2014 January 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…).

2014 January 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:

.,)( etcP

reactivityoftcoefficienPPower

CreactivityoftcoefficienCdensityCoolant

MreactivityoftcoefficienMdensityModerator

TreactivityoftcoefficienTetemperaturFuel

dd

dd

ff

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)

2014 January 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. 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].

2014 January 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.

2014 January 10

[from Nuclear Reactor Analysis, by James J. Duderstadt and Louis J. Hamilton, John Wiley & Sons, 1976]

Doppler Broadening of Resonance with Fuel Temperature

2014 January 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.

./01.0.0 0CmkbemightvaluetypicalAT f

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 ~-0.005 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:

0,.,.

dCLWRinei

2014 January 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.

2014 January 18

D2O Primary Coolant

Gas Annulus

Fuel Elements

Pressure Tube

Calandria Tube Moderator

CANDU BASIC-LATTICE CELL WITH 37-ELEMENT FUEL

Face View of a Bundlein a Fuel Channel

2014 January 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

2014 January 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

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).

Reducing Coolant-Void Reactivity

2014 January 24

Lattice-Cell Comparison

CANDU-6

Cells

ACR Cells

2014 January 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)

2014 January 26

Moderator-Poison Reactivity Coefficient

Since a moderator poison simply absorbs neutrons, we can see immediately that

GdppmmktcoefficienreactivityGadolinium

BppmmktcoefficienreactivityBoron

CANDUinfactIn

Pc

/28

/8

:

0

2014 January 27

END