Corresponding author: Vladimir I. Savander ( visavander@mephi.ru ) Academic editor: Georgy Tikhomirov
© 2020 Saleh H. Alassaf, Vladimir I. Savander, Ahmed A. Hassan.
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:
Alassaf SH, Savander VI, Hassan AA (2020) Use of erbium as a burnable absorber for the VVER reactor core life extension. Nuclear Energy and Technology 6(4): 275279. https://doi.org/10.3897/nucet.6.60563

The paper presents the results of a computational and theoretical analysis concerned with the use of erbium as a burnable absorber in VVERtype reactors. Partial refueling options for the reactor life extension to 18 and 24 months is considered, the refueling ratio being equal to three for the 18month life and to two for the 24month life. Erbium is expected to be present in all fuel elements in the FA with the same weight content. The influence of the erbium weight content on such neutronic characteristics of the reactor and fuel as burnup, reactivity coefficients, residual volume of “liquid" control, and amounts of the liquid radioactive waste (LRW) formed was assessed.
The calculations were performed using a simplified model of refueling without FA reshuffling. An infinite array of polycells consisting of FAs with different incore times was considered. The escape of neutrons from the core was taken into account by selecting the critical value K_{∞} at the end of life.
Erbium does not burn up in full for the lifetime which affects the fuel burnup as compared with the liquid excessive reactivity compensation system. The reduction is 0.7% per 0.1% of the erbium weight load in the fuel elements. This, however, also reduces the maximum content of the boron absorber in the coolant and the LRW accumulation in the ratio of 5% per 0.1% of the erbium weight load.
Erbium influences the spectral component of the coolant temperature reactivity coefficient which turns out to be negative even with its minor weight fraction in fuel elements, and a reduction in the boron absorber fraction leads to a positive value of the density reactivity coefficient. As a result, the overall coolant temperature reactivity coefficient has a negative value throughout the lifetime.
VVER, burnable absorber, erbium, reactivity margin, GETERA, liquid excessive reactivity compensation system, liquid radioactive waste (LRW)
A core life extension in reactors with partial refueling leads to an increased capacity utilization factor (CUF) and reduced unit costs of nuclear hazardous refueling operations which, combined, improves the economic efficiency of the NPP. However, an extended core life causes a proportional growth in the fuel reactivity margin that requires to be compensated throughout the reactor lifetime. To this end, along with the liquid system based on dissolution of boron absorber in the coolant, reactors of the VVER1000 type use a gadoliniumbased burnable absorber which is integrated into the fuel. With a high reactivity margin, if liquid control alone is used, the density reactivity coefficient can become negative, and the coolant temperature reactivity can become positive. Therefore, it is required to reduce the maximum concentration of the boron absorber in the coolant by increasing the share of the reactivity margin compensated through the use of burnable absorbers.
Natural gadolinium, a strong absorber of thermal neutrons, is used most extensively in Russian reactors (
There are no these drawbacks in the event of using relatively weak absorbers which can be introduced either into all fuel elements (
At the present time, reactors of the VVER1000 and VVER1200 types have an 18month life with a length of 480 days and a further extension to 510 to 540 days (
As part of a simplified fuel burnup model for a partial core refueling option, it has been assessed how the quantity of erbium absorber introduced as the burnable absorber into all fuel elements in the FA influences the unloaded fuel burnup, the coolant density and temperature reactivity coefficients, and the volume of the liquid compensation system. The major simplification consists in that refueling is considered without FA reshuffling in the core.
Computational studies were performed using the GETERA code (
The calculation model was based on identifying the periodic array of polycells consisting of FAs with different irradiation times in the core. Partial refueling is considered without reshuffling (
Primarily, a problem was considered concerning the assessment of how the weight fraction of erbium in fuel elements influences the burnup of unloaded fuel (
With loads of erbium dioxide in fuel elements being relatively small (up to 1%), the dependence of the loss in burnup on the content of erbium in fuel elements is linear and much smaller than the loss during the transition from a 12month life to an 18month or 24month life (10 to 20%).
