Contact Author:
Professor Donald Olander
fuelpr@nuc.berkeley.edu
P:(510) 642-7055
F:(510) 643-9685
Dept. of Nuclear Engineering
University of California
Berkeley, CA 94720
U. S.
Early fission gas behavior: trapping Vs release
V. Cordoliani (AREVA), D. Olander (Univ. of California)
Early Fission-gas behavior in oxide fuel: escape Vs trapping
V. Cordoliani and D. Olander
Dept. of Nuclear Engineering
University of California, Berkeley CA 94707
Fission-gas release affects LWR fuel performance for two reasons. First, escape to the plenum increases the pressure on the cladding, which can be burnup-limiting, or if incorrectly estimated, can cause cladding rupture. Second, mixing xenon fission gas with helium fill gas decreases the thermal conductivity of the fuel-cladding gap, and thus overheats the fuel.
Fission-gas release from the polycrystalline UO2 fuel occurs via several mechanisms. Fission-gas atoms migrate by intragranular diffusion from inside the grains to the grain boundaries, whence they either diffuse to a free surface and escape or are trapped in intergranular bubbles. The principal release mechanism is interconnection of these bubbles and venting of the gas through the resulting tunnels.
However, many experimental studies have shown that release via intergranular diffusion is significant before bubble nucleation and growth consumes all fission gas arriving at the grain boundaries from the grain interior. Simple qualitative reasoning demonstrates why this is so. Diffusional release is proportional to the first power of the fission-gas concentration in the grain boundary, whereas nucleation of intergranular bubbles depends on the square of the concentration. Therefore, at low burnup, diffusional release predominates, but as the gas-atom population on the grain boundary grows due to the ever-increasing rate of supply from inside the grain, nucleation and growth eventually trap all arriving fission gas. The aim of this work was to determine the burnup at which this mechanism switch occurs.
To this end, a Monte-Carlo code has been developed to investigate the behavior of fission-gas atoms on the grain boundary in the early stages of irradiation. The objective of this code is to assess the relative importance of the escape and trapping processes as a function of irradiation time (or burnup)
The code models a portion of a grain boundary as a semi-infinite two-dimensional medium on which a collection of atoms move by random walk. The direction of net diffusion is bounded on the interior by a no-flux line. The outer boundary in either direction is a line where the fission-gas concentration is zero. Every gas atom reaching this line escapes (i.e., is released). Because of symmetry, only one half of this region needs to be considered. The lateral direction (parallel to the escape line) is supposed to be infinite in extent, so that diffusion is in one dimension only. To model this lateral geometry, no-flux boundaries perpendicular to the escape line are set a finite distance apart. In sum, the grid is bounded by a rectangle with three zero-gradient (reflexive, or no-flux) sides and on side on which the gas concentration is zero.
Two initial conditions were analyzed. In the “post-irradiation” case, an areal concentration of gas atoms on the rectangular grid was specified. For the “in-pile” case, the grid initially contained no gas atoms but a flux perpendicular to the rectangle varied as t1/2 (Booth flux).
The grid superimposed on the rectangle is square, each corner of which represents an equilibrium binding site of gas atoms on the grain boundary. The sites are separated by one UO2 lattice parameter (0.547 nm). This assumes that fission gas atoms migrate by a site-to-site hopping mechanism with the above jump distance. Two or more atoms occupying contiguous sites are trapped in an immobile bubble. An atom reaching the free surface escapes. Either of the two categories of gas atoms on the grain boundary (free or trapped) can be re-solved by fission fragments that intersect the grain boundary. The simulation ends after a pre-defined number of “jumps”, the process by which all atoms hop from one site to an adjacent site. The atoms can jump in any of four perpendicular directions, except for those atoms on sites adjacent to a no-flux boundary. These atoms may jump in one of three directions, the direction into the boundary being forbidden. A typical run consists of a sufficiently large number of jumps to reduce uncertainty in the results. The number of jumps is connected to the time by the jump frequency ?, which in turn depends on the intergranular diffusion coefficient via Einstein’s equation, Dgb = _ ?2 ?, where ? is the jump distance on the grain boundary. It is set equal to the above-mentioned lattice parameter of UO2.
The validity of the code has been tested on the pure-diffusion case (i.e., no trapping) ( ). The results of the simulation showed good agreement with the analytical solution. The width of the lateral reflexive boundary was increased until the simulation results were unaffected by this parameter.
In the in-pile simulations, the concentration of trapped atoms and the number of escaped atoms is recorded at different times (or burnups). The parameters are the temperature (which controls the diffusivities D and Dgb) and the fission rate. The latter and the intragranular diffusivity D determine the flux of gas atoms to the grain boundary via the Booth model.
The concentration of trapped atoms and the number of escaped atoms evolve as ?3 and ? 1.5, respectively, where ? is the burnup. These dependences are in accord with theory. The fractional release of fission gas from the grain boundary prior to the onset of trapping is very small (~ 0.1 %).
Simulations show two distinct stages: in the first (early) period, most of the atoms are free (single atoms) on the grain boundary; a fraction of them escape but fewer form bubble nuclei; in the second stage, trapping becomes preponderant. The criterion used to characterize this shift of dominant mechanism is the “critical burnup”, ?c. This is defined as the burnup at which the trapping-to-arrival-rate ratio of gas atoms on the grain boundary attains unity. At this point a steady state is reached, as all the atoms arriving onto the grain boundary end up being trapped.
The critical burnup increases as the fission rate increases. Temperature also plays a role, as it affects the intragranular diffusivity more than intergranular diffusion coefficient. Increasing temperature decreases the critical burnup; the intragranular diffusivity grows more rapidly with temperature than the intergranular diffusivity, which increases the gas-atom supply rate to the grain boundary more than the escape rate. Consequently, the gas-atom concentration on the grain boundary grows more rapidly at high temperature than at low temperature, thus favoring bubble nucleation.
Temperature influences the relative importance of re-solution. Below ~1200 K most of the free atoms on the grain-boundary are re-solved before they can escape or form a bubble.
The distance to the free surface (i.e., the length of the rectangular grid) does not influence the critical burnup; however, increasing this parameter decreases the fractional release of fission gas, as expected.
The code is then used to predict the distance traveled by atoms between their arrival on the grain boundary and becoming trapped by another gas atom. This distance is found to increase with the concentration of gas atoms on the grain boundary. The mean free path calculated for this process shows good agreement with values derived from diffusion theory.
The spatial distribution of gas atoms shows that once the critical burnup is reached, the atom concentration profile is essentially flat except for the region of the grain boundary the closest to the free surface. At high burnup, this outermost region provides a weak source of released fission gas.
The bubble-size distribution at different stages of irradiation shows increases with time of both of the number and the size of bubbles. Re-solution is found to influence the shape of this distribution, as it tends to reduce the size of the biggest bubbles.