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Transient analysis of tritium migration in a fusion reactor vessel
Journal of Nuclear Materials 128 & 129 (1984) 739-743
739
TRANSIENT ANALYSIS OF TRITIUM MIGRATION IN A FUSION REACTOR VESSEL K. ASHIBE R & D Center, Toshiba Corporation, 4- 1, Ukishima -rho, Kawasaki- ku, Kawasaki, 210, Japan and
K. EBISAWA Nuclear Energy Group, Toshiba Corporation,
Key words: tritium permeation,
1- 1 - 6, Uchisaiwai - cho, Chiyoda - ku, Tokyo, 100, Japan
tritium inventory,
tritium outgassing,
INTOR
Transient analysis of tritium migration after implantation into the INTOR-like stainless steel first wall and W/Cu divertor is performed using a computer code TRIP. Effects of thermal diffusion, protium from (n, p) reactions, tritium decay, surface conditions and trap characters on the tritium permeation and inventory are estimated. The influence of the bakeout procedure on the outgassing and inventory through the structures after shut-down is also discussed in detail.
1. Introduction
x, [3,6,7]. For hydrogen
The first wall and divertor or limiter of the D-T reactor are exposed to a large flux of energetic tritium. It is thus possible that the tritium inventory in the walls, its permeation into the wall-coolants and its release during maintenance after shut-down will be a serious safety problem [l-5]. Recent calculations by Baskes et al. [3] have shown that for a stainless steel wall the tritium inventory, permeation rate and the time to steady state are strongly affected by the surface conditions, neutron damage traps and thermal diffusion as well as the wall temperature. Several estimates of the tritium release from stainless steel walls with or without bakeout during reactor maintenance were also made [4,5]; however, the previous estimates did not include the effects of the neutron damage traps and/or the surface recombination process of hydrogen isotopes, which can play important roles in the tritium release during maintenance. We have developed a computer code TRIP (Tritium Re-emission, Inventory and Permeation). This code is based on the formalism of the DIFFUSE [3,6] and extended to deal with three hydrogen isotopes (H, D, T) simultaneously. It also allows to apply to an arbitrary running mode like an intermittent reactor operation. Using this code, we have performed further evaluations on the above-mentioned problems for the INTOR-like, stainless steel first wall and W/Cu divertor. This report presents new results about the tritium release from these structures with or without bakeout during maintenance as well as some further sensitivity study for the tritium inventory and permeation through these structures.
ac, at=-ax
aJ.
-+G,-at,
isotope
i,
ac,T
and
ac? at
-..-L=
oic,
- CTv,, exp( - E,/kT).
p
(2) In eq. (1) C, is the mobile hydrogen concentration, Ji is the bulk hydrogen flux, Gi is the hydrogen source term which includes both the D-T implant from the plasma and H production through (n, p) reactions, and CiT is the trapped hydrogen concentration. Ci and C,r are given in atoms/ems. In eq. (2) Di is the hydrogen diffusivity, CT is the total trap concentration given in (atomic fraction), N is the atom density of the host material, X is the jump distance (taken as 2.5 A), v, is the attempt frequency for detrappinng (taken as 10” s-l), ET is the total trapping energy (the sum of the binding energy of the traps and the migration energy), T is the wall temperature and k is the Boltzmann’s constant. In the present calculations, we assume the trap concentration, CT, is initially saturated and uniformly distributed. When tritium decay is included, decay terms of - X&, and -X& are added to the right-hand sides of eqs. (1) and (2), respectively, where X, is the decay constant of tritium. The diffusivity is given by eq. (3) assuming Graham’s law for isotope dependence: Di = D,,IU-‘/~
exp( - E,/kT),
(3)
where Do is a constant, E, is the migration M, is the atomic weight of isotope i. The bulk hydrogen flux is given by
2. Method of calculation 2. I. Physical model
energy and
The TRIP solves the following coupled equations of diffusion and trapping with respect to time t and depth 0022-3115/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
11. TRAPPING
AND DIFFUSION
K. Ashibe, I(. Ebisawu / Transient anaiysis of tririum migration
740
system is integrated with respect to the time variable, t. The TRIP uses the central finite difference method for the space discretization and the GEARB code by Hindmarsh ]9] for the time integration.
