Corresponding author: Vladimir I. Savander (VISavander@mephi.ru)

Academic editor: Georgy Tikhomirov

The paper presents the results of a computational and theoretical analysis concerned with the use of erbium as a burnable absorber in VVER-type 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 18-month life and to two for the 24-month 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 burn-up, 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 in-core times was considered. The escape of neutrons from the core was taken into account by selecting the critical value _{∞} at the end of life.

Erbium does not burn up in full for the lifetime which affects the fuel burn-up 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.

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 VVER-1000 type use a gadolinium-based 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 VVER-1000 and VVER-1200 types have an 18-month life with a length of 480 days and a further extension to 510 to 540 days (

As part of a simplified fuel burn-up 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 burn-up, 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 burn-up of unloaded fuel (_{0} – _{Er}))/_{0,} where _{0} is the burn-up of fuel without erbium, and _{Er} is the weight content of erbium in fuel elements. The calculation results are presented in Fig.

Relative loss in the fuel burn-up as a function of the erbium content in fuel: 1–18-month life; 2–24-month life.

With loads of erbium dioxide in fuel elements being relatively small (up to 1%), the dependence of the loss in burn-up on the content of erbium in fuel elements is linear and much smaller than the loss during the transition from a 12-month life to an 18-month or 24-month 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

where r is reactivity, _{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 non-fissile isotopes, the dependence of the radiation capture micro-cross-section on the energy in the thermal region changes in accordance with the 1/

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 24-month 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 water-fuel 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

Polycell average neutron multiplication factor as a function of time with different erbium loads in fuel elements for the refueling ratio of two: 1 – Er 0%; 2 – Er 0.3%; 3 – Er 0.7%; 4–1.1%.

Polycell average neutron multiplication factor as a function of time with different erbium loads in fuel elements for the refueling ratio of three: 1 – Er 0%; 2 – Er 0.3%; 3 – Er 0.7%; 4–1.1%.

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 24-month 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 uranium-water system) which meets the EOL core composition (

Relative value of the density reactivity coefficient as a function of the erbium load in fuel elements: 1–18-month life, 2–24-month life.

Relative value of the temperature reactivity coefficient’s spectral component as a function of the erbium load in fuel: 1–18-month life; 2–24-month life.

Relative value of the overall coolant temperature refuel: 1–18-month life; 2–24-month life.

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 coolant-moderator 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 low-level 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 burn-up rate for this absorber is much lower than the fuel burn-up 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 _{B}(_{B}(_{B} = (_{B}(_{B}(_{K}, where _{K} is the amount of the coolant in the primary circuit. This requires the amount Δ_{B}(_{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

the solution of which looks like

where _{LRW} is the total lifetime accumulated quantity of LRW, and _{B}(

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 _{LRW} /_{K}. Given the value of this magnitude, we shall determine the final boron absorber concentration _{B}(

from which we obtain the value of the relative LRW amount reduction

depending on the concentration of erbium in fuel elements (Fig.

Relative LRW amount reduction as a function of the erbium concentration in fuel elements: 1 – Er 0.3%; 2 – Er 0.7%; 3 – Er 1.1%.

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. _{LRW}/_{K} = 2, then the LRW amount reduction change from 10 to 50% with the erbium load in fuel elements being in the above range.

The results of the computational studies for the applicability of erbium as burnable absorber for the VVER-type 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 coolant-moderator 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 burn-up 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 burn-up with the use of erbium leads to a decrease non uniformity factor of radial heat distribution in FA. However, the loss in burn-up can be reduced through an increase in the FA loading into the core’s central region with the makeup fuel (

_{2}O

_{3}in the VVER-1200 reactor fuel.

^{th}International Conference on Nuclear Option in Countries with Small and Medium Electricity Grids, INAC, 1–12.

^{th}International Scientific Conference EPE 2012. Czech Republic, 1299–1304.

* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2020, n. 3, pp. 62–71.