Keywords

1 Introduction

Lead-bismuth fast reactor is one of the six main types of the fourth generation reactor, which has the characteristics of safety, economy, continuity and nuclear non-proliferation. However, the corrosion ability of lead-bismuth alloy cannot be neglected, and the corrosion products caused by it should not be underestimated. Studies have shown that more than 90% of occupational exposure is caused by corrosion products deposited on the pipe wall from the coolant, which continue to decay and emit gamma rays in the pipe wall or coolant, in particular, some long-life nuclides in the shutdown for a period of time will still cause radiation damage to equipment maintenance workers. Therefore, it is important to study the generation and migration of corrosion products in the alkali metal coolant loop, predict the change and distribution of corrosion products for the radiation shielding design of lead-bismuth fast reactor, the inspection and maintenance of the reactor, and the accident analysis.

In view of the important influence of corrosion products on radiation protection, a great deal of research has been carried out at home and abroad, Such as the PWR-GALE program developed in the United States, the PACTOLE program in France, the Nuclear Power Institute, the Suzhou Thermal Engineering Institute, Tsinghua University, the North China Electric Power University Shanghai Jiao Tong University, and Harbin Engineering University. The above calculation program or method, the principle used is basically the same, but the simplification and assumptions used, as well as the specific treatment methods are not the same. The point reactor model is often used in the calculation, which does not take into account the influence of uneven distribution of neutron flux rate and coolant flow time, so its calculation precision is not high. In addition, the existing source item calculation program has some limitations; the calculation system and equipment are also specific, not universal. At present, the study on source term of corrosion products in water-cooled reactor is mainly focused in China, but there is no systematic study on source term of corrosion products for lead-bismuth coolant.

Based on the characteristics of lead-bismuth reactor coolant loop, the corrosion mechanism of lead-bismuth alloy and the corrosion rate of lead-bismuth alloy, the process of corrosion products generation, decay, migration and deposition in the loop are simulated in this paper; the mathematical equilibrium equation is established. The source term of corrosion products of lead-bismuth coolant was calculated by calculating the fast neutron reaction cross section of the reactor. This study provides reference data for related research in China.

2 Corrosion Source

2.1 Impurities in the Coolant

The impurities in the coolant mainly come from the raw materials and the impurities introduced in the operation. The lead-bismuth alloy was synthesized from lead and bismuth in the ratio of 44.5% and 55.5%, the impurities are mainly non-metallic impurities such as oxygen, carbon, and metallic impurities such as calcium. The pipelines and equipment of the reactor loop are processed, welded and cleaned in the process of manufacture, installation and maintenance, this process inevitably leaves behind some dirt, grease, gasoline, metal chips, welding slag, surface oxides and moisture, which is another major cause of contamination and impurities in the coolant system.

2.2 The Structural Material of the Coolant Channel

Lead and bismuth coolants have the characteristics of high melting point, high boiling point, chemical property inactivity and “Negative” cavitation reactivity. Lead and bismuth are chemically inert with fuels, low alloy steel, water and air. The structural material commonly used in contact with lead-bismuth alloys is stainless steel.

By analyzing the main components and impurities in stainless steel, the possible activation reaction types were determined. Finally, the radionuclide types of various corrosion products, the corresponding reaction types and the main sources of structural materials were counted; the results are shown in Table 1. The common active corrosion products in the main circuit are radionuclide as 24Na, 51Cr, 56Mn, 59Fe, 58Co and 60Co, and their initial nuclides are mainly Fe, Cr, Ni, Mn and Co in the structural materials.

Table 1. Source of Corrosion Products
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3 Method of Establishment

3.1 Coolant Migration Process

When calculating the source term of corrosion products in the main loop, there are two general conditions. One is that the materials in contact with the coolant in the main circuit are first corroded and dissolved in the coolant; the other is that the material in the core is first activated by radiation, and then corroded down to dissolve in the coolant. As the coolant flows, some of the activated corrosion products in the main circuit will be deposited on the equipment or pipelines in the main circuit, most of which will be cleaned by the purification system, and some will remain in the main circuit coolant. The generation and migration of corrosion product source term in the main loop can be divided into six processes as follows:

  1. (1)

    The structural material in the core is activated by irradiation;

  2. (2)

    The material in contact with the coolant in the main circuit is corroded down and dissolved in the coolant to become the corrosion product;

  3. (3)

    Non-radioactive corrosion products in the coolant flow with the coolant, in the main circuit migration and balance;

  4. (4)

    The corrosion products in the coolant are irradiated and activated as they flow through the core;

  5. (5)

    Transfer and equilibrium of radionuclide in the coolant with the coolant flow;

  6. (6)

    The radionuclide in the coolant precipitates in the main circuit equipment.

