K. LIGER, T. GILARDI
Tél : 33 (0)4 42 25 49 08 e-mail : karine.liger@cea.fr

• Theory of diffusion and mass transfer phenomena
– Fick’s law, parameters, steady state...
– Data’s for liquid Na and stainless steel: Sievert constants, permeation, diffusion
– Permeation Na/Metal/Na and Na/Metal/gas
– Equilibrium between Na and cover gas
– Cold trap and cristalisation
– Links between H and T transfers
• Mass transfer in a reactor
 System definition
 Pollution sources
 Modeling
 Estimation of the fluxes of Hydrogen and tritium
2

• Estimate :
– The distribution of H and T in the circuits and then the gaseous and liquid release of T as well as the accumulation of T in the cold traps
• SO THAT:
• During operation
– The release does not exceed release authorisation
• During conception
– A suitable release limit authorisation could be asked
3

• Hydrogen permeation includes severall phenomena
– Molecule dissociation at the interphase between metal and medium
– Adsorption, Absorption
– Diffusion in the metal
– De-absorption, De-adsorption
– Atoms combination
 In general, mass transfer is controlled by diffusion (combination is the second predominant phenomena)
 Hence, permeation can be represented by Fick’s law
4

• Équations de Fick
-
Fick’s law
- Mass conservation’s law
• For a simple geometry
• E.g.: Evolution of concentration in a plan wall after a step of concentration from C =
C2 to C1 e x o
C
1 t=0
C
2 j D C div j




C t

0 j D


C x
D



2
C x
2



C t

0
C
1 t
C
2 j : flux
D : diffusivity
C : concentration e : thickness
C
1 t=infinite
C
2
5

• When steady state and transient meet each other…
– Assumption : plan wall
– Time to reach 99,99% of the steady state flow depends on:
• D, diffusivity of material (function of temperature and nature of the material)
• e, thickness
 t p does not depends on the concentration gradient
 Time to reach 98,5% of the steady state flow: t p
/2
 p
 e
2
D
Over the lifespan of a reactor, steady state can be assumed!
6

• Nature of material: Austenic steel versurs ferritic steel, ....
– factor 100 for D at 250°C, and only 10 at 500°C
• Temperature:
– D = A exp( -E / T(K) ) , m² /s
– SS316 : factor 10 5 between room temperature and 500°C
• Surface state : Oxidised layer is a permeation barrier
• Hydrogen trapped in the metallic structure
7

Diffusion : Hydrogen/tritium trapped in metallic structure
• Gaseous adsorption on metallic surface
– external on surface
– internal on small fissuration and defect structure
• In the matrix
– Impurities
– Grain boundaries
– dislocations...
• Some of these mechanisms are irreversibles
– E.g.: during heating of metal in a vacuum oven, hydrogen release is observed up to melting temperature
• Behaviour of T similar to 1 H, but isotopic exchange may modify macroscopic behaviour of T
– In presence of hydrogen trapped in the structure:
• Shorter transient state for T diffusion
• Lower diffusion flux under steady state
8

Theory: H/T equilibrium between cover gaz and Na
Sievert constant
• Hydrogen equilibrium between Na (liquid or solid) and the cover gas
 
= K Na
SH
.
P
H
2
= K Na
ST
.
P
T
2
K
Na sH

1 , 73

K
Na sT
H
Na

1
2
H
2
( gas )
T
Na

1
2
T
2
( gas )
9

Theory: equilibrium between gas and metal
Sievert constant
• Hydrogen equilibrium between metal and the cover gas
 
= K
Ac
SH
.
P
H
2
= K
Ac .
ST
P
T
2
H in metal
 1
2
H
2
( gazeux )
T in metal
 1
2
T
2
( gazeux )
• Similar solubility of H and T in steel steel
K 
SH
K steel
ST
• Diffusion depends on atomic mass
D steel
H
D
T steel

