Reactor Physics: Design Parameters for GFRs

22.39 Elements of Reactor Design, Operations, and Safety

Fall 2006

Chris Handwerk Massachusetts Institute of Technology

Outline

• Background

• Design Philosophy

• Traditional breeder designs and traditional safety concerns

• Reactor physics design in relation to Gen IV goals

 Sustainability/Proliferation Resistance

 Economy

 Safety

 Self-controllability

Portions of this presentation are derived from the Fall 2005 version by Dr. Pavel Hejzlar

Why the renewed interest in GFRs?

• Extensive work done in 1970’s

• Carter administration ban on reprocessing

• Generation IV International Forum

 Safety

 Non-proliferation

 Economics

 Sustainability

 Resources

 Waste

6 Candidate Des igns

 GFR

 VHTR

 SCWR

 SFR

 LFR

 MSR

Reactor physics and Gen IV goals

Reactor Physi cs

Design Solution

The Engineering Pinwheel

Fast Reactor Fundamentals

• The neutrons are fast

• No moderator (most of the time)

• Coolant is non-moderating

 Liquid metal

 Gas

• Neutronic behavior governed mostly by Pu and TRU

 Much lower β than LWRs (0.0035 v. 0.0065)

• Shorter prompt neutron lifetime

• Tighter lattice than LWRs

• A LOCA will insert positive reactivity

• MTC not the chief reactivity coefficient of concern as in LWRs

Steady State Reactor Physics Parameters

Steady State T/H Parameters

The Relation between Rx Physics and T/H Design Constraints

Rx Physics Effects

Thermal Hydraulic Effects

Selection of a coolant

• Chemical compatibility

• Neutronic properties

• Thermal Properties

 Boiling/Melting Point

 Heat removal capability

 High thermal conductivity

 Large heat capacity

• Density

 Natural Circulation capability

 Required Pumping Power

• Availability/cost

• Other….

Coolant Case Study: S-CO 2

• Power Conversion System (PCS) work begat the neutronics work

 High efficiency Brayton cycle (45-50%) v. Rankine (33%)

 Allows for a direct cyc le

• Can provide better natural circulation capability than He

• Can do it all at lower temperatures (650 o C) than Helium (850 o C)

• Requires a higher pressure for Decay Heat Removal and cycle efficiency (20 MPa v. 8 MPa)

 What integrated engineering design challenges does this pose?

Traditional sodium FBR designs

• Large power rating (~3000MWt)

• Very high power density (~300kW/l)

 To reduce fuel cycle cost

 To minimize doubling time

• Short doubling time (~25 years)

• Oxide fuels - U O2-PuO2 driver

fuel, use of UO2 blankets

• Breeding ratio >1 (1.25)

• Pool type reactor

• Active safety

• Interm ediate loops

• Rankine cycle

• Difficult maintenance (opaque coolant)

• Complex and expensive

Diagram of reactor removed due to copyright restrictions.

Traditional reactor physics (safety) concerns for early liquid metal cooled FBRs

• Small effective delayed neutron fraction

 Small value of dollar unit for reactivity, hence concern that prompt critical state can be easier to reach

• Short prompt neutron lifetime

 Concern over extremely rapid power rise if reactivity increase exceeds prompt critical value

• Hy pothetical core disruptive accidents

 Core geometry not in most reactive configuration

 Loss of core geometry may hypothe tically lead to reactivity increase and large energy generation

 Although of extremely low probability, these scenarios receiv ed substantial attention

• Reactivity insertion > $1 from coolant voiding

 Local voiding is also a concern

• External blankets required for breeding

Gen IV Goals 1 & 2: Sustainability/Proliferation Resistance

• Traditionally – h igh utilization of resources (motivated

early development of fast reactors with high breeding ratio - b lankets)

• Emphases in Gen IV

 High resource utilization

 Waste minimization

 Proliferation resistance

new

• To reduce waste long-term radiotoxicity to that of natural U in <1000yrs – f ull recycling of TRU (including MA) with losses <0.1% needed

