Updating of adventitious fuel pin failure frequency in sodium-cooled fast reactors and probabilistic risk assessment on consequent severe accident in Monju

Figures & data

Table 1. Frequency of initiating events of LFs for CDFR.

Initiating event	Frequency (/ry)
Adventitious fuel pin failure	35
Inlet blockage	10^−3
Outlet blockage	10^−3
Wrapper split	2 × 10^−2
Overrated subassembly loaded	3 × 10^−2
Partially blocked subassembly loaded	2 × 10^−3
Oil in subassembly	10^−1
Non-oil debris in subassembly	10^−1

Table 2. Number of failed fuel pins and related data in SFRs based on open papers.

	JOYO
(n) Reactor	(1) Mk-II	(2) Mk-III	(3) Phenix	(4) Super Phenix	(5) PFR	(6) FFTF
(an) Total number of irradiated driver fuel pins (−)	43,434^[6]^,^[7]	16,510^[6]^,^[7]	NA	≧ 98,644^[12]	NA	≧47,500^[14]
(bn) Total number of irradiated fuel pins (−)	NA	NA	≧166,521^[10]^,^[11]	NA	∼98,000^[13]	≧63,500^[14]
(cn) Total number of failed driver fuel pins (−)	0^[6]^,^[7]	0^[6]^,^[7]	NA	0^[12]	≦18^[8]	1^[14]
(dn) Total number of failed (fuel-exposed) driver fuel pins (−)	0^[6]^,^[7]	0^[6]^,^[7]	6^[8]	0^[12]	≦14^[8]	1^[14]
(en) Total number of failed (gas-leaked) driver fuel pins (−)	0^[6]^,^[7]	0^[6]^,^[7]	NA	0^[12]	≦4^[6]	1^[14]
(fn) Total number of failed fuel pins (−)	0^[6]^,^[7]	0^[6]^,^[7]	29^[8]^,^[9]	0^[12]	22^[8]	12^[14]
(gn) Total number of failed (fuel-exposed) fuel pins (−)	0^[6]^,^[7]	0^[6]^,^[7]	15^[8]^,^[9]	0^[12]	18^[8]	NA
(hn) Total number of failed (gas-leaked) fuel pins (−)	0^[6]^,^[7]	0^[6]^,^[7]	14^[8]	0^[12]	4^[8]	NA
(in) Duration of normal operation (years)	−	−	−	4.5^[11]	−	−
(jn) Load Factor (%)	−	−	−	∼20^[11]	−	−
(kn) Cumulative equivalent full power days (days)	1828.3^[15]	701.7^[7]^,^[15]	3675^[10]	329*	∼1500^[11]	2278^[11]
(ln) Mean residence time of inner core subassemblies (days)^[12]	270	358	600	640	300	720
(mn) Mean residence time of outer core subassemblies (days)^[12]	−	439	800	640	400	600
(on) Number of inner core subassemblies in equilibrium core (−)^[12]	67	25	55	193	28	28
(pn) Number of outer core subassemblies in equilibrium core (−)^[12]	−	60	48	171	44	45
(qn) Number of fuel pins per subassembly (−)^[12]	127	127	217	271	325	217
(rn) Average achieved burnup (MWd/t)^[12]	42,000	68,500	100,000	60,000	150,000	70,000
(sn) Maximum achieved burnup (MWd/t)^[12]	84,000	86,900	150,000	90,000	200,000	155,000
(tn) Nominal full power (MWth)^[12]	100	140	563	2990	650	400

Note: NA: not available.

*Estimated based on (i) and (j).

Table 3. Number of failed fuel pins and essential related data in SFRs.

