International Conference on the Physics of Reactors “Nuclear Power: A Sustainable Resource” 

Casino-Kursaal Conference Center, Interlaken, Switzerland, September 14-19, 2008 

About the volatility of boron in aqueous solutions of borates with 

vapour in relevance to BWR-Reactors 

Steffen Böhlkea, *, Christoph Schustera, Antonio Hurtadoa

a Technische Universität Dresden, Institute of Power Engineering, 01062 Dresden, Germany 

Abstract 

In BWR-reactors a boron injection system is installed to control a total or partial ATWS accident. The 

injected boron will be spread in the fluid and some of the boron will leave the reactor with the exhausted vapour. 

To analyse the lost of boron with the vapour is the great aim of this thesis. The volatility of the boron solution 

was measured by experiments in a little autoclave vessel up to 330 °C and 13 MPa and in a circulation loop 

called BORAN up to 225 °C and 2.5 MPa. 

In the two test facilities different boron compounds in solution were analysed. Mostly, solutions of 

Disodium-Pentaborat are used because only this compound will be injected in BWR-reactors as a high 

concentrated solution. The boron concentration in the vapour depends mainly on temperature and void fraction 

of the two-phase-flow. The volatility can take values about some percent. As well the reason of the volatility of 

the analysed solutions will be discussed within a chemical background. 

 

*

 Corresponding author, steffen.boehlke@tu-dresden.de 

Tel: +49 (351) 463 39898; Fax: +49 (351) 463 37161. 

1. Introduction 

Since boron is a very good captor for thermal 

neutrons, it is used to shut down the BWR-reactor, if 

the control rods fail. To investigate the boron 

injection system of a BWR, detailed knowledge 

about the boron compound that is used in the case of 

transient conditions is necessary. The compound, 

which will be injected into the reactor pressure 

vessel (RPV), is a solution of DisodiumPentaborate-Decahydrate with a concentration not 

less than 135 g/L. For quantitative analysis of the 

boron content in the RPV during and after injection 

it is necessary to investigate the boron compound 

and the boron transport with steam. 

This boron injection system is installed at every 

BWR all over the world and is only used in state of 

emergency. Because of the very good facility 

management in the power plants the control rods 

never failed and so this injection system was never 

used up to now. That is why it is very important, 

especially for probabilistic analyses, to know the 

effectiveness of this system. 

2. Theoretical background 

Theoretically, all borate ions can be constructed 

out of boric acid and meta borate ions and also 

divided into these parts in aqueous solution. This is 

demonstrated in equations (1) to (3). In equation (1) 

1 
the penta, in equation (2) the tri and in equation (3) 

the tetra borate is originated. The compound 

Disodium-Tetraborate-Decahydrate is also called 

Borax. 

(eq. 1) 

4 B(OH)3 + B(OH)4 B5O6(OH)4 + 6 H2O

(eq. 2) 

2 B(OH)3 + B(OH)4 B3O3(OH)4 + 3 H2O

(eq. 3) 

2 B(OH)3 + 2 B(OH)4 B4O5(OH)4 + 5 H2O 2

If the solid borates dissociate in water, they are 

forming lower borates and boric acid. How much of 

each borate will be created, depends on the pHvalue of the solution. The region of interest starts for 

pH-values below 5 at approximately 100 % boric 

acid and ends with nearly 95 % meta borate for pHvalues higher than 11. For pH-values in-between 

these borders, all other borates are detectable, for 

example using Raman spectroscopy (Anderson, 

1964, Attinà, 2000) or other methods, like highfield-NMR (nuclear magnetic resonance) (Momii, 

1967, Salentine 1983). The frequency scale of the 

borates is called “Borate-Vector” (Maya, 1976, 

Maeda, 1979) (see Fig. 1). 

5 6 7 8 9 10 11 0.0

0.2

0.4

0.6

0.8

1.0

 B4O5(OH)2-

4

 B3O3(OH)2-

5

 B3O3(OH)-

4

 B5O6(OH)-

4

 B(OH)3

 B(OH)-

4

relative boron concentration

pH-value

Fig. 1. pH-dependence of the “Borate-Vector” of solutions 

of borates. 

Consequently, it is possible to create the higher 

borate ions with boric acid and hydroxide ions in 

various constitutions. The equilibrium 

concentrations of the boric acid and the hydroxide 

ions define the created borates, according to the 

mass action law. For pH-values below 10 a defined 

content of boric acid is always a present component 

in any solution of borates. This knowledge is very 

important to perform the analysis of the experiments 

about the volatility of borates in boiling aqueous 

solutions into steam.