3.2 Computational Model

In the coolant loop, the amount of the target radionuclide of the structural material decreases gradually with neutron irradiation.

$$ \begin{aligned} & \frac{{dN_{1} }}{dt} = - \overline{\sigma }_{1} \overline{\phi }_{1} N_{1} \\ & \frac{{dN_{2} }}{dt} = \overline{\sigma }_{1} \overline{\phi }_{1} N_{1} - \lambda_{2} N_{2} \\ \end{aligned} $$

In the formula, N1 is the nuclear density of the target nucleus in the structural material; t is the time;N2 is the nuclear density of the irradiated radionuclide; σ1 is the average neutron activation cross section of the target nucleus; ϕ1 is the average neutron flux rate of irradiation; λ2 is the decay constant of the irradiated radionuclide.

The increase in radionuclide in the primary circuit due to corrosion of the reactor activated materials at constant reactor power can be calculated as follows:

$$ \begin{aligned} R_{ci} & = \sum\limits_{l} {\left( {\sum\limits_{j} {\frac{{f_{ai} \cdot C_{0j} \cdot S_{j} \cdot N_{A} }}{{A_{i} }}} } \right)} \\ & = \sum\limits_{l} {\left( {\sum\limits_{j} {\frac{{f_{nll} \cdot f_{sIlj} \cdot C_{0j} \cdot S_{j} \cdot N_{A} }}{{A_{i} }}} \cdot x_{i} } \right)} \\ & = \sum\limits_{l} {\left[ {\sum\limits_{j} {\frac{{f_{nll} \cdot f_{slj} \cdot C_{0j} \cdot S_{j} \cdot N_{A} }}{{A_{i} }}} \cdot \frac{{ - \overline{\phi } \cdot \overline{\sigma }_{I} }}{{\lambda_{i} }} \cdot \left( {1 - e^{{ - \lambda_{i} tt}} } \right)} \right]} \\ & = \frac{{N_{A} \cdot \overline{\phi }}}{{A_{i} \cdot \lambda_{i} }} \cdot \left( {1 - e^{{ - \lambda_{j} \cdot t}} } \right)\sum\limits_{l} {\left[ {\overline{\sigma }_{Il} \cdot \left( {\sum\limits_{j} {f_{nnl} } \cdot f_{sIj} \cdot C_{0j} \cdot S_{j} } \right)} \right]} \\ \end{aligned} $$

In the formula, fai is the quality share of the radionuclide in the material; Coj is the material corrosion rate of module j; Sj is the corrosion area of module j; NA is the Amado Avogadro constant; Ai is the atomic weight of radionuclide I; fsILj is the mass share of the nuclide chemical element in the material composition of module j; fnIl is the natural abundance of the target nucleus; λi is the decay constant of radionuclide i.

When the reactor power is constant, the total nucleon number of the activated corrosion products in the coolant changes with time according to the following equation:

$$ \begin{aligned} & \frac{{dn_{vit} }}{dt} = R_{ci} - \lambda_{i} \cdot n_{vi} \\ & = \frac{{N_{A} \cdot \overline{\phi }}}{{A_{i} \cdot \lambda_{l} }}\left( {1 - e^{{ - \lambda_{1} \cdot t}} } \right)\sum\limits_{l} {\left[ {\overline{{\sigma_{ll} }} \left( {\sum\limits_{j} {f_{vil} } f_{sllj} C_{0} S_{j} } \right)} \right]} - \lambda_{i} \cdot n_{wt} \\ & \quad \quad R_{ci} = \frac{{N_{A} \cdot \overline{\phi }}}{{A_{1} \cdot \lambda_{l} }}\sum\limits_{l} {\left[ {\overline{{\sigma_{Il} }} \left( {\sum\limits_{j} {f_{nll} } f_{sIlj} C_{0} S_{j} } \right)} \right]} \\ & \frac{{dn_{wl} }}{dt} = R_{cl} \left( {1 - e^{{ - \lambda_{i} t}} } \right) - \lambda_{l} \cdot n_{wl} \\ \end{aligned} $$

