Reactivity Balance Calculations & Shutdown Margin

1

Section 2.2

Learning Objectives1. Relate a change in a plant parameter to its

effect on estimated critical rod position (ECP).

2. Relate a change in a plant parameter to its

2

g p peffect on estimated critical boron concentration.

Learning Objectives(continued)

3. Relate a change in a plant parameter to its effect on the value of shutdown margin.

3

g

Core Reactivities • For reactor to be critical, the algebraic

sum of all core reactivities must be zero.• Examples of core reactivities:

– Rods

4

– Boron– Xenon & samarium– Power defect– Core excess reactivity

Reactor Startup• In order to have a controlled approach to

criticality during startup, the nuclear engineers & operators must determine the core reactivities at the expected time of startup

5

startup.

• During the startup,the operators will change the reactivity values of certain parameters (rods, boron) to achieve criticality.

Reactivity Immediately FollowingRx Trip From 100% Power

Last Known Critical Condition

Control Rods-4068 pcmS/D Reactivity

6191 pcm

Keff = 1ρ = 0 pcm

Bank D at 210 StepsBoron 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 pcm

Estimated Critical Position (ECP)

• An ECP is a calculation performed to ensure criticality occurs above the rod insertion limits.

7

TS 3.1.6 - Control Bank Insertion Limits

• LCO 3.1.6: The control banks shall be w/in the insertion, sequence, & overlap limits specified in the Core Operating Limits Report (COLR).

8

p ( )

• Surveillance Requirements 3.1.6.1: verify the ECP is within the limits specified in the COLR. Within 4 hours prior to achieving criticality.

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 critical

condition (i.e. last operating condition or last startup).

• The sum of the reactivities = 0.

10

Reactivity Balance Method

• Does not require knowledge previous critical conditions.

• Requires knowledge of reference conditions of reactivity factors.

11

y

• Sum of the reactivities = 0.

• Recall than an ECP is performed to ensure criticality occurs above the rod insertion limits (RIL).

• The nuclear engineers & operators determine a critical rod height (> RIL) and adjust boron

Estimated Critical Boron Concentration

12

a critical rod height (> RIL) and adjust boron concentration.

• Rods are then withdrawn to startup the reactor.

Classroom Exercise 1 Section 2.2.6

13

Tools for Exercise 1

• Fig. 2.2-1, Rod Worth Curve.

• Fig. 2.2-2, Total Power Defect.

• Fig. 2.2-3, Boron Worth Curves.

14

g

• Fig. 2.2-4, Xenon Worth Curves.

• Fig. 2.2-5, Samarium Worth Curve.

• Fig. 2.2-6, MTC Cycle 1, BOL, ARO.

• Attachment 2.2-1

Fig. 2.2-1, Rod Worth Curve.

Integral Rod Worth

vs.

Steps Withdrawn

Banks B, C, & D.

15

100 Step Overlap.

BOL

Fig 2.2-2

Total Power Defect

Doppler & Moderator

vs.

Power

16

Fig. 2.2-3

Boron Worth Curves.

Differential Boron Worth

vs.

Boron Concentration at V i M d t

17

Various Moderator Temperatures

Cycle 1, BOL

Fig. 2.2-4

Xenon Worth Curves.

BOL Xenon Worth

vs.

Time After Shutdown

18

Fig. 2.2-5

Samarium Worth Curve

vs.

Time After Shutdown.

Samarium Reactivity after Shutdown from

19

after Shutdown from Full Power

Fig 2.2-6

MTC,Cycle 1

BOL, ARO

20

Attachment 2.2-1

(pg.1)

Estimated Critical Condition Calculation

(Delta Rho Method)

21

( )

Attachment 2.2-1

(pg. 2)

22

D 60

D 210Rod Worth

1100

50

-1050

Power Defect

1500

23

950800

Boron Worth 10.8

-1620

Classroom Exercise 1, Section 2.2.6. Attachment 2.2-1

35002800

-700

Sm Worth750

600

-150

Xe Worth

24

-1050 1500 -1620 -700 -150 -2020

Classroom Exercise 1, Section 2.2.6. Attachment 2.2-1

-2020

-10.8187

Dilute

This calculation is telling us that to take the Rx critical with CB-D at 60 steps, 26 hours after the shutdown, the RCS boron concentration must be

25

shutdown, the RCS boron concentration must be reduced by 187 ppm.

Classroom Exercise 1, Section 2.2.6. Attachment 2.2-1

Last Known Critical Condition: Bank D at 210 steps & Boron at 800 ppm.

