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PHYSICAL FOUNDATIONS OF NUCLEAR POWER SAFETY: EFFECT
OF STEAM-PHASE SOLUBILITY ON BORIC ACID ACCUMULATION
IN THE CORE OF A VVER REACTOR
Alovitdinov Khasan
Master’s student, National Research Nuclear University MEPhI (Moscow
Engineering Physics Institute)
Muinov Ulugbek
PhD student, Department of Automation and Control, Tashkent Institute of
Chemical Technology, Tashkent, Uzbekistan
https://doi.org/10.5281/zenodo.16716994
Abstract:
This thesis analyzes the risk of boric acid crystallization in the
core of a VVER reactor under prolonged beyond-design-basis accident
conditions. Unlike conservative approaches, this study uses a refined
mathematical model that accounts for the removal of boric acid due to its
solubility in steam. The aim is to evaluate the impact of this mechanism on the
final concentration of boric acid and to assess the effectiveness of a design
solution involving the reduction of initial boron concentration in Stage 3
hydroaccumulators (HA-3). The results indicate that considering steam-phase
solubility significantly reduces the crystallization risk; however, additional
measures are still required for complete elimination of the hazard.
Key words:
VVER, NPP safety, beyond-design-basis accident, boric acid,
crystallization, passive systems, steam-phase solubility, mathematical modeling.
Introduction
Ensuring the safety of VVER-based nuclear power plants (NPPs) during
severe beyond-design-basis accidents is one of the key tasks of modern nuclear
power engineering. Scenarios involving loss of coolant and long-term cooling of
the reactor core using passive systems require detailed analysis of mass transfer
processes.
One of the major hazards in such scenarios is the accumulation and
subsequent crystallization of boric acid injected into the reactor to ensure
cooling and subcriticality. The formation of solid deposits can block the flow
areas of fuel assemblies and disrupt core cooling. Previous studies have often
applied conservative approaches that do not account for boron removal via
steam. This study aims to provide a more realistic assessment of the process by
considering boric acid solubility in the steam phase.
Literature Review
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The operation of VVER passive safety systems and the problem of boron
accumulation are well covered in the scientific literature [
Ошибка! Источник
ссылки не найден.
]. The necessary physical and chemical properties of boric
acid solutions for the analysis are provided in other sources. Key to this study
are works focused on boric acid removal via steam.
Figure 1. Flow scheme of boric acid during accidents involving leakage
due to breach of the primary circuit integrity in VVER reactors [
Ошибка!
Источник ссылки не найден.
]
Experimental studies on boric acid solubility in saturated water vapor were
conducted by M.A. Styrikovich et al. [
Ошибка! Источник ссылки не найден.
]
and A.V. Pityk et al. [
Ошибка! Источник ссылки не найден.
]. These studies
established the distribution coefficient between liquid and vapor phases,
providing the basis for a more accurate model. Reference [
Ошибка! Источник
ссылки не найден.
] suggests that at near-atmospheric pressure, the
distribution coefficient (k) can be approximated as 0.0014, enabling quantitative
assessment of the boric acid mass removed with steam.
Materials and Methods
A mathematical modeling approach based on material balance equations
was used to assess boric acid accumulation. Calculations were carried out for a
72-hour accident scenario at a VVER-TOI reactor. Unlike the conservative model
that assumes zero boron removal via steam, this study uses a refined mass
balance equation for boric acid in the reactor core:
𝑀
𝑓
= 𝑀
𝑐𝑜𝑟𝑒
+ 𝑀
𝑖𝑛
− 𝑀
𝑠𝑡𝑒𝑎𝑚
, (1)
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where: M
in
– mass of solution entering from hydroaccumulators, kg;
M
steam
– mass of steam generated due to residual heat, kg; M
core
– current mass
of the fluid in the core, kg.
Using the relationship between boric acid concentration in water and
steam:
С
𝑠𝑡𝑒𝑎𝑚
= С
𝑓
∙ 𝑘
. (2)
The residual heat is assumed to be used for coolant evaporation inside the
reactor core [3].
The condensation capacity of steam generators (equal to the heat
exchangers of the passive heat removal system – SPOT) was based on large-scale
experiments conducted at JSC “SSC RF – FEI”:
𝑁
𝑆𝑃𝑂𝑇
= {
144,8 − 5,885 ∗ 10
−4
𝑡 + 3,499 ∗ 10
−9
𝑡
2
, при 𝑡 ≤ 86400
−131,25 +
7.619∗10
4
√𝑡
, 𝑡 > 86440
, (3)
Where: t – time since the accident occurred.
Calculations were performed numerically with a small-time step. The
resulting concentration values were compared with the solubility limit (≈415
g/kg) to determine the onset of crystallization and mass of precipitate.
Analysis and Results
The analysis was initially performed at a boric acid concentration of 16
g/kg, with subsequent simulations conducted for a range of concentrations
decreasing from 12 down to 1 g/kg.
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Figure 2. The accumulation of boric acid in the reactor core in
different concentrations of HA-3
The results showed that the conservative model gave a final concentration
of 1089 g/kg, while the refined model predicted approximately 974 g/kg. This
confirms that vapor solubility is an important risk reduction factor; however,
crystallization remains a major problem.
Conclusions and Recommendations
1. Accounting for boric acid solubility in steam allows for a more realistic
and less conservative assessment of boron accumulation in the VVER core. While
crystallization risk is reduced using standard design concentrations, it is not
entirely eliminated.
2. Reducing the initial concentration of boric acid in Stage 3
hydroaccumulators (HA-3) to 1–2 g/kg proves to be an effective design measure
to prevent crystallization, even within the refined model.
3. To improve prediction accuracy, additional experimental research is
needed to verify the distribution coefficient under conditions close to those of a
severe accident. The combined effect of steam-phase solubility and droplet
entrainment should also be investigated.
References:
1.
Kalyakin S.G., Remizov O.V., Morozov A.V., Yuryev Yu.S., Klimanova Yu.V.
Justification of the design functions of the passive flooding system GE-2 for the
0
100
200
300
400
500
600
700
800
900
1000
0
50000
100000 150000 200000 250000 300000
Con
cent
ra
ti
o
n
o
f
b
o
ri
c
acid
,
g
/k
g
t, s
С(ГЕ-3)=16 g/kg
С(ГЕ-3)=12 g/kg
С(ГЕ-3)=9 g/kg
С(ГЕ-3)=6 g/kg
С(ГЕ-3)=4 g/kg
С(ГЕ-3)=2 g/kg
С(ГЕ-3)=1 g/kg
ACADEMIC RESEARCH IN MODERN SCIENCE
International scientific-online conference
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advanced VVER NPP design. Izvestiya vuzov. Yadernaya energetika. 2003. No. 2.
Pp. 94–101.
2.
Styrikovich M.A., Tshvirashvili D.G., Nebieridze D.P. Investigations of the
solubility of boric acid in saturated water vapor. Doklady AN SSSR. 1960, v. 134,
no. 3, pp. 615–617.
3.
Pityk A.V., Morozov A.V., Shlepkin A.S., Sakhifgareev A.R. Experimental
study of boric acid solubility in boiling steam at atmospheric pressure. Izvestiya
vysshikh uchebnykh zavedeniy. Yadernaya energetika. 2019. No. 1. Pp. 30–40.
