Control Rod Worth: Power Dependency?

[chivasorn]

Hi

I have a question. Does the worth of control rod in a typical reactor is dependent upon power of reactor?
Thank you in advance

 

[theCandyman]

Worth is the change in reactivity divided by the change in rod movement, power isn't in the equation so I'm going to guess it doesn't have an effect.

 

[chivasorn]

thank thecandyman.

 

[Astronuc]

Hi

I have a question. Does the worth of control rod in a typical reactor is dependent upon power of reactor?
Thank you in advance

There is a difference between hot and cold shutdown margin, but that is based on a temperature dependence, which besides being power dependent depends on a number of variables including the type of fuel, type of moderation, type of reactivity control (solid and soluble burnable poison), and core loading.

 

[chivasorn]

Thanks Astronuc. Your response is very useful.

 

[QuantumPion]

Control rods have a differential rod worth, or worth per unit length inserted as a function of steps inserted. This is because the top and bottom of the core has less reactivity than the middle, so when the control rod is just starting to insert or withdraw, the first few steps have little worth compared to when the bank is half-way in. At 50% power, the control rod banks would be inserted a substantial amount (e.g. one bank half way in). So the differential worth (i.e. the worth of the next step) will be more than if the bank was completely out of the core at 100% power.

There is a dependence of integral rod worth (the total worth of a bank between fully inserted and withdrawn) and power as well. This is due to many competing effects. For example, at lower power, the fuel temperature will be lower, which will decrease resonance absorption (doppler coefficient). The moderator temperature profile will be different axially, which again has an effect on rod worth. If the core is a PWR with soluble boron, the control rods are basically competing for less neutrons with the boron or other poisons. All of these effects combine to change how the control rods effect the core reactivity.

Furthermore, there are effects due to the axial distribution of xenon. If you operate the core at 50% power with one rod bank inserted half-way for a period of hours, you will generate a xenon offset which will fluctuate up and down the core. This will cause the control rods to have a different worth depending on where the xenon is axially at any given time.

So to answer your question, yes.

 

[Astronuc]

The effect of temperature on reactivity arises from several factors:

1. moderator density (moderator temperature coefficient)
2. the relative absorption cross-sections of the control rod material vs fuel
3. strength of doppler absorption vs control rod

One has to look further into the control rod (PWR) or control blade (BWR) absorber material, which could be Ag-In-Cd, B₄C, Hf or Dy₂TiO₅. The last absorber material has been developed by the Russians.

One also has to look at which assemblies are rodded in PWR (fresh vs once-burned) and the enrichment/burnable absorber and burnup (depletion). BWRs are a bit more straightforward since most of the assemblies can be controlled during a cycle, unless a plant adopts a strict control cell strategy, as opposed to the conventional core (4-sequences) or hybrid control strategy.

Graphite moderated plants are different than LWRs, as are fast reactors, and MOX cores are different than straight UO₂ cores.