Preliminary study of the criticality monitoring method based on the simulation for the activity ratio of short half-life noble-gas fission products from fuel debris

ABSTRACT

We investigated the possibility of estimating the effective neutron multiplication factor (k_eff) of the fuel debris inside the canister and primary containment vessel (PCV) of Unit 2 of the Fukushima Daiichi Nuclear Power Station (1F) using remote gas-radioactivity measurement via Monte Carlo simulation-based calculations. Our results demonstrate an almost linear correlation between k_eff and the ⁸⁸Kr-to-¹³⁵Xe activity ratio with respect to various fuel debris compositions. This correlation is maintained regardless of geometries such as the fuel debris canister and the PCV.

KEYWORDS:

• Subcritical system
• depletion calculation
• spontaneous fission
• monte Carlo calculation
• short half-life fission product
• activity ratio; criticality

1. Introduction

The characteristics and composition of fuel debris at the Fukushima Daiichi Nuclear Power Station (1F) are considered diverse and complicated depending on the location of the debris in the primary containment vessel (PCV), differences in the fuel burn-up conditions before the accident [1], the progression of the severe accident in each unit, and other events. Fuel debris is formed during accidents when fuel mixes with other materials, such as fuel cladding (zirconium alloy), structural material (mainly steel), control blade (B₄C), air, water, concrete, and other materials inside the PCV [2]. Fuel and nonfuel materials can introduce variations in the composition of fuel debris. Internal investigations of the PCV at 1F showed fuel debris in various shapes and sizes [3].

A significant amount of the fuel debris is expected to accumulate in the lower part of the reactor pressure vessel (RPV) of 1F Unit 2, and some fuel debris will relocate from the RPV and accumulate in the pedestal area [4].

Fuel debris removal is a crucial step in the entire 1F decommissioning process. According to the road map of 1F decommissioning [5], the fuel debris retrieval method starts by inserting a special retrieval equipment through existing penetration holes in the PCV. The retrieved fuel debris is placed in a container, transferred to a storage facility in the 1F, and stored in dry conditions. Fuel debris removal will be first performed for the 1F Unit 2 as a trial.

Fuel debris must be retrieved and stored safely under stable conditions [4]. For the safety management of fuel debris and establishing stable conditions, knowing the fuel debris parameters related to safety, such as the effective neutron multiplication factor (k_eff) and the amount of fissile material, is crucial. Research related to fuel debris composition, shapes or physical form, and distribution inside the PCV is ongoing; however, detailed information on the fuel debris with respect to these parameters is not available yet [6]. Consequently, determining k_eff and other safety parameters related to fuel debris via calculations is difficult. In addition, very high gamma radiation inside the PCV limits the available options for measuring the necessary parameters, especially those needed for k_eff estimation.

The spent fuel or fuel debris contains nuclides with spontaneous fission (SF) reactions [7]. A recent study shows the possibility of quantifying SF nuclides inside the storage or canister [8]. The SF reactions produce neutrons and fission products (FPs) such as ⁸⁸Kr and ¹³⁵Xe. The neutrons subsequently trigger induced fission (IF) reactions with available fissile nuclides such as ²³⁵U and ²³⁹Pu. With the information of the quantity of SF nuclides in fuel debris, we can estimate SF reaction rate and FPs yields by relatively straightforward radioactive decay calculation. However, the estimation of IF reaction rate and FPs yields is more difficult, because we need to solve a neutron transport problem for a subcritical system with fixed neutron source (in this case from SF nuclides) by solving neutron transport equation or by particle simulation using Monte Carlo method (utilized in the current paper). Since yields of FPs such as ⁸⁸Kr and ¹³⁵Xe produced from SF nuclide such as ²⁴⁴Cm are different from the ones by IF reactions such as ²³⁵U and ²³⁹Pu [9], we can define correlation between the number of FPs such as ⁸⁸Kr and ¹³⁵Xe and the number of IF reactions which is influenced strongly by k_eff.

Naito et al. derived an equation to calculate k_eff from an activity ratio (A(⁸⁸Kr/¹³⁵Xe)) of two noble-gas radioactive nuclides (⁸⁸Kr and ¹³⁵Xe) based on an analytical approach for a simplified fuel debris model, including ²³⁵U and ²⁴⁴Cm [10]. Here, ⁸⁸Kr and ¹³⁵Xe half-life are 2.83 and 9.14 h, respectively. We consider the approach proposed by Naito et al. because of the complicated nature of fuel debris; however, it is not enough to estimate the correlation between k_eff and the A(⁸⁸Kr/¹³⁵Xe) for fuel debris.