3
1
• Hence, diffusion is « easier » for H
10

E.g.: SS316, mol(H)/m 3 (acier)/pa 1/2
– K
TISON (1983)
– K
FORCEY (1988)
– K
GRANT (1988)
= 0,9123 exp( -1352,1 / T(K) )
= 0,9424 exp( -2229 / T(K) )
= 2,2191 exp( -1890 / T(K) )
D
FORCEY (1988)
= 3,82 10 -7 exp( -5472,4 / T(K) ) , m² /s
0,25
0,2
0,15
0,1
Forcey [7]
Tison [6]
Grant [8]
0,05
T, °C
0
200 250 300 350 400 450 500 550 600
1,E-08
1,E-09
1,E-10
1,E-11
1,E-12
1,E-13
1,E-14
1,E-15
T, °C
11

C
1
Na
=
K
Na
SH
 P
1
and C
2
Na
=
K
Na
SH
 P
2
C
1 ac
=
K ac
SH
 P
1
and C
2 ac
=
K ac
SH
 P
2 then C ac
1

K ac
SH
C
Na
1
K Na
SH
and C ac
2

K ac
SH
K
Na
SH
C
Na
2
Fick’s law :

= D
A
 e
C
1 ac 
C
2 ac

( C in at/m
3
)

= D e
A
K ac
SH
K
Na
SH

C
1
Na

C
Na
2

(C in at/m
3
) then

= PE
A 
C
1
Na

C
2
Na e
PE = D .

.
K
K ac
SH
Na
SH

= pe
K
Na
SH

Plan wall e
C
1
Na
Na
C
1 ac
C
2 ac
Na
C
2
Na
Similar equations for T where

: at/s
PE : kg/m/s
C i
Na
: at/kg

: kg/m3
K
SH
Na
, K
SH ac
: at/m
3
/Pa
1/2
12

Theory: Diffusion through a wall immersed in Na and gas
C ac
1

K ac
SH
K
Na
SH
C
Na
1
C ac
2

K ac
SH
 P
2

= D
A e
K ac
SH
K
Na
SH

C
Na
1

K
Na
SH

P
2

(C in at/m
3
; P
2
in Pa)

= D.
A
.
e
K ac
SH
Na
K
SH
.

.
C
Na
1

Na
K
SH
.
 with PE = D.

.
K ac
SH
K
Na
SH
= pe

K
Na
SH and KU. C gas
2

K
Na
SH

P
2
P
2 thus 
= PE e
A

C
Na
1

KU. C gas
2

(C in at/kg) with C
1
Na : at/kg
C
2 gas : at/kg
M : kg/mol
P : Pa
C
1 e
Na
C
1 ac
C
2 ac gas
C
2
Similar equations for T
13

• In that case, diffusion flux through the surface is:
 
2

L ln r
2 r
1

1

A ml

2


2
 r
1
 r
2 ln r
1
C
2


D
A ml e

C
1

C
2
 o r1 r2 r
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• Flux of hydrogen to the cold trap: f
3
 q


C

C
(

T cold trap )

• Flux of Tritium to the cold trap:
– Co-cristallisation of tritium with H f
3
 q


C
H
Na

C
H
Na

( T cold trap )

C
T
Na
C Na
H
– Isotopic exchange and T decay neglected
Cold trap efficiency:
 
C
C


C s
C
( T
* cold trap )

0 .
5
10000
1000
100
10
1
[O ], ppm
[H], ppm
0,1
0,01
100 130 160 190 220 250 280 310 340 370 400 430 460 490 520 550 580
Te m pe r atur e , °C
C*: Solubility of H in Na
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Theory: Isotopic exchange in gas phase hydrogen - tritium
H
2 ( gaz )

T
2 ( gaz )

