1. Reactivity Coefficients
B. Rouben
McMaster University
EP 4P03/6P03
2014 Jan.-Apr.
2014 January

2. Reactivity Changes
In studying kinetics, we have seen how insertions of reactivity drive flux and power changes.
Insertions of (positive or negative) reactivity may come from:
Refuelling operations (very slow change)
Saturating-fission-product (Xe, Sm, …) transients (fairly slow change)
Sudden accidents or perturbations, which change one or more lattice parameters (e.g., fuel, coolant, or moderator temperature, coolant density, poison concentration, etc…).
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3. Definition of Reactivity Coefficient
A reactivity coefficient is defined as the derivative of the system reactivity with respect to the change in a lattice parameter.
For instance, we can define:
2014 January

4. Significance of Reactivity Coefficients
It is important to know, for any given reactor design, the sign and magnitude of the various reactivity coefficients, as these coefficients suggest the consequences of sudden changes in the operating parameters:
A positive value for a reactivity coefficient means that a positive change in that parameter will increase reactivity and tend to increase power.
A negative value for a reactivity coefficient means that a positive change in that parameter will decrease reactivity and tend to decrease power
In both cases, a larger absolute value of the reactivity coefficient  greater sensitivity to changes in that parameter.
2014 January

5. Important Reactivity Coefficients
Although they are not the only ones, the following reactivity coefficients are particularly important:
Fuel-temperature reactivity coefficient, as fuel temperatures will change in any power manoeuvres
Coolant-density reactivity coefficient, as coolant density will change with the amount of boiling, and, in safety analysis, coolant voiding (as a result of a Loss-of-Coolant Accident) is extremely important to analyze
Power coefficient of reactivity, which combines effects from the above two coefficients (and perhaps others)
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6. Units for Reactivity Coefficients
Reactivity coefficients have the units of reactivity per unit of the parameter against which the reactivity is measured.
Since reactivity is a pure, unitless number, or can alternatively be given in, say, mk, examples of units for reactivity coefficients are:
mk/C degree (or degC-1) – for a temp coefficient
mk/(g/cm3) – for a density coefficient
mk/%FP – for the power coefficient
2014 January

7. The Fuel-Temperature Reactivity Coefficient
The fuel-temperature coefficient is governed by the effect of temperature on the neutron absorption by fuel
Neutron absorption in fuel is marked by the existence of resonances, in which neutron absorption is very high at certain, very specific neutron energies (speeds) – see sketch in the next slide.
If the neutron has a speed which exactly matches the resonance energy, then there is a high probability of absorption in a collision between the neutron at that speed and the nuclide.
2014 January

8. This sketch is a log-log plot
This sketch is a log-log plot. Probability of absorption at a resonance energy is orders of magnitude higher than at neighbouring energies. A “resonance” region exists in the intermediate energy range [~1 ev -100 keV].
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9. Effect of Fuel Temperature
Fuel temperature is the reflection of the random motion of fuel nuclides – the higher the fuel temperature, the higher this random “jiggling”.
Because of the jiggling, there is a range of relative speeds between the neutron and the fuel nuclides, even for a fixed neutron speed.
This means that, at higher fuel temperatures, neutrons with speed slightly “off” the resonance energy can still be absorbed in the resonance.
The effect is that the resonance is broadened at higher temperature – this is called Doppler broadening – see next slide.
Even though the resonance peak is at the same time lowered somewhat, the overall result is that there is more absorption in the resonance at higher fuel temperature.
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10. Doppler Broadening of Resonance with Fuel Temperature
[from Nuclear Reactor Analysis, by James J. Duderstadt and Louis J. Hamilton, John Wiley & Sons, 1976]
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11. Effect on Reactivity Coefficient
Because of the Doppler broadening of the absorption resonances in fuel, the fuel-temperature reactivity coefficient is negative:
Note: The fuel-temperature coefficient is a very prompt effect – because fuel-temperature changes most quickly in a change in power.
In an accident where the power increases, a negative fuel-temperature reactivity coefficient provides a prompt negative feedback, which tends to bring power back down.
2014 January

12. Effect of Pu-239
Although the fuel-temperature reactivity coefficient is negative, the presence of Pu-239 in fuel makes it less negative.
This comes about because resonances are not always capture resonances.
There are some fission resonances, in which increased absorption means more fissions – therefore a positive reactivity effect!
Pu-239 has an important low-lying fission resonance at ~0.3 eV neutron energy. This is very important because it is within the thermal energy range, where the neutron flux is high.
As Pu-239 builds up with increased burnup, the fuel-temperature reactivity coefficient becomes less negative!
The Pu-239 component is particularly important in CANDU reactors, where the fuel is not enriched. Thus the fuel-temperature reactivity coefficient in the equilibrium CANDU core may be ~ mk/oC.
2014 January

13. Pu-239: Low-Lying Fission Resonance at 0.293 eV
2014 January

14. Reactivity Insertion on Shutdown
With a negative fuel-temperature reactivity coefficient, the reduction in temperature when the reactor is shut down will result in a positive reactivity insertion.
In CANDU, this reactivity insertion may be in the range 5-10 mk, depending on the core burnup, and depending on whether it’s a “hot” or “cold” shutdown (i.e., to the coolant temperature of ~260 oC, or to room temperature, 20 oC).
A reactivity device must be available to counter this positive reactivity on shutdown, to ensure core remains subcritical: e.g., the Mechanical Control Absorbers (MCAs), or moderator poison.
2014 January