3. Experimental investigation 

3.1. Autoclave 

To analyse the volatility of boron out of a 

solution of Sodium-Pentaborate an autoclave with a 

volume of 2 litres and the maximum experimental 

conditions of 330 °C in temperature and 13 MPa in 

pressure was used. The vessel was filled with a 

known solution (compound, concentration and pHvalue). In the cap of the vessel a steam pipe with 

valve and condenser is attached. With this valve 

steam samples can be taken out of the vessel and 

condense at all temperatures. 

3.2. BORAN – circulation loop 

The autoclave has with the exception of the 

pressure and temperature no similarities with the 

RPV of a BWR. To have a better opportunity to 

compare the collected measurement data with a real 

BWR, a circulation loop called BORAN (BOR 

ANalysis) was constructed at the Technische 

Universität Dresden (see Fig. 2). In this facility the 

lost of Boron out of boiling solutions can also be 

analysed in dependence of the void fraction in the 

two-phase-flow, as one of the most important 

thermodynamic parameter in the BWR. 

This facility is a model of the primary circuit of 

a RPV in volumetric scale 1:6000 and axial scale 

1:1. The inner volume of the facility is 70 litres. At a 

normal fill level of 5500 mm are 45 litres for fluid 

and 25 litres for steam and gas, similarly scaled like 

in a real BWR. In five 3710 mm long electrical 

heater rods an installed power of 50 kW simulates 

10 % of the scaled reactor power. A Wire-MeshSensor from Forschungszentrum DresdenRossendorf measures the void fraction above the 

heater. To enlarge the spectrum of experiments an 

additional steam generator was connected to the 

loop to increase the pressure at constant coolant 

temperatures. 

2
In BORAN it is possible to simulate the boron 

injection with a dosing pump and to investigate the 

lost of boron with the steam out of the facility. As 

well the transport of boron in the compound borate 

can be shown in fluid flow path by integrated 

measurement system of conductivity sensors. To 

simulate a LOCA (lost of coolant accident) in the 

upper part a valve connects the BORAN with the 

atmosphere with an 8 mm pipe. 

Fig. 2. Scheme of the BORAN facility to simulate a boron 

injection transient in a BWR-RPV 

(technical data: max. pressure 2.5 MPa, max. temperature 

225 °C, max. heater power 50 kW, heater height 3.71 m, 

total height 8.17 m). 

3.3. Measurement matrix and analysis 

In the autoclave the volatility of boron out of 

boiling solutions was analysed in dependence of 

temperature (100 °C to 330 °C), boron concentration 

(0.1 g/L to 20 g/L), pH-Value (3.5 to 10.2) and also 

the compound (penta borate, tetra borate and boric 

acid). Three times the pH-value of the solution was 

changed with hydrochloric acid or sodium 

hydroxide. The temperature of the BWR at normal 

operation is 270 °C. Because of an estimated cool 

down of the reactor before boron injection, the 

temperature area between 100 °C and 200 °C is for 

the boron injection transients the most important. To 

have a complete data set of the volatility of boron 

also experiments until 330 °C and 13 MPa and with 

different compounds were performed. 

In BORAN the temperature is limited to 225 °C 

at a pressure of 2.5 MPa. Because of the bigger 

volume of 50 litres only analysis with penta borate 

solution at a maximum concentration of 8 g/L was 

done, but this at different void fractions in the twophase-flow from 0 up to 70 %. 

The condensed steam samples had been 

analysed with ICP-MS (inductively coupled plasma 

- mass spectrometry) at the VKTA (Verein für 

Kernverfahrenstechnik und Analytik Rossendorf 

e.V.). 

4. Results and discussion 

The measurement data in figure 3 was 

generated with the autoclave, the data in figure 4 

with the BORAN facility. Indicated concentrations 

are pure boron concentrations. 

All the measurement data are used to calculate 

analytic coefficients (5 – 10). Out of these 

coefficients an equation (4) was constructed. With 

this equation the volatility (v) for all boron 

compounds can be calculated very easily at defined 

conditions. The volatility is described as the 

quotient of cBK and cBA (4) without any unit. 

 (4) 

L

g c

aaaaa

c

c

v

BA

voidtpHc B

BA

BK

/

⋅ ⋅⋅⋅

cBK = boron concentration in the condensate 

cBA = boron concentration in primary coolant 

cNaPBO = concentration of Sodium-Pentaborate 

To describe the influence of the boron 

concentration the coefficient ac is used. The analytic 

description is divided into two parts. 

