1. Introduction

2. Experimental Installation

2.1. Description of the Set-Up

The experimental set-up used in the plutonium temperature effect program is given in Figure 2. The experimental core consists of two concentric cylindrical vessels:

• An inner vessel that accommodates the plutonium solutions during the experiment,
• An outer vessel that provides neutron reflection by a water layer of 22 cm laterally and under the plutonium vessel. It helps to maintain a stable temperature of the device.

The inner plutonium vessel is a 0.3 cm thick, 205 cm high stainless steel cylindrical vessel with an inner radius of 37.8 cm (Figure 2). It is closed by a cover, and the bottom is manufactured to allow the complete draining of the solution at the end of the sub-critical approach (Figure 3). The plutonium solution is introduced into the core from two filling and draining pipes connected to the vessel’s bottom and sides, respectively. Another pipe located at the top of the vessel returns the plutonium solution directly to the storage tank in the event of an overflow. The vessel ensuring the neutron reflection is also a cylindrical stainless steel vessel with an inner diameter of 120.6 cm. This is a 0.3-cm thick, 232-cm high vessel surrounded from all sides by 10 cm of rock wool acting as thermal insulation. The water is introduced from two filling and draining pipes (Figure 5), respectively, connected to the bottom and sides of the vessel. Similar to the plutonium vessel, this vessel also has an overflow pipe at the top.

Figure 3. Scheme of the benchmark configuration (vertical cut).

Figure 3. Scheme of the benchmark configuration (vertical cut).

Figure 4. Principle of sub-critical approach technique.

Figure 4. Principle of sub-critical approach technique.

Figure 5. Plutonium vessel with the machined zone in the bottom for solution draining.

Figure 5. Plutonium vessel with the machined zone in the bottom for solution draining.

The covers of the two vessels house three liquid level measurement devices referred to as limnimeters. These limnimeters (Figure 6) are equipped with two needles. The first needle is used to measure the liquid level with a high accuracy (of the order of 0.001 cm). The second needle is a security needle allows the opening of the drainage valves when a predetermined level of plutonium solution is reached during a subcritical approach. Two of these limnimeters are used for measuring the level of the plutonium solution. The first one is equipped with an extension and measures the liquid level from the bottom of the vessel up to 130 cm, and the second one measures the liquid level from 100 cm up to the overflowing pipe (205 cm). The third limnimeter is used for measuring the water level in the reflector vessel.

The experimental set-up is also equipped with six temperature probes (Figure 7) in the plutonium solution and the water reflector. To regulate the temperature of the plutonium solution, the experimental set-up has also been equipped with a heating system. The storage tank for the water reflector (which has a 5000 l capacity) is equipped with six 18 kW electric heaters, a regulator system to maintain the predefined temperature, and a circulation pump to homogenize the temperature in the tank. The plutonium storage tank (enclosed in an insulated containment) is also equipped with a heating device. The solution inside the storage tank is heated by hot air with a temperature of 70 °C directed onto the outer wall of the tank. The device itself consists of a set of 6 kW resistances, a fan-coil unit, and a regulator system to maintain the predefined temperature. The previous two heating devices are used to preheat the water reflector and the plutonium solution before they are transferred to the water reflector vessel and the plutonium vessel. All transfer pipes, the water reflector vessel, and the plutonium tank storage have been thermally insulated to limit heat loss. During the course of an experiment, the temperature of the plutonium solution in the plutonium vessel is regulated by water circulation in the reflector (no heating device is in direct contact with the plutonium solution) by using the Vulcatherm. The Vulcatherm itself is equipped with a pump and several 6 kW heating resistances. The experimental set-up has also been equipped with an ultimate safety system that is triggered in the highly unlikely event that the standard safety systems (dropping both the plutonium solution and the water reflector in their respective storage tanks) do not function properly. This ultimate safety system consists of injecting an acidic solution of natural gadolinium into the plutonium solution using two independent pipes connected to the top of the plutonium vessel.

