Void Coefficient

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Course 22106

Module 12Reactivity Effects Due to TemperatureChanges and Coolant Voiding

12.1 MODULE OVERVIEW 212.2 MODULE OBJECTIVES 312.3 TEMPERATURE COEFFICIENT OF REACTIVITY 412.4 PHYSICAL BASIS FOR TEMPERATURE COEFFICIENTS 6

12.4.1 Doppler Broadening In The Fuel............................................................712.4.2 Changes In Neutron Energy Spectrum 1012.4.3 Density Changes 15

12.5 TEMPERATURE COEFFICIENTS FOR FUEL, MODERATORAND COOLANT 1612.5.1 General Expression For Temperature Coefficient 1612.5.2 The Fuel Temperature CoeffICientOf Reactivity ; 1712.5.3 The Moderator CoefficientOf Reactivity .., 1712.5.4 The Coolant CoeffICient Of Reactivity 19

12.6 PRACTICAL ASPECTS OF REACTIVITY VARIATION WITHTEMPERATURE ....................................................................2112.7 EFFECTS DUE TO VOID FORMATION 25~ ~ ~ / C ; ; I \ f ~ J : : J \ f ] r ~

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Course 22106Noles & References- 12.1 MODULE OVERVIEW

Temperature coefficient of readi'lily

Void IomIaIICIn

When the reactor operates at power, any change in power levelwill generally alter the temperatures of the fuel, moderator andcoolant. A change in the temperature of any of these componentswill cause a change in reactivity which will, in turn, affect thereactor's operating conditions. The magnitude of thisjeedback isspecified by quoting the value of the temperature coefficient ojreactivity (in J.l.kf'C) for each of the three reactor components.We begin by reviewing the principal physical mechanisms whichgive rise to the temperature coefficients. These are (a)Dopplerbroadening of the U-238 resonances; (b) changes in the energydistribution of thermal neutrons as the temperature increases(spectrum luzrdening); (c) density changes of the coolant andmoderator with temperature. The overall temperature coefficientof a given reactor component (for instance, fuel) can be regardedas the sum of the individual temperature coefficients of each termin the six-factor formula for the multiplication factor. Wedescribe how the sign of each relevant coefficient can beexplained in terms of the physical mechanisms discussed earlier.This is done for both fuel and moderator coefficients as well asfor fresh and equilibrium fuel.Finally, we look at some of the operational implications oftemperature coefficients, including the changes of reactivity thatoccur on startup and shutdown, and the importance of theDoppler effect in providing negative feedback to limit theconsequences of positive power transients.The effects of voidjormtJJion are also an important sourceoffeedback in power transients. We consider the reasons for thepositive reactivity effectof voiding channels in reactors usingheavy water as coolant, and associated practical implicationssuch as the need to maintain a high coolant isotopic.

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12.2 MODULE OBJECTIVESAfter studying this module, you should be able to:i) Define the temperature coefficient of reactivity.ii) Explain, in general, the desirability of a negativetemperature coefficient of reactivity.iii) Describe theDoppler effect in the fuel.iv) Explain what is meant by spectrum hardening, and how

this might be expected to affect the value of 11 in bothfresh and equilibrium fuel.v) Discuss the effect on reactivity of changes in moderator

or coolant density.vi) Explain why the fuel temperature coefficient is negative,and why its value changes significantly from fresh to

equilibrium fuel.vii) Explain why, in practice, the moderator temperaturecoefficient is positive for both fresh and equilibrium

fuel.viii) Given temperature coefficients for all three components

of the reactor, calculate the expected change in reactivityfrom one operational state to another (given thetemperature of each component for each state).ix ) Explain why the fuel temperature coefficient is more

important than the others in limiting power transients.x) Derme thepower coefficient and give a typical range ofvalues for a CANDU.

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Course 22106Noles & References

llildule 12 PIJI1II3


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Caul'lle 22106Notes & References- xi) Explain why coolont voiding leads to a positivereactivity in CANDU reactors, and why excessivepositive or negative void coefficients are undesirable in

reactor operation.

