Corresponding author: Petr M. Kalinichev ( kalinichevpm@gmail.com ) Academic editor: Yury Kazansky
© 2020 Igor A. Evdokimov, Andrey G. Khromov, Petr M. Kalinichev, Vladimir V. Likhanskii, Aleksey A. Kovalishin, Mikhail N. Laletin.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Evdokimov IA, Khromov AG, Kalinichev PM, Likhanskii VV, Kovalishin AA, Laletin MN (2020) Development of a criterion for assessment of fuel washout during operation of WWER power units. Nuclear Energy and Technology 6(4): 307312. https://doi.org/10.3897/nucet.6.60559

Fuel failures may occur during operation of nuclear power plants. One of the possible and most severe consequences of a fuel failure is that fuel may be washed out from the leaking fuel rod into the coolant.
Reliable detection of fuel washout is important for handling of leaking fuel assemblies after irradiation is over. Detection of fuel washout is achievable in the framework of coolant activity evaluation during reactor operation. For this purpose, ^{134}I activity is historically used in WWER power units. However, observed ^{134}I activity may increase during operation even if leaking fuel in the core is absent, and fuel deposits are the only source of the fission products release.
The paper describes a criterion which enables to reveal the cases when the increase in ^{134}I activity results from the fuel washout from the leaking fuel rods during operation of the WWERtype reactor. Some examples of applications at nuclear power plants are discussed.
WWER, fuel rod, fuel failure, fission products, technique, coolant activity, iodine radionuclides, fuel washout
Fuel failures still occur during operation of nuclear power plants (NPPs). A failure may lead to increase in the primary coolant activity, higher dose rates for personnel, a larger amount of liquid radioactive waste, and more operations required for detection and replacement of fuel assemblies (FAs) with failed fuel rods. This also involves heavy financial losses.
One of the possible and most severe consequences of a fuel failure is washing out of the fuel particles from the leaking fuel rod into the coolant. Radiological consequences of the fuel washout can persist at the power unit in the form of a high background activity for a long time (up to 10 years) (
Reliable detection of fuel washout is important because leaking fuel assemblies require specific handling.
It is permitted in some countries to continue operation of FAs with “small” defects in the leaking fuel rods unless criteria for premature fuel discharge are met (
The established fact of the fuel washout limits the conditions of the intermediate FA storage at the NPP. Leaking FA’s with fuel washout must be stored in a sealed cask in the spent fuel pool. There can be additional restrictions for shipping of these FAs from the NPP for reprocessing or longterm storage.
Some operators abroad use repair onsite technologies when the failed fuel rod is replaced by the dummy rod (
It is possible to identify fuel washout in the framework of evaluation of primary coolant activity during reactor operation (
In case of a failure, longlived fission products are released from the failed fuel rod. Shortlived radionuclides mostly decay inside the fuel rod before they are released to the coolant. In this case, the activity of shortlived radionuclides released from the failed fuel rod turns out to be smaller than the background activity level of these radionuclides released from fuel deposits. So, activities of the most shortlived radionuclides out of those accessible for detection at the NPP are used, as a rule, as an indicator of the amount of fuel deposits on the incore surfaces (
In practice, however, the activity of fission products (including the shortlived ones) can increase during reactor operation even if there is no leaking fuel in the core and the only source of the fission products release is fuel deposits. There are two factors behind this.
First, the fissile nuclide composition of fuel deposits changes in the process of irradiation. Plutonium is generated in deposits faster and reaches larger concentrations than, on the average, in fuel pellets. Such behavior is explained by a smaller effect of the ^{238}U neutron crosssection shielding in the fuel particles on the outer cladding surface (the effect of shielding in fuel pellets is described, e.g., in (
Second, the evolution of the fissile nuclide composition in deposits leads to a change in the radiation yields (probabilities of the radionuclide formation per one fission). For ^{131}I, for example, the cumulative radiation yield of ^{239}Pu fission is 30% higher than that of ^{235}U fission.
