J. Plasma Fusion Res. SERIES, Vol. 11 (2015)

Hydrogen isotopes permeation in a fluoride molten salt for nuclear fusion
blanketAkira Nakamura, Satoshi Fukada and Ryosuke Nishiumi
Department of Advanced Energy Engineering Science, Kyushu University,
6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, JAPAN(Received: 16 September 2014 / Accepted: 19 January 2015)

Mixed fluoride molten salts Flinak (LiF+NaF+KF) and Flibe (LiF+BeF 2) are expected to work as a tritium
breeder in a fusion reactor blanket along with coolant and uranium fuel dissolver in a molten salt fission reactor. In
this study, after making the molten salts in an electric furnace and purifying the salts by HF, experiments wereperformed to determine the behavior of H2 permeation through the fluoride molten salts at static conditions in therange of 500-600 °C using an apparatus composed of tertiary cylindrical Monel400 tubes. In addition, transient H2
diffusion equations in molten salts were solved, and results were compared with experimental effluent H2concentration curves. It is proved experimentally that the H2 permeability through Flibe or Flinak has linear
pressure dependence, and permeability, diffusivity and solubility of H 2 in the fluoride molten salts are correlated totheir respective Arrhenius-type equations.
Keywords: molten salt, hydrogen isotopes, permeability, diffusivity, solubility
The hydrogen fluoride concentration in the purge gas wasmeasured by a pH meter after condensing in a sample flask.
The melting point of the molten salts was measured byusing an Inconel coating thermocouple inserted in thevessel. After purifying molten salts, it was moved into thetertiary cylindrical tube system that is made of 316
stainless-steel and Monel400 nickel alloy tube. The
sectional view and the detail of the tertiary cylindricaltubes are shown in Fig. 2 and Table 1. The most internal
pipe filled with hydrogen, and the molten salt is placed
between 1st and 2nd tubes. The gas permeated to theoutside pipe was purged by argon gas. The hydrogenconcentration in the purge gas was detected by gas
chromatography. These results were used for analyzinghydrogen permeability, diffusivity and solubility in eachmolten salt.

1. Introduction

For applications of a tritium breeding material to anuclear fusion reactor, it is important to determine its
hydrogen permeability, diffusivity and solubility in thebreeding materials. In particular, fluoride molten salts arefocused here due to comparatively easy handling, because
their physical and chemical properties are appropriate. For
example, they have high tritium breeding ratio, low
reactivity with oxygen, low MHD pressure loss and theirdensity and specific heat are almost the same as that ofwater. These properties are promising as a fusion blanket
material. On the other hand, the melting point of a molten
salt is higher than other liquid breeding materials. In recentyears, a new fluoride molten salt mixture of LiF + NaF +BeF2 called Flinabe is focused because the melting point
was reported around 300 °C [1], which is around 100 °C
lower than that of Flibe. However, there are few data
relating to hydrogen behavior through Flibe, and Flinabe.
Thus, the purpose of this report is to determine hydrogen
behavior in the molten salts Flinak, and Flibe using atertiary cylindrical tube system. Moreover, these data arealso determined for preliminary experiment using Flinabe.

ExhaustMFC

Gas Chromatograph
MFC
Ni crucible

pH-meterMFC
MS-3AMS-3A

H2Ar

Thermocouple

2. Experimental

Fig. 1 shows a schematic diagram of the experimental
apparatus composed of a tertiary cylindrical tube system todetermine the permeability, diffusivity and solubility ofhydrogen in a molten salt. It is divided into two parts of thevessel storing a Ni crucible and a tertiary cylindrical tubesystem. First, the molten salt was purified by gas bubbling
using gas including 1000 ppm hydrogen fluoride.

PN2+HF(1000ppm)

Electric furnace
MFC: Mass flow controller
MS-3A: Molecular Sieve 3AFig. 1 A schematic diagram of the experimental apparatus
composed of a vessel and tertiary cylindricaltubes.

a.nakamura@aees.kyushu-u.ac.jp

25©2015 by The Japan Society of Plasma
Science and Nuclear Fusion Research

A. Nakamura et al., Hydrogen Isotopes Permeation in a Fluoride Molten Salt for Nuclear Fusion Blanket

where W [mol/s] is the molar flow rate of argon purge gas,
KH [mol/(m3Pa)] is the Henry’s constant, pt [Pa] is the totalpressure of purge gas, A [m2] is the permeation area. Thenthe steady state permeation flux, jH [mol/(m2s)], is given byMolten salt
Primary & secondary pipe:
Monel400

H2Ar purge

Tertiary pipe:
SUS316

Fig. 2 A sectional view of the tertiary cylindrical tubes.