	JOYO
(n) Reactor	(1) Mk-II	(2) Mk-III	(3) Phenix	(4) Super Phenix	(5) PFR	(6) FFTF
(An) Total number of irradiated (driver) fuel pins (−)	43,434	16,510	166,521	98,644	98,000	47,500
(Bn) Total number of failed (driver) fuel pins (−)	0	0	29	0	22	1
(Cn) Mean residence time (years)	0.7	1.1	1.9	1.8	1.0	1.8
(Dn) Cumulative equivalent full power years (years)	5.0	1.9	10.1	0.9	4.1	6.2
(En) Total number of fuel pins in equilibrium core (−)	8509	10,795	22,351	98,644	23,400	15,841
(Fn) Average achieved burnup (GWd/t)	42	68.5	100	60	150	70
(Gn) Nominal full power (MWth)	100	140	563	2990	650	400

Table 4. Frequency of AFPF in Monju by each method.

	Method 1	Method 2	Method 3	Method 4
Frequency of AFPF	7.2E−5 (/y/pin)	9.1E−5 (/EFPY/pin)	9.9E−7 (/EFPY/pin/(GWd/t))	1.0E−7 (/EFPY/pin/MWth)
Frequency of AFPF in Monju (/ry）	2.4	2.2	1.9	1.8

Table 5. Alert and reactor trip levels of detectors in CG and DN method.

Name of alert or reactor trip	Alert or reactor trip threshold
Alert of high count rate at the precipitators in CG method	FP gas release (1% of FP gas release in one fuel pin)
Alert of very high count rate at the precipitators in CG method	Fuel pin failure (0.01% fuel pin failure of total fuel pins)
Alert of high count rate at the NaI detectors in CG method	Fuel pin failure (0.02% fuel pin failure of total fuel pins)
Alert of high count rate at the DNDs in DN method	Breached cladding area (over 200 mm^2)
Alert from the TCs at the outlet of subassembly	More than 66% of flow blockage within one subassembly
Reactor trip by the DNDs in DN method	Breached cladding area (over 5000 mm^2)

Figure 1. Schematic drawing of failed fuel detectors in Monju.

Figure 2. Schematic of operating procedure after fuel pin failure in Monju.

Figure 3. Main event tree of FEFPA.

Table 6. Branching probability ranking standards.

	Qualitative	Representative	Range of
Probabilistic rank	representation	value	application	Remarks
1	Indeterminate	0.5	0.7–0.3	The occurrence frequency is almost 50%.
2	Unlikely	0.2	0.3–0.1	The possibility of occurrence is low based on engineering judgment. It corresponds to 1σ of the normal distribution.
	Likely	0.8	0.7–0.9	The possibility of occurrence is high based on engineering judgment.
3	Highly unlikely	0.05	0.1–0.01	The possibility of occurrence is completely denied based on engineering judgment. It corresponds to 2σ of the normal distribution.
	Highly likely	0.95	0.9–0.99	The possibility of occurrence is completely affirmed based on engineering judgment.
4	Extremely unlikely	<0.01	<0.01	Detailed analysis is necessary for the quantification of the probability.
	Extremely likely	>0.99	>0.99	Detailed analysis is necessary for the quantification of the probability.
5	Impossible	Ε	ϵ	The probability of occurrence is negligible.
	Certain	1–ϵ	1–ϵ	The occurrence is judged to be certain.

Table 7. Branching probability of each phenomenological headings.

Heading	Basis of engineering judgment	Branching probability rank	Representative value
(2) Cladding defect size over alert threshold of DND and precipitator	Experimental data of RBCB (run beyond cladding breach) [17]	Highly unlikely [17]	0.05
(4) Pin failure propagation to the adjacent six pins during the period until refueling	FUCALF code analyses [17]	Highly unlikely [17]	0.05
(7) Cladding defect size over reactor trip threshold of DND	Experimental data of RBCB [17]	Highly unlikely [17]	0.05
(9) Damage propagation over alert threshold of TCs at the outlet of FSA	FUCALF and SEETHE code analyses [17]	Highly unlikely [17]	0.05
(11) Failure of decay heat removal after reactor shutdown	FUCALF and SEETHE code analyses [17]	Unlikely [17]	0.2
(12) Damage propagation to the neighboring FSAs	Experimental data of Mol-7C [18] and SCARABEE [19]	Likely	0.8

Table 8. Results of fault tree analysis for common systems shared by frontline systems.

