Reactivity Coefficients

Question 1

Explain reactivity coefficients and reactivity defects and distinguish between them.

Answer 1

The change in reactivity (ρ) due to the per unit change in the associated parameter (x) is called the reactivity coefficient (α) for that parameter (x).

The term “reactivity defect” (ρx) is used to describe the total amount of reactivity added, positive or negative, due to changing a parameter by a given amount.

Question 2

Explain the effect of moderator density on each factor in the six-factor formula.

Answer 2

With a decrease in water density:

1) resonance escape probability (p) decreases.
2) thermal utilization factor (f) increases slightly
3) decreases the thermal nonleakage factor - L_th
4) decreases the fast nonleakage factor - L_f
5) The fast fission factor (ε) increases slightly due to increased slowing down length, but the effect is very small.
6) The reproduction factor (η) is not dependent on moderator density, so the reproduction factor does not change significantly

Question 3

Explain the moderator temperature coefficient (MTC) of reactivity.

Answer 3

(MTC) predicts changes in reactivity resulting from changes in moderator temperature.

MTC is defined as the change in reactivity per unit change in the temperature (°F) of the moderator.

Question 4

Describe the effect on the moderator temperature coefficient (MTC) of reactivity from changes in moderator temperature

Answer 4

The magnitude of the MTC is larger (more negative) at higher temperatures.

The moderator temperature coefficient for a 4 degree rise at a high temperature (499 to 500°F) causes a density reduction of .3 lbm/ft³ At a low temperature (99 to 100°F) a 4 degree rise causes a .04 lbm/ft³ drop in density.

Question 5

Describe the effect on the moderator temperature coefficient -α_m (MTC) of reactivity from changes in boron concentration.

Answer 5

The higher the boron concentration, the less negative (or more positive) MTC.

Conversely, as the boron concentration approaches zero, α_m tends to be more negative.

At BOL the MTC can be slightly positive, whereas at EOL, MTC will be at its most negative value.

Question 6

Describe the effect on the MTC (α_m ) of reactivity from changes in core age.

Answer 6

MTC becomes more negative as the core ages due to the significant drop in boron concentration over core life.

Boron acts as a neutron absorber, the presence of boron results in a reduction of the thermal utilization factor (f). As the boron concentration is increased, the change in (f) with respect to temperature change f/T becomes more positive, causing MTC to become less negative.

Boron concentration is a function of fuel burnup; as the reactor continues to operate, boron is withdrawn from the coolant, so MTC becomes more negative.

Question 7

Describe the effect on MTC of reactivity from control rod position.

Answer 7

As rods are inserted, MTC becomes more negative because the less dense water allows more neutrons to reach the rod to be absorbed.

Question 8

Explain the fuel temperature coefficient of reactivity.

Answer 8

The Doppler coefficient is the amount of reactivity added into the core while the fuel temperature increases by one degree.

It is sometimes referred to as the Fuel Temperature Coefficient (FTC).

It is ALWAYS negative. As fuel temperature increases, negative reactivity is always inserted.

Question 9

Explain resonance absorption.

Answer 9

It is the abnormally strong absorption by atomic nuclei of neutrons having certain definite energies.

As fuel temperature increases, the kinetic energy of fuel atoms increase. This results in neutrons of even higher and lower kinetic energy having an increased probability of resonance absorption.

Question 10

Explain Doppler broadening and self-shielding.

Answer 10

Doppler broadening is a shift in the resonant capture cross section peaks resulting from the heating of the nuclear fuel.

Self-shielding is where the fuel atoms in the outer portion of the pellet tend to shield the inner fuel atoms from the neutrons at resonant energy.

Question 11

Describe the effects on the fuel temperature (Doppler) coefficient from changes in core age.

Answer 11

The Doppler coefficient becomes more negative as the core ages.

