Keywords

1 Introduction

In order to meet the demand of peak shaving of power grid, nuclear power units will adopt load tracking operation or power reduction operation [1]. The reduced power operation mode [2], in which all the gray rods are extracted and the PWR(Pressurized Water Reactor) is reduced from full power to a specific power platform by boronization, and the low power platform runs continuously for more than 12 h, is called ELPO (Extended Low Power Operation). During ELPO, the core axial power distribution, enthalpy rise factor and power peak factor will change [3, 4], which will affect the whole core and local thermal hydraulic parameters.

The corrosion products in the primary circuit circulate with the coolant, some of which are removed by the CVCS (Chemical and Volume Control System), and the other part is deposited in the inner and outer areas of the core. The corrosion products deposited on the fuel surface are commonly known as CRUD (Chalk Rivers Unidentified Deposit). With the increase of CRUD, the heat transfer capability of fuel may decrease, and the risk of axial offset anomaly and local corrosion caused by scale will increase [5]; After irradiation, some CRUD will generate radioisotope, and these isotopes will migrate and redeposit in the primary loop after dissolving or shedding, forming coolant source term and shutdown deposition source term [6, 7].

The results of CRUD measurement data [5, 8] and mechanism study [9, 10] show that the rate of SNB (Subcooled Nucleate Boiling) on the fuel surface and the coolant temperature are the key parameters affecting the deposition and migration of corrosion products in the core. ELPO mode may have a great influence on local SNB rate and coolant temperature, which may change the distribution of corrosion products in the primary loop and change the migration of radioisotope. Therefore, it is necessary to study the migration behavior of corrosion products in the primary loop of PWR during ELPO, and evaluate the safety and economy of ELPO mode in reactor from the perspective of hydrochemistry and radiation protection.

2 Theoretical Model

2.1 Migration Model of Corrosion Products

The PWR primary loop is divided into the control volume shown in Fig. 1, in which only Fuel assembly is considered in the core, and it is finely divided along the axial direction, which is used to accurately characterize the influence of local SNB rate and coolant temperature on CRUD deposition.

The primary corrosion products are mainly composed of Ni, Fe, Cr complexes and a small amount of Co, Mn [5, 11]. For each element, the mass conservation equation in the PWR primary circuit can be listed as follows:

$$ \begin{aligned} & {\text{M}}_{{{\text{RCS}}}} \frac{{{\text{dC}}}}{{{\text{dt}}}} \cdot 10^{9} \\ & \;\; = {\text{R}}_{{{\text{release}}}} - {\text{R}}_{{{\text{CVCS}}}} - \frac{{{\text{dM}}_{{\text{c}}} }}{{{\text{dt}}}} - \frac{{{\text{dM}}_{{{\text{oc}}}} }}{{{\text{dt}}}} \\ \end{aligned} $$
(1)

Where: MRCS represents water loading capacity, in g; Rrelease represents the release rate of corrosion products, in g/s; RCVCS represents the removal rate of corrosion products by CVCS, in ppb/s; \(\frac{{{\text{dC}}}}{{{\text{dt}}}}\) indicates the change rate of corrosion products concentration, in ppb/s; \(\frac{{{\text{dM}}_{{\text{c}}} }}{{{\text{dt}}}}\) and \(\frac{{{\text{dM}}_{{{\text{oc}}}} }}{{{\text{dt}}}}\) respectively represent the deposition rate of corrosion products inside and outside the core, in g/s; t denotes time, in s.

Fig. 1.
figure 1

Schematic Diagram of Corrosion Products Migration

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The calculation formula of the items to the right of the equal sign of Eq. (1) is as follows:

$$ {\text{R}}_{{{\text{release}}}} { = }\sum\limits_{{\text{i}}} {{\text{v}}_{{\text{i}}} \cdot {\text{A}}_{{\text{i}}} } $$
(2)
$$ {\text{R}}_{{{\text{CVCS}}}} {\text{ = C}} \cdot {\upeta } \cdot {\text{w}}_{{{\text{CVCS}}}} $$
(3)
$$ \begin{aligned} \frac{{{\text{dM}}_{{\text{c}}} }}{{{\text{dt}}}} & { = }\sum\limits_{{\text{j}}} {\left( {\frac{{{\text{dm}}_{{\text{j}}} }}{{{\text{dt}}}} \cdot {\text{A}}_{{\text{j}}} } \right)} \\ & = \sum\limits_{{\text{j}}} {\left[ {{\dot{\text{m}}}_{{\text{e,j}}} \cdot {\text{C}}_{{\text{j}}} + {\text{k}}_{{\text{j}}} \cdot \left( {{\text{C}}_{{\text{j}}} - {\text{C}}_{{\text{j,0}}} } \right)} \right] \cdot {\text{A}}_{{\text{j}}} } \\ \end{aligned} $$
(4)
$$ \begin{aligned} \frac{{{\text{dM}}_{{{\text{oc}}}} }}{{{\text{dt}}}} & = \sum\limits_{{\text{k}}} {\left( {\frac{{{\text{dm}}_{{\text{k}}} }}{{{\text{dt}}}} \cdot {\text{A}}_{{\text{k}}} } \right)} \\ & = \sum\limits_{{\text{k}}} {\left[ {{\text{k}}_{{\text{k}}} \cdot \left( {{\text{C}}_{{\text{k}}} - {\text{C}}_{{\text{k,0}}} } \right)} \right] \cdot {\text{A}}_{{\text{k}}} } \\ \end{aligned} $$
(5)

Where: vi represents corrosion rate, in g/(cm2 · s); Ai represents the infiltration area of the corroded material, in cm2; C denotes the concentration of corrosion products in mainstream, in g/g; η represents the removal efficiency of corrosion products by CVCS; WCVCS represents circulating water traffic, in g/s; mj and mk respectively represent the deposition amount of corrosion products in the inner and outer areas of the core, in g; Aj and Ak represent the infiltration area inside and outside the core respectively, in cm2; \({\dot{\text{m}}}_{{\text{e,j}}}\) represents SNB rate, in g/(cm2 · s); kj and kk represent the deposition coefficients in the inner and outer regions of the core respectively, which can be calculated according to the coolant temperature [12], in g/(cm2 · s); Cj and Ck respectively represent the concentration of corrosion products in the mainstream in the inner and outer regions of the core, which is greatly affected by the local coolant temperature [13], in g/g; Cj,0 and Ck,0 respectively represent the concentration of corrosion products on the deposited surface inside and outside the core, in g/g.

2.2 Source Term Model

According to the PWR operation experience, consider the radioisotope produced by Ni, Fe, Cr and Co, as shown in Table 1 [14, 15].

Table 1. Generation of Some PWR Radioactive Nuclides
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The migration process of radioisotope can be general as follows: corrosion products are deposited in the core and irradiated to form isotopes and attach to the fuel surface, part of isotopes is dissolved into coolant to form coolant source term, and isotopes migrating with coolant is deposited outside the core to form shutdown deposition source term. In conjunction with Eqs. (1) to (5), the deposition mass of corrosion products on the fuel surface in dt time period can be obtained, and then the coolant source term and dose rate level can be calculated as follows:

$$ \frac{{{\text{d}}\upvarphi_{{\text{c}}} }}{{{\text{dt}}}}{ = }\sum\limits_{{\text{j}}} {\left[ {{\text{P}}_{{\text{j}}} - {\uplambda } \cdot {\text{n}}_{{\text{j}}} \cdot \left( {{1} - {\text{e}}^{{ - {\lambda t}}} } \right)} \right]} $$
(6)
$$ \frac{{{\text{d}}\upvarphi_{{\text{w}}} }}{{{\text{dt}}}}{\text{ = P}}_{{\text{w}}} - {\uplambda } \cdot {\text{n}}_{{\text{w}}} $$
(7)
$$ \frac{{{\text{d}}\upvarphi_{{{\text{oc}}}} }}{{{\text{dt}}}}{ = }\sum\limits_{{\text{k}}} {\left( {{\text{P}}_{{\text{k}}} - {\uplambda } \cdot {\text{n}}_{{\text{k}}} } \right)} $$
(8)

