Fuel Burn Up

8/13/2019 Fuel Burn Up

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2008 January 1

4: Neutron-Induced Fission

B. Rouben

McMaster University

Course EP 4P03/6P032008 Jan-Apr


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2008 January 2

Neutron Reactions with Matter

Scattering: the neutron

bounces off, with or withoutthe same energy (elastic orinelastic scattering)

Activation: the neutron iscaptured, & the resultingnuclide is radioactive, e.g.

16O(n,p)16N

10B(n,)7Li Radiative Capture: the

neutron is captured and agamma ray is emitted from stainless steel

40Ar(n,)41Ar Fission(follows absorption)

electronneutron

proton

Incident neutron, E1

Scattered neutron, E2

a EA

E1 = E + E2

Inelastic Scattering:

electronneutron

protonElastic Scattering:

Incident neutron, E1

Scattered neutron, E2

E1 = EA + E2

electronneutron

proton

Neutron Absorption:

Incident thermal neutron, E

Gamma Photon, E

Gamma Photon, EE ~ 7 MeV


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2008 January 3

A neutron splits a

uranium nucleus,releasing energy (quickly

turned to heat) and more

neutrons, which can

repeat the process.

The energy appears

mostly in the kinetic

energy of the fission

products and in the beta

and gamma radiation.

(neutron-induced)


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2008 January 4

Outcome of Neutron-Induced Fission Reaction

Energy is released (a small part of the nuclear mass is

turned into energy).

One neutron enters the reaction, 2 or 3 (on the average)

emerge, and can induce more fissions.

The process has the potential of being a chain reaction;this can be self-perpetuating (critical) under certain

conditions.

By judicious design, research and power reactors can be

designed for criticality; controllability is also important. The energy release is open to control by controlling the

number of fissions.

This is the operating principle of fission reactors.


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2008 January 5

Fission Process

The fission process occurs when the nucleuswhich absorbs the neutron is excited into anelongated (barbell) shape, with roughly halfthe nucleons in each part.

This excitation works against the strong forcebetween the nucleons, which tends to bring thenucleus back to a spherical shape there is afission barrier

If the energy of excitation is larger than thefission barrier, the two parts of the barbell havethe potential to completely separate: binary

fission!


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2008 January 6

Fissionable and Fissile Nuclides

Only a few nuclides can fission. A nuclide which can be induced to fission by an

incoming neutron ofanyenergy is calledfissile. There

is only one naturally occurring fissile nuclide: 235U.

Other fissile nuclides: 233U, isotopes 239Pu and 241Pu of

plutonium; none of these is present in nature to any

appreciable extent.

Fissionablenuclides: can be induced to fission, but onlyby neutrons of energy higher than a certain threshold.

e.g. 238U and 240Pu.


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2008 January 7

Fissile Nuclides: Odd-A

Notice, from the previous slide, that fissile nuclides generally havean odd value of A. This is not a coincidence.

The binding energy is greater when there are pairs of nucleons. When a neutron is absorbed in an odd-A (fissile) nucleus, its drop

in energy is relatively large (= to the binding energy of the last

nucleons in the even-A nucleus). The energy released by this drop of the neutrons energy (even if

the neutron brought no kinetic energy) is now available to changethe configuration of the nucleus the nucleus can deform bystretching and can surmount the fission barrier.

If the neutron is absorbed in an even-A (fissionable) nucleus, itsbinding energy in the odd-A nucleus is smaller, and is not sufficientfor the nucleus to surmount the fission barrier. To induce fission,the neutron needs to bring in some minimum (threshold) kinetic

energy.


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2008 January 8

Energy from Fission

Energy released per fission ~ 200 MeV [~ 3.2*10-11

J]. This is hundreds of thousands, or millions, of times

greater than energy produced by combustion, but stillonly ~0.09% of mass energy of uranium nucleus!

The energy released appears mostly (85%) as kineticenergy of the fission fragments, and in small part (15%)as the kinetic energy of the neutrons and other particles.

The energy is quickly reduced to heat (random kinetic

energy) as the fission fragments are stopped by thesurrounding atoms.

The heat is used to make steam by boiling water,

The steams turns a turbine and generates electricity.


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2008 January 10

Power from Fission

Total power (energy per unit time) generated in anuclear reactor depends on the number of fissions persecond.

