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Modelling fission gas behaviour in mixed oxide fuel under normal and off-normal conditions in fast reactors
Journal of Nuclear Materials 188 (1992) 308-311 North-Holland
Modelling fission gas behaviour in mixed oxide fuel under normal and off-normal conditions in fast reactors L. With Kernforschungszentrum Karlsruhe, Institut fiir Neutronenphysik und Reaktortechnik, Postfach 3640, W-7500 KarLsruhe I, Germany
The fission gas model LAKU has been under development in Karlsruhe since 1982. The aim of this paper is to highlight the basis of fuel properties and data on material bebaviour, which underlies and decisively influences the results of the model.
1. Introduction The Karlsruhe fission gas model LAKU has evolved over the years from an older code and incorporates modelling work performed in Karlsruhe [l-3] and elsewhere [4-61. The purpose of the model is to describe the influence of the fission products on the in-reactor pin behaviour under .off-normal conditions, which may range from the slight undercooling of a single pin to severe accident scenarios. The modelling of the radioactive source term is not the aim of the code. The main influence of the fission products on transient pin behaviour is due to their inert gas components. The model contains therefore, at least at present, only a description of the rare gas fission products residing in bubbles and in solid solution in the interior and on the surface of fuel grains. Their behaviour is modened in great detail under steady state and transient conditions in solid and - for transients only - also in melting and molten mixed oxide fast reactor fuel. A very simple description of the volatile fission product cesium, which is needed for one special aspect of transient pin behaviour, is included.
2. Model There is a quite extensive experimental basis for this kind of model: Measurements on time dependent fission gas release under various conditions, on fission gas driven swelling, spatial fission gas distributions including fission gas bubble densities and radii, and
observations of the pin behaviour under various transient conditions. There are also measurements of the material constants needed by the model, some of which have, however, a quite significant margin of uncertainty. There are, in addition, even some uncertainties concerning the exact nature of some of the physical processes involved. It is therefore indispensable to adjust the code, especially its material constants, on the basis experiments mentioned above, It follows, that the limits of the model are defined by the existing experimental evidence. Table 1 shows the different calculations steps performed by the model and the material data of importance in each step. A summary of the data to be provided for the code follows below: (1) Diffusion coefficients (gas and heavy species in the interior of the grains and on grain faces, gas bubble diffusion coefficients, the diffusion coefficient of the gas in liquid fuel); possible dependence of these data on fuel stoichiometry and burnup. (2) Fuel grain growth data. (3) Densities of intra- and intergranular bubbles. (4) Probability for resolution of bubble gas. (5) Fuel behaviour under cracking conditions (yield strength of the fuel, width of crack). (6) Fuel surface tension, especially its temperature dependence in molten fuel. (7) Viscosity of liquid fuel and its enthalpy dependence between solidus and liquidus. Many of these data values (e.g. fuel surface tension in liquid fuel, grain growth laws) are sufficiently well known, but others, especially the various diffusion co-
0022-3115/92/%05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved
L. V&h / Modelling fusion gas behaviour in mixed oxide fuel
efficients have a wide margin of uncertainty due to, partly, their dependence on fuel fabrication specifications. It must be noted in this context, that the steadystate part of the code has been verified mainly on fast reactor irradiations. A change of the diffusion coeffi-
cients might be warranted when modelling thermal reactor fuel, due to its different stoichiometry: Stoichiometty (or burnup) dependent material constants are so far not taken into account. Another remark must be made concerning the
Table 1 Modelling steps and main material parameters of the fission gas model LAKU Object
Model
Important parameters
Grains
Initially idealized as spherical, but elongation at high irradiation temperatures taken into account As atoms in the fuel matrix Modelled as resolved gas (in supersaturated solution) and, at higher temperatures, as small gas bubbles; one class of bubbles, with a mean radius, gas content and bubble density; precipitation into bubbles by diffusion of atomic gas, resolution fission induced (some authors postulate thermally induced resolution) Low temperatures: migration of atomic gas; intermediate temperatures: migration effect mitigated by trapping in intragranular bubbles; onset of sweeping by grain growth; high temperatures: additional gas sweeping by mobile intragranular bubbles and by moving gas pores LAKU model: enhanced bubble migration velocity as main physical process with, additionally, atomic gas diffusion (low temperatures) and grain boundary sweeping (long transients at