Reactivity Balance Calculations & Shutdown Margin

Reactivity Balance Calculations &Shutdown MarginSection 2.21

Learning Objectives1. Relate a change in a plant parameter to itseffect on estimated critical rod position (ECP).2. Relate a changeg in a pplant pparameter to itseffect on estimated critical boronconcentration.2

Learning Objectives(continued)3. Relate a change in a plant parameter toits effect on the value of shutdownmargin.g3

Core Reactivities For reactor to be critical, the algebraicsum of all core reactivities must be zero. Examples of core reactivities:– Rods– Boron– Xenon & samarium– Power defect– Core excess reactivity4

Reactor Startup In order to have a controlled approach tocriticality during startup, the nuclearengineers & operators must determine thecore reactivities at the expected time ofstartupstartup. During the startup,the operators will changethe reactivity values of certain parameters(rods, boron) to achieve criticality.5

Reactivity Immediately FollowingRx Trip From 100% PowerLast Known Critical ConditionBank D at 210 StepsBoron Concentration 800 ppmS/D Reactivity6191 pcm-6191Keff 1ρ 0 pcmControl Rods-4068 pcmTotal Rod Worth-7741 pcmReactivity 1550 pcmBank D @ 210 50 pcmPower Defect 1500 pcmShutdown Rods-3673 pcm6

Estimated Critical Position (ECP) An ECP is a calculation performed toensure criticality occurs above the rodinsertion limits.7

TS 3.1.6 - Control Bank Insertion Limits LCO 3.1.6: The control banks shall be w/inthe insertion, sequence, & overlap limitsspecified in the Core Operating LimitsReportp ((COLR).) Surveillance Requirements 3.1.6.1: verifythe ECP is within the limits specified in theCOLR. Within 4 hours prior to achievingcriticality.8

ECP Calculations Two methods:– Delta Rho (Section 2.2.2.1)– Reactivity Balance (Section 2.2.2.2)9

Delta Rho Method Requires knowledge of previous criticalcondition (i.e. last operating condition orlast startup). The sum of the reactivities 0.10

Reactivity Balance Method Does not require knowledge previous criticalconditions. Requires knowledge of reference conditionsof reactivityy factors. Sum of the reactivities 0.11

Estimated Critical Boron Concentration Recall than an ECP is performed to ensurecriticality occurs above the rod insertion limits(RIL). The nuclear engineers & operators determinea critical rod height ( RIL) and adjust boronconcentration. Rods are then withdrawn to startup thereactor.12

ClassroomExercise 1Section 2.2.613

Tools for Exercise 1 Fig. 2.2-1, Rod Worth Curve.Fig. 2.2-2, Total Power Defect.Fig.g 2.2-3, Boron Worth Curves.Fig. 2.2-4, Xenon Worth Curves.Fig. 2.2-5, Samarium Worth Curve.Fig. 2.2-6, MTC Cycle 1, BOL, ARO.Attachment 2.2-114

Fig. 2.2-1, Rod Worth Curve.Integral Rod Worthvs.Steps WithdrawnBanks B, C, & D.100 Step Overlap.BOL15

Fig 2.2-2Total Power DefectDoppler & Moderatorvs.Power16

Fig. 2.2-3Boron Worth Curves.Differential Boron Worthvs.Boron Concentration atV iVariousM d tModeratorTemperaturesCycle 1, BOL17

Fig. 2.2-4Xenon Worth Curves.BOL Xenon Worthvs.Time After Shutdown18

Fig. 2.2-5Samarium Worth Curvevs.Time After Shutdown.Samarium Reactivityafter Shutdown fromFull Power19

Fig 2.2-6MTC,Cycle 1BOL, ARO20

Attachment 2.2-1(pg.1)Estimated CriticalConditionCalculation((Delta Rho Method))21

Attachment 2.2-1(pg. 2)22

D60D2101100Rod Worth50-10501500Power DefectBoron WorthClassroom Exercise 1, Section 2.2.6.Attachment 2.2-195080010.8-162023

Xe Worth28003500-700750600-10501500-1620-700-150Sm Worth-150-2020Classroom Exercise 1, Section 2.2.6. Attachment 2.2-124

-2020-10.8187DiluteThis calculation is telling us that to take the Rxcritical with CB-D at 60 steps, 26 hours after theshutdown, the RCS boron concentration must bereduced by 187 ppm.Classroom Exercise 1, Section 2.2.6. Attachment 2.2-125

ECC - Reactor Startup (w/ CB-D at 60 steps)26 Hours Following Rx Trip From 100% Power(Delta Rho Method)Last Known Critical Condition: Bank D at 210 steps & Boron at 800 ppm.Critical BoronConcentrationNeed to Dilute 2020 pcm950-187 763 ppmPower Defect 1500 pcmKeff 1ρ 0 pcmΔ Control Rod ReactivityBank D 60 steps-1050 pcmΔ Xenon Reactivity -700 pcmΔ Samarium Reactivity -150 pcmΔ Boron Reactivity -1620 pcm(800-950ppm)

