1. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
Fuel Depletion
Time scale:
Days and months.
More depletion  change steady state flux by means of control rods.
For a given fuel isotope
For constant flux 0 the solution is
For time varying flux
Neutron fluence N 
Solve numerically.
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

2. Fuel Depletion Constant power.   Linear depletion!  
Power ~ flux only over short time periods during which Nf is constant.
The solution is obviously
 
Energy released per fission
Fission rate
Linear depletion!
 
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

3. Fuel Depletion
HW 31
Do the calculations for different flux and power levels.
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

4. Poisoning and Fuel Depletion
Infinite, critical homogeneous reactor. 
  
Constant power
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

5. Poisoning and Fuel Depletion
Constant
Constant
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

6. Poisoning and Fuel Depletion
Now we know all macroscopic cross sections. 
 
When there are no absorbers left to remove, we need to refuel.
Absorbers are not only control rods.
All fuel nuclei should be considered.
For each species, all sources and sinks should be taken into account.
Until = 0.
Solve for t to get upper limit for “core loading lifetime”
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

7. Poisoning and Fuel Depletion
Some poisons are intentionally introduced into the reactor.
Fixed burnable poisons.
B, Gd.
More uniform distribution than rods, more intentionally localized than shim.
Soluble poisons (chemical shim).
Boric acid (soluble boron, solbor) in coolant.
Boration and dilution.
Emergency shutdown (sodium polyborate or gadolinium nitrate).
Non-burnable poisons.
Chain of absorbers or self shielding.
Flatter flux.
Power shaping.
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

8. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
Delayed Precursors
For one-group
What about delayed neutrons?
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

9. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
Delayed Precursors
(s)
< 0.7%
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

10. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
Delayed Precursors
The multi-group equation now becomes
Different energy spectra
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).

11. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
Delayed Precursors
In steady state
Appearance of ggg depends on whether we have fine or course energy groups.
Nuclear Reactors, BAU, 1st Semester, (Saed Dababneh).