In our previous study, we developed a new depletion calculation code to estimate the A(⁸⁸Kr/¹³⁵Xe) [11]. This code can solve neutron transport and depletion calculations of subcritical systems with an inherent neutron external-source problem by using particle simulation (Monte Carlo method). The code contains a function for evaluating the quantity of short half-life FPs buildup due to SF and IF. In Ref [11], A(⁸⁸Kr/¹³⁵Xe) was estimated for a canister with a hypothetical nuclear material comprising UO₂ and 0.1 wt.% ²⁴⁴Cm for code validation.

This paper applies the depletion code to many fuel debris conditions in the decommissioning process in the fuel debris canister and the PCV [12]. We model the fuel debris canister to investigate the correlation between the k_eff and the A(⁸⁸Kr/¹³⁵Xe) for many fuel debris compositions. We also model the PCV to study the k_eff–A(⁸⁸Kr/¹³⁵Xe) correlation in different geometry models.

Figure 1 shows the image of applications of ⁸⁸Kr and ¹³⁵Xe measurements to estimate the k_eff of the PCV and the fuel debris canisters. Noble gases such as ⁸⁸Kr and ¹³⁵Xe are chemically inert and will be released easily from fuel debris into the surrounding air [13]. An additional advantage of short half-life FP (⁸⁸Kr and ¹³⁵Xe) gamma-ray emitting gas measurement is that it can be performed remotely in place with lower gamma-ray backgrounds.

Figure 1. The k_eff estimation method using the activity ratio between ⁸⁸Kr and ¹³⁵Xe.

In this preliminary study, it is assumed that all or the same rate of ⁸⁸Kr and ¹³⁵Xe released from fuel debris will be detected without time-delay of their migration times to a measurement point. The validity of this assumption and the appropriate correction methods [14] will need to be confirmed in advance of 1F implementation.

This study aims to find correlations between the A(⁸⁸Kr/¹³⁵Xe) and the k_eff for the fuel debris canister and the PCV without requiring prior detailed knowledge of the fuel debris compositions and shapes.

2. Calculation methods

2.1. Geometry model

2.1.1. Fuel debris canister

We used an existing design for investigating the canister-geometry model and materials [12]. The canister contains vent valves to allow hydrogen gas to flow out. However, these valves are omitted in the model geometry shown in Figure 2.

Figure 2. Canister-geometry model.

Reference [12]-predicted fuel debris filling rate accounts for 22% of the canister volume, including 11% water and 67% air. This is the conservative filling rate. However, we investigated the influence of the filling rate and water fraction on the k_eff–A(⁸⁸Kr/¹³⁵Xe) correlation by calculating cases involving filling rates other than the conservative filling rate.

The canister used in the calculation herein has an inner diameter of 220mm, an inner height of 800mm, and an internal volume of 0.030m³. The canister material is stainless steel SS316L with a thickness of 10mm.

2.1.2. The PCV

The PCV geometry model and material compositions of the 1F Unit 2 used in this study are based on those reported in a previous study conducted by our group [15]. Figure 3 shows the PCV geometry model used for calculations in this study. In this model, only the fuel debris from the lower part of the pedestal is considered for calculations. The fuel debris is assumed to fill up two PCV floor sump pits having a flat surface with a depth of 40cm (excluding fuel debris in the sump pit).

Figure 3. The PCV of the 1F unit 2 geometry model.

2.2. Calculation case description

In this study, we perform a fixed-source subcritical depletion calculation to obtain the A(⁸⁸Kr/¹³⁵Xe) value of the canister and the PCV. Moreover, an eigenvalue calculation is performed to obtain the k_eff of the canister.

Herein, we use several general assumptions and calculation conditions as follows. (1) The fuel debris used in the calculation herein is the fuel debris from 1F Unit 2, with 10 years of storage time. (2) The subcritical depletion calculation period is two months, divided into two depletion-time intervals of one month. Therefore, the A(⁸⁸Kr/¹³⁵Xe) in the calculation indicates the data after the fuel debris has resided in the canister or the PCV for two months. (3) The fuel debris, water, and air are homogeneously mixed inside the canister and the PCV. (4) As in our previous paper, all horizontal boundary condition calculations are reflective, and vacuum boundary condition calculations are set at the bottom and top parts of the fuel debris canister. This model represents an infinite array of the same subcritical canister with a 300-mm lattice pitch.