2 HT
( gaz )
• Isotopic exchange reaction:
• Equilibrium constant is: k

2
P
HT
P
H 2

P
T 2
Ln k
 
133
5
4
3
2
1
0
100 300
T, °C
500 700
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Assumptions:
1.
Steady state calculation
2.
Homogeneity of concentrations in the circuits
3.
Isotopic exchange in cold traps neglected as well as T decay
4.
Source of T:
– In primary circuit:
• Ternary fission reactions
• Control rod reactions
• Activation of impurities: B, Li
 Estimation of the source on the base of Superphenix and Phenix past experience
5.
Source of H:
– In primary circuit: fission reactions.
– In secondary circuit:
• Gaz in the ternary circuit: source = 0
• Water in the ternary circuit
– Aqueous corrosion of GV
– Thermal decomposition of N2H4 used in water to limit presence of O :
3 N
2
H
4
= 2 NH
3
+ 2 N
2
+ 3 H
2 for T>250°C
 Estimation of the source on the base of Superphenix and Phenix past experience
17

SPX:reference case
Schematic view of the reactors
PF I
PF II
Ar
I II
III
BPR
GV Turbine
RUR
Na/Na
RUR
Na/Air
Improvement of the models for Tritium transfer in other SFR concepts
Y - H
2
O
- He-N
2
- SCO
2
And for other fission reactors (EPR, HTR, VHTR…)
~
18

for Hydrogen:
• Diffusion through heat exchangers
• Diffusion through GV
• Diffusion through pipes and volumes
• Trapping in cold traps (for H in Na) / Sources in the circuits
• H exchange with covering gas for Tritium:
• Diffusion through heat exchangers
• Diffusion through GV
• Diffusion through pipes and volumes
• Trapping in cold traps (for T in Na) / Sources in the circuits
• H/T exchange with covering gas
19

Localisation of exchange in the different concepts
SFR Na/Na/H2O
Localisation
Primary cold traps
Secondary cold traps
GV
Intermediate heat exchanger
Pipes and volumes
SFR Na/Na/SCO2
Localisation
Primary cold traps
Secondary cold traps
GV
Intermediate heat exchanger
Pipes and volumes
SFR Na/Na/He-N2
Localisation
Primary cold traps
Secondary cold traps
GV
Intermediate heat exchanger
Pipes and volumes
T flux%
28
35

36

T flux%
41
19
3
26
7
T flux%
31
14
30
19
3
H flux %
6
89

5

H flux %
46
23
7
9
10
H flux %
35
16
30
8
7
20

SFR Na/Na/H2O, Na/Na/SCO2, Na/Na/He-N2
• Presence of H2O in the ternary circuit leads to a source of H, which is benefit to reduce gaseous leakage:
• Release of T for Na/Na/H2O: 65 kBq/s
• Release of T for other concepts: nearly 1200 kBq/s
• Presence of:
• secondary cold traps of great importance for Na/Na/H2O concept
• primary cold traps of great importance for other concepts
• Permeation through GV:
• is of great importance for Na/Na/H20 concept. Great PE lowers gaseous release
• has no effect for other concepts
• Addition of secondary hydrogen source minimises T release
21

– Diffusion
– T release depends on the concept
– Importance of cold traps
– Importance of Hydrogen source
– Ways of limitation of diffusion: nature of metal, oxydised layer, thickness, temperatures, aeras
– Modeling partially validated on Phenix and Superphenix former results
– Modeling Improvement needed:
• Colds traps modeling should be improved
• Transient state should be implemented
• Measurement of H/T diffusivity through metals
22

[1] Paul TISON
Influence de l’hydrogène sur le comportement des métaux.
Rapport CEA-R-5240 ; Thèse présentée à l’université Paris 6 le 9 Juin 1983
[2] K.S. FORCEY ; D.K. ROSS ; J.C.B. SIMPSON ;D.S. EVANS
Hydrogen transport and solubility in 316L and 1.4914 steels for fusion reactor applications.
Journal of Nuclear Materials 160 (1988), North Holland, Amsterdam.
[3] D.M.GRANT ;D.L. CUMMINGS and D.A. BLACKBURN
Hydrogen in 316 steel ; diffusion, permeation and surface reaction.
Journal of Nuclear Materials 152 (1988), North Holland, Amsterdam.
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