QuestionsAbout the ECP Calculations?27

Reactivity Anomaly (Section 2.2.5) With the Rx critical at rated thermal powerand program Tave, the excess positivereactivity from the fuel is compensated by:– burnable poisons (if any),– control rods,– poisons in fuel (mainly Xe & Sm),– and boron. As fuel is depleted, the excess positivereactivity decreases.28

Reactivity Anomaly (continued) Over core life, boron is reduced to decreasenegative reactivity and to maintain ratedthermal power.29

TS 3.1.2 - Core Reactivity LCO: The measured core reactivity shall bew/in 1% delta K/K (1000 pcm) of predicted.– Performed at 60 EFPD (after refueling) & every31 EFPDs afterwards.– Ensures accident analyses remains valid.30

Critical Boron Concentrationvs.BurnupHFP, ARO,Equilibrium Xe Conditions.31

Core Reactivity Surveillance Rx stable & reactivities balanced. Eq. Xe & Sm, all rods out, Tave @ program. Usually compare actual boron concentrationw/ ppredicted for time in core life.32

Core Reactivity Surveillance (cont) If actual differs from predicted too much:– could potentially be a loss of SDM or operationbeyond fuel design limits.– accident analysis for rod withdrawal or rodejectionj ti may no llonger bbe valid.lid– must be in Mode 3 w/in 6 hrs.– If don’t have adequate SDM, borate as required.33

V.C. SummerInadvertent CriticalitySection 7.234

Shutdown Margin (SDM) TS defines SDM as the instantaneous amount ofreactivity by which the Rx is subcritical or would besubcritical from its present condition assuming:– All RCCAs are fully inserted except for the single RCCA ofhighest reactivity worth, which is assumed to be fullywithdrawn. However,, with all RCCAs verified fullyy insertedby two independent means, it is not necessary to accountfor a stuck RCCA in the SDM calculation. With any RCCAnot capable of being fully inserted, the reactivity worth ofthe RCCA must be accounted for in the determination ofSDM, and– In MODES 1 and 2, the fuel and moderator temperaturesare changed to the nominal zero power design level.35

SDM Technical Specifications TS 3.1.1Mode 2 w/ Keff 1.0 & in Modes 3, 4 and 5.SDM 1.3 % ΔK/K with TAVG 350 FSDM 1.6% with with TAVG 350 FIn MODES 1 and 2, SDM is verified by observingthat the requirements of LCO 3.1.5 andLCO 3.1.6 are met .– In the event that a rod is known to be untrippable,SDM verification must account for the worth of theuntrippable rod as well as another rod of maximumworth.36

Shutdown margin for an operating reactorSDM ρ rods ρ mod ρ fuel37

Control rod positionTAVGPowerBoronXenonSamarium38

Exercise 2 - Section 2.2.639

Exercise 2 (continued-1)40

Exercise 2 (continued-2)41

Tools for Exercise 2 Table 2.2-1 (pg. 2.2-4)Fig. 2.2-1, Rod Worth Curve.Fig. 2.2-2, Total Power Defect.Fi 2Fig.2.2-3,23 BBoron WWorthhCCurves.Fig. 2.2-4, Xenon Worth Curves.Fig. 2.2-5, Samarium Worth Curve.Fig. 2.2-6, MTC Curves.Attachment 2.2-242

Attachment 2.2-2(pg. 1)SDM Calculation.A Reactivity Balance43

Attachment 2.2-2(pg. 2)44

Attachment 2.2-2(pg. 3)45

Exercise 2 - Section 2.2.646

Exercise 2, Part 1rod worth tablerod worth curve- 5144 pcm -5.144 % delta K/Kpower defect77441040107501550-5144Exercise 2, Part 1: Determine the Shutdown Margin usingAttachment 2.2-2, Section I.47

Exercise 2, Part 248

-5144Xe worth15502800 1250Sm worth840600-24049

Exercise 2, Part 2; 40 hrs after trip, 547 oF Tave54707MTC0750750011.2boron worth050

Exercise 2, Part 2; 40 hrs after trip, 547 oF Tave.-5144 125000-240-4134Exercise 2, part 2:Determinei theh ShutdownSh dMargini 40 hourshafterf theh tripi usingiAttachment 2-2-2, Section II.-4134 pcm - 4.134 % delta K/K51

Exercise 2, Part 352

Exercise 2, Part 3; 40 hrs after trip, 547 oF Tave.Shutdown Banks are Withdrawn.-4134table 2.2-110403676-149853