where the second term on the right is due to the thermal diffusion (the Soret effect), with Q* being the heat of transport. The surface boundary conditions for eq. (1) are J,= -CK,,C& .i and
atx=O,
(5)
2.2. A reference parameter set for calculations
J, = C KijCiCj at x = 1, (6) j where Kij is the hydrogen molecular recombination coefficient for isotope i combining with isotope j, 1 is the wall thickness and we take x = 0 at the inner wall (plasma side) surface, and x = I at the outer wall (coolant side) surface. Baskes’ phenomenological formula [S] for the re~mbination coefficient is used with its mass and temperature dependence. For an endothermic metal, K,j = 4c(u( MijT) -1’2S-2
exp[-(Es+E,)/kT],
(7)
where c is a constant (2.635 X 1O25K1i2 AMUt/2 atm-’ cm-2 s-l), a is the molecular sticking coefficient, Es is the hydrogen heat of solution, Mij is the atomic weight of the molecule being formed ( Mij = Mj + Mj), and S is the hydrogen solubility. The solubility is given by S = Se exp( - E,/kT),
03)
where Se is a constant (Sieverts’ constant). At the interface of a composite wall such as the W/Cu divertor, the hydrogen flux, 4, and the mobile and trapped concentrations, C, and CiT, are assumed to be continuous. The coupled system of eqs. (1) and (2) is solved numerically by “the method of lines”; i.e., first, the system is discretized with respect to the space variable, x, and then the resulting ordinary differential equation
For the calculations presented in this report, we used a parameter set summarized in table 1, as a reference. The parameters on the wall structures and the operating conditions were taken from a representative INTGR design [5]. The diffusivity in stainless steel was obtained from ref. [lo]. An average literature value was used for the solubility in stainless steel. The diffusivities and solubilities in tungsten and copper were taken from refs. [II] and [12], respectively. The heat of transport, Q*, in stainless steel is based on data for hydrogen in y-Fe-Ni alloy [13]. Although Baskes et al. [3] used a fixed value (Q* = - 0.065 ev) based on the same data, the data clearly show a linear dependency on temperature. We adopted, therefore, the temperature dependent expression obtained by fitting the data. For tungsten and copper, no data on the heat of transport are available. The trapping characteristics and the surface conditions are highly uncertain and very little data are available for the divertor materials. The trapping energy in stainless steel was taken from ref. 171. The values for tungsten and copper were tentatively assumed. The trap concentrations are based on the discussion in ref. [3]. For the inner surface, we assumed a condition with medium cleanness based on the stainless steel data [14]. Recently, Causey et al. (151 have shown that the recombination coefficient through stainless steel is increased
Table 1 Reference parameter set for first wall and divertor calculations Parameters Diffusivity
Be (cm2sV1) ED
(ev)
Q* WI Solubility Trapping Surface condition Thickness Area Temperature
Implant flux Implant energy ‘) -0.467+4.72x10-4
S, (at. cmY3 atm-‘/2) Es (eV) ET (ev) C, (at. fr.) ainner
%“M 1 (cm) cm21 Tinnr (K) q:l.fcTrz,a(Kf =,, 6) (D-T cm-’ s-l> (ev)
T(K).
First wall 316 ss
Divertor W
cu
2.15x10-2 0.59
4.1x10-3 0.39
2.3x10-’ 0.49
1.01 x 1020 0.094 0.85 0.01 5x10-3 0.5 1.2 380 623 _
5.1 x 1020 1.04 1.5 0.01 5x10-3 _ 0.5 33 523 453 403 7X10’S 135
2.8X 1020 0.38 1.0 0.01
a)
393 3.4 x 10’6 200
_
0.5 0.5
K. Ash&e, K. Ebisawa / Transient analysis of tritium migration
with the bombarding ion fluence. Therefore, our reference value for the inner surface may be rather conservative. The effects of outer surface conditions on the tritium inventory and permeation are far less than those of the inner surface because of the flow toward the outer surface nearly determined by the bulk diffusion. In the reference case, b-decay of tritium and H production through (n, p) reactions are not considered. For the D-T implant source terms, G{(x), about the first wall, we used the calculated profile [16] for 200 eV D-T implanted into stainless steel. The same profile corrected with a calculated reflection coefficient [17] for 135 eV D-T onto tungsten was assumed for the divertor case.
741
-0467*4,72xiO*
TIME
3. Results and &eussion For the results presented below, we assume a continuous plasma bum to save computer time, though the actual plasma bum is intermittent; for example, the INTOR stage-III [5] is to be operated with a bum duty of 0.4 (if we contain availability of 0.5). For such intermittent operation our preliminary calculation showed that the tritium migration during the pause of plasma bum had only little influence on tritium permeation increase and shortening of time to steady state if the wall was cooled down enough to below lOO* C during the pause. Therefore, the calculated results presented below can presumably be applied to ~te~tt~t operation by means of simply enlarging the time scale by the reciprocal of the duty factor. In such an application, it is noticed that the permeation rate should be reduced by the duty factor. 3. I. First wall permeation and i~ve~~v~ For the reference case, the steady-state permeation rate and inventory and the time to 0.9 steady-state permeation, under continuous plasma bum, are calculated to be 29 Ci/day, 0.46 kg and 1 x lo9 s, respectively. The permeation rate is remarkably low and the time to steady state far exceeds the total bum time (1.3 x 10’ s) of INTOR. It is noticed that the reference case values of permeation rate and inventory are comparable to the “nominal case” values of ref. [3], although more dirty inner surface conditions, lower inner wall temperature and larger implant flw compared with those of ref. [3] were assumed in our case. The reason is partly due to differences in the diffusivity and wall thickness used, and partly due to different assumptions on the heat of transport, Q*, in the thermal diffusion term. Fig. 1 shows the effects of Q* on the tritium permeation and inventory. As is demonstrated by the curves of fig. 1, choice of the temperature-dependent Q* leads to a remarkable reduction in inventory and especially in permeation rate compared with the other choices, because of its large negative value in the lower temperature region.