We model the characteristics and composition of the fuel debris at the 1F Unit 2 using the fuel-inventory data before the accidents provided by authors [16] and consider the FPs released during the accidents based on Phebus FPT4 [13]. The fuel (mainly UO₂) in the fuel debris contains FPs and actinides specifically modeling the 1F Unit 2 average core compositions before the accident. The A(⁸⁸Kr/¹³⁵Xe) of the current work was derived using a total yield of ⁸⁸Kr and ¹³⁵Xe produced from SF reactions of ²⁴⁴Cm mainly and IF reactions of ²³⁵U, ²³⁹Pu, and a trace of other fissile nuclides. The following subsections present several calculation cases to illustrate the fuel debris compositions for the canisters and the PCV.

2.2.1. Fuel debris types

The nonfuel materials included in the 1F Unit 2 PCV, such as zirconium alloy, structural material, air, water, concrete, and other materials, can be mixed with fuel and form fuel debris. We categorize the fuel debris types roughly in to four types (Table 1). The molten core–concrete interaction (MCCI) is a byproduct of the concrete interaction with the fuel.

Table 1. Fuel debris types.

No	Fuel debris types	Compositions
1	Fuel only	UO2
2	Uranium-rich	UO2 75 vol%+ZrO2 25 vol%
3	Molten fuel	UO2 50 vol%+ZrO2 50 vol%
4	MCCI	UO2 20 vol%+concrete 80 vol%

The UO₂ contains actinides and FPs.

We investigate the correlation among the fuel debris types, canister criticality, and the A(⁸⁸Kr/¹³⁵Xe) for the averaged core compositions (an average burn up of 24 GWd/t) with the conservative filling rate.

2.2.2. Canister filling rate and water contents

Since the fuel debris can have different shapes, sizes [3], and water contents [12], we must investigate the canister filling rate and water content influence on the k_eff–A(⁸⁸Kr/¹³⁵Xe) correlation.

We vary the canister filling rates of fuel debris from 10 vol% to 70 vol% of the canister volume with 3 vol% interval. The water volume fraction of the canister is 11 vol%, and the rest represents air. Because water is likely to be present in the fuel debris, we calculate cases where the water volume fraction varies from 1% to 15% while the fuel debris is kept constant at 22% of the canister volume. The fuel debris type used is the molten fuel in Table 1 at the averaged core compositions.

2.2.3. Fuel debris inside the PCV of the 1F unit 2

We assume the fuel debris inside the PCV also has an averaged core composition, and all the fuel debris shown in Table 1 could be distributed. However, with the current information, knowing the fuel debris location, fuel debris type, and distribution inside the PCV is challenging. We simulate various fuel debris compositions by varying the fraction of UO₂ in the fuel debris from 1 vol% to 70 vol% and the ZrO₂ from 69 vol% to 0 vol%. The water volume fraction is 10 vol%, and the rest (20 vol%) is filled with structural materials. The k_eff–A(⁸⁸Kr/¹³⁵Xe) correlation for the fuel debris in the PCV are estimated for two conditions: submerged in water or air.

2.2.4. Fuel debris with fuel components of non-average core compositions

Based on refueling and operation history before the accident, fuel burn-up in the reactor core varied roughly at 3, 15, 20, 30, and 40 GWd/t. After the accident, almost all fuels melted, mixed, and relocated. As a result, we expect fuel debris will have fuel of average core compositions. However, fuel debris stored in the canisters may not have an average core composition because of its small capacity. There is a possibility that stored fuel debris in different canisters will have different compositions (e.g. with higher or lower burn-up) compared to the average core. Therefore, to clarify the characteristics of fuel debris of non-average core compositions, we utilize fuel of varied fuel burn-up (e.g. 3.31, 15.7, 24.0, and 41.0 GWd/t) with fuel debris compositions similar to Section 2.2.1 and 2.2.2.

3. Results and discussion

3.1. Canister filling rate, water content, and types of fuel debris

Figure 4 shows the correlation between k_eff and A(⁸⁸Kr/¹³⁵Xe) under a fuel debris variation based on filling rate, water fraction, and fuel debris type listed in Table 1. The influence of a fuel debris type having the conservative filling rate for the core-averaged compositions on the k_eff–A(⁸⁸Kr/¹³⁵Xe) correlation is linear.

Figure 4. Canister activity ratio of ⁸⁸Kr-to-¹³⁵Xe versus criticality (k_eff) with respect to various mixing parameters at the average core composition.