For the reliable identification of the fuel washout during reactor operation, one needs to differentiate between cases when the growth in the activity of shortlived fission products is caused by the fuel washout from leaking fuel rods and when this results from the evolution of fissile nuclide composition in fuel deposits.
A criterion is proposed below for detection of fuel washout during WWER operation in the event of a fuel failure. Some examples of practical applications at NPPs are provided.
Balance equations are used to describe the activity of fission products in the primary circuit (
A ∝ R, (1)
where A is the activity of ^{134}I; and R is the rate of the ^{134}I release into the coolant from fuel deposits.
Dependences were obtained in (
R ∝ YF, (2)
where Y is the cumulative yield of ^{134}I per fission; and F is the fission rate (the number of heavy nuclei fissions per unit of time in a unit of the fuel deposits amount in the core).
The dependence of F on the nuclide composition of fuel in deposits can be roughly represented as
F ≈ Φ (σ_{Pu}c_{Pu} + σ_{U}c_{U}), (3)
where σ_{Pu}, c_{Pu} are the effective crosssection and the concentration of ^{239}Pu nuclei in deposits; σ_{U}, c_{U} are the same for ^{235}U; and Φ is the neutron flux.
Uranium burns up and plutonium is accumulated in fuel deposits in the process of the reactor operation. Under certain conditions, with regard for the fact that σ_{Pu} > σ_{U}, the accumulation of plutonium in deposits may lead to a growth in the fission rate F and, as it follows from Eqs. (1) and (2), to a growth in the background activity.
Generation of plutonium in fuel is defined by the resonance capture of epithermal neutrons by ^{238}U nuclei. We shall consider a model problem to demonstrate the differences between the accumulation of plutonium in fuel deposits and in fuel pellets.
Let there be a flat layer of fuel of a certain thickness with the epithermal neutron flux Φ falling onto it at the right angle. We shall estimate how the plutonium generation rate changes in fuel through the depth x (Fig.
With the given energy of neutrons, the probability dp of the neutron capture at the depth x in the layer dx (
dp = σ×c×exp(–σ×c×x)dx, (4)
where с is the concentration of ^{238}U nuclei; and σ is the crosssection of the neutron capture by ^{238}U nuclei.
When expressed in a unit of surface and in a unit of time, the number of the neutron resonance capture reactions dN (x) in the energy interval dE at the depth x is found by the expression
dN = c×σ×exp(–c×σ×x)dx[φ(E)dE], (5)
where φ is the energy density of the incident flux.
A high macroscopic crosssection of the neutron capture by ^{238}U nuclei leads to the flux of nearresonant neutrons attenuating through the fuel layer. And a convenient way to calculate the intensity of the neutron flux interaction with fuel is to introduce the value σ_{eff} (x) as the “effective” neutron capture crosssection:
${\sigma}_{eff}\left(x\right)=\frac{1}{\Phi}{\int}_{{E}_{1}}^{{E}_{2}}\sigma \left(E\right){e}^{c\sigma \left(E\right)x}\phi \left(E\right)dE$, (6)
$\Phi ={\int}_{{E}_{1}}^{{E}_{2}}\phi \left(E\right)dE$, (7)
where Е_{1}, Е_{2} are the epithermal neutron energy range limits. And expression (5) can be rewritten as
dN = Φ×σ_{eff} (x)×c×dx. (8)
The crosssection of the neutron absorption σ(E) by ^{238}U nuclei includes a number of resonance peaks in the spectrum’s epithermal region. The most notable peak is that being the first at the energy E_{r} ≈ 6.67 eV. Its contribution to the integral resonance crosssection is about 40% (
It can be roughly considered that φ ∝ 1/E in the epithermal region of the neutron spectrum. Substituting in expression (6) the dependence of the crosssection on energy for one resonance peak, according to the BreitWigner formula (
$\frac{{\sigma}_{eff}\left(x\right)}{{\sigma}_{eff}\left(0\right)}=\mathrm{exp}\left({\sigma}_{0}cx/2\right){\mathrm{I}}_{0}\left({\sigma}_{0}cx/2\right)$, (9)
where I_{0} is the modified Bessel function of the first order; and σ_{0} = σ(E_{r}) is the resonance peak amplitude.