Quantities of interest: Fission power (total power generated in fission) Thermal power (the power (heat) removed by the

coolant) Electric power (the power changed to electrical

form) In the CANDU 6:

Fission power = 2156 MWf Thermal Power = 2061 MWth Gross Electric Power 680-730 MWe


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2008 January 11

Exercises

Given that one fission releases 200 MeV, howmany fissions occur per second in a CANDU 6 atfull power?

How many fissions occur in 1 year at full power?

Compare this to the number of uranium nuclei inthe reactor.


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Neutron Flux

Imagine all neutrons in unit volume at a given instant. Let the neutron population density be n neutrons/cm3.

Sum all the distances (path lengths) which would be

traversed by these neutrons per unit time. This is defined

as the total neutron flux, denoted f. In the (hypothetical) case in which all neutrons are

travelling at the same speed v, the flux is the product of

the density nof the neutron population and the speed v:

f(v) = nv [For a distribution of neutron speeds, integrate over v]

fhas units of (neutrons.cm-3*cm.s-1) = (neutrons.cm-2.s-1)


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Calculating Reaction Rates

Recall that the macroscopic cross section is theprobability of reaction per distance travelled. Putting together the concepts of neutron flux

and cross section, one can calculate reaction rates.

The reaction rate for a given reaction type (e.g.,fission) for neutrons of speed v is the product ofthe path length of neutrons of speed v[i.e., the fluxf(v)]by the macroscopic cross section:

Rate of reactions of type i (per unit volume)for neutrons of speed v= Si(v)f(v)

If there is a distribution of neutron speeds,

reaction rate must be integrated over speed v.


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Concept of Irradiation

The irradiation w(or exposure, or fluence) of the reactorfuel or other material is a measure of the time spent by the

material in a given neutron flux f. Mathematically, it is

defined as the product of flux by time:

w= f.t fhas units of neutrons.cm-2.s-1

Therefore the units of irradiation w are neutrons/cm2.

In these units, whas very small values. It is more

convenient therefore to use the nuclear unit of area, thebarn (b) = 10-24cm2, or even the kb = 1,000 b.

wthen hasunits ofneutrons per kilobarn [n/kb].


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Concept of Fuel Burnup

Fuel burnup is defined as the (cumulative) quantity of

fission energy produced per mass of uranium during its

residence time in the reactor.

Fuel burnup starts at 0 for fuel which has just entered the

reactor, and builds up as the fuel produces energy. The exit (or discharge) burnup is the burnup of the fuel as

it exits the reactor.

The two most commonly used units for fuel burnup are

Megawatt-hours per kilogram of uranium, i.e.,MW.h/kg(U), and Megawatt-days per Megagram (or

Tonne) of uranium, i.e., MW.d/Mg(U). 1 MW.h/kg(U) = 1,000/24 MW.d/Mg(U) = 41.67 MW.d/Mg(U)


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Fuel Burnup

The exit fuel burnup is an important economic quantity: itis essentially the inverse of fuel consumption [units, e.g.,Mg(U)/GW(e).a].

For a given fissile content (fuel enrichment), a highburnup signifies low fuel consumption, and therefore a

small refuelling-cost component. Note, however: the true measure of a reactors efficiency

is not fuel burnup, but uranium utilization, the amount ofuranium from the ground needed to produce a certain

amount of energy. Typical fuel burnup attained in CANDU 6 = 7,500

MW.d/Mg(U), or 175-180 MW.h/kg(U). However, this can vary, because burnup depends on

operational parameters, mostly the moderator purity.


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Fuel Requirements

Energy in fission immense:1 kg (U) in CANDU = ~180 MW.h(th)

= 60 MW.h(e).

Typical 4-person households electricity use

= 1,000 kW.h/month = 12 MW.h/year

Then a mere 200 g (< 0.5 lb) (U) [6 to 8 pellets]

serves 1 household for an entire year. [Cf: If from

fossil, ~ 30,000 times as large, ~ 6,000 kg coal.]Cost of nuclear electricity insensitive to

fluctuations in price of U.


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Reactor Multiplication Constant

Several processes compete for neutrons in a nuclearreactor:

productive absorptions, which end in fission

non-productive absorptions (in fuel or in

structural material), which do not end in fission leakage out of the reactor

Self-sustainability of chain reaction depends on

relative rates of production and loss of neutrons.

Measured by the effective reactor multiplicationconstant:

)( leakagesabsorptionlossneutronofRate

productionneutronofRatekeff


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Reactor Multiplication Constant

Three possibilities for keff: keff < 1: Fewer neutrons being produced than lost.