T(K)
(IV
cREFERENCE )
ilO
S)
Fig. 1.Effects of different choice regarding the heat of transport, Q*, on tritium permeation rate and inventory for the first wall. Another interesting problem on tritium permeation and inventory is the synergistic effect of protium, ‘H, which is produced uniformly in the wall by the neutron flux during the plasma bum due to (n, p) reactions. Assuming the H production rate of 1 X 10” atom cme3 S -’ based on our nucleonic calculation for the stainless steel wall under the neutron wall loading of 1.3 MW/m* in the INTOR [5], effects of the H-incorporation have been calculated. The H-incorporation to the reference case results in d ecmasing of the tritium inventory to 0.43 kg and shortening of the time to steady state to 7 x 10s s, mainly because of the competition for traps. The influence is, however, not so strong under the condition of INTOR neutron wall loading. The steadystate permeation is not affected by the incorporation of H. The reason is that the incorporation of H does not affect the recombinative release process of tritium on the inner surface, owing to the much lower concentration of H in the near surface region compared with those of the implant D-T. The tritium permeation rate is also affected by &decay of tritium, especially in cases where the trapping lengthens the residence of tritium in the wall. Incorporation of the decay term decreases the steady-state permeation rate by a factor of 2.4 from the reference case. On the other hand, reduction of the steady-state inventory is only by a factor of 1.2. The inventory and the time to steady state depend strongly on trapping characteristics (3,5]. We calculated the trap concentration effects. If the trap concentration is decreased to 0.1 at%, the tritium inventory decreases to 0.11 kg, and the time to steady state is shortened to 1 x lo* s, which is comparable to the total bum time of INTOR. 3.2. f)ivertor ideation
and inventory
For the reference case, the steady-state permeation rate and inventory through the divertor are calculated to 11. TRAPPING
AND DIFFUSION
K. A.&be, K. Ebisawa / Transient ana&tsisof triiium ~jg~atIo3?
742
be 53 a/day and 0.59 kg, respectively. The time to steady-state permeation is 2 x lo9 s under continuous plasma burn, and far exceeds the total burn time (1.3 x lo8 s) of INTOR. These results are comparable to those of the previous study for the INTOR-like W&u divertor [IS]. The dependence of ~rmeation and inventory evolution on trap concentration are shown in fig. 2, with the reference case. A decrease in the trap concentration to 0.1 at% simply results in a tenfold decrease of the inventory and the time to steady state from the reference case. The time to steady state, however, still exceeds the total bum time of INTOR. If the trapping is not incorporated, the steady state of permeation is reached in the fairly early days of INTOR operation. It is noticed that the steady-state permeation rate and inventory in the reference case are comparable to those of the first wall, although the D-T flux to the total area of the divertor is about twentyfold larger than that of the first wall. Such circumstances mainly result from a rapid recombination release at the inner surface of the divertor. The molecular recombination coefficient for tungsten is much larger than that for stainless steel because. of the very low hydrogen solubility of tungsten (see eq. (7)). On this point, additional calculations have shown the permeation and inventory to be essentially independent of the inner surface condition (einner: 0.5-5 x lo-s). A decrease in the trapping energy for tungsten from 1.5 eV to 1.0 eV results in no change in the inventory and the time to steady state.
of the bakeout procedure
3.3. 1njIuences
As is shown in the preceding sections, a large amount of tritium is retained in the first wall and divertor during reactor operations. It is thus possible that the tritium outgassing from the structures after shut-down 1mo.
lwk.
WlCu
iooyr.
toyr
IYC.
I /
produces difficulties in the opening of the reactor vessel and/or maintenance of the structures. We have evaluated influences of bakeout procedures on the outgassing and the inventory reduction based on the following scenario; i.e., (1) the reactor runs for two years with duty factor 0.8 and availability 0.5 and then it is shut down for m~ntenance, and (2) temperature of the structures after shut-down is uniformly kept at 70 *C if any special bakeout procedure is not carried out. For the results presented below, we used a result of 0.8 year continuous bum calculation for the above two year intermittent operation. The reference set of parameters shown in table 1 was used as material parameters and operation conditions except for the sensitivity studies with respect to surface condition. In the case of no bakeout procedure, calculations have shown the outgassing rate from the inner surface of the first wall to be 53 Ci/day nearly constantly for one month. This value is larger by 3 orders of magnitude than that of [4]. The reason is presumably due to different assumptions on the reactor operating scenario and/or on the surface cleanness. On the other hand, the outgassing rate from the inner surface of the divertor has been shown to change from 320 Ci/day at one hour after shut-down to 10 Ci/day after a month. Fig. 3 shows the effects of bakeout procedures on the outgassing from the inner surface of the first wall. The outgassing rate during the maintenance period after 2 days bakeout at 15O’C is still larger than the rate after one hour bakeout at 250 ‘C. A similar relation is also obtained between the bakeout temperature of 25OOC and 400 o C. These results imply that if the amount of outgassing tritium into the maintenance hall is limited by a capacity of atmospheric tritium recovery system, a longer bakeout period or a higher bakeout temperature is required to allow the personnel access during maintenance.
_ -
,
/
I
1
l\.
10
.-
\ ‘1
klO,~++
WALL
”
INNER
SURFACE
-
.-.-.
,500c
o---o
250°C
-
‘-*
4oo”c
;
.\ ty*@_.\*\ -
b+.
.-.