3. Description of the Program

3.2. Proposed Experiments

The plutonium solutions were prepared at three target concentrations from a mother solution initially prepared in 1993. ²⁴¹Am had to be removed from the solution. The acid normality was set to 1N, and the targeted plutonium concentrations were: 14.3 g/L, 15 g/L, and 20 g/L (see Table 1), and two phases of experiments were defined:

• Phase I comprised fourteen experiments (five at 20 g/l, four at 15 g/l, and five at 14.3 g/l). Four of these phase I experiments were terminated prematurely due to technical issues. For some experiments (2998, 2999A, 3001A, and 3002A), the approach to critical was stopped too far away from criticality. In fact, the last solution height was far from the extrapolated height to criticality. Because the uncertainty of extrapolation was large in comparison with the obtained critical height, the experiments were not considered to constitute proper benchmarks by the experimentalists and were therefore discarded from the selection.
• Phase II comprised three experiments (at 14.3 g/l).

Table 1. Characteristics of the plutonium solution for the various experiments (the uncertainties given correspond to 2σ).

Table 1. Characteristics of the plutonium solution for the various experiments (the uncertainties given correspond to 2σ).

Experiment	T[°C]	C(Pu) [g/l] at 21 °C	Dilation Factor	Critical Mass (kg) ± 3σ	H+ (mol/l) at 21 °C	ρ[g/cm3] at 21 °C	Average Extrapolated Critical Height [cm]
2997	22.20 ± 010	19.665 ± 0.095		3.43 ± 0.04	1.0700 ± 0.011	1.06678 ± 0.00004	38.869 ± 0.075
2999B	39.84 ± 0.07	20.146 ± 0.042	0.99243	3.45 ± 0.04	1.0707 ± 0.021	1.06787 ± 0.00005	38.104 ± 0.086
3000	22.18 ± 0.08	20.111 ± 0.044		3.40 ± 0.04	1.059 ± 0.041	1.06760 ± 0.00003	37.630 ± 0.066
3001B	40.00 ± 0.07	15.001 ± 0.013		5.83 ± 0.04	1.032 ± 0.011	1.05804 ± 0.00006	86.583 ± 0.217
3002B	39.97 ± 0.07	14.895 ± 0.045	0.99241	5.80 ± 0.04	1.032 ± 0.020	1.05798 ± 0.00007	86.778 ± 0.181
3003	22.15 ± 0.08	15.010 ± 0.098		5.74 ± 0.04	1.042 ± 0.005	1.05812 ± 0.00003	85.191 ± 0.200
3004	22.19 ± 0.09	14.246 ± 0.023		8.65 ± 0.04	1.034 ± 0.006	1.05699 ± 0.00007	135.255 ± 0.024
3005	39.99 ± 0.08	14.290 ± 0.020	0.99238	8.48 ± 0.04	1.036 ± 0.005	1.05707 ± 0.00003	132.142 ± 0.030
3006	30.09 ± 0.09	14.285 ± 0.036		8.36 ± 0.04	1.032 ± 0.004	1.05709 ± 0.00001	130.374 ± 0.027
3007A	22.21 ± 0.09	14.294 ± 0.010		8.55 ± 0.04	1.033 ± 0.008	1.05681 ± 0.00004	133.254 ± 0.031
3007B	28.14 ± 0.07	14.294 ± 0.010	0.99735	8.47 ± 0.04	1.033 ± 0.008	1.05681 ± 0.00004	131.997 ± 0.118
3008	28.13 ± 0.08	14.277 ± 0.023		8.83 ± 0.04	1.039 ± 0.007	1.05707 ± 0.00002	137.751 ± 0.025
3009	40.01 ± 0.10	14.067 ± 0.015		8.63 ± 0.04	1.038 ± 0.011	1.05648 ± 0.00001	136.710 ± 0.032

At the beginning of the program, only separate sub-critical approaches were planned for safety reasons. In fact, the command control system could not be modified easily to drain some solution from the tank. Since phase I experiments are entirely independent of one another, even if the experimental uncertainties are very low (see Table 2), a potential reactivity effect, lower than the level of uncertainties would not be significant in comparison with the uncertainties associated with the two separate approaches. Moreover, it should be noted that the two solutions at 14.3 g/l, even if they are assumed to be identical, have been drained into the storage tank and could have been contaminated differently.