• Enhanced proliferation resistance favors elimination of depleted U blankets, avoidance of Pu separation and

maintenance of dirty plutonium isotopics throughout the cycle

Impact of recycling TRUs

Sustainability-driven design choices

GFR for both waste management and resource utilization

• Use accumul a ted TRU fr om spent LW R for 1 st FR core

• Design GFR with BR=1 , no blankets to avoid clean Pu

• Recycle TRU without Pu separ ation, Depleted U feed

• If enough GFRs deployed, LW R legac y TRU inventory eliminated

• After full transition to GFR, enrichment could be eliminated

Today

Nat - U

Enriched U

UO 2

U +TRU + F P

(1 st core)

U +TRU + F P

Conversion & Enrichment Plant

LWR Fuel Fabri c ation Plant

LWR

Reproc essing Plant

GFR

Storage of LWR spen t fuel

Depleted U

0.1% TRU loss

+ FPs

Storage of Depleted U

High -Level Waste S t orage

Consequences of sustainability-driven choices

• Small effective delayed neutron fraction

 TR Us have small 

 TR Us in LWR spent fuel 49%Pu239 , 23%Pu240,

7%Pu241, 6.6%Np237,

5%Pu242, 4.7%Am241,

2.7%Pu238

 Smaller marg in to

superprompt criticality, hence reactor control more challenging

 What can be done to increase

 eff?

 Not much

 Harden spectrum to fission more U238, but this worsens coolant vo id worth

 Increase leakage, but this hurts neutron economy

Graph removed due to copyright restrictions.

Consequences of sustainability-driven choices (Cont’)

• Increased positive coolant void worth

 Safety issue

 Typically much smaller in GFR than in LMRs

 Can be fast

 Smaller β makes coolant void worth larger in terms of reactivity in dollars

 More positive coolant void worth is due to TRU loading (primarily Pu239, Np237 and Am241)

 Why?

Neutron spectrum in GFR

CO2-cooled, Zr matrix UZr fuel Na cooled, TRU fuel

LBE-co oled , TRU fue l

0.04

0.03

0.02

0.01

0.00

10 -4 10 -3 10 -2 10 -1 10 0 10 1

Energy (MeV)

Positive coolant void worth in FRs

Three components of coolant void worth

1. Spectrum hardening

Pu239 capture and fission cross sections

Fission

Capture

•Neutron population shifts

•Spectrum hardening

•Fission/capture ratio increases

•Reactivity increas es

Major neutron

population

Positive coolant void worth in FRs

• This differs from U235, hence much lower void worth for U235 fueled core

U235 capture and fission cross sections

Fission Capture

Positive coolant void worth in FRs

Minor actinides (mainly Np237 and Am241) exacerbate the problem

Np237 capture and fission cross sections

Capture

Fission

Shift upon C oolant voiding

Major neutron population

• Am 241 same behavior

• What about U238? Also an issue but  f comes up after 1MeV and only to 0.5barn

Positive coolant void worth in FRs (cont)

2. Coolant absorption

 Less coolant  smaller parasitic absorption, hence reactivity increases (same for over-moderated LWRs)

 Small for GFR but can be significant for LMRs – coolants with higher absorption cross section worse

3. Neutron leakage

 Less coolant  increased neutron leakage, hence reduced reactivity

 Smaller or pancake cores have lower coolant void worth

 Coolants with larger scattering cross section have larger reactivity reduction from leakage

Ways to reduce CVW in GFRs

• A lthough CVW is small (in comparison to LMRs) , its reduction is difficult . Why?

• L eakage component is very small (neg ligible for some gases, such as He)

• P ossibilities :

1. Use core and reflector materi als th at exhibit an increase in absorpt i on cross section/reduction in refl ection upon spectrum hardening

2. Use gas that has high scattering ma croscopic cross secti on to increase benefit of leakage effect

3. Minimize coolant fraction in the core

4. Soften the spectrum

1. CVW solution: Titanium reflector

Scattering xs

Absorption xs

This would be nice core material

but nature does not provide such

Ti capture and scattering cross sections

2. CVW Solution: Leakage effect for He and SCO 2

Coolant void reactivity for (U-TRU)C pin fuel with Ti cladding and Ti reflector

0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1

1 .1

2. 00

1. 50

1. 00

0. 50

0. 00

-0 . 5 0

S - C O 2 @ 20 M P a

He @ 8 M P a

-1 . 0 0

-1 . 5 0

-2 . 0 0

-2 . 5 0

H ei g h t t o D i am e t er R a t i o

3. CVW solution:

Tube-In-Duct (TID) Fuel Assembly

• Hexagonal duct with coolant tubes

Duct W a l l

Cladding

• Compatible wit h vibrat ionally

(ODS MA956)

compacted (VIPAC) or specially formed “hexnut” pellet fuel

• Vented to reduce pressure- induced stresses in cladding and

duct wall (as in GCFR of 1970’s)

• Very high fuel volume fraction (~63%) with tolerable core pressure drop.

