted in dissolution tests. A 1-dm³ glass flask covered with heater was used in this study, as shown in Figure 2. A specified amount of fuel (sheared with a length of 10 mm) and nitric acid were poured into the flask at room temperature (25–30°C), and the mixture was heated up to and maintained at 95 ± 5°C. While the dissolution proceeded, samples of the dissolver solution in the flask were removed periodically in the tests A, C, and E, and the concentrations of U, Pu, and FP nuclides in the solution were measured using absorption spectroscopy for U and Pu and gamma spectrometry for FP nuclides. Meanwhile, the reaction progression was also monitored by counting the ⁸⁵Kr released from the fuel matrices using a NaI scintillator placed on the off-gas system of the test apparatus. We assumed the reaction had finished when the count number of released ⁸⁵Kr dropped to and stayed at the level of the background count. In each test, the dissolution reaction finished within 3 h.

Figure 1. Schematic flow of sample separations (underlined samples were analyzed to determine their chemical composition).

Figure 2. Schematic diagram of apparatus for dissolution tests.

3.3. Measurement of composition of the dissolver solutions and the insoluble residues

After the test had finished and the dissolver solution had been cooled to room temperature, and solid components dispersed in the dissolver solution, such as hulls, non-dissolved fuels, and other components consisting of FPs, were collected by suction filtration on a glass-fiber filter with 1-μm pore diameter. Concentrations of U, Pu, and FPs in the product solution were measured using same method as the sample measurement for U, Pu, and FP nuclides, and using Inductively Coupled Plasma-Atomic Emission Spectroscopy (ICP-AES) for FP elements. The collected solid components were immersed in 0.25 dm³ of 3 M nitric acid at 95°C for up to 2 h to recover the non-dissolved fuels. After this additional dissolution treatment, the treated solution was clarified by using the same procedure as described above. Concentrations of U, Pu, and FPs in the post-treatment solution and those in the insoluble residue were measured using same method as the product solution measurement for U and FPs, and alpha spectrometry for Pu. Prior to the measurement, the insoluble residue was treated by melting at 750°C with sodium peroxide and sodium carbonate, and the mixture was dissolved into 3 M nitric acid solution.

4. Results and discussion

4.1. Comparison among dissolution behaviors of U, Pu, and FP nuclides

Tables 2 and 3 list the elemental compositions of dissolver solutions (samples and product solutions) and insoluble residue through dissolution tests A–F. According to the measured concentrations in post-treatment solutions, up to 1% of initial mass of heavy metal and negligibly small amount of FPs were estimated to be dissolved by the additional dissolution treatment. The dissolution ratios of each nuclide were calculated from the measured concentration by using the following formula:

Figure 3 shows the typical temporal changes on the dissolution ratios of U, Pu, and FP nuclides (⁸⁵Kr, ¹⁰⁶Ru, ¹²⁵Sb, ¹³⁷Cs, and ¹⁴⁴Ce) in dissolution test E ([HM]_p ∼ 510 g dm⁻³). Uranium and plutonium showed similar dissolution rates to each other. The results in the other tests had similar tendencies and are not shown here. Thus, U and Pu seemed to dissolve congruently, and no significant preferable dissolution of UO₂ occurred.

Figure 3. Release of ⁸⁵Kr and dissolution behavior of U, Pu, and FP nuclides in test E.