1stComponent ratio(%)
65Ni-33Cu-2Fe

Diameter(mm)
3.18

Thickness(mm)
0.7

Length(mm)
750

2nd
3rd

65Ni-33Cu-2Fe
18Cr-12Ni-2.5Mo

12.7
25.4

1.0
1.65

530
300

PH24.1 Purification and a melting point
Flibe needs to be purified because BeF2 includes asmall amount of BeO as impurities. To reduce BeO to BeF2,the following chemical reaction is used:

Thus, Flibe is highly purified by HF bubbling. Fig. 3
shows the cooling curve of Flinak and Flibe. Two curves
on Flibe are compared between cooling curves before andafter the purification. From these results, the melting pointof Flinak was measured 450s2 °C. that of Flibe is alsomeasured 450s2 °C. These value are comparable to thereference data of TLiF46.5-NaF11.5-KF42 = 454 °C [3] andTLiF67.2-BeF232.8 = 459 °C [4]. There are slight difference
550

FlinakFlibe before HF bubbling
Flibe after HF bubbling500

Temperature [Υ]

450

400
350
300

(2a)
(2b)

Kc,

(6)

BeO  2HF o BeF2  H 2O

where c [mol/m3] is the molar concentration of hydrogen,DH [m2/s] is the diffusivity of hydrogen in the molten salt,
x [m] is the direction perpendicular to surface of the molten
salt layer and t [sec] is time. The initial and boundary
conditions are as follows:x(5)4. Results and discussion(1)

WcK H 2 pt A

fc0 K2c0 K
¦KL n 1 § KL D 2 ·1Zn ¸ cos Zn¨1 DD KL ¹©

These equations are used to determine the hydrogen
permeability, diffusivity and solubility from experimentaldata.

Transient hydrogen diffusion behavior was analyzed
using the rectangular coordinate system for simplicity. A
one-dimensional unsteady diffusion equation is describedas follows:wc,  DH 2wx(4)

Dt ·§u exp ¨ Zn2 2 ¸L ¹©

3. Analysis

t 0, c 0,x 0, c c0 ,(3)DH2  K H2

jH 2

Table 2 Component ratio of each molten salt.
Molten salt
Component ratio (%)
Flinak
46.5LiF-11.5NaF-42KF
Flibe
67.2LiF-32.8BeF2w 2cwx 2

pH 2 ,up  pH 2 ,down

An analytical solution to Eq. (1) for H2 permeation
through a molten salt is expressed as follows:

The outside diameter and thickness of 1st Monel-400
pipe are 3.18 mm and 0.7 mm. Those of 2nd pipe are 12.7mm and 1.0 mm, and those of 3rd pipe are 25.4 mm and1.65 mm. Thus, the thickness of the molten salt is 3.76 mm
and the permeation area is 8.4×10-3 m2. The argon flow rate
was maintained at 30 cm3/min. The temperature ranges
500-600 °C. Preliminary experiment was performed underconditions without the molten salt in order to determine therate of hydrogen permeation through the Monel alloy. The
temperature distribution of the tertiary cylindrical tubes
and soundness of apparatus were confirmed. Table 2 shows
the component ratio of the molten salt made for thisexperiment.

DH 2L

where L [m] is the thickness of the molten salt, pH2,up andpH2,down [Pa] are the hydrogen partial pressures at upstream
and downstream sides, respectively. The hydrogen
permeability through molten salt, PH2, becomes a productof the diffusivity and the solubility as follows:

Table 1 The detail data of the tertiary cylindrical tubes.

wcwt

DH 2  K H 2

jH 2

250

00.5

11.5

2Time [hr](2c)Fig. 3 Cooling curve of Flinak and Flibe.

262.5

A. Nakamura et al., Hydrogen Isotopes Permeation in a Fluoride Molten Salt for Nuclear Fusion Blanket

between results before and after HF bubbling. Thus, it wasconfirmed that BeO was efficiently reduced to BeF2 by HF
bubbling.

H2 permeation flux, jH2 [mol/(m2s)]

1E-04

4.2 Hydrogen permeation experiment to determine
permeability, diffusivity and solubility.
Fig. 4 shows comparison of hydrogen permeability ofMonel400 between the experimental data and the previous
reference [2]. It is found that these results are almost thesame as the data of the reference. We confirmed thattemperature is uniform in the apparatus.
Fig. 5 compares the results of hydrogen permeation
flux in the experimental apparatus. Square marks shown inthe blank experiment, which corresponds to the Monelpermeability, and the rest correspond to that of the molten
salts, Flinak or Flibe, at 500 °C. This results shows thathydrogen permeation through the molten salt is therate-determining process.
Fig. 6 shows the relationship between steady-statehydrogen permeation flux through Flibe, (jH)steady-state, andthe upstream hydrogen partial pressure, pH2,up in the range
from 104 to 6 × 105 Pa. In the experiment at 600 °C, it
investigated only two pressure condition in 104 Pa and 3 ×105 Pa, because the experimental apparatus broke. Thus,
the broken line virtually show the line of slope equals unity
the same as 500 °C and 550 °C.
Permeability of H2 in Monel [mol/(msPa0.5)]