(Horizontal Cross Section)

Coolant Channels

Fuel

Courtesy of CEA Cadarache. Used with permission.

4. CVW solution:

Use of diluent to soften spectrum

 

  VOID   c 

   c 

 

 f  UNVOIDED

 

 f  VOIDED

Neutron Energy Spectra of Fuel with BeO Diluent

N o r m a l i z ed S p ec t r u m - 1 0 % B e O

N or m al i z e d S pe c t r um - 40% B eO

N or m al i z e d S pe c t r um - 20% B eO

N or m al i z e d S pe c t r um - 50% B eO

N or m al i z ed S p ec t r u m - 30% B eO

N or m al i z ed S p ec t r u m - N o B eO

2. 50 E - 0 2

2. 00 E - 0 2

1. 5 0 E - 0 2

1. 0 0 E - 0 2

5. 00 E - 0 3

0. 00 E + 00

1 . 00 E - 05 1 . 00E - 04 1 . 00 E - 03 1 . 0 0E - 02 1 . 00E - 01 1 . 00E + 0 0 1 . 00E + 01

En e r g y ( M e V)

The Diluent Approach

• Without diluent, enrichment zoning

 BOL CVW=1.6$, radial peaking = 1.56

With BeO d iluent, enrichment and diluent zoning

 BOL CVW=0.5$, radial peaking = 1.15

Diluent can also reduce axial peaking

• Shapes power by:

 Displacing fuel

 Minor effect

 Softening neutron energy spectrum

 Reduces neutron energy below fast fission thres hold

 Dominant effect

• BeO

 Moderating effect

 Thermal conductivity enhancement

 Best CVR reduction among candidate options

• Other candidates

 SiC

 TiC

Radial Power Shaping Using BeO

Other effects of diluent

Consequences of sustainability-driven choices (Cont’)

• Difficult to achieve conversion ratio (CR) of

1.0 in the absence of blankets

 Balance between leakage/neutron economy and CVW

 Balance thermal hydraulics and neutronics through coolant and fuel volume fractions

Why high heavy metal density?

• Unit cell calculatio ns

• U fuels

• Heavier density fuels

achieve higher BOL

reactivity

Gen IV Goals 3: Economy

• Indirect link

 Capital cost via safety - e xamples

 Reduced peaking allows higher power density for given structural material temperature limits, hence more energy from the same vessel and lower cost

 Low reactivity swing reduces number of control rods (CRDs expensive)

• Direct link

 Fuel cycle cost

 Strive for low enrichment (TRU weight fraction)

 Strive for high specific power

Example of long life, low power density design

Inner reflector

Shield

reflector

Active core

• Synergistic twin to thermal GT- MHR

• Same low power density – 8 kW/l

• Pass ive decay heat removal by conduction and radiation

• Excellent sa fety

• Neutronic a lly f easible

• Very long core life – 50 years

1400

1200

1000

800

600

400

0 50 1 00 150 200 250

Time (hours)

1.02

1.00

0.98

0.96

0 2 0 4 0 6 0 8 0

Effect ive full power years

Bd = 5 0 M W d / k g

Bd = 1 8 0 MW d/ k g

FCC 

C

xT

8 . 766 pL  T 1  e  xT

T- P W R T- G C F R

FCC-PWR (4%)

FCC-GC FR (13 % )

40 But very high fuel cycle cost!!!

25

20

15

10

5

0

0 2.5

12 0

10 0

80

60

40

20

0

2 0 4 0 6 0 8 0 1 0 0 1 2 0

S p ec i f i c po we r ( k W / k g HM )