Fuel debris types with high fuel content (fuel only) exhibit high A(⁸⁸Kr/¹³⁵Xe) and k_eff, followed by uranium-rich molten fuel and MCCI (the lowest fuel content). Despite of the fuel debris type, the k_eff–A(⁸⁸Kr/¹³⁵Xe) has a linear relationship.

The filling rate of the fuel debris canisters depends on the fuel debris size and dimensions. The number of IF decreases when the quantity of nuclear material (fuel) in the fuel debris is low. Hence, the SF nuclides dominate the short half-life FPs production. For burn up>15 GWd/t, ²⁴⁴Cm accounts for more than 94% of the total SF sources, followed by ²⁴⁰Pu, accounting for<5% and ²⁴²Pu, accounting for<1% [7]. Therefore, the A(⁸⁸Kr/¹³⁵Xe) value is determined by the ²⁴⁴Cm SF yields related to ⁸⁸Kr and ¹³⁵Xe.

Owing to the increasing filling rate of the canisters, subsequent number of IF increases. The ²³⁵U IF fission yields related to ⁸⁸Kr and ¹³⁵Xe differ from the one given by ²⁴⁴Cm. Figure 4 shows an increase in the filling rate from 10 vol% to 70 vol%, resulting in an approximate change in the A(⁸⁸Kr/¹³⁵Xe) value from 0.17 (mostly SF) to 0.22 (a combination of SF and IF).

The k_eff value of the canisters increases with the quantity of nuclear material that improves with the increasing filling rate of the canisters. As shown in Figure 4, the k_eff roughly increases from 0.16 to 0.36. Hence, the correlation between the k_eff and A(⁸⁸Kr/¹³⁵Xe) values is linear.

Because of the high likelihood of water being present in the fuel debris, as mentioned in section 2.2.1, water has a significant influence on the k_eff–A(⁸⁸Kr/¹³⁵Xe) correlation of the canisters. With increasing water fraction inside the canister, the A(⁸⁸Kr/¹³⁵Xe) value increases, even though the nuclear material including contribution of the A(⁸⁸Kr/¹³⁵Xe) from SF nuclides e.g. ²⁴⁴Cm remained constant. Owing to the increasing quantity of the water fraction inside the canisters, the k_eff value of the canister increases roughly from 0.08 to 0.32. Because water acts as a moderator, increasing water quantity increases the population of thermal neutrons. These thermal neutrons are highly likely triggering IF of fissile materials (e.g.²³⁵U and ²³⁹Pu) and increase the A(⁸⁸Kr/¹³⁵Xe) value. Figure 4 shows the increase in the water fraction from 1 vol% to 15 vol%, resulting in the A(⁸⁸Kr/¹³⁵Xe) value changing from approximately 0.14 (influence of mostly SF) to 0.21 (influence of SF and IF).

Therefore, as shown in Figure 4, under a specific burn-up degree, the variation in the composition of fuel debris based on the canister filling rate, fuel debris type, water content, or combinations of these three mixing parameters produces a linear correlation between the k_eff and A(⁸⁸Kr/¹³⁵Xe) values, with similar slopes.

3.2. Correlation among the mixing parameters of fuel debris inside the PCV of 1F unit 2

Figure 5 shows the correlation between the k_eff and A(⁸⁸Kr/¹³⁵Xe) values for a variety of fuel debris compositions based on the description provided in section 2.2.3.

Figure 5. Correlation between the activity ratio of ⁸⁸Kr/¹³⁵Xe and k_eff for various types of fuel debris in the PCV and the canister at the average core composition.

In section 2.2.3, we assumed the fuel debris had water mixed inside. We compare two cases: fuel debris exposed to air and fuel debris submerged in water, inside the pedestal. Figure 5 shows a graph submerged in air and water are almost similar, therefore the effect of water outside fuel debris is relatively small.

The correlations between the k_eff and the A(⁸⁸Kr/¹³⁵Xe) values are linear for both submerged in water or air. For comparison, we include the graph of the fuel debris canister presented in Figure 4 to demonstrate the similarity of the correlation between the k_eff–A(⁸⁸Kr/¹³⁵Xe) values with respect to the fuel debris canister and PCV. Figure 5 shows that the correlation between the k_eff and A(⁸⁸Kr/¹³⁵Xe) values is not sensitive to geometry.