intermediate temperatures); release mechanisms postulated by other authors: bubble movement in stress gradients; thermally induced resolution with atomic gas diffusion; sweeping by moving lattice defects Diffusion to pores at low irradiation temperatures; at higher temperatures formation of lenticular bubbles, interlinkage and venting to the pores; modelled with one bubble class similar to the intragranular model; gas content at the grain faces always small, but grain face bubble swelling not negligible Grain boundary separation due to saturation with bubbles; grain boundary cracking by overpressurized bubble Model for formation of interlinking channels, pore venting, channel closure by sintering; pores contain bigger fraction of intergranular gas 3 bubble classes + resolved gas, precipitation and resolution; forces acting on bubbles: Brownian motion, capillary forces, buoyancy, inertia
As fabricated grain size; law of grain growth
Gas formation Gas behaviour inside the grains (as intragranular gas)
Migration to grain surface under steady state conditions
Migration to grain surface under transient conditions
Gas behaviour on grain face under steady state conditions
Gas behaviour on grain face under transient conditions Gas in pores (fabricated and restructured) Gas in melting and molten fuel
Gas driven swelling caused by bubbles and pores
309
Follows from the parameters of the bubbles resp. pores (densities and radius) calculated by the model
Number of gas atoms per fission diffusion constant of atomic gas (irradiation induced for low temperatures, and thermally activated); resolution constant; intragranular bubble density
Same as above; steady-state velocity of intragranular bubble; pore velocity
Surface diffusion coefficient of the heavy species; self-diffusion coefficient of the heavy species; yield strength of fuel
Density of grain face pores
Crack opening displacement; self-diffusion coefficient of heavy species in grain faces Channel width; intra- and intergranular self-diffusion coefficient of heavy species Viscosity of liquid fuel and of fuel between solids and liquids; temperature dependent liquid fuel surface tension; diffusion coefficient of gas in liquid fuel
L. V&h / ModeNinl:fission gas behaciour in mixed oxide fuel
310 Table 2 Experimental ejection
results of the FD experiments
Experiment name
Preirradiation conditions Linear power (MW,‘cm)
Burnup (at%)
FD2.8
151
-8
FD4.3
251
-5
with solid fuel
Transient: experimental result
Fuel sputtering starting at 6.233 s Start of solid-state fuel ejection at 5.459 s
model for steady-state irradiation: As stated above, the main purpose of the code is modelling the fission gas behaviour under transient conditions. It has been found, however, that this part of the model is quite sensitive to changes in the starting conditions, i.e. the representation of the gas distribution in the pin after steady-state irradiation. Therefore a considerable effort has to be spent for devising an accurate model of the fission gas behaviour during normal reactor operation. Fuel restructuring processes influence the gas behaviour and have therefore to be taken into account. Tables 2 and 3 show one example of the parameter fitting implicit in the code. The mode1 has been used to recalculate some of the FD-experiments [7], which are transient experiments on irradiated fast reactor fuel with the aim of investigating the mode of transient fuel failure. Fuel breakup in the still solid state occurred in some of these tests. Table 2 gives the main results for these tests, tabIe 3 the results of the model, employing the uranium self-diffusion coefficient O,* measured by Reynolds and Burton [8]. Also shown are the results for varying this value by a factor of five in both directions, which is the uncertainty given by the authors. It is evident that the original value gives acceptable re-
Table 3 LAKU-recalculations heavy species Experiment name
sults for both experiments, and that the results for one experiment become worse when the diffusion coefficient is changed so as to ameliorate the results for the other one. This difficulty may be due to a difference in the pretest fuel configuration not modelled by LAKU: Unfortunately no post-irradiation examinations were carried out for the samples used in the tests. One part of the code that has recently been refined is the model of gas behaviour in molten and especially melting fuel. A smooth transition of the most important material constants from those of solid to those of liquid fuel has been realized for the melting process. Capillary effects have been included among the forces acting on the fission gas bubbles in molten fuel. They turn out to be the most important driving force for the coalescence of bigger bubbles, and their magnitude is directly proportional to the decrease with increasing temperatures of the fuel surface tension. There is unfortunately very little experimental basis to verify the model for melting and molten fuel. One is thus reduced to a more or less qualitative evaluation of integral experiments, e.g. those of the CABRI series [9] involving fuel melting but no pin failure. The results [3] demonstrate a satisfactory agreement of the experimental evidence - mainly from post-test examinations - with the results of the model.