15. Coolant-Density Reactivity Coefficient
In LWRs, where the coolant and the moderator are not separated, a reduction in coolant density is equivalent to a reduction in moderator density, which is a negative reactivity effect.
Turning this around, an increase in coolant density is a positive reactivity effect in the LWRs:
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16. Coolant-Void Reactivity
In reactor physics, one often speaks of the coolant-void reactivity (CVR). This is not a coefficient, but rather it is the reactivity effect of losing all the coolant. It is important to know this effect in the reactor safety analysis.
While it is not a coefficient (i.e., a derivative), we can see that the void reactivity will generally have the opposite sign to the coolant density reactivity coefficient (since it corresponds to a reduction – not an increase - in coolant density).
Therefore, in LWRs, CVR < 0 (and large in absolute value).
However, in the standard CANDU, CVR >0.
This is because in the standard CANDU a loss of coolant is not equivalent to a loss of moderator. There are subtle reactivity effects explained in the next slides.
CVR > 0 does not make standard CANDU reactors unsafe! There are 2 fast-acting, fully-capable, independent emergency shutdown systems, each of which can mitigate the power excursion from a loss-of-coolant accident.
2014 January

17. Differential Effects on Voiding
In a pressure-vessel reactor, the coolant and moderator are not separated. Here coolant voiding is equivalent to loss of moderator,  large negative reactivity, reactor shuts down.
But CANDU is a pressure-tube reactor  the loss of coolant is not a loss of moderator.
In fact, in the standard CANDU, the coolant contributes little to moderation, and coolant loss gives a positive void reactivity.
We will consider how neutron events are changed when coolant is lost, and the effect on reactivity.
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18. CANDU BASIC-LATTICE CELL WITH 37-ELEMENT FUEL
Face View of a Bundle
in a Fuel Channel
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19. Standard-CANDU Coolant-Void Reactivity
Before Neutrons Leave a Channel
Before escaping from the channel where they are born, some fission neutrons are normally slowed by coolant into the resonance energy region and are absorbed.
Now imagine the coolant is lost. Without coolant, the following will happen:
Fewer fast neutrons will be slowed into the resonance region, therefore there will be more opportunities for fast neutrons to induce fission (more fast-fission production):  > 0, and
More fast neutrons will escape resonance capture and reach the moderator (less absorption): p > 0
Both phenomena increase reactivity
cont’d
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20. Standard-CANDU Coolant-Void Reactivity
After Neutrons Re-enter a Channel
Upon entering a channel from the moderator, some thermalized neutrons are scattered by hot coolant to higher energies and resonance capture.
Now imagine the coolant is lost. Without coolant, scattering to higher energies does not occur, and more neutrons escape resonance capture.
This gives rise to a positive reactivity change from U-238: pU-235 > 0, but
To a negative reactivity change from Pu-239 (on account of the resonance at 0.3 eV): pPu-239 < 0
cont’d
2014 January

21. Standard-CANDU Coolant-Void Reactivity
The overall result of the 3 positive components and the 1 negative component is that the net CVR of the standard CANDU is positive, but decreases as Pu-239 builds up with burnup:
CVR (initial core – all fuel fresh)  +20 mk
CVR (equilibrium core – mixture of burnups) +15 mk
Note that it is not physically possible to lose all the coolant instantaneously – therefore there cannot be an instantaneous insertion of +15 mk.
In addition, reactivity insertion in a large LOCA can be reduced by subdividing the coolant into more than one loop (and having bidirectional flow) - see next slide.
Therefore, the reactivity insertion in a large LOCA may be of the order of 4-5 mk in the first second after the break.
Each shutdown system can be actuated within 1 s, and can insert a large negative reactivity (e.g., -50 mk) in the first second after actuation.
2014 January

22. Non-Uniform Voiding Transient
Coolant voiding in a large LOCA is not uniform.
For instance, in the CANDU 6, the heat transport system is subdivided into two side-by-side loops, each servicing one half of the cylindrical reactor.
Side-by-Side Heat-Transport-System Loops in CANDU 6
2014 January

23. Reducing Coolant-Void Reactivity
Even though a positive CVR may not mean poor safety, there may be a negative perception of a positive CVR. Then how would one go about reducing the CVR to deal with this perception?
One way: Give coolant greater role in moderation. Increase ratio of coolant volume to moderator volume, e.g. by reducing lattice pitch, and/or increasing outer diameter of pressure tube. Would reduce reactivity even in cooled state  need fuel enrichment.
Another way: Make use of flux redistribution on coolant voiding (relative flux increase in centre of bundle). Inserting poison material in central pin will increase absorption on coolant loss  reduced void reactivity.
Poison in central pin used in Low-Void-Reactivity Fuel
All these options used for ACR-1000 (see comparison of basic cells in next Figure).
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24. Lattice-Cell Comparison
CANDU-6
Cells
ACR Cells
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25. Power Coefficient of Reactivity
An increase in power results in a prompt increase in fuel temperature, and may result in an increase in coolant boiling.
Thus, the power coefficient of reactivity will in general be a combination of an increase in fuel temperature ( < 0) and a reduction in coolant density ( < 0 in LWR, >0 in standard CANDU)
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26. Moderator-Poison Reactivity Coefficient
Since a moderator poison simply absorbs neutrons, we can see immediately that
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27. END
2014 January