	Headings	Failure probability
I	Support systems (i.e., power supply) required for manual reactor shutdown	2.30E−06
II	Common system required for manual reactor shutdown by the alert from precipitators or NaI detectors (argon gas sampling line)	7.60E−04
III	Common component required for precipitators (three signal line and calibration error)	4.01E−04
IV	Common component required for precipitators (two signal line)	1.69E−08
V	Prevention of common cause failure and calibration error in manual and automatic shutdown using DN method	4.01E−04
VI	Single channel commonly required in both manual and automatic shutdown using DN method (i.e., detector, control circuits and power supply for loop-A)	2.71E−06
VII	Support system required in manual and automatic shutdown using DN method (i.e., power supply for loop-B)	1.95E−06
VIII	Support system required in manual and automatic shutdown using DN method (i.e., power supply for loop-C)	1.95E−06
IX	Components required only for manual shutdown	2.91E−06
X	Components required for reactor shutdown (i.e., reactor trip breakers and control rods)	6.41E−08

Table 9. Results of fault tree analysis for main event tree headings (frontline systems).

	Headings	Probability	Prerequisites for common shared system^*1
(3)	Failure of manual reactor shutdown by the alert from DNDs and precipitators	4.26E−04	Success in I, II, III, IV, V, VI, (VII or VIII), IX and X
		4.27E−04	Success in I, II, III, IV, V, VII, VIII, IX, and X and Failure in VI
		1.0	Failure in I, II, III, IV, V, (VI and VII), (VI and VIII), (VII and VIII), IX or X
(5)	Failure of normal reactor shutdown by the second alert from precipitators	4.26E−04	Success in I, II, III, IX and X
		1.0	Failure in I, II, III, IX or X
(6)	Failure of normal rector shutdown by the alert from NaI detectors	8.28E−04	Success in I, II, IX and X
		1.0	Failure in I, II, IX or X
(8)	Failure of automatic reactor shutdown by the trip signal from DNDs	5.77E−13	Success in V, VI, (VII or VIII) and X
		7.60E−07	Success in V, VII, VIII and X; and failure in VI
		1.0	Failure in V, (VI and VII), (VI and VIII), (VII and VIII) or X
(10)	Failure of manual reactor shutdown by the alert from TCs at the outlet of FSA	1.42E−03	Success in I, IX and X
		1.0	Failure in I, IX or X

^*1 “Success in I”, for example, denotes here that the support systems (i.e., power supply) required for manual reactor shutdown, shown in Table 8 as “I”, are available, and “Failure in I” means that they are unavailable.

Table 10. Results of event tree analysis for FEFPA in Monju compared with those in existing PRA.

	Vaughan (CDFR) [3]	Schleisiek (SNR 300) [2]	JNES (Monju) [4]	This study (Monju)
Adventitious fuel pin failure (/ry)	35	No estimation (1)	4.4	2.4
Bulk boiling in one FSA (/ry)	−	6.5 × 10^−6	−	−
Fuel melting in a substantial part of the incident FSA (/ry)	1.9 × 10^−6	−	−	−
Damage propagation to the neighboring FSAs (/ry)	−	1.0 × 10^−7	−	1.7 × 10^−12
Untripped states (limited damage) (/ry)	2.0 × 10^−7	−	−	−
Damage propagation to more than 37 FSAs (/ry)	−	−	5.6 × 10^−8	−
Whole core accident (/ry)	1.9 × 10^−9	−	−	−

Table 11. CDF from FEFPA compared with those from ATWS and PLOHS.

		With scram
	Without	(failure of decay
	scram	heat removal)
CDF from FEFPA (/ry)	∼9.6 × 10^−13	∼7.3 × 10^−13
CDF from ATWS and PLOHS (/ry)	∼3 × 10^−8 in ATWS	∼5 × 10^−8 in PLOHS

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