3. Conclusions Though the main modelling work for the gaseous fission products has been accomplished to date, some additional efforts may become necessary for high burnup pins. There is evidence from the more recent CABRI-2 series of experiments, that the fuel structure at high values of burnup (10 at% and more) can be quite different from that at lower values. This is possibly due to the accumulation of fission product composites in the fuel to sheath gap and a different growth
of the FD experiments with solid fuel ejection, using different grain boundary diffusion coefficients of the LAKU results Event
With diffusion coefficient 5xD:
FD2.8 FD4.3
Partial grain boundary cracking at General grain boundary cracking at Partial grain boundary cracking at General grain boundary cracking at
5.450 s 5.504 s
Lx+
W/S
6.288 s
6.277 s
5.442 s 5.459 s
5.439 s 5.454 s
L. Viith / Modelling fusion gas behaviour in
behaviour of the fuel grains. The CABRI-2 follow-on program will probably serve to broaden the experimental experience in this respect. This may entail additions to the modelling, e.g. a more refined model for cesium and possibly other fission products. The modelling of the burnup dependence of diffusion coefficients, grain growth and possibly other aspects of material behaviour may also become necessary.
References [l] L. Vath, KfK 3753, Kernforschungszentrum Karlsruhe, Germany, 1984.
Karlsruhe,
mixed oxidefuel
311
[2] L. Vlth and E.A. Fischer, Nucl. Technol. 71 (1985) 246. [3] L. VIth, Proc. 1990 Int. Fast Reactor Safety Meeting, Snowbird, Utah, August 12-16, 1990, vol. IV (American Nuclear Society, 1990) p. 375. [4] E.E. Gruber, Nucl. Technol. 35 (1977) 617. [5] J. Rest and SM. Gehl, Nucl. Eng. Des. 56 (1980) 233. [6] D.H. Worledge, SANDBO-0328, Sandia National Laboratories (1980). [7] S.A. Wright, E.A. Fisher, P.K. Mast and G. Schumacher, Nucl. Technol. 71 (1985) 326. [8] G.L. Reynolds and B. Burton, J. Nucl. Mater. 82 (1979) 22. [9] G. Heusener et al., Proc. 1990 Int. Fast Reactor Safety Meeting, Snowbird, Utah, August 12-16, 1990, vol. II (American Nuclear Society, 1990) p. 197.
Modelling fission gas behaviour in mixed oxide fuel under normal and off-normal conditions in fast reactors L. With Kernforschungszentrum Karlsruhe, Institut fiir Neutronenphysik und Reaktortechnik, Postfach 3640, W-7500 KarLsruhe I, Germany
The fission gas model LAKU has been under development in Karlsruhe since 1982. The aim of this paper is to highlight the basis of fuel properties and data on material bebaviour, which underlies and decisively influences the results of the model.
1. Introduction The Karlsruhe fission gas model LAKU has evolved over the years from an older code and incorporates modelling work performed in Karlsruhe [l-3] and elsewhere [4-61. The purpose of the model is to describe the influence of the fission products on the in-reactor pin behaviour under .off-normal conditions, which may range from the slight undercooling of a single pin to severe accident scenarios. The modelling of the radioactive source term is not the aim of the code. The main influence of the fission products on transient pin behaviour is due to their inert gas components. The model contains therefore, at least at present, only a description of the rare gas fission products residing in bubbles and in solid solution in the interior and on the surface of fuel grains. Their behaviour is modened in great detail under steady state and transient conditions in solid and - for transients only - also in melting and molten mixed oxide fast reactor fuel. A very simple description of the volatile fission product cesium, which is needed for one special aspect of transient pin behaviour, is included.