%
(REFERENCE)
FIRST
TB
“. (x100)
“\ 0%.
B B vr
LEVEL
‘yixl)
u p
BAKECXJT
-*-,
5 7
DIVERTOR
-NO
‘,“.
P
“-;y... \
% I I
I
I
I111111
I
TIME
(S)
1 I,,,,,,
I 102
IO BAKEOUT
Fig. 2. Effects of trap concentration on tritium permeation rate and inventory for tbe ‘w/Cu divertor.
‘.
.
-2
TIME
I
-
I ,,& ld
(hour)
Fig. 3. Influence of bakeout procedure at different temperatures (7’a) on tritium outgassing from the inner surface of the first wall during a later maintenance at wall temperature of 7o*c.
K. Ash&e, K. Ebisawa / Transient analysis of tritium migration
TIME
(months)
Fig. 4. Reduction of tritium inventory of the first waII by the bakeout procedure.
For the divertor, a one-hour bakeout at 250° C results in a four-order decrease of outgassing rate. On the other hand, a one-day bakeout at 150” C leads to a delayed outgassing having a peak of 30 Ci/day at about one day after bakeout. Calculations have also shown that, if the inner surface sticking coefficient is decreased due to an exposure to air, the outgassing rates from the first wall are decreased in proportion to the value of the sticking coefficient. On the other hand, the outgassing from the divertor is not affected by the change of sticking coefficient after bakeout ( ainna: OS-5 X lo-‘). The outgassing rates from the inner surface of the First wall at various temperatures after shut-down are calculated. The results suggest to us that the outgassing rate during maintenance will be more than lo3 Ci/day when the temperature of the structure is ~te~ttently raised at 150°C due to the decay heat. The tritium inventory is also influenced by the bakeout procedure. Fig. 4 shows the tritium inventory in the first wall during bakeout. The 400 QC bakeout for the first wall is capable of reducing the bulk inventory. The one month bakeout at 400 o C reduces the inventory in the first wall from 0.27 kg after the two year operation to 0.01 kg. It is noticed, however, that about 30% (70 g) of the total inventory is released into the coolant through the outer surface. On the other hand, for the W/Cu divertor, almost all of the trapped tritium is retained in the bulk traps even after the one month bakeout at 400 o C.
4. Summary
The calculations presented above show that the tritium permeation rate and the inventory for the stainless steel wall are remarkably reduced by adoption of the
743
temperature dependent heat of transport. The effects of protium produced from (n, p) reactions are not so strong under the INTOR conditions of neutron wall loading. The permeation rate and inventory for the W/Cu divertor are comparable to those of the first wall although the D-T implant flux for the divertor is much larger than that for the first wall. This result is mainly due to a rapid recombinative release at the inner tungsten surface. Although the time to reach steady-state permeation completely depends on the assumed trapping characteristics, steady state is not presumably attained during the life of INOR. The tritium outgassing from the inner surface after shut-down is comparatively large for both structures if an appropriate bakeout procedure is not employed. The tritium inventory in the first wall is almost completely reduced by a bakeout at 400’ C for one month. On the other hand, the inventory in the W/Cu divertor is hardly reduced by even a 400 o C bakeout.
Referen= [l] P. Wienhold, M. Profand, F. Waelbroeck and J. Winter, J. Nucl. Mater. 93/94 (1980) 866. [2] D.F. Holland and B.J. Merrill, Proc. 9th Symp. on Engineering Problems of Fusion Research, Chicago (1981) 1209. [3] MI. Baskes, W. Bauer and K.L. W&on, J. Nucl. Mater.
111/112 (1982) 663. [4] P. Wienhold, F. Waelbrceck and J. Winter, J. Nucl. Mater. 111/112 (1982) 248. [5] INTOR Group, International Tokamak Reactor: Phase Two A, Part I (Rep. Int. Tokamak Reactor Workshop Vienna, 1981-83), (IAEA. Vienna, 1983). [6] M.I. Baskes, Sandia National Laboratories Rep. SAND 80-8201 (1980). [‘7] K.L. Wilson and M.I. Baskes, J. Nucl. Mater. 76/77 (1978) 291. [8] M.I. Baskes, J. Nucl. Mater. 92 (1980) 318. [9] A.C. Hindmarsh, Lawrence Livermore Laboratory Rep., UCID-30059 Rev. 2 (1977). [lo] K.F. Chancy and G.W. PoweII, Met. Trans. 1 (1970) 2356. [ll] R. Frauenfelder, J. Vacuum Sci. Te&noi. 6 (1969) 388. [12] Y.I. Belyakov and Y.I. Zveydin, Uch. Zap. Leningrad Gos. Univ. Ser. Fii. Nauk. 345 (1%8) 44. [13] O.D. Gonzalez and R.A. Oriani, Trans. Met. Sot. AIME 233 (1965) 1878. [14] K.L. Wilson, J. Nucl. Mater. 103/104 (1981) 453. [lS] R.A. Causey, D.F. Holland and M.L. Sattler, Nucl. Technol. Fusion 4 (1983) 64. [16] G.W. Look and ML Baskes, J. Nucl. Mater. 85/86 (1979) 995. [17] L.G. Haggmark and J.P. Biersack, J. Nucl. Mater. 85/86 (1979) 1031. [18] M.A. Abdou et aI., Tritium and Safety, USA Input to INTOR Workshop Session V, Phase ZA, FED-INTOR/ TRIT,‘824 (1982).