3.3. Fuel debris with non-average core compositions

As mentioned in the Introduction and Section 2.2, the fuel components inside fuel debris contain various fissiles and SF nuclides. Each has a different yield of ⁸⁸Kr and ¹³⁵Xe so values of A(⁸⁸Kr/¹³⁵Xe) for individual fission-capable nuclides are constant and tend to be specific. The overall A(⁸⁸Kr/¹³⁵Xe) of the canister or the PCV is defined by the type and quantity of SF and IF.

Figures 4 and 5 show an intuitively simple correlation between the k_eff and A(⁸⁸Kr/¹³⁵Xe). When the k_eff is low, the A(⁸⁸Kr/¹³⁵Xe) also gives a low value and vice versa. We describe the detailed mechanism in the followings, when the k_eff values are relatively low, the majority of ⁸⁸Kr and ¹³⁵Xe yields will come from SF of mainly ²⁴⁴Cm (>95%). Since the A(⁸⁸Kr/¹³⁵Xe) of ²⁴⁴Cm is low (~0.1), the overall A(⁸⁸Kr/¹³⁵Xe) approaches 0.1. On the contrary, when the k_eff is relatively high, ⁸⁸Kr and ¹³⁵Xe from IF of mainly ²³⁵U became dominant. As a result, the A(⁸⁸Kr/¹³⁵Xe) will approach 0.5, because A(⁸⁸Kr/¹³⁵Xe) of ²³⁵U is~0.5.

²³⁹Pu in the fuel debris of the average core is~20% of ²³⁵U mass, other fissile nuclide such as ²⁴¹Pu and ²³³U has collective mass below 2% of ²³⁵U. The A(⁸⁸Kr/¹³⁵Xe) of ²³⁹Pu IF is ~ 0.2, which is smaller than the one of ²³⁵U, therefore, when the k_eff is high, the overall A(⁸⁸Kr/¹³⁵Xe) is approaching value<0.5.

Difference in the correlations between k_eff and A(⁸⁸Kr/¹³⁵Xe) appear when compositions of SF nuclides and IF fissile nuclides in the fuel debris change, Figure 6 shows the relationship between the k_eff and A(⁸⁸Kr/¹³⁵Xe) at several different fuel burn-up (e.g. 3.31, 15.7, 24.0, and 41.0 GWd/t). Each specific burn-up graph shows a linear correlation between the canister k_eff and A(⁸⁸Kr/¹³⁵Xe) similar to Figures 4 and 5.

Figure 6. Canister activity ratio of ⁸⁸Kr-to-¹³⁵Xe versus criticality (k_eff) under various conditions at different fuel burn-up.

As mentioned above, each canister in this Section filled with fuel debris with a single burn-up fuel. In reality, these conditions are less probable because after all fuels melted, mixed with non-fuel material, and relocated to the bottom of RPV and inside the pedestal, the fuel with different burn-up values is likely to be mixed and its compositions will be closer to the average core conditions. Figure 6 also gives possibility of the A(⁸⁸Kr/¹³⁵Xe) measurement to predict burn-up or fissile nuclide contents in the fuel debris.

4. Conclusions and future works

We investigated the correlation between the k_eff and A(⁸⁸Kr/¹³⁵Xe) values with respect to canisters and the PCV under different fuel debris compositions using a novel depletion calculation code. The calculation results showed that the correlation between canister criticality and A(⁸⁸Kr/¹³⁵Xe) was linear, with similar slopes for various mixing parameters, such as fuel debris filling rates, water fractions, and fuel debris types, when the fuel isotope composition remained unchanged. Moreover, the k_eff–A(⁸⁸Kr/¹³⁵Xe) correlation is not sensitive to geometry such as in the fuel debris canister or in the PCV. These results indicate that the activity ratio A(⁸⁸Kr/¹³⁵Xe), which can be measured from a place nearly free from gamma ray backgrounds, can be employed for monitoring criticality.

We assume ⁸⁸Kr and ¹³⁵Xe migration from fuel debris to its surrounding air is relatively fast compared to its half-life, therefore ⁸⁸Kr and ¹³⁵Xe released from fuel debris will be detected without time-delay of their migration times to a measurement point. We also assume the similarity of chemical and physical behaviors between ⁸⁸Kr and ¹³⁵Xe. In future work, we will perform a detailed analysis of ⁸⁸Kr and ¹³⁵Xe migration in the PCV or another large container to accurately predict the k_eff. In addition, we will carry out experiments for code validation, assess the practicality of ⁸⁸Kr and ¹³⁵Xe measurements, and explore the possibility of the proposed method to predict burn-up or fissile nuclide contents in the fuel debris.

Disclosure statement

No potential conflict of interest was reported by the author(s).