12.3 TEMPERATURE COEFFICIENT OFREACTIVITY

In the module on reactor kinetics (Module 8), we ignored anyvariations in reactivity due to changes in power. As we saw inModule II, there are marked changes in reactivity due to xenon,which occur over a period ofminutes to hours after an overallpower change. Changes in reactor power also cause changes inthe temperature of the fuel, moderator, and coolant. These toohave an effect on reactivity-an effect which acts on a muchshorter time scale than the xenon. We begin by.discussiIig anexperiment which demonstrates the importance of these feedbackreactivity effects.In 1949, the NRX reactor atAEeL, Chalk River, was allowed to"run away". NRX was a heavy water moderated reactor whichused control rods for reactor regulation. The heavy water levelwas set somewhat above the height at which the reactor would becritical at low power with the rods withdrawn. Reactor powerwas allowed to increase unchecked, and the manner in which itincreased is rather unexpected (see Figure 12.1).The power initially increased exponentially with a period of33 seconds (' t= 33 s, & =+1.6 mk). As the temperature of thefuel rods increased, however, the reactivity decreased and thiscaused the rate of power increase to slow. Later, the reactivitydecreased at a faster rate as the heavy water became warmer.The total decrease in reactivity was enough to make the reactorsubcritical, and the end result was that the power reached amaximum value and then started to decrease.

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Thus the reactor was self-regulating, since temperature changesinduced by a power increase reduced reactivity and so preventedpower from increasing indefinitely. Of course, in thisexperiment, the initial excess reactivity was quite small; if morereactivity had been inserted at the start, it is quite possible thatthe power would have continued to rise.The temperature coefficient of reactivity is defined as the changein reactivity per unit increase in temperature. Its units are mkf'Cor ~ o ( l J.1k =1O-3mk). The coefficient may be positive ornegative. In the example just described, it was negative becausean increase in temperature led to a loss of reactivity.Mathematically the temperature coefficient is written

ldk- -t l l '..__._-_._--------_._-

Course22106Notes & References

Selfregulating reactor

Temperature ooefficienl

10

oFigure 12.1 :

200


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Course22106Noles & References

Temperature changes occur in the fuel, coolant and moderatormore or less independently, and there will therefore be atemperature coefficient of reactivity associated with each. It isvery desirable for the overall temperature coefficientof a reactorto be negative to provide the self-regulating feature illustrated byNRX. It is particularly advantageous if the fuel coefficient isnegative because in a transient the fuel will heat up more rapidlythan other components of the core.

12.4 PHYSICAL BASIS FORTEMPERATURE COEFFICIENTSIn a later section, we look at the individual temperaturecoefficients of the fuel, moderator and coolant, and we describethe effects of temperature on the terms in the six-factor formula.Before we do this, it is useful to consider the physical basis forsome of the more significant contributions to the temperaturecoefficients. In the following sections, we look 'Ilt threeparticularly important effects.We can see how each of these effects influences the factors inequation (3.7) for the reaction rate (R) in the reactor for a givennuclide

where (J refers to either the fission or the absorption crosssection, as appropriate.

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The three effects considered include:1. Doppler broadening in the fuel, which increases the

absorption of neutrons in the resonance region of theU-238 microscopic cross-section;2. Changes in the energy spectrum of the thermal neutronflux, which affect the microscopic cross-sections for thevarious scattering, absorption and fission processes;3. Density changes which directly affect N, the numberdensity of the nuclides present in the reactor.

12.4.1 Doppler Broadening In The FuelThe Doppler effect arises directly from a temperature change inthe fuel. A rise in fuel temperature increases the resonancecapture in U-238 for the following reason. We know that theabsorption cross-section ofU-238 in the resonance regionconsists of a set of fairly sharp peaks of the sort shown inFigure 12.2, where the probability of a neutron being absorbeddepends critically on the exact value of its kinetic energy or, whatamounts to the same thing, the speed at which the neutron ismoving. Actually, it's more complicated than that because theimportant factor in determining the probability of absorption isthe speed of the neutron reltltive to the U-238 nucleus. Sinceheating the fuel will make the atoms ofU-238 vibrate morevigorously, it isn't surprising that it has an effect on the relativespeeds of the neutrons and the U-238 nuclei, consequentlychanging the shape of the peak.