Table 2. Experimental uncertainties of the PU+ program.

Table 2. Experimental uncertainties of the PU+ program.

Parameter		Variation In the Calculation	Uncertainty (1σ)	Δkeff(1σ) × 105
Temperature (°C)	Doppler effect	3	0.13	Negligible
	Solution density			Negligible
	Water density			Negligible
Acidity (mol/l)		0.1	0.004	5
Plutonium concentration (g/l) – Systematic*		0.1	0.033	89
Plutonium concentration (g/l) - Statistical			0.005	14
Plutonium valence		100 %	5.77 %	7
Density of solution (g/cm3) - Systematic		0.01	0.00065	Negligible
Density of solution (g/cm3) - Statistical			0.00002	Negligible
Am concentration (%)		20	11.55	9
Isotopic Composition 240Pu (%) (a)		0.1	0.01	9
Isotopic Composition 241Pu (%) (b)		0.1	0.0025	Negligible
Tank wall composition (%)		1	0.58	9
Detected impurities (boron) (mg/l)		0.44	0.25	Negligible
Impurities below the detection limit (mg/l)		2	0.29	79
Solution height (cm)		0.24	0.05	8
Tank radius (cm)		0.2	0.062	17
Tank thickness (cm)		0.05	0.006	Negligible
TOTAL				123

In 2006, a new technical solution was studied in order to make the draining of the solution possible. After approval by the safety authorities, new sub-critical approaches (experiments 3007A and 3007B) were proposed. Contrary to previous experiments, those experiments were perfectly correlated.

In order to highlight a significant PU+ effect with regard to the experimental uncertainties, it was paramount to dispose of experiments as correlated as possible with one another.

The idea was to use the same solution at various temperatures (without draining the plutonium solution from the vessel) as follows:

• First, a standard sub-critical approach at the initial temperature was performed;
• For safety reasons, a small amount of the solution was drained to reduce the plutonium mass because the positive temperature effect would lead to a reactivity increase (roughly 1 % of the initial solution will have to be drained);
• The temperature of the solution was increased slowly by heating the water reflector; and finally, a standard sub-critical approach is performed at the final temperature.

This idea was used for the design of experiments 3007A and 3007B. Except for the temperature discrepancy, the experiments were fully correlated, which allowed magnifying the effect of the reactivity effect caused by the temperature increase. It is crucial when observing minor effects compared to the experimental uncertainties (see Table 2).

3.2. Characterization of the Plutonium Solutions

The plutonium solutions were prepared by nitric dilution of an initial plutonium nitrate solution at 28.86 g/l. The program started with a plutonium solution at 20 g/l and continued with solutions with a decreasing plutonium content (15 and 14.3 g/l). The list of the experiments with the corresponding plutonium concentrations and temperatures is given in Table 1.

The bulk density of the solution was determined through helium pycnometry technique. Moreover, the solutions were fully characterized through a dosage using the Davis & Townsed method. This method consists of reducing plutonium at valency III by an excess of copper. Then, copper is oxidized by potassium dichromate. A first equivalent point is obtained. After adding a mixture of acid, plutonium is oxidized at valency IV by potassium dichromate. A second equivalent point is obtained. The mass of plutonium in the sample is determined through the mass of potassium dichromate necessary between the first and the second equivalent point.

$$\mathit{C}\left(\mathrm{Pu}\right)=\frac{({\mathit{m}}_1-{\mathit{m}}_2)\times {\mathit{T}}_{\mathrm{Cr}}\times \mathrm{M}{\mathrm{A}}_{\mathrm{Pu}}}{\mathrm{PE}}\times 1000$$

(1)

where:

m₁ is the mass of potassium dichromate of the first equivalent point

m₂ is the mass of potassium dichromate of the second equivalent point

T_Cr is the concentration of potassium dichromate in (N/g)

MA_Pu is the average atomic mass of plutonium (g/mol)

PE is the mass of the sample

C(Pu) is given in (g/kg)

The plutonium isotopic composition is reported in Table 3. The impurities were measured using the ICP-MS and ICP-AES techniques (see Table 4).

