Transcript Theory of Diffusion

Hydrogen-tritium
transfer
in SFR Concepts
K. LIGER, T. GILARDI
Tél : 33 (0)4 42 25 49 08
e-mail : [email protected]
OUTLINES
• 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
General goal for tritium transfer estimation
•
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
Theory: Mass transfer through a wall
•
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
Theory of Diffusion : Fick ’s law
•
 j  D C
 div j   C  0

t
Équations de Fick
- Fick’s law
- Mass conservation’s law
•
For a simple geometry
C
j  D
x
 2C  C
D

0
 x2  t



x
•
E.g.: Evolution of concentration in a plan
wall after a step of concentration from C =
C2 to C1
j : flux
D : diffusivity
C : concentration
e : thickness
C2
C2
C2
e
o
C1
C1
C1
t=0
t
t=infinite
5
Steady state vs transient state ?
• 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
 tp does not depends on the concentration gradient
e2
p 
D
 Time to reach 98,5% of the steady state flow: tp /2
Over the lifespan of a reactor, steady state can be assumed!
6
Theory: Diffusion depends on…
• 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 105 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 1H, 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
H = K SHNa .
PH2
T = K STNa .
PT2
H
Na
T
Na
K sH
 1,73 K sTNa
Na

1 H ( gas)
2 2

1 T ( gas)
2 2
9
Theory: equilibrium between gas and metal
Sievert constant
•
Hydrogen equilibrium between metal and the cover gas
H = K SHAc .
PH2
T = K STAc.
PT2

 1 H (gazeux)
2 2
in metal
H
T
in metal
•
Similar solubility of H and T in steel
steel
K SH
•

steel
K ST
Diffusion depends on atomic mass
DHsteel
DTsteel
•

 1 T (gazeux)
2 2

3
1
Hence, diffusion is « easier » for H
10
Solubility in metal : Sievert constant
E.g.: SS316,
–
–
–
mol(H)/m3(acier)/pa1/2
KTISON (1983) = 0,9123 exp( -1352,1 / T(K) )
KFORCEY (1988) = 0,9424 exp( -2229 / T(K) )
KGRANT (1988) = 2,2191 exp( -1890 / T(K) )
mol(H)/m3/Pa1/2
0,25
Forcey [7]
Tison [6]
Grant [8]
0,2
0,15
0,1
0,05
T, °C
0
200
250
300
350
400
450
500
550
600
1,E-08
1,E-10
1,E-11
1,E-12
1,E-13
1,E-14
550
450
350
250
150
1,E-15
25
DFORCEY (1988) = 3,82 10-7 exp( -5472,4 / T(K) ) , m² /s
D, m²/s
1,E-09
T, °C
11
Theory: Diffusion through a wall immersed in Na
Na
Na
C1Na = KNa
SH  P1 and C2 = K SH  P2
ac
ac
C1ac = K ac
SH  P1 and C2 = K SH  P2
ac
ac
KSH
KSH
ac
Na
Na
then C  Na C1 and C2  Na C2
KSH
KSH
ac
1
Plan wall
e
C1Na
C1ac
Fick’s law :
A
 = D C1ac  C2ac ( C in at/m3)
e


Na
A K acSH Na
Na
3
=D
Na C1  C 2  (C in at/m )
e K SH
then
A Na
 = PE C1  C 2Na 
e

K ac
SH
PE = D. . Na = pe Na
K SH
K SH
Na
C2ac
C2Na
Similar equations for T
where
 : at/s
PE : kg/m/s
CiNa : at/kg
 : kg/m3
KSHNa, KSHac : at/m3/Pa1/2
12
Theory: Diffusion through a wall immersed in Na and gas
ac
KSH
C  Na C1Na
KSH
ac
ac
 P2
C2  KSH
ac
1
e
C1


ac
A KSH
3
Na
Na
 = D
Na C1  KSH  P2 (C in at/m ; P2 in Pa)
e KSH
Na
A KacSH  Na KSH
 = D. . Na . . C1 
.
e KSH 

C1ac
Na
gas
C2ac
C2


P2  (C in at/kg)

K ac
SH
with PE = D. . Na = pe Na
K SH
K SH
and
gas
2
KU. C


Na
K SH

P2
A
thus  = PE C1Na  KU. Cgas
2
e

with C1Na: at/kg
C2gas : at/kg
M : kg/mol
P : Pa
Similar equations for T
13
Theory: Diffusion through pipes
•
In that case, diffusion flux through the surface is:

2 L
A
DC1  C2   D ml C1  C2 
r
e
ln 2
r1
Aml 
r1
o
r2
r
2  L r2  r1 
r
ln 2
r1
14
Cold traps :
•
Flux of hydrogen to the cold trap:
f 3 q CC( T cold trap ) 

Cold trap efficiency:  
C  Cs
 0.5
*
C  C(T cold trap )
10000
Flux of Tritium to the cold trap:
1000
– Co-cristallisation of tritium with H
CT
f 3 q CH CH (T cold trap )  Na
CH
Na
Na 
Na
100
[O], ppm
[H], ppm
10
1
0,1
0
0
0
0
0
0
0
58
55
52
49
46
43
0
0
0
0
0
0
0
0
0
40
37
34
31
28
25
22
19
16
0
0,01
13
– Isotopic exchange and T decay neglected
10
•
Te m pe r atur e , °C
C*: Solubility of H in Na
15
Theory: Isotopic exchange in gas phase
hydrogen - tritium
•
Isotopic exchange reaction:
•
Equilibrium constant is:
H2 ( gaz )  T2 ( gaz )  2 HT( gaz )
5
2
PHT
PH 2  PT 2
4
3
k
k
2
Ln k  1,4966 
133
T ( K)
1
0
100
300
500
700
T, °C
16
Tritium transfer in a Reactor
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 N2H4 = 2 NH3 + 2 N2 + 3 H2 for T>250°C
 Estimation of the source on the base of Superphenix and Phenix past experience
17
Schematic view of the reactors
PF I
SPX:reference case
PF II
Ar
I
RUR
Na/Na
~
III
II
GV
Turbine
BPR
RUR
Na/Air
Improvement of the models for Tritium transfer in other SFR concepts
Y - H2O
- He-N2
- SCO2
And for other fission reactors (EPR, HTR, VHTR…)
18
SFR: Mass balance
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
T flux%
28
35

36

H flux %
6
89

5

SFR Na/Na/SCO2
Localisation
Primary cold traps
Secondary cold traps
GV
Intermediate heat exchanger
Pipes and volumes
T flux%
41
19
3
26
7
H flux %
46
23
7
9
10
SFR Na/Na/He-N2
Localisation
Primary cold traps
Secondary cold traps
GV
Intermediate heat exchanger
Pipes and volumes
T flux%
31
14
30
19
3
H flux %
35
16
30
8
7
20
Concepts comparison
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
Conclusion ...
– 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
References
[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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