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.
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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
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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.
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– 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
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, 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
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• 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
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Control rod positionTAVG
Power
38
BoronXenon
Samarium
Exercise 2 - Section 2.2.6
39
Exercise 2 (continued-1)
40
Exercise 2 (continued-2)
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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
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• 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
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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
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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
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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
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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
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Fig 2.2-2
Total Power Defect
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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
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Fig. 2.2-4
Xenon Worth Curves.
BOL Xenon Worth
vs.
Time After Shutdown
Eq. Xe @ 100%
2800 pcm
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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