Table 3. Isotopic composition of plutonium.

Table 3. Isotopic composition of plutonium.

Isotope	238Pu	239Pu	240Pu	241Pu	242Pu
Content in%	0.1940 +/- 0.0050	76.9410 +/- 0.0200	20.6980 +/- 0.0200	1.0800 +/- 0.0050	1.0870 +/- 0.0050

Table 4. Measured impurities using Inductive Coupled Plasma Mass Spectrometry (ICP-MS) and Inductive Coupled Plasma Absorption and Emission Mass Spectrometry (ICP-AES) for the plutonium solution (19.67 g/l) measured on February 2, 2007.

Table 4. Measured impurities using Inductive Coupled Plasma Mass Spectrometry (ICP-MS) and Inductive Coupled Plasma Absorption and Emission Mass Spectrometry (ICP-AES) for the plutonium solution (19.67 g/l) measured on February 2, 2007.

Element	Concentration [mg/l]	Element	Concentration [mg/l]
241Am	16	Mg	2.3
B	2.2	Ni	19.6
Ba	1.5	Pb	0.4
Ca	4.8	Th	2
Cr	6.7	Zn	3.5
Fe	34
The elements with content lower than 1 mg/l include Ag, Al, As, Au, Be, Cd, Ce, Co, Cs, Cu, Dy, Er, Eu, Ga, Gd, Ge, Hf, Hg, Ho, Ir, La, Li, Lu, Mn, Mo, Nb, Nd, Os, Pd, Pr, Pt, Rb, Re, Rh, Ru, Sb (not detected), Sc, Se, Sm, Sn (not detected), Sr, Ta, Tb, Te, Ti, Tl, Tm, U, V, W, Y, Yb, and Zr.

It should be noted that, for easiness in using the benchmark model, the instrumentation immersed in the solution tank monitoring the temperature and the level of the solution was not modeled. The critical height of the solution had to be modified to account for that removal.

4. Evaluation of Experimental Data

5. Analysis of the Experimental Results

5.4. Calculated Temperature Coefficients

Only the 3007A configuration was considered since it is the only one where the initial and perturbed cases are strongly correlated, the approach-to-critical for the 28 °C configuration (3007B) being performed in one run after draining the water level and increasing the temperature of the plutonium nitrate solution. The contribution of the Doppler, thermal expansion, and thermal scattering data effects were evaluated.

The temperature coefficients were calculated using the multi-group codes APOLLO2-MORET 4 and APOLLO2-MORET 5 using respectively nuclear data based on the JEF2.2 and JEFF-3.1.1 evaluations and also continuous energy code MORET 5.D.1. For MORET 5.D.1, the JEFF-3.3 library was employed for all nuclides, except for hydrogen in water, where thermal scattering data from various evaluations or by regenerating at correct temperatures based on new experimental data were used.

The geometry is assumed not to vary between 22 °C and 28 °C. The only discrepancy between the two configurations is the composition of the plutonium and water reflector after expansion solution (when the expansion effect is accounted for), their temperatures, and the thermal scattering data of hydrogen in water.

A first analysis of Table 5 shows that positive temperature coefficients are obtained for the multi-group APOLLO2-MORET 4 and APOLLO2-MORET 5 codes. Indeed, for these codes, the thermal scattering data of hydrogen are calculated at a tabulated temperature if the temperature of the benchmark is less than 2 °C from the tabulated temperature, otherwise an interpolation at the benchmark temperature is performed.

Table 5. Temperature coefficients (pcm/K) calculated with CRISTAL package codes (multi-group) and libraries.

Table 5. Temperature coefficients (pcm/K) calculated with CRISTAL package codes (multi-group) and libraries.