At the outer boundary of the fuel layer (x = 0), the righthand part of Eq. (9) is equal to unity. For a flat geometry (see Fig.
With σ_{0}cx >> 1 (for the first resonance peak of ^{238}U and uranium dioxide fuel, this corresponds to x >> 1×10^{–5} m), the righthand part of Eq. (9) decreases as x^{–0.5}. This means that, with scales of about several millimeters (the fuel pellet size), the average value of σ_{eff} will be by many times smaller than in the nearsurface layer. As a result, the intensity of the neutron resonance interaction with ^{238}U and, therefore, the concentration of plutonium on the fuel pellet periphery should be notably larger than the pellet average values. This is confirmed by postirradiation examinations (
An approach is proposed in (
The conditions on the fuel pellet periphery are close to the fuel deposit irradiation conditions on the fuel cladding surface. The considered model shows that, due to a larger crosssection, σ_{eff}, plutonium is generated in fuel deposits faster and reaches larger concentrations than in the fuel pellets on the average. This circumstance may lead to a notable increase in the fission rate F in deposits during the reactor operation, and, as a consequence, to a gradual growth in the coolant background activity in the course of the fuel cycle.
The maximum rate of activity growth, with a fixed amount of fuel deposits, can be estimated for any core configuration. If a fuel rod fails during operation and the recorded growth in the ^{134}I activity exceeds the calculated threshold value, a conclusion can be made that there is a source of fuel particles in the core. This forms the basis for the criterion of the fuel washout from leaking fuel rods.
The approximate relation as follows is valid for the neutron flux Φ in expression (3)
Φ ∝ LP/(ε_{Pu} σ_{Pu}n_{Pu} + ε_{U} σ_{U}n_{U}), (10)
where n_{Pu}, ε_{Pu} are the concentration in fuel pellets and the fission energy for ^{239}Pu nuclei; and n_{U}, ε_{U} are the same for ^{235}U.
It follows from Eq. (10) that the neutron flux and the concentrations c_{Pu} and c_{U} in fuel deposits are defined by the fissile nuclide composition (and, therefore, by the burnup and enrichment) in fuel rods.
Then, with Eqs. (2) and (3) taken into account, expression (1) for the activity caused by the release of fission products from fuel deposits can be approximately written as
A ∝ F ∝ LPf (Bu). (11)
The function f (Bu) has the meaning of a relative growth in the activity due to fission products release from the fuel deposits on the fuel rod of a given enrichment in course of irradiation.
It should be noted that the generation of plutonium in fuel pellets depends on the spectrum of neutrons which is influenced, in particular, by the evolution of the boric acid concentration in the coolant, and by the coolant temperature and density. To study these parameters, calculations were performed using a certified neutronic code, SVL (Multigroup Program for the Calculation of WWER Reactor Cells and Assemblies. Certificate No. 248, dated 18.12.2008). A computational analysis has shown that variations in the above parameters have a relatively slight impact on the form of the function f. It can be therefore considered that the function f depends only on the burnup Bu for the given fuel type with the given enrichment.
Examples of the function f calculated using the SVL code for two different enrichments are shown in Fig.
We shall consider that most of the fuel deposits are on the fuel cladding surfaces. To build the fuel washout criterion, it is required to take into account that the core contains deposits on fuel rods with a different burnup. With regard for the contribution of each i^{th} fuel rod, the growth in the activity A^{*} in the course of the fuel cycle can be described using relation (11):
$A\left(t\right)\propto \sum _{i}{m}_{i}K{q}_{i}\left(t\right){f}_{i}\left(B{u}_{i}\left({t}_{0}\right)+\Delta B{u}_{i}\left(t\right)\right)$ (12)
where m_{i} is the effective mass of the fuel deposits on the i^{th} fuel rod (the mass of deposits in the form of a “monolayer” capable to ensure the same ^{134}I release rate); Kq_{i} (t) is the relative heat rate of the i^{th} fuel rod (the ratio of the current fuel rod power to the current value of the average power of the fuel rods in the reactor); Bu_{i} (t_{0}) is the fuel burnup in the i^{th} fuel rod at the initial time; and ∆Bu_{i} (t) is the increment of the fuel burnup in the i^{th} fuel rod between the time t_{0} and the time t.