Exercise 2, Part 3; 40 hrs after trip, 547 oF Tave.Shutdown Banks are Withdrawn (continued).A. Will the Rx go critical?No. There is 1498 pcm of negative reactivity in the Rx.g requirementsqbe met?B. Will the TS Shutdown MarginYes, assuming the plant is in Mode 3. Recall that TSdefines SDM as the instantaneous amount of reactivity bywhich the Rx is subcritical or would be subcritical fromits present condition.54

Exercise 2, Part 3; 40 hrs after trip, 547 oF Tave.Shutdown Banks are Withdrawn (continued - 1).C. Is the plant still in Mode 3?Yes, assuming the plant meets the definition of Mode 3.Mode 3 is Keff 0.99 and Tave 350 o F.-1498 pcm -1.4981 498 % deltad lt K/K - 0.014980 01498 deltad lt K/Kρ Keff 1KeffΔK KA little algebra,Keff 0.98555

Exercise 2, Part 3; 40 hrs after trip, 547 oFTave.Shutdown Banks are Withdrawn (continued - 1).4. From the above condition, assume the licensee withdraws theshutdown banks , then takes no further action. What willhappen over the next two days?See Figure 2.2-4. The Rx is presently subcritical by 1498 pcm.In 6-7 hours the plant will enter MODE 2 due to xenondecay. In about 35 hours the Rx may go critical (it will be closeconsidering samarium buildup and xenon decay). If the reactordoes go critical, it will trip on high SR count rate.56

Exercise 3; Four days after trip, 300 oF Tave.57

Exercise 3; Four days after trip, 300 oF Tave.-5144Xe worth02800Sm worth950600 2800-35058

Ex. 3; Four days after trip, 300 oF Tave. (continued)300-247MTC7 1739Recall that we want to find out how much positive reactivity wasadded by the 247 oF cooldown.Also recall that MTC changes as temperature changes.Because we don’t have an integral MTC curve, use the no-loadTave value for MTC to be conservative.59

Ex. 3; Four days after trip, 300 oF Tave. (continued - 1)750750013.5boron worth0-5144 1739 2800-350-96560

Ex. 3; Four days after trip, 300 oF Tave. (continued - 2)-965-965 335 635-13.5 63547-13.5Exercise 3: Determine the boron concentration changerequired to meet the SDM requirements for this condition.Is the SDM requirement met?No.This calculation is telling us that 47 ppm of boron must beadded to the RCS to meet the SDM requirements.61

Fig. 2.2-1, Rod Worth Curve.D @ 21050 pcmD @ 601100pcm62

Fig 2.2-2Total Power DefectDoppler & Moderatorvs.Power800 ppm;- 1500 pcm63

Fig. 2.2-3Boron Worth Curves.Differential Boron Worth950 ppm:10.8pcm/ppmvs.Boron Concentration atV iVariousModeratorM d tTemperatures64

Fig. 2.2-4Eq. Xe @100%2800 pcm26 hours;3500 pcm65

Fig. 2.2-5Samarium Worth Curvevs.Time After Shutdown.Samarium Reactivityafter Shutdown fromFull Power26 hours;750 pcmEq. Sm @ 100%600 pcm66

67

Fig. 2.2-1, Rod Worth Curve.D @ 22010 pcm68

Fig 2.2-2Total Power Defect750 ppm;1550 pcm69

Fig. 2.2-4Eq. Xe @100%2800 pcm40 hours;1550 pcm70

Fig. 2.2-5Samarium Worth Curvevs.Time After Shutdown.Samarium Reactivityafter Shutdown fromFull Power40 hours;840 pcmEq. Sm @ 100%600 pcm71

Fig. 2.2-6MTCCycle 1,BOL, AOL750 ppm;547 oFMTC - 7 pcm/ oF72

Fig. 2.2-3Boron Worth Curve750 ppm; 547 oF TaveBoron Worth -11.2 pcm/ppm73

Eq. Xe @100%2800 pcmFig. 2.2-4Xenon Worth Curves.BOL Xenon Worthvs.Time After ShutdownAt 96 hrs, the Xe iseffectively gone.74

Fig. 2.2-5Samarium Worth Curve96 hrs:950 ppcmEq. Sm @ 100%600 pcm75

750 ppm;547 oFMTC - 7 pcm/ oF750 ppm;300 oFMTC 0 pcm/ oFFig.g 2.2-6MTCCycle 1,BOL, AOL76

Fig. 2.2-3Boron Worth Curve750 ppm; 300 oF TaveBoron Worth -13.5 pcm/ppm77

S/D Reactivity -4068 pcm 6191 pcm Keff 1 ρ 0 pcm Bank D at 210 Steps Boron Concentration 800 ppm 6 Power Defect 1500 pcm Shutdown Rods-3673 pcm-6191 pcm Reactivity 1550 pcm Total Rod Worth-7741 pcm Bank D @ 210 50