Reactivity Coefficients

Question 1

What is the difference between Reactivity Coefficients and Reactivity Defects?

Answer 1

Coefficients are rate of change of reactivity per unit of parameter change.
Defects are total amount of reactivity change for a given total change in a parameter.
mph vs total miles traveled.

Question 2

What is Moderator Temperature Coefficient (MTC)?

Answer 2

Amount of reactivity added (pcm or delta k/k) per degree change of the moderator.
Typical value of -10 pcm, or 0.0001 delta k/k

Function of mod/fuel ratio, density of moderator and boron concentration.

Question 3

Describe Undermoderated.

Answer 3

Typically at higher Moderator temps and lower boron concentration.
MTC is negative.
Rise in T(mod) causes:
1. Density of water lowers. Neutrons travel farther and are more likely to be captured by resonance kidnappers. Therefore Resonance kidnapping escape probability goes down. (Larger effect)
2. Boron is pushed out of the core leaving less in the core for absorption, therefore more neutrons absorbed by fuel. Thermal utilization factor rises. (Smaller effect)

Question 4

Describe Overmoderated.

Answer 4

Typically at lower moderator temperatures and higher boron concentration.
Same logic applies for Resonance escape and Thermal Utilization, however, in this condition Thermal Utilization factor has a larger effect on reactivity.
This causes MTC to be positive in this condition.

Question 5

How is MTC affected by changes in the Moderator temperature?

Answer 5

Density.
At lower T(mod), a given temp change changes density a lot less than the same temp change at higher T(mod).
Therefore at higher T(mod), the magnitude of MTC change is greater for a given change in temp vs lower T(mod).

Question 6

How does Boron Concentration affect MTC?

Answer 6

At higher boron concentration, more boron in the moderator is available to absorb neutrons. This causes less neutrons to be absorbed by the fuel. Thermal Utilization factor lowers as a result.
With boron concentration increasing, Thermal Utilization factor rises more and more by reduction in Mod Density, therefore as boron concentration rises-> MTC becomes less negative (shifts toward positive).

Question 7

Another way to look at boron affect on MTC

Answer 7

High boron concentration:
Given rise in T(mod) pushes more boron atoms out of core and thermal utilization rises greater than resonance escape lowers. Positive reactivity addition. (Positive MTC)

Low boron concentration:
Given rise in T(mod) pushes less boron atoms out of the core and thermal utilization rises less than resonance escape lowers. Negative reactivity addition. (Negative MTC)

Question 8

How does control rod position affect MTC?

Answer 8

With control rods partially inserted, a given rise in T(mod) will allow more neutrons to be absorbed by the rods (due to lower moderator density), therefore MTC is more negative with rods inserted.
Fully withdrawing rods has the opposite effect.

Question 9

How does Core Age affect MTC?

Answer 9

At BOL, higher boron concentration.
At EOL, lower boron concentration.
Resonance escape probability is bigger factor with lower boron concentration and thermal utilization factor rise lowers more and more as boron concentration lowers, therefore MTC gets more negative over core life.

Question 10

What is the Void Coefficient?

Answer 10

Takes into account steam voids in MTC. Essentially the same principle as density changes of the MTC.
As more voids form, less neutrons reach thermal energies and negative reactivity is added.
Void coefficient is negative.

Effect of this coefficient is negligible.
Typical value is large @ -100 pcm/%change in void, however, in PWRs, the voids are negligible.

Question 11

What is the Pressure Coefficient?

Answer 11

Same concept as MTC.
Higher pressure causes more dense moderator. If MTC is negative, then a pressure rise is a positive coefficient.

This coefficient is negligible.

Question 12

What is Fuel Temperature Coefficient?
Also called Doppler Reactivity Coefficient.

Answer 12

Change in reactivity per degree change in fuel temperature. Always negative.

Responds quicker to increase in power than MTC.

Typical value of -1 pcm/degree change in fuel temp.

Question 13

What is Doppler Broadening?

Answer 13

At low fuel temps, resonance peaks are high and skinny. As fuel temp rises, the peaks lower and widen while the area under the peaks remains the same. This causes more epithermal neutrons to be absorbed by isotopes at resonance energies.
Higher temp causes resonance escape to lower. Negative reactivity.

Question 14

What is Doppler Defect?

Answer 14

Total amount of negative reactivity added as power rises (fuel temp rises).

Question 15

What is Self Shielding?

Answer 15

At low fuel temps, higher resonance escape probability due to higher, skinnier resonance peaks
Therefore shielding against resonance absorption. (Higher self shielding).

At higher temps the reverse is true.

Question 16

How does moderator temperature affect FTC?

Answer 16

If moderator density is high, neutrons slow down faster and resonance escape rises. Because of this the change I Doppler effect will be less significant to changes in resonance escape probability. The opposite is true for low moderator density.
Therefore at higher T(mod)-> FTC is more negative.

Question 17

Fuel Temperature Effects on FTC.

Answer 17

At lower fuel temp, resonance peaks are tall and skinny, therefore a given change in fuel temp cause greater broadening of the peaks. More negative FTC.
At higher fuel temps, the peaks are already broadened and don’t broaden as quickly, therefore worth the same given change in temp, less negative reactivity is added. FTC is less negative

Question 18

How does Core Age Effect FTC?

Answer 18

Pu240 is produced over core life which has a higher microscopic cross section for absorption at resonance peaks than U235/238. Therefore as the core ages, FTC becomes more negative.

Question 19

What is the Power Coefficient?

Answer 19

Combined effects of MTC, FTC and Void coefficient.
Should always be negative even if MTC is slightly positive.
If not, BOOM!

Question 20

What are Differential and Integrated Boron Worth?

Answer 20

Differential: reactivity added per ppm boron change

Integrated: total reactivity added from total ppm boron change.

Question 21

How does Boron Worth change with boron concentration?

Answer 21

At lower boron concentrations, for the same change in ppm, a higher percentage of ppm will change, therefore more reactivity will be added per ppm change at lower boron concentrations.

Question 22

How is Boron Worth affected by changes in moderator temperature?

Answer 22

At higher temp, moderator is less dense causing less boron to be in the core for a given ppm. Therefore a given change in ppm will have less effect on reactivity as it would at colder temps because less boron atoms will be in the core.
Boron worth lowers as T(mod) rises.