With a fixed mass of fuel deposits, expression (12) can be rewritten as
A (t) ≤ A (t_{0})×kφ, (13)
where the product kφ describes the maximum negative activity growth in the interval [t_{0}, t]. And
φ = max ((f_{i} (Bu_{i} (t_{0}) + ∆Bu_{i} (t)) / f_{i} (Bu_{i} (t_{0}))), (14)
k = max (Kq_{i} (t) / Kq_{i} (t_{0})). (15)
Inequality (13) should be satisfied in any interval [t_{0}, t] for which there is no fuel washout into the coolant.
As shown by an analysis of the WWER NPP cycles, the activity of fission products caused by the release from fuel deposits, provided there is no leaking fuel in the course of cycle, is fairly well approximated by a linear function if the reactor operates with a constant power:
A (t) ≈ α(t – t_{0}) + A (t_{0}), (16)
where α is the linear approximation coefficient that characterizes the activity growth rate.
Let t_{0} ≤ t ≤ t_{1} be the interval of an approximately linear activity growth, so the inequality as given below follows from (13) and (16)
α ≤ α_{cr} = (kφ – 1)×A (t_{0}) / (t_{1} – t_{0}). (17)
Testing of inequality (17) can be used as the fuel washout criterion. A violation of condition (17) is an evidence of the fuel washout from the failed fuel rod.
The value φ can be determined based on the neutronic calculation data for the analyzed fuel cycle. If the reactor operates in a steadystate fuel cycle, estimation can be based on the reactor standard fuel loading pattern and standard FA loading histories.
The criterion application algorithm is as follows.
To demonstrate the operability of the proposed criterion, we shall consider data for a number of WWER fuel cycles both with and without fuel failures. The calculated ratios of the actual ^{134}I activity growth rate α to the critical one, α_{cr}, for the above cycles are shown in Fig.
It can be seen in the figure that, for all cycles during which there were no fuel failures, the ratio α/α_{cr} < 1. This is exactly what one can expect with an invariable amount of fuel deposits in the core.
The ratio α/α_{cr} did not exceed unity as well for some fuel cycles with fuel failures. This is in accordance with the ideas that not any fuel failure entails a fuel washout into the coolant.
Fuel washout was shown with the use of the criterion for some of the analyzed cycles with leaking fuel in the core. Such cycles are marked by diamondshaped symbols. Ovals are used to mark the cycles for which fuel washout into the coolant may be regarded as confirmed experimentally.
The activity of ^{134}I is used traditionally in WWER reactors to estimate the amount of fuel deposits. It has been demonstrated in the study that the activity of ^{134}I tends to grow in the course of the failure free fuel cycles even with an invariable mass of fuel deposits in the core. This may happen due to a high rate of plutonium generation in fuel deposits. Dependence has been obtained which allows upperbound estimation of the respective maximum ^{134}I activity growth rate.
A criterion has been proposed which makes it possible to differentiate cases when the ^{134}I activity growth is caused by the washout of fuel and when it is explained by the evolution of the fissile nuclide composition in fuel deposits.
A number of fuel cycles at WWER1000 NPPs have been analyzed comparatively. It has been shown that the ^{134}I activity growth rate turns out to be smaller than the criterion threshold for the failure free fuel cycles. In the fuel cycles, for which fuel washout was confirmed experimentally, the ^{134}I activity growth rate exceeds the value set by the criterion.
The research was carried out with the financial support of the RFBR as part of the Project No. 203890081.