C ==

3
for cBA < 1.5 g/L: 

100 150 200 250 300 350 0.00

0.02

0.04

0.06

0.08

0.10

Boric Acid

 0.5 g/L pH = 5.5

 4.9 g/L pH = 4.1

Sodium-Tetraborate

 3.3 g/L pH = 9.15

 + HCl pH = 8.15

temperature / °C

volatility cBK/cBA

©

TU Dresden, chair of Hydrogen and Nuclear Power Engineering

Sodium-Pentaborate

 0.2 g/L pH = 8.5

 1.4 g/L pH = 8.4

 2.0 g/L pH = 8.3

 3.9 g/L pH = 8.1

 + NaOH pH = 10.2

 + HCl pH = 3.7

 9 g/L pH = 7.8

20 g/L pH = 7.3

100 150 200 0,00

0,01

0,02

©

TU Dresden, chair of Hydrogen and Nuclear Power Engineering

temperature / °C

volatility = cBK / cBA

 void nearly 0

 void ca. 0,25 - 0,35

 void > 0,60

 for comparison:

 autoclave

L

g

c a BA

c 0036.0 ⋅=

 

else: (5) 

as information: (6) 

Table 1 

Calculation of KMol for equation (6) 

Boron comp. nBor·MBor / 

g/mol MComp. / g/mol KMol

boric acid 10.8 61.8 0.175 

penta borate 108 590 0.183 

tetra borate 43.2 424.2 0.102 

The dependence of the pH-value, the 

temperature and the void fraction can be calculated 

with the following equations (7 – 9). The linear 

influence of the void fraction is exponentially 

weighted by the temperature (9). 

 

 (7)

 

 (8) 

 (9) 

Because boron acid has a higher volatility a 

fifth coefficient has to be constructed. The 

coefficient aBC is 1.35 in the case of boron acid. For 

all the other compounds it is 1. (10) 

By this method it is possible to predict the 

volatility of different borates with steam in the range 

of the experimental data and therefore also in the 

range of BWR- and PWR-reactors. It should be 

noted that the volatility of boron out of a boric acid 

solution was verified nearly 100 years ago by 

Gmelin (1922), but there are no quantitative data for 

temperature above 100 °C available in the literature. 

The equation for the calculation of the void 

influence (9) is currently only valid for the BORAN 

facility. The value of the void was measured by the 

Wire-Mesh-Sensor for many working points before 

the experiments with borates has been started. At a 

known working point the void can be estimated at 

this position only. For a transmission on a plant it is 

necessary to have more information about the 

geometry of the fluid channel. 

7.0

0038.0

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛

⋅=

L

g

c

a BA

c

BA NaPBO Mol cc ⋅

Fig. 3. Volatility of boron out of boiling solution with 

defined boron contents from different boron compounds – 

measurements with autoclave. 

Another possibility to get the void fraction in 

the facility is a calculation with a thermal hydraulic 

code like the ATHLET-Code from the Gesellschaft 

für Anlagen- und Reaktorsicherheit (GRS) mbH. A 

second possibility to measure the local void fraction 

in the heating duct with conductivity sensors is now 

under way. 

Fig. 4. Volatility of boron out of boiling pentaborate 

solution with a defined boron content (cboron = 1.3 g/L) at 

various void fractions– measurements with BORAN. 

= K

−1

⎛ ⎛ ⎞

327.0

54.9

1

874.7 906.8 −

⎟

⎟

⎟

⎠ ⎜

⎜

⎜

⎝ ⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝ +

− += pH pH

e

a

C

t at 1⋅+=

° − 009.008.0

C

t

a ° void = ⋅⋅+ evoid 60 2.01

4
Following influences and dependences can be 

extracted out of the measurement data in figure 3 

and 4: 

• Exponential temperature dependence for all 

temperatures 

• Saturation effect in volatility by increasing 

the boron concentration over 5 g/L 

• A decreasing pH-value increases the 

volatility and inverted 

• Different boron compounds create nearly 

the same volatilities at the same 

concentration and pH-value 

• Boric acid is 35 % more volatile than penta 

borates 

• A increasing void fraction increases the 

volatility of the boron up to a factor 5 in 

comparison to a vapour-free fluid-flow 

5. The influence of the void fraction 

The result of the measurements of the volatility 

with the BORAN facility is a very important 

dependence on the void fraction in the two-phaseflow (see fig. 4). The higher the void fraction the 

higher the interfacial area between fluid and vapour. 

At a bigger surface the probability is higher for 

a boric acid molecule to change from the fluid into 

the vapour. Prasser et al. (2007) have done some 

measurements about the interfacial area density in 

dependence on the volumetric gas content of a 

water-air-flow. They measured a nearly linear 

relation between air-content and interfacial area 

density. In this work this method was transferred to 

a flow of water and vapour. 