The fission products showed specific behavior as shown in Figure 3. The release of the noble gas ⁸⁵Kr was similar to the behavior found for the dissolution of U or Pu, indicating that ⁸⁵Kr was distributed homogeneously in the fuel matrices [7]. Past research showed that the ratio of released ⁸⁵Kr can adequately represent the dissolution ratio calculated from the dissolved mass of fuel [5]. Thus, the dissolution ratio can be described as the ratio of released ⁸⁵Kr. The dissolution of lanthanide FP nuclides, represented as ¹⁴⁴Ce in Figure 3, also showed similar behavior to that of U and Pu. ¹³⁷Cs showed a relatively high dissolution ratio in the early phase of dissolution, which meant that dissolution was suppressed in the late phase. The reason for this depression of Cs is still unclear, but it could be explained by the precipitation of dicesium tetravalent plutonium hexanitrate, PuCs₂(NO₃)₆, in the sample solution upon cooling for measurement [8]. However, since the molecular ratio of Cs to Pu in the fuel is estimated to be less than 4% from the calculation with ORIGEN, the impact of the precipitate on the dissolution rate of fuel is expected to be negligibly small. The dissolution ratio of ¹²⁵Sb was 85% at the end of the reaction, while 15% was detected from the insoluble residue. The dissolution ratio of ¹⁰⁶Ru was extremely low compared to those of the other nuclides. Most Ru is expected to be transferred to the insoluble residue, forming metallic alloys with other noble metals such as Mo, Tc, Pd, and Rh [7,9].

Therefore, the FP nuclides noted here are expected to have little impact on the dissolution of U and Pu because these fuel components seem to behave independently. Hence, we describe only the dissolution of U and Pu [10] or ⁸⁵Kr, which describe the dissolution of fuel matrices well. The impacts of the Pu content, HM concentration, and fuel form on the dissolution rate are discussed in the following sections.

4.2. Impact of Pu content on dissolution rate of irradiated MOX fuels

4.2.1. Pu content effect in surface-area model

It has been reported that the Pu content has an enormous impact on the fuel dissolution rate. Uriate et al. [1] noted that non-irradiated MOX pellets become more refractory as their Pu content increases. This relationship is expressed by the following equation:

The symbols n, d _MOX, , , and r _MOX indicate the Pu content (–), density of MOX fuel (g cm⁻³), and the instantaneous dissolution rates (mg cm⁻² min⁻¹) of non-irradiated UO₂, PuO₂, and MOX fuel pellets, respectively. The impact of the Pu content on the dissolution rate, however, has not yet been clarified quantitatively, especially for irradiated MOX fuel. From previous studies, it is expected that irradiation might enhance the dissolution rate of fuels. Ikeda et al. [11] showed that the dissolution rate of UO₂ powder irradiated in an LWR reactor up to 54 GWD/t is 48 times faster than that of non-irradiated powder. Schiefelbein and Lerch [12] reported that UO₂-2 wt% PuO₂ fuels irradiated in a thermal reactor up to 9630 MWD/MTM showed an improvement in the dissolution ratio after 6 h of exposure to boiling 12 M HNO₃ compared to non-irradiated fuels. In this section, the relationship between the dissolution rate of irradiated MOX fuel and its Pu content is investigated using the dissolution test results obtained in this work and previous studies. The results for fuels with intermediate burn-up from 40,100 to 63,700 MWD/t are specifically referenced to eliminate the effect of the irradiation level. The experimental conditions in the previous works [3,13] are shown in Table 4.

Table 4. Experimental conditions in previous studies with sheared pieces (30-mm in length).

Test no.	Fuel type	Pu content (%)	Final [HM] (g/dm^3)	Mass of fuel (and HM) (g)	Initial HNO3 volume (dm^3)	Initial [HNO3] (mol/dm^3)	Reference
Prev-1	Mk-II	26.5	560	141 (116)	0.205	10	[3]
Prev-2	Mk-II	26.5	280	145 (118)	0.410	10	[3]
Prev-3	Mk-I	17.6	150	576 (480)	3.7	3.3	[13]

If the Pu content changes, each value of k, y and E mentioned in Equation (2) may be different. Because there are not sufficient data enough to determine those parameters systematically, we solely introduced an adjustment parameter, c, which can be affected by Pu content, on Equation (2).