2. Model There is a quite extensive experimental basis for this kind of model: Measurements on time dependent fission gas release under various conditions, on fission gas driven swelling, spatial fission gas distributions including fission gas bubble densities and radii, and
observations of the pin behaviour under various transient conditions. There are also measurements of the material constants needed by the model, some of which have, however, a quite significant margin of uncertainty. There are, in addition, even some uncertainties concerning the exact nature of some of the physical processes involved. It is therefore indispensable to adjust the code, especially its material constants, on the basis experiments mentioned above, It follows, that the limits of the model are defined by the existing experimental evidence. Table 1 shows the different calculations steps performed by the model and the material data of importance in each step. A summary of the data to be provided for the code follows below: (1) Diffusion coefficients (gas and heavy species in the interior of the grains and on grain faces, gas bubble diffusion coefficients, the diffusion coefficient of the gas in liquid fuel); possible dependence of these data on fuel stoichiometry and burnup. (2) Fuel grain growth data. (3) Densities of intra- and intergranular bubbles. (4) Probability for resolution of bubble gas. (5) Fuel behaviour under cracking conditions (yield strength of the fuel, width of crack). (6) Fuel surface tension, especially its temperature dependence in molten fuel. (7) Viscosity of liquid fuel and its enthalpy dependence between solidus and liquidus. Many of these data values (e.g. fuel surface tension in liquid fuel, grain growth laws) are sufficiently well known, but others, especially the various diffusion co-
0022-3115/92/%05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved
L. V&h / Modelling fusion gas behaviour in mixed oxide fuel
efficients have a wide margin of uncertainty due to, partly, their dependence on fuel fabrication specifications. It must be noted in this context, that the steadystate part of the code has been verified mainly on fast reactor irradiations. A change of the diffusion coeffi-
cients might be warranted when modelling thermal reactor fuel, due to its different stoichiometry: Stoichiometty (or burnup) dependent material constants are so far not taken into account. Another remark must be made concerning the
Table 1 Modelling steps and main material parameters of the fission gas model LAKU Object
Model
Important parameters
Grains
Initially idealized as spherical, but elongation at high irradiation temperatures taken into account As atoms in the fuel matrix Modelled as resolved gas (in supersaturated solution) and, at higher temperatures, as small gas bubbles; one class of bubbles, with a mean radius, gas content and bubble density; precipitation into bubbles by diffusion of atomic gas, resolution fission induced (some authors postulate thermally induced resolution) Low temperatures: migration of atomic gas; intermediate temperatures: migration effect mitigated by trapping in intragranular bubbles; onset of sweeping by grain growth; high temperatures: additional gas sweeping by mobile intragranular bubbles and by moving gas pores LAKU model: enhanced bubble migration velocity as main physical process with, additionally, atomic gas diffusion (low temperatures) and grain boundary sweeping (long transients at intermediate temperatures); release mechanisms postulated by other authors: bubble movement in stress gradients; thermally induced resolution with atomic gas diffusion; sweeping by moving lattice defects Diffusion to pores at low irradiation temperatures; at higher temperatures formation of lenticular bubbles, interlinkage and venting to the pores; modelled with one bubble class similar to the intragranular model; gas content at the grain faces always small, but grain face bubble swelling not negligible Grain boundary separation due to saturation with bubbles; grain boundary cracking by overpressurized bubble Model for formation of interlinking channels, pore venting, channel closure by sintering; pores contain bigger fraction of intergranular gas 3 bubble classes + resolved gas, precipitation and resolution; forces acting on bubbles: Brownian motion, capillary forces, buoyancy, inertia
As fabricated grain size; law of grain growth
Gas formation Gas behaviour inside the grains (as intragranular gas)
Migration to grain surface under steady state conditions
Migration to grain surface under transient conditions
Gas behaviour on grain face under steady state conditions
Gas behaviour on grain face under transient conditions Gas in pores (fabricated and restructured) Gas in melting and molten fuel
Gas driven swelling caused by bubbles and pores
309
Follows from the parameters of the bubbles resp. pores (densities and radius) calculated by the model
Number of gas atoms per fission diffusion constant of atomic gas (irradiation induced for low temperatures, and thermally activated); resolution constant; intragranular bubble density
Same as above; steady-state velocity of intragranular bubble; pore velocity
Surface diffusion coefficient of the heavy species; self-diffusion coefficient of the heavy species; yield strength of fuel
Density of grain face pores