Experiment	C(Pu) in g/L	APOLLO2-MORET 4	APOLLO2-MORET 5
		JEF2.2	JEFF-3.1.1
3007A/B	14.294	15.5 ± 2.4	16.2 ± 2.4

However, it can be seen in Table 5 that the obtained temperature coefficient is significantly higher than the experimentally measured value. One of the reasons that can be attributed to this huge discrepancy is the interpolation of thermal scattering cross sections by APOLLO2 between two broad temperature grids available in the JEFF-2.2 and JEFF 3.1.1 TSL evaluation for light water, i.e., 293.6 K and 350.0 K.

The same calculation was performed using the MORET 5.D.1 continuous energy codes with nuclear data based on JEFF-3.3 processed for the temperatures encountered in the PU+ program (28 °C), the thermal scattering data being obtained from JEFF-3.3, ENDF/B-VIII.0 at the temperatures available in the ENDF files (293.15 K and 300 K for ENDF/B-VIII.0 and 293.15 K for JEFF-3.3), and the newly developed TSL based on the SNS data at the required temperatures (295.15 K and 301.15 K). The temperature coefficients obtained are reported in Table 6.

Table 6. Temperature coefficients (pcm/K) calculated with MORET 5 (continuous energy) and libraries (expansion effect of solution taken into account) - – Monte Carlo Standard deviation = 0.0005.

Table 6. Temperature coefficients (pcm/K) calculated with MORET 5 (continuous energy) and libraries (expansion effect of solution taken into account) - – Monte Carlo Standard deviation = 0.0005.

C(Pu) in g/L (3007 A)	Temperature effect	TSL from JEFF-3.3 at 293.6 K and 293.6 K	TSL from ENDF/B-VIII.0 at 293.15 K and 300 K	TSL with new evaluation from SNS [11] at 295.15 K and 301.15 K
		MORET 5
14.294	Thermal expansion	+0.33	+0.33	+0.33
	Doppler	+3.67	+3.67	+3.67
	S(α,β)	0	+7.17	+5.83
	Total	+3.33	+9.67	+11.83

As expected, when referring to the experimental results, a positive temperature coefficient is obtained (see Table 7) when using the TSL data from JEFF-3.3; only a +3.33 pcm/K effect is observed as the same TSL data at 293.6 K was utilized for both the simulations at 22 °C and 28 °C. The effect is larger when using TSL data from ENDF/B-VIII.0 (9.67 pcm/K) and from SNS (+11.83 pcm/K). Considering their uncertainties, these values are consistent with the reactivity worth of the solution level decrease due to the temperature effect (+5.17 pcm/K in Table 7).

Table 7. Effect of temperature on the critical height and translation in reactivity worth (SNS).

Table 7. Effect of temperature on the critical height and translation in reactivity worth (SNS).

Experiment	C(Pu) in g/L	Critical height (cm)	Difference in the critical height (mm)	Reactivity worth of 1 mm of solution (pcm)	Reactivity worth corresponding to the temperature effect (pcm)	Reactivity worth corresponding to the temperature effect (pcm/K)
3007A	14.294	133.254	-12.57	2.47	31	5.17

Another conclusion is that the main contributor to the temperature effect is the thermal scattering data effect followed by the Doppler effect. The expansion effect is calculated to be negligible.

Indeed, when looking only at the effect of TSL data without considering the expansion effect of the Pu solution, it appears that the effect of TSL data is negligible for TSL data from JEFF-3.3 but larger for TSL data from ENDF/B-VIII.0 (+7.17 pcm/K) and from SNS (+5.83 pcm/K).

This observed negligible effect of TSL data for JEFF-3.3 is evident due to the unavailability of TSL data for a fine temperature grid in the evaluation. A close observation of the larger positive temperature coefficient obtained using ENDF/B-VIII.0 and the new TSL data highlights the importance of having either a fine grid in TSL temperatures in the nuclear data evaluation or regeneration of TSLs at the required temperature for benchmarks sensitive to TSL temperatures.

6. Conclusions

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