To have a better possibility to compare 

measurement data between various facilities, it will 

be the best to use only the interfacial area and not 

the void fraction because of different geometries. At 

this time it is not possible to measure the interfacial 

area density of a vapour-water flow; only data of a 

gas-water flow are available. 

6. About the reason of volatility 

6.1. Chemistry and consideration 

The dissociation of the borates in lower borates 

and boric acid is the basic fact for the description of 

the volatility of boron out of boiling solutions of 

borates. Gmelin (1922) implied that the boron in 

solutions of boric acid can left the boiling solution. 

The volatility by sublimation of solid boric acid in 

the glass industry is generally known while melting. 

The sublimation pressure of boric acid at room 

temperature is 280 Pa. 

More investigation of the volatility of solid 

boric acid was done by Stackelberg et al. (1937). He 

predicted the volatility of solid boric acid without 

water. But if the temperature gets higher than 

130 °C the ortho boric acid will lost its content of 

water and becomes meta boric acid and for 

temperatures about 400 °C boron oxide (H3BO3 Æ

OBOH Æ B2O3). The monomers of meta boric acid 

are connecting each other to a fibrous polymer 

chain. This effect stops the volatility. 

Under pressure the solutions of boric acid are 

always in the liquid phase to have ortho boric acid 

for all temperatures and every time without any dry 

out. That is why the boric acid is available as ortho 

boric acid with huge water content at every 

temperature. It is volatile. The correlation between 

the vapour pressure of water and the sublimation 

pressure of boric acid is a result of the mass action 

law. The proportionality factor depends on the 

temperature. 

Also Stackelberg et al. (1937) demonstrated a 

correlation between the boron concentration in the 

solution and in the condensate of the vapour. 

Therefore the influence of the concentration and 

temperature on the volatility can be established. 

At the end Stackelberg et al. (1937) published 

volatility data of boiling solutions with boric acid at 

different concentrations at nearly 100 °C. He 

measured a volatility of about 30 %, 60 times bigger 

than the measured values of the current work of 

nearly 0.5 %. Stackelberg et al. (1937) used the 

titration against barium hydroxide, a very errorprone method in comparison to the analysis by ICPMS of the current samples. Furthermore the 

experimental conditions in the 1930s are particularly 

not traceable and completely different from the 

conditions now. The measurement data of this work 

are from two facilities and they accord. Therefore 

5
this data have a higher plausibility in comparison to 

the literature data. 

6.2. Physical Data of volatility 

Gmelin (1922) collected the data of sublimation 

pressure from different papers. Two temperaturepressure-points can be used for the calculation of the 

volatility for this analysis. At first for 100 °C results 

a pressure of 8 kPa, for 128 °C a pressure of 

32.3 kPa. For water the saturation pressures are 

higher, 101 kPa for 100 °C and 254 kPa for 128 °C 

(Schmidt, 1989). Menzel et al. (1934) and Thiel et 

al. (1934) measured the sublimation pressure of 

boric acid, too. The data of Menzel et al. (1934) are 

only for temperatures until 75 °C. Thiel et al. (1934) 

describes at first the correlation between the 

saturation pressure of water and the sublimation 

pressure of boric acid in solution. The publicised 

sublimation pressures are smaller than in Gmelin 

(1922). 

Another physical parameter, which influences 

the volatility, is the sublimation enthalpy of boric 

acid. Pankajavalli et al. (2007) reported a value of 

(174.1 ± 4.7) kJ mol-1 at a mean temperature of 

72 °C. Stackelberg et al. (1937) measured a value of 

105.6 kJ mol-1 over the temperature range 109 – 

140 °C. The enthalpy of the evaporation of water is 

nearly 40 kJ mol-1 (20 kJ mol-1 for each hydrogen 

bridge bond) and depends, like every physically 

parameter, on the temperature. 

The high molar enthalpy of sublimation of boric 

acid depends on the high number of the strong 

hydrogen bridge bonds between the three hydroxylgroups of the boric acid. To crack each bond there 

are 20 kJ mol-1 necessary. The high enthalpy of 

evaporation of water has the same reason. 

A third factor, which influences the volatility of 

a solution of borates, is the “Borate-Vector”. It 

describes the distribution of the boron atoms on the 

ions and the boric acid in the solution in the 

dependence of the pH-value. The pH-value of the 

used solution is 8.3. The result is that only 30 % of 

all boron atoms are compounded in the boric acid 

and contribute to the volatility of the boiling 

solution (see Fig. 1). The boron acid molecules are 

un-dissociated because of their very week acidity, 

another assumption for the volatility. Dissociated 

acids cannot leave the fluid with the vapour. There 

will be a division of charge, which is physically 

forbidden. 