When Pu content is equal to 30%, c is unity. If the dissolution rate is assumed to decrease exponentially with increasing the Pu content, c can be described by:

where a and n are an empirical parameter and the Pu content, respectively. The value of c in each experiment with varying Pu content was determined by minimizing the squared difference between the dissolution ratios calculated using Equations (1), (3), and (10) and experimental ones for each of the test condition. The appropriate c values obtained in each test in this study are detailed in Table 5. The value of S ₀ in Equation (1) was calculated considering the cross section of sheared pieces to be circular shape and also shown in Table 5. As shown in Figure 4, the calculated values of the dissolution ratio using the appropriate c value agree well with the experimental values.

Figure 4. Comparison of dissolution ratios calculated by surface-area model with the experimental values (released ratios of ⁸⁵Kr).

Table 5. Calculated instantaneous dissolution rates with different Pu contents by surface-area model.

Dissolution test	S 0 (cm^2)	c value (–)	r at [H^+] = 8 M and T = 95°C (×10^−3 mol · cm^−2 · min^−1)
This study
Test A	28.9	5.5 ± 1.6	2.1 ± 0.6
Test B	18.3	5.6 ± 1.2	2.1 ± 0.4
Test C	28.9	5.7 ± 0.9	2.1 ± 0.4
Test D	18.3	4.5 ± 0.9	1.7 ± 0.4
Test E	58.5	2.0 ± 0.2	0.74 ± 0.08
Test F	18.9	2.7 ± 0.4	1.0 ± 0.2
Previous studies
Prev-1	14.0	0.90 ± 0.26	0.33 ± 0.10
Prev-2	14.0	1.2 ± 0.3	0.43 ± 0.12
Prev-3	39.4	9.0 ± 1.6	3.3 ± 0.6

In this section, we directly compared the c values obtained from the dissolution tests with the different HM concentrations and the different fuel forms. This evaluation procedure is thought to be reasonable due to following two reasons. First, though a minor depression of the c value was observed at the HM concentration of higher than 500 g dm⁻³, e.g., comparison between test E (c = 2.0 ± 0.2) and test F (c = 2.7 ± 0.4), this difference is expected to be much trivial than the effect of Pu content. Second, the length of fuel is expected to have little impact on the dissolution rate described with surface-area model because we assumed the homogeneous surface reaction being based on the observation of the aspect of cross section (see section 3.1.). Therefore, we evaluated the effect of Pu content on the c values, neglecting the effects of the HM concentration and the fuel form.

As shown in Figure 5, the c values tend to decrease with increasing Pu content at the range from 0.18 to 0.30. The “a” in Equation (11) was determined to be approximately 19 by minimizing the squared difference between the c values listed in Table 5 and the values calculated from Equation (11). The calculated values were described as a solid line in Figure 5. The instantaneous dissolution rate at unit surface area is expressed as follows:

where n is the Pu content (–) ranging from 0.18 to 0.30.

Figure 5. Pu content dependence of the adjustment parameter, c, in the surface-area model.