11. TRAPPING
AND DIFFUSION
739
TRANSIENT ANALYSIS OF TRITIUM MIGRATION IN A FUSION REACTOR VESSEL K. ASHIBE R & D Center, Toshiba Corporation, 4- 1, Ukishima -rho, Kawasaki- ku, Kawasaki, 210, Japan and
K. EBISAWA Nuclear Energy Group, Toshiba Corporation,
Key words: tritium permeation,
1- 1 - 6, Uchisaiwai - cho, Chiyoda - ku, Tokyo, 100, Japan
tritium inventory,
tritium outgassing,
INTOR
Transient analysis of tritium migration after implantation into the INTOR-like stainless steel first wall and W/Cu divertor is performed using a computer code TRIP. Effects of thermal diffusion, protium from (n, p) reactions, tritium decay, surface conditions and trap characters on the tritium permeation and inventory are estimated. The influence of the bakeout procedure on the outgassing and inventory through the structures after shut-down is also discussed in detail.
1. Introduction
x, [3,6,7]. For hydrogen
The first wall and divertor or limiter of the D-T reactor are exposed to a large flux of energetic tritium. It is thus possible that the tritium inventory in the walls, its permeation into the wall-coolants and its release during maintenance after shut-down will be a serious safety problem [l-5]. Recent calculations by Baskes et al. [3] have shown that for a stainless steel wall the tritium inventory, permeation rate and the time to steady state are strongly affected by the surface conditions, neutron damage traps and thermal diffusion as well as the wall temperature. Several estimates of the tritium release from stainless steel walls with or without bakeout during reactor maintenance were also made [4,5]; however, the previous estimates did not include the effects of the neutron damage traps and/or the surface recombination process of hydrogen isotopes, which can play important roles in the tritium release during maintenance. We have developed a computer code TRIP (Tritium Re-emission, Inventory and Permeation). This code is based on the formalism of the DIFFUSE [3,6] and extended to deal with three hydrogen isotopes (H, D, T) simultaneously. It also allows to apply to an arbitrary running mode like an intermittent reactor operation. Using this code, we have performed further evaluations on the above-mentioned problems for the INTOR-like, stainless steel first wall and W/Cu divertor. This report presents new results about the tritium release from these structures with or without bakeout during maintenance as well as some further sensitivity study for the tritium inventory and permeation through these structures.
ac, at=-ax
aJ.
-+G,-at,
isotope
i,
ac,T
and
ac? at
-..-L=
oic,
- CTv,, exp( - E,/kT).
p
(2) In eq. (1) C, is the mobile hydrogen concentration, Ji is the bulk hydrogen flux, Gi is the hydrogen source term which includes both the D-T implant from the plasma and H production through (n, p) reactions, and CiT is the trapped hydrogen concentration. Ci and C,r are given in atoms/ems. In eq. (2) Di is the hydrogen diffusivity, CT is the total trap concentration given in (atomic fraction), N is the atom density of the host material, X is the jump distance (taken as 2.5 A), v, is the attempt frequency for detrappinng (taken as 10” s-l), ET is the total trapping energy (the sum of the binding energy of the traps and the migration energy), T is the wall temperature and k is the Boltzmann’s constant. In the present calculations, we assume the trap concentration, CT, is initially saturated and uniformly distributed. When tritium decay is included, decay terms of - X&, and -X& are added to the right-hand sides of eqs. (1) and (2), respectively, where X, is the decay constant of tritium. The diffusivity is given by eq. (3) assuming Graham’s law for isotope dependence: Di = D,,IU-‘/~
exp( - E,/kT),
(3)
where Do is a constant, E, is the migration M, is the atomic weight of isotope i. The bulk hydrogen flux is given by
2. Method of calculation 2. I. Physical model
energy and
The TRIP solves the following coupled equations of diffusion and trapping with respect to time t and depth 0022-3115/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
11. TRAPPING
AND DIFFUSION
K. Ashibe, I(. Ebisawu / Transient anaiysis of tririum migration
740
system is integrated with respect to the time variable, t. The TRIP uses the central finite difference method for the space discretization and the GEARB code by Hindmarsh ]9] for the time integration.