To leave the fluid the boron has to go over the 

interfacial area between the fluid and the vapour. 

This is a barrier for the boron. 

6.3. Calculation 

With the combination of all these influences the 

concentration in the condensed vapour can be 

estimated. Because of the lower vapour pressure of 

boric acid in comparison to water the part of the lost 

water is higher than the part of boric acid. The 

quotient is described in equation (11). 

boricacidV

waterV

p p

p f

,

, = (11) 

The quotient of the molar enthalpies in equation 

(12) describes the energy distribution of the 

molecules of the added energy for boiling. Because 

of the higher enthalpy of boric acid much more 

water will leave the boiling solution. 

watermol

mol boricacid

h h

h

f

,

, = (12) 

The two quotients fp and fh depend on the 

temperature! If they will be multiplied with each 

other and with the ratio of boric acid (for 

pentaborate and a pH-value of 8.3 is the ratio nearly 

0.3) in the solution the boron concentration in the 

vapour can be estimated. For an example 

temperature of 128 °C the volatility is estimated in 

the following equation 13. 

( ) %86.03.0

1.174 /

/2.39

3.254

3.32 128 =° ⋅ =⋅ molkJ

molkJ

kPa

kPa Cf (13) 

The measurement data at 128 °C for different 

void fractions are 0.3 % for a void at nearly 0 % and 

0.6 % for a void of 60 %. This values are in the near 

of the calculate ones. If the interfacial area will be 

bigger, more boron can escape the solution and the 

calculated value can be achieved. 

7. Future work - connection to BWR 

For a better quality of the extracted equations 

out of the measurement data it is necessary to have 

6
more data points. At this way the model about the 

lost of boron will become better. It is fundamental 

that the model is conservative at every measurement 

or calculation point. That means the result of the 

calculation gives a bigger lost of boron than the 

measurement at every time. 

For the ATHLET-Code from the GRS an input 

data for the BORAN facility was created. With this 

integral thermal hydraulic code nearly all 

parameters like temperature, pressure, mass flow 

and boron concentration in each node of the test 

facility can be calculated. The whole test facility is 

described in approximately 200 nodes. The 

calculation of the lost of boron with exhausted 

steam with the ATHLET-Code is not possible. The 

boron transport with the vapour cannot be 

calculated, only in the liquid phase. Some changes 

in the code are inescapable. But the code is suitable 

for the calculation of the thermo hydraulic 

parameter. 

The next step is to simulate some transients 

with the test facility BORAN and the ATHLETcode. By the use of the valve, which connects the 

vapour-chamber of the facility with the atmosphere, 

a LOCA-experiment can be performed. 

Based on the ATHLET-calculation of a real 

reactor the lost of boron with exhausted steam can 

be estimated. All parameter for calculation of the 

lost of boron can be get out of the main edit of 

ATHLET. 

The great aim of this analysis is a new 

validation of the effectiveness of the boron injection 

system in a boiling water reactor to decrease the 

reactivity of the core. The higher the boron 

concentration the lower is the reactivity of the core. 

That is why the calculation has to be conservative! 

8. Summary 

In this paper the lost of boron out of sodium 

borate and boric acid solutions was investigated. 

The volatility was studied with two facilities; an 

autoclave and the BORAN test facility. The result of 

the measurement data are correlations to the 

concentration, the temperature, the pH-value, the 

compound and the void fraction in the two-phase 

flow of BORAN. Out of these correlations some 

equations were derived. The boron concentration in 

the vapour can be about some percent of the boron 

concentration in the borate solution. 

In addition to the measurement of the volatility 

the physical and chemical reasons of the transfer of 

boron from the liquid in the gaseous phase was 

shown. The built boric acid after solving the sodium 

borate sublimates. That is why the boron can leave 

the solution over the interfacial surface. 

The aim of this project is to estimate the lost of 

boron out of a real BWR with boron-treated feed 

water. The volatility correlation will be 

implemented in the ATHLET-code and therefore 

applied for the calculation of boron injection 

transients at a real BWR. This work will be done at 

the Forschungszentrum Dresden-Rossendorf. 

9. Acknowledgement 

This work is funded by Vattenfall Europe 

Nuclear Energy (VENE) GmbH, Hamburg, 

Germany. Many thanks to the Institut für 

Sicherheitsforschung at the Forschungszentrum 

Dresden - Rossendorf for measuring the void 

fraction and for the great help to find some literature 

about interfacial area density.

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