If t ≤ t1, the analytical solution of the equation is:

$$ {\text{n}}_{wi} ({\text{t}}) = \frac{{R_{ct} }}{{\lambda_{t} }} - \frac{{R_{ct} \lambda_{t} t + R_{ct} }}{{\lambda_{l} }}e^{{ - \lambda_{1} t}} $$

if t > t1, The power of the reactor has changed, the average neutron flux rate of the reactor has changed, The solution of the equation is:

$$ \begin{aligned} & {\text{n}}_{{{\text{wt}}}} ({\text{t}}) = \frac{{R_{ci2} }}{{\lambda_{l} }}\left[ {1 - {\text{e}}^{{\lambda_{i} \left( {t_{1} - t} \right)}} } \right] - R_{cc2} \left( {t - t_{1} } \right){\text{e}}^{{ - \lambda_{t} t}} \\ & + \frac{{R_{ci1} }}{{\lambda_{l} }}\left[ {{\text{e}}^{{\lambda_{l} \left( {t_{1} - t} \right)}} - {\text{e}}^{{ - \lambda_{l} t}} } \right] - R_{ct1} t_{1} {\text{e}}^{{ - \lambda_{l} t}} \\ \end{aligned} $$

3.3 Example Description

The type of this example is a compact pool structure, as shown in Fig. 1; the main parameters are shown in Table 2. Under normal operating conditions, the circulation flow of lead-bismuth medium in the first circuit is as follows: Lead and Bismuth are heated from bottom to top by the core in the internal components of the reactor, and then enter the upper steam generator of the collector chamber through openings in the upper part of the containment vessel, After the heat transfer is completed from the top to the bottom of the primary side of the steam generator and the secondary side, the secondary side outlet is reintegrated into the lower collecting cavity of the side shield, and the inner opening of the side shield returns to the upper collecting cavity from the bottom to the top, Then flow down the annular passage between the side shield and the main vessel and enter the main pump inlet, under the pumping of the main pump, the annular passage between the lower shield and the lower head of the main vessel enters the lower collecting cavity of the core along the flow distribution mechanism, and finally returns to the core.

Fig. 1.
figure 1

Schematic Diagram of Pool-type Structure of Lead-bismuth Fast Reactor

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Table 2. Main Parameters
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3.4 Calculation Results and Comparative Analysis

The fast neutron average reaction cross sections for various reactions were calculated using the MCNP code, as shown in Table 3. The radioactivity of the corrosion products in the model coolant is calculated using the formula in Sect. 3.2, and a comparison with the results of the same type of reactor is shown in Table 4.

Table 3. Fast Neutron Average Reaction Cross Section
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Table 4. Results and Comparison of Radioactive Activity of Corrosion Products
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As can be seen from Table 4, the total activity of corrosion products in the lead-bismuth coolant circuit is 1.97E+15Bq. Among them, 51Cr, 54Mn, 58Co and 60Co have the largest proportion, but 51Cr and 58Co are short-lived nuclides, which can decay rapidly after shut down for a period of time, and 54Mn and 60Co have longer lifetime, which are the main contributors to the total activity.

Compared with ClEAR-1, the model has same life, but different power, temperature, flow, and structural materials. These factors cause the total amount of corrosion products to be more than ClEAR-1.

4 Conclusions

The sediment source term of corrosion products is the main source of occupational irradiation, and it is also the key and difficult point in the source term analysis of nuclear facilities. Based on the characteristics of lead-bismuth coolant system, the release, migration, decay and deposition of corrosion products in the coolant loop are fully considered, a method for calculating the source term of corrosion products in lead-bismuth coolant loop is developed, The method is used to simulate the coolant loop of lead-bismuth fast reactor, and the source term of corrosion products is calculated. The results show that the source terms of the corrosion products are mainly composed of 51Cr, 54Mn, 56Mn, 58Co, 60Co and 59Fe, among which the long-lived nuclides 60Co and 54Mn are the main contributors to the radioactive activity. The analytical methods and conclusions of this paper can provide theoretical support for relevant domestic research.