where the second term on the right is due to the thermal diffusion (the Soret effect), with Q* being the heat of transport. The surface boundary conditions for eq. (1) are J,= -CK,,C& .i and
atx=O,
(5)
2.2. A reference parameter set for calculations
J, = C KijCiCj at x = 1, (6) j where Kij is the hydrogen molecular recombination coefficient for isotope i combining with isotope j, 1 is the wall thickness and we take x = 0 at the inner wall (plasma side) surface, and x = I at the outer wall (coolant side) surface. Baskes’ phenomenological formula [S] for the re~mbination coefficient is used with its mass and temperature dependence. For an endothermic metal, K,j = 4c(u( MijT) -1’2S-2
exp[-(Es+E,)/kT],
(7)
where c is a constant (2.635 X 1O25K1i2 AMUt/2 atm-’ cm-2 s-l), a is the molecular sticking coefficient, Es is the hydrogen heat of solution, Mij is the atomic weight of the molecule being formed ( Mij = Mj + Mj), and S is the hydrogen solubility. The solubility is given by S = Se exp( - E,/kT),
03)
where Se is a constant (Sieverts’ constant). At the interface of a composite wall such as the W/Cu divertor, the hydrogen flux, 4, and the mobile and trapped concentrations, C, and CiT, are assumed to be continuous. The coupled system of eqs. (1) and (2) is solved numerically by “the method of lines”; i.e., first, the system is discretized with respect to the space variable, x, and then the resulting ordinary differential equation
For the calculations presented in this report, we used a parameter set summarized in table 1, as a reference. The parameters on the wall structures and the operating conditions were taken from a representative INTGR design [5]. The diffusivity in stainless steel was obtained from ref. [lo]. An average literature value was used for the solubility in stainless steel. The diffusivities and solubilities in tungsten and copper were taken from refs. [II] and [12], respectively. The heat of transport, Q*, in stainless steel is based on data for hydrogen in y-Fe-Ni alloy [13]. Although Baskes et al. [3] used a fixed value (Q* = - 0.065 ev) based on the same data, the data clearly show a linear dependency on temperature. We adopted, therefore, the temperature dependent expression obtained by fitting the data. For tungsten and copper, no data on the heat of transport are available. The trapping characteristics and the surface conditions are highly uncertain and very little data are available for the divertor materials. The trapping energy in stainless steel was taken from ref. 171. The values for tungsten and copper were tentatively assumed. The trap concentrations are based on the discussion in ref. [3]. For the inner surface, we assumed a condition with medium cleanness based on the stainless steel data [14]. Recently, Causey et al. (151 have shown that the recombination coefficient through stainless steel is increased
Table 1 Reference parameter set for first wall and divertor calculations Parameters Diffusivity
Be (cm2sV1) ED
(ev)
Q* WI Solubility Trapping Surface condition Thickness Area Temperature
Implant flux Implant energy ‘) -0.467+4.72x10-4
S, (at. cmY3 atm-‘/2) Es (eV) ET (ev) C, (at. fr.) ainner
%“M 1 (cm) cm21 Tinnr (K) q:l.fcTrz,a(Kf =,, 6) (D-T cm-’ s-l> (ev)
T(K).
First wall 316 ss
Divertor W
cu
2.15x10-2 0.59
4.1x10-3 0.39
2.3x10-’ 0.49
1.01 x 1020 0.094 0.85 0.01 5x10-3 0.5 1.2 380 623 _
5.1 x 1020 1.04 1.5 0.01 5x10-3 _ 0.5 33 523 453 403 7X10’S 135
2.8X 1020 0.38 1.0 0.01
a)
393 3.4 x 10’6 200
_
0.5 0.5
K. Ash&e, K. Ebisawa / Transient analysis of tritium migration
with the bombarding ion fluence. Therefore, our reference value for the inner surface may be rather conservative. The effects of outer surface conditions on the tritium inventory and permeation are far less than those of the inner surface because of the flow toward the outer surface nearly determined by the bulk diffusion. In the reference case, b-decay of tritium and H production through (n, p) reactions are not considered. For the D-T implant source terms, G{(x), about the first wall, we used the calculated profile [16] for 200 eV D-T implanted into stainless steel. The same profile corrected with a calculated reflection coefficient [17] for 135 eV D-T onto tungsten was assumed for the divertor case.
741
-0467*4,72xiO*
TIME
3. Results and &eussion For the results presented below, we assume a continuous plasma bum to save computer time, though the actual plasma bum is intermittent; for example, the INTOR stage-III [5] is to be operated with a bum duty of 0.4 (if we contain availability of 0.5). For such intermittent operation our preliminary calculation showed that the tritium migration during the pause of plasma bum had only little influence on tritium permeation increase and shortening of time to steady state if the wall was cooled down enough to below lOO* C during the pause. Therefore, the calculated results presented below can presumably be applied to ~te~tt~t operation by means of simply enlarging the time scale by the reciprocal of the duty factor. In such an application, it is noticed that the permeation rate should be reduced by the duty factor. 3. I. First wall permeation and i~ve~~v~ For the reference case, the steady-state permeation rate and inventory and the time to 0.9 steady-state permeation, under continuous plasma bum, are calculated to be 29 Ci/day, 0.46 kg and 1 x lo9 s, respectively. The permeation rate is remarkably low and the time to steady state far exceeds the total bum time (1.3 x 10’ s) of INTOR. It is noticed that the reference case values of permeation rate and inventory are comparable to the “nominal case” values of ref. [3], although more dirty inner surface conditions, lower inner wall temperature and larger implant flw compared with those of ref. [3] were assumed in our case. The reason is partly due to differences in the diffusivity and wall thickness used, and partly due to different assumptions on the heat of transport, Q*, in the thermal diffusion term. Fig. 1 shows the effects of Q* on the tritium permeation and inventory. As is demonstrated by the curves of fig. 1, choice of the temperature-dependent Q* leads to a remarkable reduction in inventory and especially in permeation rate compared with the other choices, because of its large negative value in the lower temperature region.