Crack opening displacement; self-diffusion coefficient of heavy species in grain faces Channel width; intra- and intergranular self-diffusion coefficient of heavy species Viscosity of liquid fuel and of fuel between solids and liquids; temperature dependent liquid fuel surface tension; diffusion coefficient of gas in liquid fuel
L. V&h / ModeNinl:fission gas behaciour in mixed oxide fuel
310 Table 2 Experimental ejection
results of the FD experiments
Experiment name
Preirradiation conditions Linear power (MW,‘cm)
Burnup (at%)
FD2.8
151
-8
FD4.3
251
-5
with solid fuel
Transient: experimental result
Fuel sputtering starting at 6.233 s Start of solid-state fuel ejection at 5.459 s
model for steady-state irradiation: As stated above, the main purpose of the code is modelling the fission gas behaviour under transient conditions. It has been found, however, that this part of the model is quite sensitive to changes in the starting conditions, i.e. the representation of the gas distribution in the pin after steady-state irradiation. Therefore a considerable effort has to be spent for devising an accurate model of the fission gas behaviour during normal reactor operation. Fuel restructuring processes influence the gas behaviour and have therefore to be taken into account. Tables 2 and 3 show one example of the parameter fitting implicit in the code. The mode1 has been used to recalculate some of the FD-experiments [7], which are transient experiments on irradiated fast reactor fuel with the aim of investigating the mode of transient fuel failure. Fuel breakup in the still solid state occurred in some of these tests. Table 2 gives the main results for these tests, tabIe 3 the results of the model, employing the uranium self-diffusion coefficient O,* measured by Reynolds and Burton [8]. Also shown are the results for varying this value by a factor of five in both directions, which is the uncertainty given by the authors. It is evident that the original value gives acceptable re-
Table 3 LAKU-recalculations heavy species Experiment name
sults for both experiments, and that the results for one experiment become worse when the diffusion coefficient is changed so as to ameliorate the results for the other one. This difficulty may be due to a difference in the pretest fuel configuration not modelled by LAKU: Unfortunately no post-irradiation examinations were carried out for the samples used in the tests. One part of the code that has recently been refined is the model of gas behaviour in molten and especially melting fuel. A smooth transition of the most important material constants from those of solid to those of liquid fuel has been realized for the melting process. Capillary effects have been included among the forces acting on the fission gas bubbles in molten fuel. They turn out to be the most important driving force for the coalescence of bigger bubbles, and their magnitude is directly proportional to the decrease with increasing temperatures of the fuel surface tension. There is unfortunately very little experimental basis to verify the model for melting and molten fuel. One is thus reduced to a more or less qualitative evaluation of integral experiments, e.g. those of the CABRI series [9] involving fuel melting but no pin failure. The results [3] demonstrate a satisfactory agreement of the experimental evidence - mainly from post-test examinations - with the results of the model.
3. Conclusions Though the main modelling work for the gaseous fission products has been accomplished to date, some additional efforts may become necessary for high burnup pins. There is evidence from the more recent CABRI-2 series of experiments, that the fuel structure at high values of burnup (10 at% and more) can be quite different from that at lower values. This is possibly due to the accumulation of fission product composites in the fuel to sheath gap and a different growth
of the FD experiments with solid fuel ejection, using different grain boundary diffusion coefficients of the LAKU results Event
With diffusion coefficient 5xD:
FD2.8 FD4.3
Partial grain boundary cracking at General grain boundary cracking at Partial grain boundary cracking at General grain boundary cracking at
5.450 s 5.504 s
Lx+
W/S
6.288 s
6.277 s
5.442 s 5.459 s
5.439 s 5.454 s
L. Viith / Modelling fusion gas behaviour in
behaviour of the fuel grains. The CABRI-2 follow-on program will probably serve to broaden the experimental experience in this respect. This may entail additions to the modelling, e.g. a more refined model for cesium and possibly other fission products. The modelling of the burnup dependence of diffusion coefficients, grain growth and possibly other aspects of material behaviour may also become necessary.
References [l] L. Vath, KfK 3753, Kernforschungszentrum Karlsruhe, Germany, 1984.
Karlsruhe,
mixed oxidefuel
311
[2] L. Vlth and E.A. Fischer, Nucl. Technol. 71 (1985) 246. [3] L. VIth, Proc. 1990 Int. Fast Reactor Safety Meeting, Snowbird, Utah, August 12-16, 1990, vol. IV (American Nuclear Society, 1990) p. 375. [4] E.E. Gruber, Nucl. Technol. 35 (1977) 617. [5] J. Rest and SM. Gehl, Nucl. Eng. Des. 56 (1980) 233. [6] D.H. Worledge, SANDBO-0328, Sandia National Laboratories (1980). [7] S.A. Wright, E.A. Fisher, P.K. Mast and G. Schumacher, Nucl. Technol. 71 (1985) 326. [8] G.L. Reynolds and B. Burton, J. Nucl. Mater. 82 (1979) 22. [9] G. Heusener et al., Proc. 1990 Int. Fast Reactor Safety Meeting, Snowbird, Utah, August 12-16, 1990, vol. II (American Nuclear Society, 1990) p. 197.