Where: \(\frac{{{\text{d}}\upvarphi_{{\text{c}}} }}{{{\text{dt}}}}\), \(\frac{{{\text{d}}\upvarphi_{{\text{w}}} }}{{{\text{dt}}}}\) and \(\frac{{{\text{d}}\upvarphi_{{{\text{oc}}}} }}{{{\text{dt}}}}\) represent the radioisotope change rate on the fuel surface, coolant and outside the core respectively, in Bq/s; Pj, Pw and Pk represent the radioisotope generation rates on the fuel surface, coolant and outside the core respectively, in Bq/s; NJ, NW and NK denote the radioisotope activity on the fuel surface, coolant and outside the core respectively, calculated from the amount of corrosion products deposited and the nuclear reactions shown in Table 1, in Bq; λ represents decay constant, in s−1.

3 Calculation Results and Analysis

3.1 Analytical Methods

Using LINDEN software [16] and CAMPSIS software [17] independently developed by CGN (China General Nuclear power group), the migration behavior of corrosion products of a million kilowatt PWR during one cycle running on 75% power and 50% power platforms was evaluated. Among them, LINDEN is used to calculate the thermal hydraulic parameters of each control body in the primary loop, including SNB rate and coolant temperature; CAMPSIS based on LINDEN calculations, analog corrosion products in the various control body deposition, dissolution, activation and redeposition migration process.

3.2 Migration of Corrosion Products

Figure 2 shows the migration of corrosion products in the primary loop under ELPO mode. The calculation results show that:

  1. 1)

    Compared with full power operation, when ELPO is carried out with 75% power and 50% power platform, the total amount of CRUD is significantly reduced, and more corrosion products will be deposited outside the core or removed by CVCS. From Eq. (4), it can be seen that this is because ELPO reduces SNB rate, thus inhibiting the deposition of corrosion products on the fuel surface;

  2. 2)

    The total CRUD of 50% power platform is higher than the total CRUD of 75% power platform. The reason for this phenomenon is that although the SNB rate decreases at lower power platform, the local coolant temperature of fuel also decreases, the concentration of corrosion products increases, and the CRUD deposition rate increases instead.

Fig. 2.
figure 2

Calculation Results of Corrosion Product Migration

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3.3 Distribution of Primary Loop Source Terms

Figure 3 shows the distribution of primary loop source terms in ELPO mode. The calculation results show that:

  1. 1)

    With the decrease of core power, the coolant source term gradually increases. This is because the decrease of core power causes the radioisotope deposited on the fuel surface to dissolve into the coolant, thus increasing the coolant source term;

  2. 2)

    Compared with full power operation, the dose rate decreases slightly in ELPO mode. The main reason is that ELPO reduces the total amount of CRUD and inhibits the formation of radioisotope under the premise of constant irradiation level;

  3. 3)

    The dose rate of the 50% power platform is slightly higher than that of the 75% power platform. The reason for this phenomenon is the same as the migration trend of corrosion products. The superposition of the effects of lower power platform on SNB rate and corrosion product concentration may lead to the increase of CRUD total, radioisotope and dose rate.

Fig. 3.
figure 3

Calculation Results of Source Term Distribution in Primary Loop

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4 Conclusions

In this paper, a model of corrosion product migration and radioisotope formation in the primary circuit of Analog PWR is established, and the migration behavior of corrosion products during ELPO mode of a PWR is evaluated. The main conclusions are as follows:

  1. 1)

    ELPO can restrain CRUD deposition and alleviate the influence of CRUD on fuel capability by reducing SNB rate and changing local coolant temperature;

  2. 2)

    Compared with full power operation, ELPO will cause the coolant source term to rise, and the radioisotope deposited on the fuel surface will enter the coolant and be gradually removed by CVCS;

  3. 3)

    The total amount of CRUD, coolant source term and dose rate increased slightly when the power platform was reduced from 75% to 50%, which indicated that the ELPO power platform had a great influence on the migration behavior of corrosion products in the primary circuit.