4.2.2. Promotion effect by irradiation

For comparison with non-irradiated fuels from previous studies, the dissolution rates under standard dissolution conditions, i.e., initial HNO₃ concentration of 8 M and temperature of 95°C, with different Pu contents were estimated. As for the irradiated MOX fuel, the instantaneous dissolution rate (mol cm⁻² min⁻¹) under standard dissolution conditions was calculated for each Pu content by applying Equation (10) with the c values listed in Table 5, [H⁺] = 8 M, and T = 368.15 K. Meanwhile, the dissolution rate of non-irradiated fuel had been reported by many workers under several temperature conditions [1,14–16]. For calculation of the rate at 95°C, the activation energy that had been reported for UO₂ dissolution and estimated to be approximately 60 kJ/mol [14] was used accordingly. The instantaneous dissolution rates calculated for the irradiated fuels are shown in Figure 6 compared with those for the non-irradiated fuels. The dissolution rate equation for the non-irradiated fuels was also calculated using Equation (9) and shown in Figure 6. It is clear that the irradiated MOX fuels dissolved 10²–10³ times faster than the non-irradiated ones with the same Pu content. The possible reasons for the enhanced dissolution of irradiated fuels are expected to be, for example, the catalytic effect of noble metal fission products such as Pd on the oxidizing dissolution of UO₂, the evolution of the effective surface area of the fuels by irradiation, or a decrease in the solid density of the fuels upon irradiation. As for the catalytic effect of noble metals, Trummer et al. [17] reported that UO₂ powders containing 3 wt% of Pd dissolved five to six times faster than non-Pd powders in H₂O₂ + HCO₃ solution. The same effect of noble metals was also reported by Ikeda et al. [18]. However, from the reports in the previous papers mentioned above, the effects of noble metals seem to be too weak to explain the 10²–10³ order of enhancement obtained in this study. The effect of density deterioration is also expected to be small. Therefore, the most probable explanation is the evolution of the surface geometry upon irradiation. Nevertheless, it was clarified that an increased Pu content decreases the dissolution rate of irradiated MOX fuels, as reported in previous studies using non-irradiated fuels.

Figure 6. Comparison of instantaneous dissolution rate calculated at [H⁺] = 8 mol dm⁻³ and T = 95°C between non-irradiated and irradiated MOX fuel.

4.3. Impact of heavy metal concentration in product solution

4.3.1. Dissolution rate at high HM concentration

It is generally said that the amount of solute in a dissolver solution has two opposing impacts on the dissolution rate. The promoting effect appears when a solute species, particularly UO₂ ^2 +, shows catalytic behavior toward its dissolution reaction. The catalytic interaction of the UO₂ ²⁺ ion was indicated in some previous works [1,14], but the reaction mechanism is not clear. Ikeda et al. [15] claimed that the uranyl ion itself does not have a catalytic effect, but that the nitric acid ion accompanied by a uranyl ion acts as a reactant in the dissolution reaction. On the contrary, the inhibiting effect appears when the amount of solute in the dissolver solution approaches the solubility of these species and the chemical reaction is suppressed. By comparing the results of tests A–D, in which the HM concentration varied from 260 to 400 g dm⁻³, the dissolution rates were comparable to one another within a range from 1.7 ± 0.4 to 2.1 ± 0.6 mmol cm⁻² min⁻¹ (see Table 5), and no significant effect of HM concentration was observed. On the other hand, on comparing tests E and F, the instantaneous dissolution rate obtained at 510 g dm⁻³ (0.74 ± 0.08 mmol cm⁻² min⁻¹) was found to be slightly lower than that at 260 g dm⁻³ (1.0 ± 0.2 mmol cm⁻² min⁻¹). This result seems to show that the inhibiting effect is stronger than the promoting effect. The uranium concentration of the dissolver solution tested in this study, however, is up to 510 g dm⁻³, which is far less than the solubility of uranyl nitrate in nitric acid [19]. Under such conditions, the inhibiting effect on the chemical reaction is evaluated to be negligibly small. Therefore, we should take physical transport processes such as the diffusion and penetration of nitric acid into the fuel matrices into account. These transport processes are macroscopic, not microscopic ones such as the transport through the diffusion layer near the surface. Another kinetic approach for the dissolution behavior of irradiated MOX fuels is needed for the application of these macroscopic transport processes such as the diffusion and penetration of nitric acid.