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Course 22106Notes & References

Doppler eUect

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-Cou,..e22106Notes & ReferenceslU.r_---------.....,I :7.0I E

I . . . . . . U L7 U U 7.0

NMlInEnIlgy leV)Figure 12.2: Doppler broadening ofU-238 resonance------------_._-_.._--_ .._----_._-._.__ ._._----_._-

o-Q E"cE.Note: HereE, represenlS !he kinetic energy of !he neulrOlI and E,. !heenergy at lhepeaIc of !he 1eSOIIIIIICC. AU three lICUll'Ons appear 10 lhe nucleus as having !he

IeSOIIIIIICC energy.Figure 12.3: Mechanism ofDoppler broadening

------_._-

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To illustrate, consider a nucleus at rest, as shown at the left ofFigure 12.3. A neutron that happens to have a speedcorresponding to the peak of the resonance will have a highprobability of being absorbed, while one that is travelling slightlyslower or faster will have a much reduced probability. Now thinkabout what happens when the fuel is heated and the U-238 nucleiare vibrating back and forth. A neutron whose speed is such thatit previously lay well outside the peakmay encounter a U-238nucleus that is moving at that instant in such a way that the speedof the neutron re14tille to the nucleus coincides with the peak.The centre diagram in Figure 12.3 shows a neutron whose speedis above where the peak would be located if the U-238 nucleuswere at rest, but which encounters a nucleus moving in the samedirection at a speed that makes the neutron's speed of approachthe same as it was in the fIrst diagram. To the nucleus, thisneutron would appear to be within the peak of the resonance.The same thing could happen to a neutron whose speed is suchthat it would be below the peak when the nucleus was at rest, butwhich happens to encounter a "hot" uranium nucleus movingtowards it at exactly the right speed (right-hand diagram).The net result of heating the fuel is therefore that the resonancecan be considered as being "broadened" as shown in Figure 12.2.Although the height of the peak has been reduced (becauseneutrons that were originally moving at exactly the correct speedfor the peak are no longer moving at the correct speed), theU-238 cross-section is in any case so high that any neutron withinthe overall peak region is virtually certain to be absorbed in thefuel (the mean free path in fuel of a neutron at the energy of thepeak is about 0.025 mm). The net effect of heating is to broadenthe range of energies over which the neutrons have a highprobability of being absorbed. When the fuel is heated, therefore,there will be a reduction in the resonance escape probability (p)and consequently in the reactivity.

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(;Qurse22106Notes & References

Resonance broadening


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C o u , . . ~ 1 0 6

Notes & References- 12.4.2 Changes In Neutron Energy SpectrumAn alteration to the temperature and/or density of any componentof the reactor affects the energy distribution of the neutrons (theenergy spectrum). This, in turn, changes the fission andabsorption rates in other components, owing to the fact that theseare sensitive to the neutron energy.

Thennal neutrons We know that neutrons in the reactor start off at a high energy(up to severalMeV) and then bounce around in the moderatoruntil they reach relatively low speeds where they are in thermalequilibrium with their surroundings. At this point, they are aslikely to gain energy in a collision with a nucleus as they are tolose energy.Thermal neutrons are characterized by a distribution of energies,described by a rather complicatedmathematical expressionknown as the thermal energy spectrum (Figure 12.4.). At roomtemperature, the most probable value for a thermal neutronenergy is 0.0253 eV. Since the kinetic energies of the atoms ofany material depend on its temperature, changes in thetemperature of the moderator, coolant or fuel will affect theneutron spectrum, and thus the average thermal neutron energy.Figure 12.4 shows the shift in the spectrum for a change inmoderator temperature from 20C to 300C. The averageneutron energy is proportional to the absolute temperature of themoderator, so it is approximately doubled by going from 293 Kto 573 K. This move towards higher neutron energies is oftenreferred to as an increase in the neutron temperature.

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IIS1

Course 22106Noles & References

0.005 0.01 0.02 0.05 0.1 0.2NIInn EneIgy (IV)

Figure 12.4: Neutron energy shift with changing moderatortemperature--_._...._-----_._-------

The change in the thermal neutron spectrumwith temperaturewill alter the balance between the fission and absorption rates inthe core, because the fission and absorption cross-sections areboth functions of the neutron energy. The parameter chieflyaffected is the reproduction factor (Tl) as discussed below.