Chain reaction not self-sustaining, reactor

eventually shuts down. Reactor is subcritical.

keff= 1: Neutrons produced at same rate as lost.Chain reaction exactly self-sustaining, reactor

in steady state. Reactor is critical.

keff> 1: More neutrons being produced than lost.

Chain reaction more than self-sustaining,reactor power increases. Reactor is supercritical.


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Critical Mass

Because leakage of neutrons out of reactorincreases as size of reactor decreases, reactormust have a minimum size for criticality.

Below minimum size (critical mass), leakage is

too high and keffcannot possibly be equal to 1. Critical mass depends on:

shape of the reactor composition of the fuel other materials in the reactor.

Shape with lowest relative leakage, i.e. for whichcritical mass is least, is shape with smallestsurface-to-volume ratio: a sphere.


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Reactivity

Reactivity (r)is a quantity closely related toreactor multiplication constant. It is defined as

r= 1-1/ keff

= (Neutron production-loss)/Production

=Netrelative neutron production

Central value is 0:r< 0 : reactor subcritical

r= 0 : reactor criticalr> 0 : reactor supercritical


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Units of Reactivity

Reactivity measured in milli-k (mk).

1 mk = one part in one thousand

= 0.001

r= 1 mk meansneutron production > loss by 1 part in 1000

1 mk may seem small, but one must consider the timescale on which the chain reaction operates.


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Control of Chain Reaction

To operate reactor: Most of the time we want keff= 1 to keep power

steady.

To reduce power, or shut the reactor down, we

need ways to make keff< 1:

done by inserting neutron absorbers, e.g. water,

cadmium, boron, gadolinium.

To increase power, we need to make keffslightly>1 for a short time:

usually done by removing a bit of absorption.


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Control of Chain Reaction

In a reactor, we dont want to make keffmuch greater than1, or > 1 for long time, or power could increase to high

values, potentially with undesirable consequences, e.g.

melting of the fuel.

Even when we want to keep keff= 1, we need reactivitydevices to counteract perturbations to the chain reaction.

The movement of reactivity devices allows absorption to

be added or removed in order to manipulate keff.

Every nuclear reactor contains regulating and shutdownsystems to do the job of keeping keffsteady or increasing

or decreasing it, as desired.


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2008 January 27

Products of Fission

The fission products (fission fragments) are nuclides ofroughly half the mass of uranium.

They are not always the same in every fission. There are

a great number of different fission products, each

produced in a certain percentage of the fissions (theirfission yield).

Most fission-product nuclides are neutron rich; they

disintegrate typically by - or - decay, and are therefore

radioactive, with various half-lives.


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2008 January 28

Decay Heat

Many fission products are still decaying long after the originating

fission reaction.

Energy (heat) from this nuclear decay is actually produced in the

reactor for many hours, days, even months after the chain reaction

is stopped. This decay heat is not negligible.

When the reactor is in steady operation, decay heat representsabout 7% of the total heat generated.

Even after reactor shutdown, decay heat must be dissipated

safely, otherwise the fuel and reactor core can seriously overheat.

Next Figure shows the variation of decay heat with time. Also, the used fuel which is removed from the reactor must be

safely stored, to cool it and to contain its radioactivity.


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2008 January 29

Decay Power vs. Time

RatioofS

hutdowntoOperatingP

ower(P/Po)

1.0 10 102 103 104 105

Time After Shutdown (s)

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.03

0.02

0.01

Decay HeatORIGENincludes actinides, and

fission products from U-238, U-235,Pu-239, Pu-241

Scale on left Scale on right


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2008 January 30

Formation of Transuranics (Actinides)

Transuranics areproduced in the reactor by absorption ofneutrons by 238U: plutonium, americium, curium, etc.

e.g., production of 239Pu:

238U +n 239U 239Np + 239Pu + 2

238U is said to befertilebecause it yields fissile239Pu

239Pu can participate in fissions; it can also continue to

absorb neutrons to yield 240Pu and 241Pu (latter is fissile)

Half the energy eventually produced in CANDU is from

plutonium created in situ!

Actinides tend to have long half-lives, e.g. for 239Pu

24,000 y.


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CANDU

6

Reactor

(700-

MWe

Class)


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2008 January 32

Calandria, Showing Fuel Channels


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Long-Term Reactivity Control

For long-term maintenance of reactivity: Refuellingis required because reactivity eventually

decreases as fuel is irradiated: fission productsaccumulate and total fissile content decreases.

In CANDU 6, average refuelling rate ~ 2 channelsper Full-Power Day (FPD), using the 8-bundle-shiftrefuelling scheme (8 new bundles pushed in channel,8 irradiated bundles pushed out).

