FUEL PERFORMANCE CODES

1
Fuel performance
8 Fission-gas (fg)release

• the fuel stack is divided into J x K isothermal
  cylindrical annuli (sections) of length ?z and
  radial thickness ?r
• Dvj,k volume of section j,k 2?r?r?z

moles fg produced in time t in section j,k
?(zj) axial power-shape function Efiss
3.2x10-11 J/fiss

• mj,k cumulative moles of fg released from
  sect. j,k

2
Fission-gas release (UO2)

• Production in grain at a rate
  atoms fg/cm3-s
• 2a. fg diffuses towards grain boundary diff.
  coef. D
• 2b. Some fg trapped in intragranular bubbles
• 3a. fg atoms arrive at grain boundary (gb)
• 3b. fg trapped in intergranular bubbles N
  atoms fg /cm2 gb
• 4. Bubble interlinkage on gb leads to release
  to rod interior

3
Intragranular diffusion
C fg concentration in matrix of fuel,
atoms/cm3 D fission-gas diffusivity in fuel,
cm2/s a radius of equivalent spherical grain
5 ?m BC at ? 0 ?C/?? 0
BC at ? a C(a,t) 0 (if re-solution
neglected)
(each gb is fed by two grains)
4
Re-solution from intergranular bubbles

• ff or O,U recoil collision with fg in bubble
• If 300 eV transferred to fg atom it is
  re-solved
• re-solution depth ?10 nm
• re-solution parameter probability/s of an atom
  being re-solved b 10-5

5
New BC at grain surface (? a) fg
balances on re-solution layer
at re-solution plane
N fg atoms/cm2
6
New grain-surface BC (very difficult to solve )
and
simplification The flux J is obtained by
applying a correction factor to the flux without
re-solution, ? J Correction factor to J (1
C(a,t)/?t)
Results in ODE
where
7
Intergranular bubbles

• fg on the grain boundaries is mainly trapped in
  lenticular bubbles
• These grow but keep the same shape

• p 2?/Rb pressure in bubble

• B bubbles/unit area, the nucleation density

nbfb/Ab fg atoms/unit gb area

• N nbB

3.8x1015 fb
8
At what value of fb do the bubbles interlink?

• If fb,sat (interlinkage) is known, Nsat
  3.8x1015 fb,sat
• The irradiation time for interlinkage/release
  given by equation for N(t) on slide 6

Monte Carlo analysis
F fraction of bubbles in largest cluster
9

• Results of Monte-Carlo calculation using the
  second method
• Note the sharp increase in F at fb ? 0.45
• This is taken as the coverage at which
  inter-linkage and fg release occurs
• Using the eqn at the bottom of slide 7, the fg
  concentration is

Fraction of all bubbles in the largest cluster F
Fraction of gb surface covered by bubbles fb
Nrelease 3.8x1015x0.45 1.7x1015 fg atoms/cm2
10
Release times
trel(i) time of release at step i
11
Example of fg release calculation
- ? 10 nm 10-6 cm b 10-5 s-1? ?b 10-11
cm/s
- D 8x10-17 cm2/s (1000oC) 8x10-16 cm2/s
(1200oC)
-
- A 5x1013 atoms/cm2 (1000oC) 5x1015 (1200oC)
- S 2.5x10-3 s-1/2 (1000oC) 8.0x10-4 s-1/2
(1200oC)
following release, the voids (formerly bubbles)
collapse and the fg collection process repeats
12
fg released upon interlinkage of bubbles
Dvj,k volume of section j,k 2?r?r?z
a grain radius 5x10-4 cm

• grains in ?vj,k ?vj,k /(4/3)?a3
• area of gbs in ?vj,k ½ x 4?a2?vj,k /(4/3)?a3
  3?vj,k/2a
• B bubbles per unit gb area
• fg bubbles in ?vj,k B x gb area 3B?vj,k/2a
• mj,k moles fg released when bubbles in sect.
  j,k interlink
• mj,k fg bubbles in ?vj,k x moles fg in bubble
  (sl. 7)
• mj,k (3B?vj,k/2a)

13
Cumulative fg release

• For all sections i,k
• count release events
• multiply by fg release from each
• add to give cumulative release

Continue example T0 1300oC TS 400oC
Both sections Dz 10 cm R 5 mm
Sect. A 1150 1250oC rin 1.2 mm rout 2.0
mm Sect. B 950 1050oC rin 2.7 mm rout
3.1 mm
14
Release computation(see plot on slide 6)
fg released, moles x 105
15
Cumulative fg release, cont
Moles fg released (20 mos.) Sect. A
21.6x10-5 Sect. B 2.9x10-5 Total 24.5x10-5
sect. B
sect. A