Keff = 1ρ = 0 pcm

Δ Control Rod Reactivity Bank D 60 steps

-1050 pcm

ECC - Reactor Startup (w/ CB-D at 60 steps)26 Hours Following Rx Trip From 100% Power

(Delta Rho Method)

Critical Boron Concentration

Power Defect+1500 pcm

Δ Xenon Reactivity -700 pcm

Δ Samarium Reactivity -150 pcm

Δ Boron Reactivity -1620 pcm(800-950ppm)

Need to Dilute+2020 pcm

950-187=763 ppm

Questions About the ECP Calculations?

27

Reactivity Anomaly (Section 2.2.5)

• With the Rx critical at rated thermal power and program Tave, the excess positive reactivity from the fuel is compensated by:– burnable poisons (if any), – control rods,

28

– poisons in fuel (mainly Xe & Sm), – and boron.

• As fuel is depleted, the excess positive reactivity decreases.

• Over core life, boron is reduced to decrease negative reactivity and to maintain rated thermal power.

Reactivity Anomaly (continued)

29

TS 3.1.2 - Core Reactivity

• LCO: The measured core reactivity shall be w/in 1% delta K/K (1000 pcm) of predicted. – Performed at 60 EFPD (after refueling) & every

31 EFPDs afterwards.

30

– Ensures accident analyses remains valid.

Critical Boron Concentration

vs.

Burnup

HFP, ARO,

Equilibrium Xe Conditions.

31

Core Reactivity Surveillance

• Rx stable & reactivities balanced.

• Eq. Xe & Sm, all rods out, Tave @ program.

• Usually compare actual boron concentration w/ predicted for time in core life.

32

p

Core Reactivity Surveillance (cont)

• If actual differs from predicted too much:– could potentially be a loss of SDM or operation

beyond fuel design limits.

– accident analysis for rod withdrawal or rod j ti l b lid

33

ejection may no longer be valid.

– must be in Mode 3 w/in 6 hrs.

– If don’t have adequate SDM, borate as required.

V.C. SummerInadvertent Criticality

Section 7.2

34

Shutdown Margin (SDM)• TS defines SDM as the instantaneous amount of

reactivity by which the Rx is subcritical or would besubcritical from its present condition assuming:– All RCCAs are fully inserted except for the single RCCA of

highest reactivity worth, which is assumed to be fully withdrawn. However, with all RCCAs verified fully inserted

35

, yby two independent means, it is not necessary to account for a stuck RCCA in the SDM calculation. With any RCCA not capable of being fully inserted, the reactivity worth of the RCCA must be accounted for in the determination of SDM, and

– In MODES 1 and 2, the fuel and moderator temperatures are changed to the nominal zero power design level.

SDM Technical Specifications

• TS 3.1.1• Mode 2 w/ Keff < 1.0 & in Modes 3, 4 and 5.• SDM > 1.3 % ΔK/K with TAVG > 350°F• SDM > 1.6% with with TAVG < 350°F

36

• In MODES 1 and 2, SDM is verified by observing that the requirements of LCO 3.1.5 and LCO 3.1.6 are met . – In the event that a rod is known to be untrippable,

SDM verification must account for the worth of the untrippable rod as well as another rod of maximum worth.

fuelrodsSDM ρρρ −−= mod

Shutdown margin for an operating reactor

37

Control rod positionTAVG

Power

38

BoronXenon

Samarium

Exercise 2 - Section 2.2.6

39

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 2 2 3 B W h C

42

• Fig. 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 Curves.

• Attachment 2.2-2

Attachment 2.2-2

(pg. 1)

SDM Calculation.

A Reactivity Balance

43

Attachment 2.2-2

(pg. 2)

44

Attachment 2.2-2

(pg. 3)

45

Exercise 2 - Section 2.2.6

46

rod worth table 7744

1040

rod worth curve 10

750

Exercise 2, Part 1

- 5144 pcm = -5.144 % delta K/K

47

power defect 1550

-5144

Exercise 2, Part 1: Determine the Shutdown Margin using Attachment 2.2-2, Section I.

Exercise 2, Part 2

48

Xe worth1550

2800+1250

-5144

49

Sm worth

840

600

-240

MTC

547

0

7

Exercise 2, Part 2; 40 hrs after trip, 547 oF Tave

0

750

50

750750

0boron worth11.2

0

Exercise 2, Part 2; 40 hrs after trip, 547 oF Tave.

-5144 +1250 -2400 0 -4134

Exercise 2, part 2:

i h Sh d i 40 h f h i i

51

Determine the Shutdown Margin 40 hours after the trip using Attachment 2-2-2, Section II.