4-bundle-shift and 10-bundle-shift refuelling schemeshave also been used in other CANDUs.

Selection of channels is the job of the stationphysicist.

F lli hi t b th d f th t


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2008 January 34

Fuelling machines at both ends of the reactor

remove spent fuel, insert new fuel.


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Reactor Regulating System

The reactivity devices used for controlpurposes by the Reactor Regulating System

(RRS) in the standard CANDU-6 design

are the following: 14 liquid-zone-control compartments (H2O

filled)

21 adjuster rods 4 mechanical control absorbers

moderator poison.

S i l S f t S t


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Special Safety Systems

There are in addition two spatially, logically, and

functionally separate special shutdown systems (SDS):

SDS-1, consisting of 28 cadmium shutoff rodswhich

fall into the core from above

SDS-2, consisting of high-pressure poison injectionintothe moderator through 6 horizontally oriented nozzles.

Each shutdown system can insert > 50 mk of negative

reactivityin approximately 1 s.

Next Figure summarizes the reactivity worths and

reactivity-insertion rates of the various CANDU-6

reactivity devices.


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REACTIVITY WORTHS OF CANDU REACTIVITY DEVICES

Function Device Total ReactivityWorth (mk)

MaximumReactivity

Rate (mk/s)

Control 14 ZoneControllers

7 0.14

Control 21 Adjusters 15 0.10

Control 4 MechanicalControl Absorbers

10 0.075(driving)- 3.5 (dropping)

Control Moderator Poison -0.01(extracting)

Safety 28 Shutoff Units -80 -50

Safety 6 Poison-Injection Nozzles

>-300 -50


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CANDU Reactivity Devices

All reactivity devices are located or introduced into guidetubes permanently positioned in the low-pressure

moderator environment.

These guide tubes are located interstitially between rows

of calandria tubes (see next Figure). Maximum positive reactivity insertion rate achievable by

driving all control devices together is about 0.35 mk/s,

well within the design capability of the shutdown

systems.


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Liquid Zone Controllers

For fine control of reactivity:14 zone-control compartments, containing variableamounts of light water (H2O used as absorber!)

The water fills are manipulated:

all in same direction, to keep reactor critical for steady operation, or

to provide small positive or negative reactivity toincrease or decrease power in a controlled manner

differentially, to shape3-d power distribution towardsdesired reference shape


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Liquid Zone-Control Units


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Liquid Zone-Control Compartments

h i l l b b


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Mechanical Control Absorbers

For fast power reduction:

4 mechanical absorbers (MCA), tubes of cadmium

sandwiched in stainless steelphysically same as

shutoff rods.

The MCAs are normally parked fully outside the coreunder steady-state reactor operation.

They are moved into the core only for rapid reduction of

reactor power, at a rate or over a range that cannot be

accomplished by filling the liquid zone-control systemat the maximum possible rate.

Can be driven in pairs, or all four dropped in by gravity

following release of an electromagnetic clutch.

X = Mechanical Control Absorbers


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Adj d


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Adjuster Rods

When refuelling unavailable (fuelling machine down)

for long period, or for xenon override: 21 adjuster rods, made of stainless steel or cobalt (to

produce 60Co for medical applications). Adjusters are normally in-core, and are driven out

(vertically) when extra positive reactivity is required. The reactivity worth of the complete system is about

15 mk. Maximum rate of change of reactivity for 1 bank of

adjusters is < 0.1 mk per second. The adjusters also help toflatten the power distribution,

so that more total power can be produced withoutexceeding channel and bundle power limits.


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CANDU Special Shutdown Systems


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2008 January 48

CANDU Special Shutdown Systems

Two independent,

fully capable

shutdown systems:

SDS-1 (rods enter

core from top)

SDS-2 (injection of

neutron poisonfrom side.


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SDS 2


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SDS-2

SDS-2: high-pressure injection of solution of

gadoliniuminto the moderator in the calandria. Gadolinium solution normally held at high pressure in

vessels outside of the calandria. Concentration is~8000 g of gadolinium per Mg of heavy water.

Injection accomplished by opening high-speed valveswhich are normally closed.

When the valves open, the poison is injected into themoderator through 6 horizontally oriented nozzles that

span the core (see next Figure). Nozzles inject poison in four different directions in the

form of a large number of individual jets. Poison disperses rapidly throughout large fraction of

core.


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2008 January 52Positions of Liquid-Poison-Injection Nozzles


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