1E-11

1.1

1.2

1.3

1.4
1.5
1000/T [1/K]

1.6

1.7

1.8

Fig. 4 Comparison of H2 permeability of Monel between
the present study and the previous ones.
Ar flow rate: 30cm3/min, pH2,up: 3.01㽢105Pa
Temperature: 500Υ

8E-06

Monel

6E-06

FlinakFlibe

4E-06

550Υ
500Υ
1E+04

1E+05

1E+06

1E+07

The relationship between permeation flux andpartial pressure of H2 from 104 to 6 × 105 Pa.

1j/C0(L/D+1/K) [-]H2 permeation flux, jH2 [mol/(m2s)]

1E-05

600Υ

1E-07

The values of (jH)steady-state are linearly proportional tothe pressure, pH2,up. The results proved experimentally thehydrogen sorption into Flibe obeys the Henry’s law, whichmeans hydrogen has moved through a molten salt in amolecular form. The reason why the result of jH in 104 Pa
is higher than others is that it used hydrogen (10%) andargon (90%) mixed gas, and the gas flows in slightly overatmospheric pressure condition, others are performed using
pure hydrogen gas. The permeation flux is proportional tohydrogen partial pressure, this effect cannot explain thegap. However, it is considered that it is experimented under
different conditions between 104 Pa and the range from 105
to 6 × 105 Pa due to the structure of this experimentalapparatus. The effect of differential pressure between inlet
and outlet gas may affect the gap. Therefore, it isconcluded that permeation flux in Flibe is linearly
proportional to the pressure using data of the range from105 to 6 × 105 Pa.
Fig. 7 shows comparison of the hydrogen permeation
flux in Flinak at 500 °C between experimental data and theanalytical solution. The vertical axis represents thehydrogen permeation flux normalized by its steady statevalue. The horizontal axis represents normalized time.

Reference (by J.K.Gorman et al.)1( )Fig. 6this work (1/2inch Monel)

1E-12

1E-06

Upstream hydrogen pressure, pH2,up [Pa]this work (1/8inch Monel)

1E-10

( )
( )

1E-08
1E+03

300 [Υ]

400

500

1E-09

line of slope = 1

1E-05

0.80.6
LFlinak: 3.78mm, pH2,up: 3.01㽢105Pa
Temperature: 500Υ

0.4

2E-06

0.2

0E+00

0Experiment

Analytical solution
0246810Time [hr]

00.2

0.4

0.6

0.8

1Dt/L2 [-]Fig. 7 Comparison of the H2 permeation flux in Flinak
between experiment and analytical solution.

Fig. 5 Comparison between H2 permeation flux of Moneland the molten salt, Flinak and Flibe.

27

A. Nakamura et al., Hydrogen Isotopes Permeation in a Fluoride Molten Salt for Nuclear Fusion Blanket

Permeability of H2 in molten salt [mol/(msPa)]

j/C0(L/D+1/K) [-]

10.8
0.6
LFlibe: 3.78mm, pH2,up: 3.01㽢105Pa
Temperature: 500Υ

0.4Experiment

0.2

0Analytical solution
00.2

0.4

0.6

0.8

1Dt/L2 [-]1E-12

H2 in Flinak

D2 in Flibe

1E-13

H2 in Flibe
H2 in Flinak

1E-14

11.04

1.08

1.12

1.16

1.2

1.24

1.28

1.32

Fig. 9 Comparison of permeability of H2 between thepresent study and previous ones.

Close agreement was obtained between experimental
data and the analytical solution. The hydrogen diffusivity
can be estimated from these results. The analysis at 550 °C
and 600 °C is done in a similar way.
Fig. 8 shows comparison of the hydrogen permeation
flux in Flibe at 500 °C between the experimental data andthe analytical solution. Judging from this result, we
confirmed that the analytical solution is almost in goodagainst with the experimental data.
Fig. 9 shows a comparison of the permeability
between Flinak and Flibe, and previous experimental data
[5-7]. Our permeability data of Flinak and Flibe, PH2[mol/msPa], are correlated to the following equations:Diffusivity of H2 in molten salt [m2/s]

650

700

1E-07

600

H΃ in Flinak (by present study)H΃ in Flibe (by present study)H΃ in Flinak (by S.Fukada et al.)H2 in Flinak

D΃ in Flibe (by R.A.Anderl et al.)T΃ in Flibe (by P.Calderoni et al.)