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-Course 22106Notes & References

2.072.06 j-------__ ~ 1 1 ~ 5 ! . . : - : V ~ 5 ] ~2.05 IJv

20 60 100 140 180 220 260 300

Figure 12.5: Deviation of absorption("C) -section of U-235from Uv, and variation of 11" with moderator temperature.(Upper curve normalized so that ratio =1 at 20C)

1.&8

1.010

1.32

1.21

1.16

1.08

1.00 w::::-- '_-- ' -_.. . .L._........_. l . - - - ' ' - - - - - ' _20 60 100 u,o 180 220 260 3002.06

2.02

1.98

l.'.

N........ leJIlpenIuro ( 'C)

1. '0 L--J'--L_...l.._..L._-'- L-.::>.I._20 60 100 140 180 220 260 300

- . . . . . . . . . . . . . . ("C)Figure 12.6: Deviation of absorption cross-section of Pu-239from Uv, and variation of 11., with moderator temperature(Upper curve normalired so that ratio = 1 at 20"C)

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As mentioned in Section 3.8, many of the materials in the reactorhave absorption cross-sections which vary inversely with theneutron speed, that is, Ga"" Ilv. I fal lmaterials exhibited thesame Vv dependence on neutron speed (or energy), the relativereaction rates would be unaffected by a change in neutrontemperature. However, both U-235 and Pu-239 have absorptioncross-sections which depart significantly from Vv behavior. Oneway to illustrate this is to plot the ratio of the absorption crosssection of each isotope to the absorption cross-section of U-238,which is approximately Vv, as a function of neutron temperature.The departure of the absorption cross-sections ofU-235 andPu-239 from Vv is illustrated by the upper curve in Figures 12.5and 12.6 respectively. It can be seen that the absorption rate ofU-235, relative, for example, to the U-238 which forms themajority of the fuel, will drop as the neutron temperatureincreases. For Pu-239, on the other hand, an increase in neutrontemperature will cause a marked increase in the absorption rate ofPu-239 relative to the Vv absorbers. This increase is due to themovement of neutrons at the higher end of the thermal spectruminto the large resonance at 0.3 eV in Pu-239(see Figure 12.7).Unfortunately, the situation is more complicated than this,because the fission and absorption cross-sections of each fissileisotope vary in II different way with neutron energy.Consequently, knowing how absorption in the fissile isotopeschanges with temperature does not, by itself, explain how 1'\behaves. The most convenient way to illustrate this is to look atthe values of 1'\ for each material, considered as an individualisotope; for instance, the 1'\-value for U-235, 1'\s, is defined asTIs = Vs x (Grs/G.s), by analogy with the definition of TI in thesix-factor formula (equation 5.4) which applies to the fuel as awhole. The variation of the TI-values ofU-235 and Pu-239 isshown in the lower curves in Figures 12.5 and 12.6. Over therange shown, each isotope demonstrates a decrease in TI withincreasing neutron temperature, the decrease of Pu-239 beingmuch steeper.

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CouI'Se22106Notes & References

Variation of T1 with neutron energy


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CtJurse22106Noles & References

We can now look at what we would expect to happen to theoverall TI-value of the fuel, which is equal to the number offission neutrons produced per thermal neutron absorbed in thefuel (where "fuel" includes U-238, fission products, etc.). For afreshly-fuelled reactor, the situation is fairly straightforward. Asthe neutron temperature increases, the neutron absorption rate inU-235 will decrease relative to the Vv components of the fuel,such as U-238. In addition, the decrease of TIs with neutrontemperature means that the absorptions which do take place inU-235 will be less effective in causing fissions. Consequently, itis clear that the contribution ofU-235 to the temperaturecoefficient of T) will be negative, so that in a freshly-fuelled coredT)/dT will also be negative.In an equilibrium core, U-235 will still, of course, make anegative contribution to the temperature coefficient of T). For thePu-239 which is now also present, the pronounced increase of theabsorption cross-section with temperature will lead to a markedincrease in absorptions in Pu-239 relative to the othercomponents of the fuel. On the other hand, the decrease of 1'\9will make these absorptions less effective in causing fissions. Itturns out, in practice, that the former effect predominates, so thatthe contribution of Pu-239 to the overall temperature coefficientof 1'\ is positive. The magnitude of this positive contribution issuch that, for equilibrium fuel, it predominates over the negativeU-235 contribution. so that the overall dT)/dT for equilibrium fuelis positive.