-4134 pcm = - 4.134 % delta K/K

Exercise 2, Part 3

52

Exercise 2, Part 3; 40 hrs after trip, 547 oF Tave.

Shutdown Banks are Withdrawn.

-4134

table 2.2-110403676

53

-1498

Exercise 2, Part 3; 40 hrs after trip, 547 oF Tave.Shutdown Banks are Withdrawn (continued).

A. Will the Rx go critical?

B. Will the TS Shutdown Margin requirements be met?

No. There is 1498 pcm of negative reactivity in the Rx.

54

g q

Yes, assuming the plant is in Mode 3. Recall that TS defines SDM as the instantaneous amount of reactivity by which the Rx is subcritical or would be subcritical from its present condition.

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 1 498 % d lt K/K 0 01498 d lt K/K

55

Keff = 0.985

A little algebra,

-1498 pcm = -1.498 % delta K/K = - 0.01498 delta K/K

ρ =−

=KK

KK

eff

eff

1 Δ

4. From the above condition, assume the licensee withdraws the shutdown banks , then takes no further action. What will happen over the next two days?

Exercise 2, Part 3; 40 hrs after trip, 547 oF Tave.Shutdown Banks are Withdrawn (continued - 1).

56

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 close considering samarium buildup and xenon decay). If the reactordoes go critical, it will trip on high SR count rate.

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

57

-5144

Xe worth

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

58

Xe worth

02800

+2800

Sm worth950

600

-350

Ex. 3; Four days after trip, 300 oF Tave. (continued)

MTC

300

-247

7

+1739

59

1739

Recall that we want to find out how much positive reactivity was added 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-load Tave value for MTC to be conservative.

Ex. 3; Four days after trip, 300 oF Tave. (continued - 1)

750750

0

0

boron worth13.5

60

-5144 +2800 -350

+1739 -965

Ex. 3; Four days after trip, 300 oF Tave. (continued - 2)

-965

-965

+335

+635

-13.5

61

+635-13.5

47

Exercise 3: Determine the boron concentration change required 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 be added to the RCS to meet the SDM requirements.

Fig. 2.2-1, Rod Worth Curve.

D @ 21050 pcm

D @ 60

62

D @ 601100pcm

Fig 2.2-2

Total Power Defect

Doppler & Moderator

vs.

Power

63

800 ppm;

- 1500 pcm

Fig. 2.2-3

Boron Worth Curves.

Differential Boron Worth

vs.

Boron Concentration at V i M d t

950 ppm:10.8

64

Various Moderator Temperatures

pcm/ppm

26 hours;3500 pcm

Eq. Xe @ 100%

2800 pcm

Fig. 2.2-4

65

Fig. 2.2-5

Samarium Worth Curve

vs.

Time After Shutdown.

Samarium Reactivity after Shutdown from

26 hours;750 pcm

66

after Shutdown from Full Power

Eq. Sm @ 100%600 pcm

750 pcm

67

Fig. 2.2-1, Rod Worth Curve.

D @ 22010 pcm

68

Fig 2.2-2

Total Power Defect

69

750 ppm;1550 pcm

40 hours;1550 pcm

Eq. Xe @ 100%

2800 pcm

Fig. 2.2-4

70

Fig. 2.2-5

Samarium Worth Curve

vs.

Time After Shutdown.

Samarium Reactivity after Shutdown from

40 hours;840 pcm

71

after Shutdown from Full Power

Eq. Sm @ 100%600 pcm

840 pcm

Fig. 2.2-6

MTC

Cycle 1,

BOL, AOL 750 ppm;547 oF

72

MTC= - 7 pcm/ oF

Fig. 2.2-3

Boron Worth Curve

750 ppm; 547 oF TaveBoron Worth =-11.2 pcm/ppm

73

Fig. 2.2-4

Xenon Worth Curves.

BOL Xenon Worth

vs.

Time After Shutdown

Eq. Xe @ 100%

2800 pcm

74

At 96 hrs, the Xe is effectively gone.

Fig. 2.2-5

Samarium Worth Curve

96 hrs:950 pcm

75

p

Eq. Sm @ 100%600 pcm

Fig. 2.2-6

750 ppm;547 oF

MTC= - 7 pcm/ oF

750

76

g

MTC

Cycle 1,

BOL, AOL

750 ppm;300 oF

MTC= 0 pcm/ oF

Fig. 2.2-3

Boron Worth Curve

77

750 ppm; 300 oF TaveBoron Worth =-13.5 pcm/ppm