Corresponding author: Petr M. Kalinichev (kalinichevpm@gmail.com)
Academic editor: Yury Kazansky
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, 134I activity is historically used in WWER power units. However, observed 134I 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 134I activity results from the fuel washout from the leaking fuel rods during operation of the WWER-type reactor. Some examples of applications at nuclear power plants are discussed.
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 long-term storage.
Some operators abroad use repair on-site 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, long-lived fission products are released from the failed fuel rod. Short-lived radionuclides mostly decay inside the fuel rod before they are released to the coolant. In this case, the activity of short-lived 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 short-lived 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 in-core surfaces (
In practice, however, the activity of fission products (including the short-lived 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 238U neutron cross-section 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 131I, for example, the cumulative radiation yield of 239Pu fission is 30% higher than that of 235U 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 short-lived 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 (
where
Dependences were obtained in (
where
The dependence of
where σPu,
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 σPu > σU, the accumulation of plutonium in deposits may lead to a growth in the fission rate
Generation of plutonium in fuel is defined by the resonance capture of epithermal neutrons by 238U 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
Schematic illustration of the model problem that describes the neutron capture by 238U nuclei.
With the given energy of neutrons, the probability
where
When expressed in a unit of surface and in a unit of time, the number of the neutron resonance capture reactions
where φ is the energy density of the incident flux.
A high macroscopic cross-section of the neutron capture by 238U nuclei leads to the flux of near-resonant 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
where
The cross-section of the neutron absorption σ(
It can be roughly considered that φ ∝ 1/
where I0 is the modified Bessel function of the first order; and σ0 = σ(
At the outer boundary of the fuel layer (
With σ0
Distribution of the mass fraction of plutonium in a uranium dioxide fuel pellet at a burnup of ~ 59 MW×day/kgU
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 cross-section, σ
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 134I 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 ∝
where
It follows from Eq. (10) that the neutron flux and the concentrations
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
The function
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 (Multi-group 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
Examples of the function
Dependences f of the relative 134I activity growth on the burnup increment: 1–2.4% fuel enrichment; 2–3.6% fuel enrichment.
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
where
With a fixed mass of fuel deposits, expression (12) can be rewritten as
where the product
φ = max ((
Inequality (13) should be satisfied in any interval [
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:
where α is the linear approximation coefficient that characterizes the activity growth rate.
Let
α ≤ αcr = (
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 steady-state 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.
Time intervals of steady-state reactor operation are selected within the fuel cycle.
The data on 134I activity for the given time interval is approximated by linear dependence (16); the value α is determined using the least squares method.
The so obtained value of the activity growth rate α is compared with the criterion value α cr calculated in accordance with the right-hand part in (17). If α/α cr > 1, a conclusion is made that there is fuel washout.
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 134I activity growth rate α to the critical one, αcr, for the above cycles are shown in Fig.
Results of calculations based on the criterion for 134I. Shown on the vertical axis is the ratio of the actual slope α for the linear trend of the 134I activity to the critical slope αcr.
It can be seen in the figure that, for all cycles during which there were no fuel failures, the ratio α/αcr < 1. This is exactly what one can expect with an invariable amount of fuel deposits in the core.
The ratio α/αcr 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 diamond-shaped symbols. Ovals are used to mark the cycles for which fuel washout into the coolant may be regarded as confirmed experimentally.
One leaking FA was detected during reactor outage after cycle 2 at unit С. This FA was examined in RIAR hot cells. One failed fuel rod (with gadolinium) was found in the FA by examination. A lengthy opened defect was found in the failed fuel rod. The fuel pellet was heavily oxidized on the grain boundaries opposite the defect which led to the grain leaching. A large-size piece of the fuel pellet was absent at that point. This is an evidence of the fuel being washed out from the gadolinium fuel rod into the coolant.
There were eight leaking fuel assemblies found after cycle 3 at unit В after the reactor shutdown for preventive maintenance. It was found by a visual examination of one of them that a cladding fragment was absent in one of the peripheral fuel rods. The extent of the fuel rod damage allowed a suggestion that there was fuel washout into the coolant during operation.
The activity of 134I is used traditionally in WWER reactors to estimate the amount of fuel deposits. It has been demonstrated in the study that the activity of 134I 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 upper-bound estimation of the respective maximum 134I activity growth rate.
A criterion has been proposed which makes it possible to differentiate cases when the 134I 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 WWER-1000 NPPs have been analyzed comparatively. It has been shown that the 134I 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 134I 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. 20-38-90081.
* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2020, n. 3, pp. 50–61.