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10000 , . . . - - - r - - r - - - r - - , - - - r - - r - . . ,

10 1 - - - + - - - + - - - + - - = = - - \ - - l 4 t - - + - - - : : : ~ f - - - ;

I 1000J 1001 - - - + - - + - - - \ - 1 - -A

0.001 0.01 0.1 1 10 100 1000 10000NIIARIn Energy (tY)Figure 12.7: Fission and total (G t = G. + G,) cross-sections ofPu-239

12.4.3 Density ChangesAs the temperature of the moderator or coolant increases, itsdensity will decrease. Since the numberof atoms per unitvolume decreases, neutrons will travel further between collisionsand therefore have an increased chance of leaking out of thereactor. Both the fast and thermal non-leakage probabilities willconsequently decrease, tending to lower the reactivity. On theother hand, the reduction in atomic density will lower theItUlCFO'COPU: absorption cross-sectionof the moderator orcoolant, which will increase the thermal utilization (f), thustending to increase reactivity. For the moderator, the effect of thereduction in atomic density will be particularly strong i f i tcontains an appreciable quantity of poison. It will therefore bemost pronounced for a fresh core, where a significant quantity of.poison is required to compensate for the high inherent reactivity.

DtnsiIy effects

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12.5 TEMPERATURE COEFFICIENTSFOR FUEL, MODERATOR ANDCOOLANT12.5.1 General Expression For TemperatureCoefficientAs stated in Section 12.3, the temperature coefficient is defmedin general as the change in reactivity per unit (0C) change intemperature, that is,

dlclk I dIc--=--dT k dT

where the multiplication factor is given by the formula(Section 5.4)

It can be shownmathematically that(12.1)

I dIc I de I dp I dfJ I df I dA f I dA t- - = - -+- -+- -+- -+ - -+ - --k dT e fIT p dT fJ dT f tlI' A , fIT At dTwhich means that we can obtain the overall temperaturecoefficient by adding the contributions of the six factors in theformula.

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12.5.2 The Fuel Temperature Coefficient OfReactivityThe fuel temperature coefficient arises principally from twofactors: one is the Doppler effect and the other the effect due tothe fact that the neutron spectrum is slightly hardened by theincrease in fuel temperature. For fresh fuel, the contributionsfrom changes in p and 1'\ are both negative, the predominant onebeing the reduction in p due to the Doppler broadening. Forequilibrium fuel, the strong negative Doppler contribution ispartly compensated by the fact that the coefficientof 71 ispositive, owing to the presence ofPu-239. as discussed inSection 12.4.2. Calculations of the fuel temperature coefficientin a typical CANDU yield the following values:Fresh fuel: Fuel temperature coefficient = -15 Jlkf'CEquilibrium fuel: Fuel temperature coefficient = - 4Jlkf'C

12.5.3 The Moderator Coefficient OfReactivity

The main effects produced by heating the moderator are (a) adecrease in moderator density, and (b) an increase in the averageneutron energy. The temperature of the moderator affects theneutron temperature much more than the temperature of the fuelor the coolant does. since the moderator is principally responsiblefor thermaljzjng the neutrons in the first place.

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Fuel temperature coefficient

Moderator coefflclent

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Figure 12.8: Change in reactivity with moderator temperature

For both fresh and equilibrium fuel, calculations show that pdecreases with an increase of moderator temperature (whichdecreases moderator density and so increases the distance aneutron travels while it is slowing down). Fastand thermalleakage both increase for the same reason. The thermalutilization makes a positive contribution because of the decreasein moderator absorption at the lower moderator density. Theimportant difference between the fresh and equilibrium fuel casesis that the coefficient of 11 is strongly negative for fresh fuel andstrongly positive for equilibrium fuel as indicated inSection 12.4.2. The result is that, while the calCulations predict astrong negative moderator temperature coefficient for fresh fuel,the coefficient for equilibrium fueHs positive. This may be seenby comparing the upper and the lowest curves in Figure 12.8 (thecoefficient is given by the 110pe of the line in each case). Itshould be noted, however, that the calculations for the freshlyfuelled coredo not include the effect due to the boron which inpractice must be added to the moderator to hold down thereactivity of the fresh core.