We shall consider the influence of the erbium absorber on the overall coolant temperature reactivity coefficient. It is known to consist of two terms
$\frac{d\rho}{d{T}_{th}}=\frac{d\rho}{d{T}_{th}}\left({\gamma}_{th}=\text{const}\right)+\frac{d\rho}{d{\gamma}_{th}}\left({T}_{th}=\text{const}\right)\frac{d{\gamma}_{th}}{d{T}_{th}}$, (1)
where r is reactivity, Т_{th} is the coolant temperature, and γ_{th} is the coolant density.
The first term we shall designate α_{m} is the spectral component which is connected with the neutron gas temperature variation in response to the moderator temperature variation. For nonfissile isotopes, the dependence of the radiation capture microcrosssection on the energy in the thermal region changes in accordance with the 1/V law such that the thermal spectrum average microcrosssection will decrease as the moderator temperature increases. Fissionable isotopes have a resonance in the spectrum’s thermal region (Е = 0.3 eV), which results in the averaged radiation capture and fission crosssections growing with the moderator temperature increase. This reactivity coefficient will be positive in the absence of erbium. However, since even erbium isotopes also have a resonance at the energy Е = 0.41 eV, the cumulative effect can be negative. So this coefficient depends largely on the concentration of erbium in fuel. Therefore, this term will have a negative sign if there is a certain quantity of erbium in fuel.
The second term designated a_{g} is the density reactivity coefficient which, with a liquid system used for the excessive reactivity compensation, is defined to a great extent by the content of boron in the coolant. The higher is the concentration of boron in the coolant, the smaller is the value of the density reactivity coefficient. The calculation has shown that this value proved to be negative at the beginning of a regular life in the event of a purely liquid excessive reactivity compensation system for a 24month life. For this case, as a result, the overall temperature reactivity coefficient turned out to be positive.
Since a simplified partial refueling model is used in the study, then relative reactivity coefficient values are presented for the computational analysis. Temperature reactivity coefficient and its components, which meet the end reactor state prior to refueling with only a liquid system employed for the excessive reactivity compensation, are used as normalizing values. In this state, the concentration of the boron absorber is equal to zero, and the reactivity coefficients are defined only by the waterfuel ratio value which is equal for all considered options. In particular, the values of these coefficients do not depend on the refueling ratio.
The largest concentration of the boron absorber in the core is normally achieved at the beginning of a regular life. This value was calculated for all options under consideration. Figs
Such boron absorber concentration was added into the coolant for the calculation of reactivity coefficients as ensures the polycell criticality at the initial time. After that, the spectral and density components of the overall temperature reactivity coefficient for all considered life duration and fuel erbium load options were determined by simply varying the coolant temperature and density. The relative calculated values are presented in Figs
The results of the computational studies agree with the conclusion that a longer life and a larger initial concentration of boron in the coolant affect adversely the density reactivity coefficient reducing it to negative values for a 24month life. When erbium is used, the initial concentration of boron in the coolant decreases and the density reactivity coefficient grows linearly reaching substantially positive values (up to 50 to 70% of its value in a purely uraniumwater system) which meets the EOL core composition (
The spectral component of the reactivity coefficient ensures that negative values are achieved already with a small content of erbium in fuel elements and grows linearly in modulus with the growth in the erbium load in fuel, as it increases in modulus by a factor of 2.5 to 3, this effect being dependent on the life duration.
It is natural that the overall coolantmoderator temperature reactivity coefficient also grows in modulus in a linear manner with the increase in the erbium load in fuel elements as it remains negative.
A major drawback of a liquid excessive reactivity compensation system is large amounts of lowlevel LRW accumulated at the NPP as the result of the coolant dilution for keeping the reactor critical. A comprehensive reduction in this LRW amount is a vital task involved in the VVER reactor improvement (
The physical peculiarity of the liquid reactivity margin regulation system is that the absorber is dissolved in the coolant and the coolant circulates in the primary circuit. As a result, the boron absorber is outside the core for much of the time. Therefore, the burnup rate for this absorber is much lower than the fuel burnup rate in the core, and regulation consists in reducing the quantity of the boron absorber in the coolant by diluting it with distilled coolant.