GFR

•For U235 enriched fuel

•  =45%, L=0.90

•Bd=180MWd/kgHM

•discount rate x=10%/yr

•C=3936 $/kg for e=13%

PWR

•  =33%, L=0.90

•Bd=50MWd/kgHM

•discount rate x=10%/yr

•C=1200 $/kg for e=4.5%

•Fabrication 200$/kg

•SP=38kW/kgHM

•Twin to MHR-GT not economically feasible

•Specific power should not be much below 20kW/kg, Shoot for 25kW/kgHM (BWR)

• SUPERSAFE reactor of no use without a buyer

• What works for thermal reactor may not work for fast reactor

Gen IV Goals 4: Safety

• Reactivity increase from coolant depressurization

• Primary issue is post LOCA decay heat removal

 Gen IV emphasis is on enhanced safety

 Current trend – r ely on passive means

Water cooling

Em ergency cooling Heat Exch an ger

R eactor vessel

Guard containment

Hexagonal bl ocks with coolant chann el s

reflector

Cor e

GFR with natural circulation decay heat removal at elevated pressure

•4x50% cooling loops

•after depressurization of primary system, containment pressure increases and provides elevated pressure needed for natural circulation

Requires

Low pressure drop core , hence large coolant volume fraction – but neutronics favors small coolant volume fractions

Approaches to reconcile neutronics thermal hydraulic requirements

• Problem

 Neutronics needs high fuel volume fraction

 Post-LOCA thermal hydraulics favors low pressure drop

• Use inverted fuel assembly or plate fuel assembly

MIT approach CEA approach

Courtesy of CEA Cadarache. Used with permission.

Neutronic Design for Safety

• Most GFRs have slightly positive CVW

• Is this acceptable?

• How to assure safety with slightly positive CVW?

 Rely on other reactivity coefficients, which are negative

 Doppler feedback

 Fuel thermal expansion coefficient

 Core radial expansion coefficient

 CRD driveline expansions coefficient

 Strive for a design with such a combination of reactivity coefficients that can achieve reactor shutdown without exceeding structural materials and fuel temperature limits

Possible Safety Approach

• Follow IFR approach of reactor self-controllability

• Goal: reactor should have sufficiently strong passive regulation of power to compensate for operator errors or equipment failures even if the scram fails .

• Core designed such that it inherently achieves safe shutdown state without exceeding temperature limits that

would lead to core or vessel damage

• This must be achieved under the most restricting anticipated transients without scram (ATWS)

 Unprotected (without scram) loss of flow (ULOF)

 Unprotected loss of heat sink (ULOHS)

 Unprotected overpower (UTOP) –

 largest worth CRD withdrawal

Possible Safety Approach (cont’)

• Note that this is much stronger requirement than for LWRs

• Loss of coolant is not credible in IFR since coolant under no pressure and if vessel fails, the coolant

remains in guard vessel ( but it is an issue in GFR, hence it needs to be accommodated )

• Inherent shutdown is determined by:

 Reactivity feedbacks

 Materi al and coolant -related limits (e.g., clad, boiling, freezing T for IFR)

• Need to find such combination of reactivity feedbacks and limits that makes it possible to achieve self- controllability

Safety Approach (cont’)

• Quasi-static balance for reactivity encompassing all paths that affect

reactivity is

   CVW

for GFR

0    power

  

flow

   temp

   external

• Since time constants of heat flow changes and temperature induced geometry changes and of delayed neutr ons are in the range of half second to several minutes, and transients are slower, most feedbacks are linear

permitting above equation to be represented as

   CVW

for GFR

0   

 ( P

 1 ) A  ( P / F

 1 ) B

  T inlet C

   external

P,F – p ower and coolant flow nor malized to full power and fl ow

 Tin – c hange from normal coolant temperature

A,B,C – i ntegral reactivity parameters that arise from temperature and structural changes - d iscussed next

Three criteria for A,B,C can be derive d to achieve self-controllability

Wade and Chang, “The IFR Concept Physics of Operation and Safe ty, Nucl. Sci. Eng., Vol. 100, p. 507, 1988

Self-controllability criteria for LMRs

• ABR – f ertile free, lead cooled actinide burner

• LMRs can be designed to sa tisfy these criteria in spite of positive C VW

• Transient calculations still nee ded to confirm the performance

2.0

1.0

IFR

ABR

IFR

Limits Actual values

IFR ABR

S1: A/B

S2: C  Tc/B

S3:  TOP / | B |

criterion

Controls Tc rise in ULOFs Balance between ULOHs

and chilled Tinlet

Controls UTOP

GFR self controllability

• Designing a GFR with self controllability is a challenge

• Differences

 Additional term in reactivity balance to account for CVW

 Direct cycle – s eparate ULOHS and ULOF may not be possible – l oss of heat sink (precooler) may lead to loss of flow to prevent compressor surge or stall, hence ULOF and ULOHS will be always combined