4.3.2. Evaluation by fragmentation model

In this study, the appropriate f values in the fragmentation model were determined by using the minimized squared difference between the dissolution ratios calculated using Equations (4)–(6) and experimental ones for each of the test condition. Typical examples of calculation results are shown in Figure 7, and the appropriate f values calculated in tests A–F (10-mm length) are shown in Table 6. The volume ratios of nitric acid () to the MOX fuel (V _MOX) are also listed as “L/S ratio” in Table 6. The values of are referred from the initial volume of nitric acid (dm³) listed in Table 1. The values of V _MOX are calculated dividing the mass of MOX fuel (g) in Table 1 by the solid density of MOX fuel, which is assumed as approximately 10⁴ g dm⁻³ [1]. By comparing the results of tests A–D, no significant change of the f value was observed, even though the L/S ratio was decreased from 31.7 to 22.6 as the HM concentration in the product solution increased from 260 to 400 g dm⁻³. By comparing the results of tests E and F, we see that the f value decreased significantly from 0.20 to 0.11 as the HM concentration in the product solution increased from 260 to 510 g dm⁻³, where the L/S ratio was decreased from 30.0 to 13.9. The relationship between calculated f value and the L/S ratio with tests A–F (10-mm length) is summarized in Figure 8. The L/S ratio seems to have negligibly small impact on the f value with the HM concentrations less than 400 g dm⁻³, where the L/S ratio is larger than ∼20. However, at the highly concentrated condition, where the HM concentration is more than 500 g dm⁻³, the decrease of L/S ratio is expected to have a great impact on the dissolution rate of the irradiated MOX fuel, making the penetration and diffusion of nitric acid into the fuel matrices less efficient significantly.

Figure 7. Comparison of dissolution ratios calculated by the fragmentation model with the experimental values (released ratios of ⁸⁵Kr).

Figure 8. Dependence of the f value on the L/S ratio.

Table 6. Calculated f values for different fuel forms and heavy-metal concentrations by fragmentation model.

Dissolution test	[HM] p (g/dm^3)	L/S ratio, V HNO3/V MOX (–)	A/m ratio, N MOX, S /N HNO3, R (–)	f value (–)
10-mm length (this study)
Test A	390	22.6	4.3 × 10^−8	0.22 ± 0.05
Test B	260	31.7	4.6 × 10^−8	0.26 ± 0.03
Test C	400	22.8	4.2 × 10^−8	0.24 ± 0.04
Test D	∼280	31.4	4.0 × 10^−8	0.25 ± 0.04
Test E	∼510	13.9	4.2 × 10^−8	0.11 ± 0.02
Test F	260	30.0	3.9 × 10^−8	0.20 ± 0.02
20-mm length (this study)
Test G	∼270	33.8	2.6 × 10^−8	0.06 ± 0.02
30-mm length (previous studies)
Prev-1	560	15.0	1.9 × 10^−8	0.032 ± 0.010
Prev-2	280	29.2	2.0 × 10^−8	0.046 ± 0.006

4.4. Effect of short stroke shearing on dissolution performance

The form of the fuel pieces can affect the penetration and diffusion of nitric acid into the fuel rather more than the chemical reaction via the surface of the sheared fuel. Since the f value is also expected to be affected by the physical configurations of the dissolution test apparatus such as the shape of the dissolver cell and the agitation conditions, we used only data obtained with similar experimental apparatus to that used in this work, i.e., small-scale apparatus and agitation by air bubbling. The f values obtained for the dissolution tests using sheared pieces of 20-mm length (test G) and pieces of 30-mm length (Prev-1, and Prev-2) are shown in Table 6 and Figure 8, being compared with those of 10-mm length. It is noted that the f values of 10-mm length are larger by 3–5 times than those of 20-mm length and 30-mm length with similar L/S ratio. Even at the HM concentration higher than 500 g dm⁻³ where the L/S ratio are 14–15, the f value of 10-mm length, 0.11 ± 0.02, is larger than that of 30-mm length, 0.032 ± 0.010. This improvement in f value is expected to be due to the enlargement of the effective surface area exposed to solution by short stroke shearing. Since the penetration and diffusion of nitric acid are initiated with the path through the external surface of the sheared pieces exposed to the solution, the f value can be affected not only by the L/S ratio but also by the ratio of the number of moles of (U, Pu)O₂ on the effective surface area of the sheared pieces exposed to the solution (N _{MOX, S} ) to the number of moles of nitric acid which have reacted with MOX fuel (N _{HNO3, R} ). The value of N _{MOX, S} was calculated from following equation:

where d _MOX, M _W, and L are the density (∼10 g cm⁻³), molecular weight (∼270 g mol⁻¹), and lattice constant of (U, Pu)O₂ (cm), respectively. In this study, the value of L was assumed to be approximately 5.5 × 10⁻⁸ cm as reported by Sari et al. [20]. The value of N _{HNO3, R} was estimated from the number of moles of U and Pu dissolved, assuming following chemical reaction:

The mole ratio of N _{MOX, S} to N _{HNO3, R} was calculated and shown in Table 6 as “A/m ratio”. It is clearly shown that the shorter the length of fuel becomes from 30-mm to 10-mm, the larger the A/m ratio becomes from 2 × 10⁻⁸ to 4 × 10⁻⁸ even at low L/S ratio (“test E” and “Prev-1” in Table 6). This improvement in the A/m ratio is expected to cause the enlargement of f value.

The relationship among the f value, the L/S ratio, and the A/m ratio can be expressed by the following formula:

The symbols “α”, “β”, and “γ” are empirical numbers which are expected to be dependent on the physical configurations of the dissolution test apparatus. Because the decrease of L/S ratio is found to affect the f value only at relatively low L/S ratio, the value of “β” is expected to be less than unity. On the other hand, the value of “γ” expected to be larger than unity on the basis of the relationship between A/m ratio and f values listed in Table 6. In this study, those parameters were determined by fitting the Equation (14) to the f value listed in Table 6. As shown in Figure 9, the empirical numbers “α”, “β” and “γ” were determined to be 3 × 10²⁰, 0.7, and 3, respectively. These numbers will vary with experimental configuration, as described above. Nevertheless, there are not enough data for a systematic analysis of the effects of these factors.

Figure 9. Calculated f values modeled as a function of the L/S ratio and the A/m ratio.

As a consequence, under highly concentrated conditions where the HM concentration reaches more than 500 g dm⁻³, as the L/S ratio decreases, the penetration and diffusion of nitric acid through fuel matrices are depressed significantly. However, by shearing the fuel pins with short strokes, i.e., 10-mm length, dissolution can be enhanced through the enlargement of the effective surface areas of the fuels. The relationship between the penetration and diffusion rates of nitric acid, the L/S ratio, and the effective surface area is expressed by Equation (14), in which the empirical numbers are determined for the test apparatus configuration.

5. Conclusion

The dissolution kinetics of spent MOX fuels were investigated through dissolution tests using fuel pieces irradiated in the “JOYO” fast reactor. The effects of the Pu content, HM concentration, and fuel form on the dissolution rate were discussed. The dissolution rate of irradiated fuel was shown to be 10²–10³ times higher than that of non-irradiated fuel, but the rate decreased with Pu content, as expected from the results of previous reports using non-irradiated pellets or powders. Kinetic analysis by the fragmentation model, which considers the processes of the penetration and diffusion of nitric acid through the fuel matrices, indicated that the dissolution rate of irradiated fuel is affected not only by the volume ratio of liquid to solid (L/S ratio), which decreases the penetration rate of nitric acid, but also by the exposed surface area per unit mole of nitric acid (A/m ratio). The penetration rate of nitric acid, which controls the dissolution rate of the fuel, was expected to be depressed at high HM concentrations, but enhanced for fuel pieces sheared with short strokes (i.e., with an enlarged specific surface area of fuel). Then, the dissolution process with short stroke shearing can be applied to maintain the dissolution efficiency of MOX fuels with high Pu contents of up to 30% at high concentrations of up to 500 g dm⁻³.

Acknowledgements

In this study, all of the dissolution tests using irradiated mixed-oxide fuels were conducted in the Chemical Processing Facility (CPF) of Japan Atomic Energy Agency.