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

Abstract

Experimental studies, deterministic approaches and probabilistic risk assessments (PRAs) on local fault (LF) propagation in sodium-cooled fast reactors (SFRs) have been performed in many countries because LFs have been historically considered as one of the possible causes of severe accidents. Adventitious-fuel-pin-failures (AFPFs) have been considered to be the most dominant initiators of LFs in these PRAs because of their high frequency of occurrence during reactor operation and possibility of fuel-element-failure-propagation (FEFP). A PRA on FEFP from AFPF (FEFPA) in the Japanese prototype SFR (Monju) was performed in this study based on the state-of-the-art knowledge, reflecting the most recent operation procedures under off-normal conditions. Frequency of occurrence of AFPF in SFRs which was the initiating event of the event tree in this PRA was updated using a variety of methods based on the above-mentioned latest review on experiences of this phenomenon. As a result, the frequency of occurrence of, and the core damage frequency (CDF) from, AFPF in Monju was significantly reduced to a negligible magnitude compared with those in the existing PRAs. It was, therefore concluded that the CDF of FEFPA in Monju could be comprised in that of anticipated transient without scram or protected loss of heat sink events from both the viewpoint of occurrence probability and consequences.

Keywords:

• SFR
• sodium cooled fast reactor
• Monju
• safety
• probabilistic risk assessments
• severe accident
• LF
• local subassembly fault

1. Introduction

Local fault (LF) has been considered as one of the possible causes of core-disruptive accidents or severe accidents in sodium-cooled fast reactors (SFRs) for a long time. Fuel-element-failure-propagation (FEFP) was considered to be of greater importance in safety evaluation of SFRs because fuel elements are generally densely arranged in the fuel subassemblies (FSAs) in this type of reactors and power densities are higher compared with those in light water reactors (LWRs) [1]. Therefore, probabilistic risk assessments (PRAs) [2–4], deterministic safety analyses and experimental studies on LF accidents have been performed in many countries historically.

Table 1 shows frequencies of initiating events for LFs in the British commercial demonstration fast reactor (CDFR) [3]. Among the different initiators, adventitious-fuel-pin-failure (AFPF) was the most dominant one because of its high frequency of occurrence during reactor operation and possibility of FEFP [5]. Therefore, FEFP from AFPF (FEFPA) is identified to be the main theme of event tree analysis in SFRs for assessing LFs from a probabilistic point of view. An event tree analysis of FEFPA in the Japanese prototype fast breeder reactor (Monju), in this context, was performed in this study based on the state-of-the-art knowledge of experimental and analytical studies [6], reflecting the most recent operation procedures under off-normal conditions.

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

Frequency of AFPF in SFRs was updated also based on an up-to-date review of open papers concerning experiences of this phenomenon, whereas the probabilities used in the existing PRAs [2–4] were based on the past experiences until 1985.

2. Updating of adventitious fuel pin failure frequency based on a state-of-the-art review of experiences in SFRs

Experiences of AFPFs in SFRs were thoroughly investigated based on a wide range of related open papers [6–15] in order to quantify the most up-to-date frequency of this phenomenon.

Table 2 shows numbers of failed fuel pins and related data in SFRs summarized by this investigation. Experiences in small-sized experimental reactors with the nominal full power of less than 100 MWth were excluded from this table. This considers the fact that these experiences in are to be used in the event tree analysis for a mid-sized prototype reactor, Monju, with the nominal full power of 714 MWth.

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).

Essential information was extracted in Table 3 from the data in Table 2, in order to quantify the probability of AFPF. Experimental fuel pins were basically excluded from this table since they were generally different from driver fuel pins in their specifications and irradiation conditions. Mean residence times (C_n) in Table 3 were estimated by the following equation based on the values of (l_n), (m_n), (o_n) and (p_n) in Table 2: (1) $$C_n=\frac{l_n{o}_n+m_n{p}_n}{o_n+p_n}÷365.24$$(1)

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

Numbers of fuel pins in equilibrium core (E_n) in Table 3 were also calculated by the following equation using the values of (o_n), (p_n) and (q_n) in Table 2: (2) $$E_n=(o_n+p_n)q_n$$(2)

Estimated frequency of fuel pin failure can be obtained by a variety of methods as follows. The results are then to be compared with each other and the largest one among all of them is to be employed in the event tree analysis in Chapter 3, for conservatism.

2.1. Method 1

The estimated frequency of AFPF in this method (P₁) is defined by the following equation based on the values of (A_n), (B_n) and (C_n) in Table 3. The fuel pin failure ratio as a simple arithmetic average is normalized to that per unit residence time, where the total number of irradiated fuel pins in each reactor is considered as a weighting coefficient: (3) $$P_1=\frac{\sum B_n}{\sum A_n}÷\frac{\sum A_n{C}_n}{\sum A_n}$$(3) where A_n is the total number of irradiated (driver) fuel pins in a reactor n (−), B_n is the total number of failed (driver) fuel pins in a reactor n (−) and C_n is the mean residence time of fuel pins in a reactor n (years).