As a result of Pu-240 production over core life, the Doppler temperature coefficient will become more negative because Pu-240 has a very high capture cross section (about 1 × 10⁵ barns) for 1 eV kinetic energy incident neutrons. Therefore, as Pu-240 builds up, the value for α_D becomes more negative later in core life

Question 12

Describe the effects on the fuel temperature (Doppler) coefficient from changes in fuel temperature.

Answer 12

As temperature rises, the resonance peaks broaden, allowing the fuel to resonantly capture neutrons over a larger range of energy levels.

At low fuel temperatures the resonance absorption peaks are very narrow, and only a small fraction of the neutrons passing through the resonance energy spectrum are absorbed.

A small increase in the fuel temperature causes a significant fractional increase in the number of neutrons resonantly absorbed in the fuel (U-238, Pu-240). Also, because of their small increase in energy, a slightly lower number of thermal neutrons are absorbed in the fuel (U-235).

The magnitude of the Doppler coefficient is larger at low fuel temperatures.

Question 13

Describe the effects on the fuel temperature (Doppler) coefficient from changes in moderator temperature.

Answer 13

If the moderator density is high (low temperature), the slowing down length and the slowing down time of a neutron are very short.

Changes in resonant peaks will cause a relatively small effect compared to the effects observed at a lower moderator density (high temperature).

When the moderator is hot or contains voids, the slowing down length and the slowing down time for neutrons are longer. Any change in the resonance peaks will be more significant since the neutrons spend relatively longer periods of time in the resonance region.

This means the Doppler coefficient is more negative at high moderator temperatures and is most negative at high void fractions.

Question 14

What are the components of the power coefficient?

Answer 14

The coefficients are associated with fuel temperature, moderator temperature, and voids,

α_{<span>Power </span>}= (Delta ρ_fuel + Delta ρ_moderator + Delta ρ_voids)/Delta % Power

Question 15

Explain and describe the effect of power defect and Doppler defect on reactivity?

Answer 15

The term “reactivity defect” (ρ_x) is used to describe the total amount of reactivity added, positive or negative, due to changing a parameter by a given amount.

For the PWR core, as fuel temperature and power increase, negative reactivity will always be inserted.

This results in a negative effect on power and keff. In fact, because the effect of resonance absorption is occurring at the source of fission (the fuel), Doppler will be the quickest negative reactivity insertion to help turn a power upswing or power excursion.

This negative reactivity insertion as a function of power is referred to as the Doppler defect,

Question 16

Describe the effects of boration/dilution on reactivity

Answer 16

The effect of the chemical shim is to increase the macroscopic absorption of the moderator throughout the core. As a result, the thermal utilization (f) of the fuel is decreased, reducing reactivity in the core.

As the reactor operates and fuel is burned up, reactivity in the core decreases. By removing some of the chemical shim (dilution), which decreases boron concentration in the core, reactivity is increased to compensate for the loss of fuel due to burnup.

Changing the concentration of soluble poison dissolved in the coolant is a slow process. The maximum rate of change of reactivity for this system is approximately 3 pcm/second.

Question 17

Compare boron reactivity worth versus boron concentration

Answer 17

Note that the highest differential boron worth occurs for low boron concentrations. This is because boron atoms are not competing with as many other boron atoms.

Question 18

Compare boron reactivity worth versus moderator temperature.

Answer 18

At higher temperatures the reactor core contains a smaller mass of water due to expansion of the water at constant pressure within the reactor core.

The reactor core pressure is automatically maintained. The smaller mass of water results in a smaller mass of boron in the core at the given value of ppm.

This causes a lower boron density in the core, resulting in a lower differential worth.

Question 19

Explain the change in reactivity addition rate due to boration/dilution over core life.

Answer 19

The concentration of boron dissolved in the coolant will be much lower at EOL compared to BOL.

Every gallon of borated water removed from the core through dilution will carry with it much less boron at EOL than at BOL.

Over core life, boron concentration is reduced by approximately a factor of 10.

Question 20

Draw the under/over moderated core moderator to fuel ratio chart for thermal utilization factor (f) and density.

Answer 20