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The reduction in the density of thepoisoned mode{ator producesa large increase in thermal utilization (f ) when the moderator isheated. This increased contribution is sufficient to change thesign of the overall moderator coefficient from negative topositive. This effect is shown by the third curve in Figure 12.8.The approximate values of the moderator coefficient (over therange 40C to 70C) are:

CoUrH22106

Notes & References

Fresh fuel: (no boron in moderator)Fresh fuel: (poisoned moderator)Equilibrium fuel:

===

While the rust case has no practical significance for the operatingreactor, it is interesting in that it shows the significance of thechange in sign of the coefficient of 11 in going from fresh toequilibrium fuel.

12.5.4 The Coolant Coefficient Of ReactiVityThe reactivity effect associated with a change in coolanttemperature is more complicated in its make-up than the othertwo coefficients we've been considering, so thatwe won'tdiscuss this in detail. The calculated effect of changing thecoolant temperature in a CANDU 600 is shown in Figure 12.9.The coefficient for the equilibrium fuel case is positivethroughout the whole temperature range but, for reasons that aretoo complex to explain here, the coolant coefficient with freshfuel starts off negative bu t changes to positive at a coolanttemperature of about 250"C. (The coefficient, again, is given bythe slope of the curve at any point).

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Coolant coefficient

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COurse 22106

-Noles & References321 All.CooIInIo t - - - - : r - - : ~ - . . : : ~ . . . . ; , ; T .....~ ( " C ) = = : : ; : : ~ ~[ .1 SI 100 lSI 200 300 I, ,

I 47..

Figure 12.9: Change in reactivity with instantaneous change incoolant temperature (calculated for CANDU 600)----------_.._---_._._--_..__ ..

~ -

1 ' I ~ o

1111 1111 . .CCI*t' 0 nRrq

Figure 12.10: Comparison of measured and calculated reactivitychanges due to fuel and coolant temperature changes inPickering A (fresh fuel)

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It is difficult to detennine the coolant coefficient frommeasurements on the r e a c t o r ~ because you can't change thecoolant temperature without simultaneously changing the fueltemperature. It is possible to get an overall check on thecalculation methods by measuring reactivity as the coolant andfuel are heated simultaneously. Figure 12.10 demonstrates acomparison of theory and measurement for Pickering A. Theheat transport system was heated by running the primary pumpswhile the reactor was held critical at low power. Since theheating took place slowly, one can assume that the fueltemperature kept in step with the coolant. The results weretherefore a combination of the fuel and coolant coefficients. Itcan be seen that there is good agreement between the calculatedand measured reactivity changes.

12.6 PRACTICAL ASPECTS OFREACTIVITY VARIATION WITHTEMPERATUREWe have already mentioned that it is desirable for thetemperature coefficients to be negative so that a self-regulatingfeature is provided. We must, however, consider more than justthe values of the three temperature coefficients. Two veryimportant factors are (a) the magnitude of the temperaturechanges that take place in each component for a given powerchange, and (b) the time taken for each component to heat up.

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Course 22106Notes &References

lIodule 12 P8gfItl1


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-Course 22106Notes & ReferencesTABLE 12.1

Typical temperatures of reactor components (GC)Component Cold ShutdownFuel 25Coolant 25Moderator 25

Hot Shutdown29026570

Full Power69029070

The typical temperatures of the reactor components for three"standard" conditions are provided in Table 12.1. Variations inoverall reactivity as a CANDU 600 is taken from cold shutdownto full power are illustrated in Figure 12.11 for the fresh fuel andequilibrium fuel cases. With equilibrium fuel, the net reactivitychange in going from cold shutdown to full power is less than2 mk. For fresh fuel, however, there is a loss of about 8.5mk inmoving from cold to hot shutdown and a further loss of 6.5 mk ingoing from hot shutdown to full power. Since the reactor willregain this reactivity when it is shut down again, allowance mustbe made for this when estimating the amount of negativereactivity that must be inserted to keep the system safelysubcritical even after complete cooling has taken place. Caremust also be taken in going from cold shutdown to hot shutdownwith an equilibrium core because of the reactivity gain of about3 mk that occurs during the change.

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Fresh Fuel

900

805m!

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Void Coefficient