To estimate the LRW amount reduction, the lifetime boron concentration in the coolant required for the criticality was calculated. The LRW amount can be estimated based on this data since the LRW quantity is equal to the quantity of the distillate introduced into the circuit. We shall assume that the concentration of boron in the coolant was C_{B}(t) at the time t, and is expected to be C_{B}(t + Δt)е by the time t + Δt. And the quantity of the boron absorber to be removed from the circuit will be equal to ΔM_{B} = (C_{B}(t) – C_{B}(t + Δt))V_{K}, where V_{K} is the amount of the coolant in the primary circuit. This requires the amount ΔV (t), which is determined from the equality C_{B}(t)∙ΔV (t) = ΔM_{B}, to be taken from the circuit with boron. The same quantity of distillate needs to be added into the circuit to replace the separated coolant quantity. By equating these values, we shall have the equation for the LRW amount determination
$\frac{d{V}_{\mathrm{LRW}}}{{V}_{\mathrm{K}}}=\frac{d{C}_{\mathrm{B}}\left(t\right)}{{C}_{\mathrm{B}}\left(t\right)}$ (2)
the solution of which looks like
${V}_{\mathrm{LRW}}={V}_{\mathrm{K}}\mathrm{ln}\left(\frac{{C}_{\mathrm{B}}\left(0\right)}{{C}_{\mathrm{B}}\left(T\right)}\right)$ (3)
where V_{LRW} is the total lifetime accumulated quantity of LRW, and C_{B}(T) is the end concentration of boron at the boron control termination time.
The calculation results depend greatly on the assumed value of the residual boron absorber concentration in the coolant. This study uses the quantity of the LRW formed in the reactor with no burnable absorber, that is, for the case of purely boron control relative to the circuit volume, namely n = V_{LRW} /V_{K}. Given the value of this magnitude, we shall determine the final boron absorber concentration С_{B}(T) and shall further use this value for all options of the erbium load in fuel elements. This results in the equation
${V}_{\mathrm{LRW}}\left({x}_{\mathrm{Er}}\right)={V}_{\mathrm{LRW}}\left(0\right)+{V}_{\mathrm{K}}\mathrm{ln}\left(\frac{{C}_{\mathrm{B}}\left({x}_{\mathrm{Er}},t=0\right)}{{C}_{\mathrm{B}}(0,t=0)}\right)$ (4)
from which we obtain the value of the relative LRW amount reduction
${\delta}_{\mathrm{LRW}}\left({x}_{\mathrm{Er}}\right)=\frac{{V}_{\mathrm{LRW}}\left(0\right){V}_{\mathrm{LRW}}\left({x}_{\mathrm{Er}}\right)}{{V}_{\mathrm{LRW}}\left(0\right)}=\frac{1}{n}\mathrm{ln}\left(\frac{{C}_{\mathrm{B}}(0,t=0)}{{C}_{\mathrm{B}}\left({x}_{\mathrm{Er}},t=0\right)}\right)$
depending on the concentration of erbium in fuel elements (Fig.
Since the fuel enrichment values for both partial refueling cases turned out to be close, the dependences of the relative reduction practically coincided as well, this being shown in Fig.
The results of the computational studies for the applicability of erbium as burnable absorber for the VVERtype reactor life extension have been obtained using a simplified model of partial refueling without the FAs reshuffled in the core. Options were considered with the core life extended to 18 to 24 months but with an integer refueling ratio which required an increased initial enrichment of the makeup fuel. Calculations have shown that varying the quantity of the erbium loaded into the fuel elements makes it possible to control the coolantmoderator temperature reactivity coefficient and ensures inherent safety properties (negative values of temperature reactivity coefficients).
It has been shown using a simple water exchange model for the boron absorber critical concentration control that the use of erbium as a burnable absorber makes it possible to reduce the LRW amount to 50%. An increase in the erbium load in fuel elements reduces the burnup of unloaded fuel by about 0.7% with the erbium load in fuel elements increased by 0.1 of wt. % as the reduction of the LRW amount in this case is about 5%. A reduction in the fuel burnup with the use of erbium leads to a decrease non uniformity factor of radial heat distribution in FA. However, the loss in burnup can be reduced through an increase in the FA loading into the core’s central region with the makeup fuel (