1E-08

T2 in Flibe

D2 in Flibe

1E-09

H2 in Flinak

H2 in Flibe

1E-10

11.04

1.08

1.12

1.16

1.2

1.24

1.28

1.32

1000/T [1/K]§ 76.4 > kJ / mol@ ·(7)2.03 u109 exp ¨ ¸¸¨RTg©
¹§ 129.7 > kJ / mol@ ·PFlibe  H 2 1.37 u105 exp ¨ 
¸¸(8)
¨RgT
©
¹
where Rg [J/mol] is the universal gas constant, and T istemperature in [K].
Fig. 10 shows a comparison of the diffusivity in
Flinak and Flibe, and previous experimental data. The
diffusivity data of hydrogen in Flinak and Flibe, DH2 [m2/s],
are correlated to the following equations:Fig. 10Solubility of H2 in molten salt [mol/(m3Pa)]

PFlinak  H 2§ 4.9 > kJ / mol@ ·(9)3.59 u1010 exp ¨¸¸¨RTg©
¹§ 25.2 > kJ / mol@ ·DFlibe  H 2 2.09 u108 exp ¨ ¸¸(10)¨Rg T©
¹Fig. 11 shows a comparison of the solubility in Flinakand Flibe, and previous experimental data. The solubility
data of hydrogen in Flinak and Flibe, KH2 [mol/m3Pa], arecalculated by Eq. (4) and correlated to the followingequations:§ 81.3> kJ / mol@ ·K Flinak  H 2 5.64 exp ¨ ¸¸(11)¨Rg T©
¹DFlinak  H 2§ 104.8 > kJ / mol@ ·6.57 u102 exp ¨ ¸¸¨RgT©
¹

T2 in Flibe

1000/T [1/K]

Fig. 8 Comparison of the H2 permeation flux in Flibe
between experiment and analytical solution.

K Flibe  H 2

H΃ in Flinak (by present study)H΃ in Flibe (by present study)H΃ in Flinak (by S.Fukada et al.)D΃ in Flibe (by R.A.Anderl et al.)T΃ in Flibe (by P.Calderoni et al.)

650

700

1E-11

Comparison of diffusivity of H2 between thepresent study and previous ones.
H΃ in Flinak (by present study)H΃ in Flibe (by present study)H΃ in Flinak (by S.Fukada et al.)D΃ in Flibe (by R.A.Anderl et al.)T΃ in Flibe (by P.Calderoni et al.)T2 in Flibe

1E-03

D2 in Flibe

H2 in Flibe

1E-04

H2 in Flinak

H2 in Flinak

1E-05

Fig. 111

1.04

500 [Υ]

550

600

650

700

1E-02

1.08

1.12

1.16

1.2

1000/T [1/K]

1.24

1.28

1.32

Comparison of solubility of H2 between thepresent study and previous ones.

There are one-order magnitude differences between
previous reference data and the present ones, respectively.
The difference may come from difference in permeation
area or configuration of apparatus. Previous experiment isperformed using almost the same. Another reason is theeffect of impurities included in molten salt, and the other isthe effect of temperature distribution. When the tertiary
cylindrical tube is heated, three separate electric furnaces
are used. According to these effects, the one-order

(12)

28

A. Nakamura et al., Hydrogen Isotopes Permeation in a Fluoride Molten Salt for Nuclear Fusion Blanket

magnitude difference may be observed. The activationenergy for hydrogen permeation in Flinak is smaller thanthat of Flibe. It has been already proved by previous report[5] that it is affected by interaction with ions of respectivecomponents.

5. Conclusions

Hydrogen permeability, diffusivity and solubility inthe molten salt Flinak and Flibe were determined by using
a tertiary cylindrical tube system. The hydrogen solution inFlibe obeys the Henry’s law. The analytical solution values
are in good agreement with the experimental data. The
hydrogen permeability in Flibe is higher than that in Flinak.
The permeability, diffusivity and solubility obtained
experimentally are correlated to the following equations,
respectively:

Qi , H 2§ B > kJ/mol@ ·Ai exp ¨  i¸¸¨RgT©
¹(13)Table 3 The values of Ai and Bi appearing in Eq. (13)i = Flinak
i = Flibe
QAiBiAi
BiP 2.0310-9 76.4
1.3710-5 129.7
D 3.5910-10 -4.9
2.0910-8 25.2
K 5.6481.3
104.8
6.57102

6. References[1][2][3][4][5][6][7]R. E. Nygren, Fusion Sci. Technol., 47, 549 (2005).
J. K. Gorman et al., vacuum, 12, 19 (19862).
J. Lumsden, Discuss. Faraday Soc., 32, 138 (1961)
K. A. Romberger et al., J. Phys. Chem., 76, 1154 (1972)
S. Fukada et al., J. Nucl. Mater., 358, 235 (2006)
R. A. Anderl et al., J. Nucl. Mater., 329-333, 1327 (2004)
P. Calderoni et al., Fusion Eng. Des., 83, 1331 (2008)29