T(K)
(IV
cREFERENCE )
ilO
S)
Fig. 1.Effects of different choice regarding the heat of transport, Q*, on tritium permeation rate and inventory for the first wall. Another interesting problem on tritium permeation and inventory is the synergistic effect of protium, ‘H, which is produced uniformly in the wall by the neutron flux during the plasma bum due to (n, p) reactions. Assuming the H production rate of 1 X 10” atom cme3 S -’ based on our nucleonic calculation for the stainless steel wall under the neutron wall loading of 1.3 MW/m* in the INTOR [5], effects of the H-incorporation have been calculated. The H-incorporation to the reference case results in d ecmasing of the tritium inventory to 0.43 kg and shortening of the time to steady state to 7 x 10s s, mainly because of the competition for traps. The influence is, however, not so strong under the condition of INTOR neutron wall loading. The steadystate permeation is not affected by the incorporation of H. The reason is that the incorporation of H does not affect the recombinative release process of tritium on the inner surface, owing to the much lower concentration of H in the near surface region compared with those of the implant D-T. The tritium permeation rate is also affected by &decay of tritium, especially in cases where the trapping lengthens the residence of tritium in the wall. Incorporation of the decay term decreases the steady-state permeation rate by a factor of 2.4 from the reference case. On the other hand, reduction of the steady-state inventory is only by a factor of 1.2. The inventory and the time to steady state depend strongly on trapping characteristics (3,5]. We calculated the trap concentration effects. If the trap concentration is decreased to 0.1 at%, the tritium inventory decreases to 0.11 kg, and the time to steady state is shortened to 1 x lo* s, which is comparable to the total bum time of INTOR. 3.2. f)ivertor ideation
and inventory
For the reference case, the steady-state permeation rate and inventory through the divertor are calculated to 11. TRAPPING
AND DIFFUSION
K. A.&be, K. Ebisawa / Transient ana&tsisof triiium ~jg~atIo3?
742
be 53 a/day and 0.59 kg, respectively. The time to steady-state permeation is 2 x lo9 s under continuous plasma burn, and far exceeds the total burn time (1.3 x lo8 s) of INTOR. These results are comparable to those of the previous study for the INTOR-like W&u divertor [IS]. The dependence of ~rmeation and inventory evolution on trap concentration are shown in fig. 2, with the reference case. A decrease in the trap concentration to 0.1 at% simply results in a tenfold decrease of the inventory and the time to steady state from the reference case. The time to steady state, however, still exceeds the total bum time of INTOR. If the trapping is not incorporated, the steady state of permeation is reached in the fairly early days of INTOR operation. It is noticed that the steady-state permeation rate and inventory in the reference case are comparable to those of the first wall, although the D-T flux to the total area of the divertor is about twentyfold larger than that of the first wall. Such circumstances mainly result from a rapid recombination release at the inner surface of the divertor. The molecular recombination coefficient for tungsten is much larger than that for stainless steel because. of the very low hydrogen solubility of tungsten (see eq. (7)). On this point, additional calculations have shown the permeation and inventory to be essentially independent of the inner surface condition (einner: 0.5-5 x lo-s). A decrease in the trapping energy for tungsten from 1.5 eV to 1.0 eV results in no change in the inventory and the time to steady state.
of the bakeout procedure
3.3. 1njIuences
As is shown in the preceding sections, a large amount of tritium is retained in the first wall and divertor during reactor operations. It is thus possible that the tritium outgassing from the structures after shut-down 1mo.
lwk.
WlCu
iooyr.
toyr
IYC.
I /
produces difficulties in the opening of the reactor vessel and/or maintenance of the structures. We have evaluated influences of bakeout procedures on the outgassing and the inventory reduction based on the following scenario; i.e., (1) the reactor runs for two years with duty factor 0.8 and availability 0.5 and then it is shut down for m~ntenance, and (2) temperature of the structures after shut-down is uniformly kept at 70 *C if any special bakeout procedure is not carried out. For the results presented below, we used a result of 0.8 year continuous bum calculation for the above two year intermittent operation. The reference set of parameters shown in table 1 was used as material parameters and operation conditions except for the sensitivity studies with respect to surface condition. In the case of no bakeout procedure, calculations have shown the outgassing rate from the inner surface of the first wall to be 53 Ci/day nearly constantly for one month. This value is larger by 3 orders of magnitude than that of [4]. The reason is presumably due to different assumptions on the reactor operating scenario and/or on the surface cleanness. On the other hand, the outgassing rate from the inner surface of the divertor has been shown to change from 320 Ci/day at one hour after shut-down to 10 Ci/day after a month. Fig. 3 shows the effects of bakeout procedures on the outgassing from the inner surface of the first wall. The outgassing rate during the maintenance period after 2 days bakeout at 15O’C is still larger than the rate after one hour bakeout at 250 ‘C. A similar relation is also obtained between the bakeout temperature of 25OOC and 400 o C. These results imply that if the amount of outgassing tritium into the maintenance hall is limited by a capacity of atmospheric tritium recovery system, a longer bakeout period or a higher bakeout temperature is required to allow the personnel access during maintenance.
_ -
,
/
I
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.-
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SURFACE
-
.-.-.
,500c
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250°C
-
‘-*
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;
.\ ty*@_.\*\ -
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.-.
%
(REFERENCE)
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“. (x100)
“\ 0%.