 Self-controllability criteria need to be updated

 Decay heat removal may not be fully passive

• Issues

 MIT design with UO2 fuel has too large Doppler feedback (low conductivity, softer spectrum)

Questions

Extra Slides

Natural circulation performance - C O 2 and He

Post LOCA core temperature profiles

13 00

12 00

11 00

10 00

90 0

80 0

70 0

60 0

50 0

40 0

30 0

20 0

10 0

0 . 0 0 .2 0 .4 0 .6 0 .8 1 . 0 1 . 2 1 .4

C o re A x ia l L o c a tio n ( m )

1300

Av er ag e C ha nne l C oo l a nt Av er ag e C ha nne l W a l l H ot C ha nn el C o ol ant

H o t C h an ne l W al l

P = 5. 0 ba r s

m d ot = 78 . 9 7 k g/ s

1200

1100

1000

900

800

700

600

500

400

300

200

100

0

Av er ag e C hann el C ool ant Av er ag e C hann el W al l H ot C han nel C ool ant

H ot C han nel W al l

P = 13 bar s

m dot = 1 3. 8 7 k g/ s

0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4

C o r e Ax i a l Lo c a t i on ( m )

CO 2 Heli um

•Limits – peak cladding temperature=1200  C, maximum core-average outlet T=850  C

•2% decay heat can be removed by natural circulation

•CO2 much better than He – requires backup pressure of 5bars versus 13 bars for He

•Helium – i ssue of excursion type instabilities

IFR criteria for passive self-regulation

• A-net power reactivity coefficient (Doppler, fuel thermal expans ion) A=( α d + α th )  T f [¢]

• B-pow e r/flow coefficient of reactivi ty - c ontrols asymptotic temperature

rise in ULOF (coolant density, CRD- driveline, core radial expans ion

coefficients

B = [ α d + α th + α den +2( α crd + 2/3 α rad )]  T c /2 [¢]

• Key strategies:

 Small negative A - metallic fuel, hard spectrum

 Large negative B - m inimi ze coolant density coefficient

• Large B also favors large tem perature rise across the core

• But penalties on efficiency, hence compromis e needed

IFR criteria for passive self-regulation

• C –inlet temperature coef. of reactivity

      /  T in 

• provides balance between the ULOHS and the chilled inlet temperature inherent response (Doppler, fuel thermal exp., coolant density core, radial exp.)

C= ( α d + α th + α den + α rad ) [¢/K]

• range comes from cladding limit and coolant temperature rise

• Main efforts:

 Minimize coolant density coefficient

 Increase core radial expansion coefficient, if needed

IFR criteria for passive self-regulation

• Controls asymptotic temperature rise in UTOP

• The rod worth of the most reactive control rod must be limited

• Strategies:

 Minimize reactivity swing

 Use fertile, maximize  , C R=1 is a good candidate

 Increase Vf - limited by cladding stress constraint

 Low-leakage core favored, but hurts coolant void worth

 Large B - minimize coolant density coefficient

 Increase number of CRDs

Feasibility domain for plate core at 50kW/l

• Feasibility domain for carbide CERCER (50/50) 2400MWth core q’’’= 50W/cc

CE A result s

Core

design possible

52

Courtesy of CEA Cadarache. Used with permission.

Feasibility domain for plate core at 100kW/l

• Feasibility domain for carbide CERCER (50/50) 2400MWth core q’’’= 100W/cc

CEA results

Courtesy of CEA Cadarache. Used with permission. 53

Typical reactor response to ULOF

Fue l Cl a d

Cor e Out l e t C o re In let

Clad temperature limit

Time [sec]

• Cladding must remain below temperature limit

Example of GFR design for passive decay heat removal

Guard co n f in em en t

Courtesy of CEA Cadarache. Used with permission.

CEA and Framatome h elium cooled design 55

Example – n eutronic data for CEA design

Example – key design data for CEA design