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I
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TIME
(S)
1 I,,,,,,
I 102
IO BAKEOUT
Fig. 2. Effects of trap concentration on tritium permeation rate and inventory for tbe ‘w/Cu divertor.
‘.
.
-2
TIME
I
-
I ,,& ld
(hour)
Fig. 3. Influence of bakeout procedure at different temperatures (7’a) on tritium outgassing from the inner surface of the first wall during a later maintenance at wall temperature of 7o*c.
K. Ash&e, K. Ebisawa / Transient analysis of tritium migration
TIME
(months)
Fig. 4. Reduction of tritium inventory of the first waII by the bakeout procedure.
For the divertor, a one-hour bakeout at 250° C results in a four-order decrease of outgassing rate. On the other hand, a one-day bakeout at 150” C leads to a delayed outgassing having a peak of 30 Ci/day at about one day after bakeout. Calculations have also shown that, if the inner surface sticking coefficient is decreased due to an exposure to air, the outgassing rates from the first wall are decreased in proportion to the value of the sticking coefficient. On the other hand, the outgassing from the divertor is not affected by the change of sticking coefficient after bakeout ( ainna: OS-5 X lo-‘). The outgassing rates from the inner surface of the First wall at various temperatures after shut-down are calculated. The results suggest to us that the outgassing rate during maintenance will be more than lo3 Ci/day when the temperature of the structure is ~te~ttently raised at 150°C due to the decay heat. The tritium inventory is also influenced by the bakeout procedure. Fig. 4 shows the tritium inventory in the first wall during bakeout. The 400 QC bakeout for the first wall is capable of reducing the bulk inventory. The one month bakeout at 400 o C reduces the inventory in the first wall from 0.27 kg after the two year operation to 0.01 kg. It is noticed, however, that about 30% (70 g) of the total inventory is released into the coolant through the outer surface. On the other hand, for the W/Cu divertor, almost all of the trapped tritium is retained in the bulk traps even after the one month bakeout at 400 o C.
4. Summary
The calculations presented above show that the tritium permeation rate and the inventory for the stainless steel wall are remarkably reduced by adoption of the
743
temperature dependent heat of transport. The effects of protium produced from (n, p) reactions are not so strong under the INTOR conditions of neutron wall loading. The permeation rate and inventory for the W/Cu divertor are comparable to those of the first wall although the D-T implant flux for the divertor is much larger than that for the first wall. This result is mainly due to a rapid recombinative release at the inner tungsten surface. Although the time to reach steady-state permeation completely depends on the assumed trapping characteristics, steady state is not presumably attained during the life of INOR. The tritium outgassing from the inner surface after shut-down is comparatively large for both structures if an appropriate bakeout procedure is not employed. The tritium inventory in the first wall is almost completely reduced by a bakeout at 400’ C for one month. On the other hand, the inventory in the W/Cu divertor is hardly reduced by even a 400 o C bakeout.
Referen= [l] P. Wienhold, M. Profand, F. Waelbroeck and J. Winter, J. Nucl. Mater. 93/94 (1980) 866. [2] D.F. Holland and B.J. Merrill, Proc. 9th Symp. on Engineering Problems of Fusion Research, Chicago (1981) 1209. [3] MI. Baskes, W. Bauer and K.L. W&on, J. Nucl. Mater.
111/112 (1982) 663. [4] P. Wienhold, F. Waelbrceck and J. Winter, J. Nucl. Mater. 111/112 (1982) 248. [5] INTOR Group, International Tokamak Reactor: Phase Two A, Part I (Rep. Int. Tokamak Reactor Workshop Vienna, 1981-83), (IAEA. Vienna, 1983). [6] M.I. Baskes, Sandia National Laboratories Rep. SAND 80-8201 (1980). [‘7] K.L. Wilson and M.I. Baskes, J. Nucl. Mater. 76/77 (1978) 291. [8] M.I. Baskes, J. Nucl. Mater. 92 (1980) 318. [9] A.C. Hindmarsh, Lawrence Livermore Laboratory Rep., UCID-30059 Rev. 2 (1977). [lo] K.F. Chancy and G.W. PoweII, Met. Trans. 1 (1970) 2356. [ll] R. Frauenfelder, J. Vacuum Sci. Te&noi. 6 (1969) 388. [12] Y.I. Belyakov and Y.I. Zveydin, Uch. Zap. Leningrad Gos. Univ. Ser. Fii. Nauk. 345 (1%8) 44. [13] O.D. Gonzalez and R.A. Oriani, Trans. Met. Sot. AIME 233 (1965) 1878. [14] K.L. Wilson, J. Nucl. Mater. 103/104 (1981) 453. [lS] R.A. Causey, D.F. Holland and M.L. Sattler, Nucl. Technol. Fusion 4 (1983) 64. [16] G.W. Look and ML Baskes, J. Nucl. Mater. 85/86 (1979) 995. [17] L.G. Haggmark and J.P. Biersack, J. Nucl. Mater. 85/86 (1979) 1031. [18] M.A. Abdou et aI., Tritium and Safety, USA Input to INTOR Workshop Session V, Phase ZA, FED-INTOR/ TRIT,‘824 (1982).
11. TRAPPING
AND DIFFUSION