The frequency of occurrence of AFPF in Monju by this method (P_M1) can be calculated according to the following equation: (4) $$P_{M1}=P_1\times N_{\mathrm{SA}}\times N_{\mathrm{pin}}$$(4) where the number of FSAs in the core (N_SA) is 198, and the number of fuel pins in one FSA (N_Pin) is 169, respectively [16].

2.2. Method 2

This method defines the estimated frequency (P₂) by the following equation using the values of (B_n), (D_n) and (E_n) in Table 3. The frequency of AFPF for each reactor is defined by using a product of the number of fuel pins in equilibrium core and cumulative equivalent full power years as the denominator, instead of the total number of irradiated fuel pins and mean residence time in method 1, considering the substantial irradiation duration of the pins. The overall frequency is calculated as a weighted average of the frequencies for each reactor using the same product as a weighting coefficient: (5) $$P_2=\frac{\sum \left(\frac{B_n}{D_n{E}_n}\times D_n{E}_n\right)}{\sum D_n{E}_n}$$(5) where D_n is the cumulative equivalent full power years in a reactor n (years) and E_n is the number of fuel pins in equilibrium core in a reactor n (−).

The frequency in Monju (P_M2) can be calculated using the following equation: (6) $$P_{M2}=P_2\times N_{\mathrm{SA}}\times N_{\mathrm{pin}}\times {\mathrm{LF}}_m$$(6)

The mean load factor of Monju (LF_m) is conservatively assumed to be 0.71 in this study based on the presumption of 148 days of operation in a cycle [16] and 60 days of interval for periodic inspection and refueling as an average.

2.3. Method 3

The estimated frequency in this method (P₃) is normalized to that per unit burnup, in addition to method 2, using the average achieved burnups of irradiated fuel pins. The frequency is then defined by the following equation based on the values of (B_n), (D_n), (E_n) and (F_n) in Table 3: (7) $$P_3=\frac{\sum \left(\frac{B_n}{D_n{E}_n}\times D_n{E}_n\right)}{\sum D_n{E}_n{F}_n}$$(7) where F_n is the average achieved burnup in a reactor n (GWd/t).

The frequency in Monju (P_M3) is given by the following equation: (8) $$P_{M3}=P_3\times N_{\mathrm{SA}}\times N_{\mathrm{pin}}\times {\mathrm{LF}}_m\times {\mathrm{BU}}_m$$(8)

The average burnup of Monju (BU_m) to be achieved in the future high-burnup core is 80 GWd/t [16] and this value is employed in this study.

2.4. Method 4

This method defines the estimated frequency (P₄) as a reactor-power-dependent quantity, in addition to method 2, using the nominal full power of each reactor. The frequency is given by the following equation using the values of (B_n), (D_n), (E_n) and (G_n) in Table 3: (9) $$P_4=\frac{\sum \left(\frac{B_n}{D_n{E}_n}\times D_n{E}_n\right)}{\sum D_n{E}_n{G}_n}$$(9) where G_n is the nominal full power in a reactor n (MWth).

The frequency in Monju (P_M4) can be calculated using the following equation: (10) $$P_{M4}=P_4\times N_{\mathrm{SA}}\times N_{\mathrm{pin}}\times {\mathrm{LF}}_m\times {\mathrm{NFP}}_m$$(10) where the nominal full power of Monju (NFP_m) is 714 MWth [16].

Table 4 exhibits the calculated frequencies of fuel pin failure by each method. The frequency of occurrence of AFPF in Monju by method 1 is to be conservatively employed in the event tree analysis to be mentioned below because the frequency is the largest among all the methods.

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

3. Event tree analysis for failure propagation from adventitious fuel pin failure

Damage propagation from fuel pin failure to be evolved to whole core damage prevented by an automatic reactor trip triggered by delayed neutron detectors (DNDs) was considered to be the main sequence of events in the existing PRAs [2–4]. Not only automatic rector trip by DNDs but also multiple reactor shutdown measures by various kinds of detectors such as precipitators or NaI detectors in cover gas (CG) method are equipped in Monju as shown in Figure 1. The most recent schematic of operation procedures after a fuel pin failure, and alert and reactor trip levels of detectors against fuel pin failures are shown in Figure 2 and Table 5, respectively.

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.

The following sequence of events to be evolved to whole core damage is then conceivable [17], based on this information, from phenomenological considerations on reactor shutdown operation procedures corresponding to each alert or reactor trip level of detectors mentioned above:

1. initiating event (AFPF),

2. cladding defect size over alert threshold of DNDs and precipitators,

3. failure of manual reactor shutdown by the alert from DNDs and precipitators,

4. pin failure propagation to the adjacent 6 pins during the period until refueling,

5. failure of normal reactor shutdown by the second alert from precipitators,

6. failure of normal rector shutdown by the alert from NaI detectors,

7. cladding defect size over reactor trip threshold of DNDs,

8. failure of automatic reactor shutdown by the trip signal from DNDs,

9. damage propagation over alert threshold of thermo couples (TCs) at the outlet of FSA,

10. failure of manual reactor shutdown by the alert from TCs at the outlet of FSA,

11. failure of decay heat removal after reactor shutdown and

12. damage propagation to the neighboring FSAs.

It should be noted that damaged FSAs will be removed after reactor shutdown and replaced with fresh ones.

The event tree reflecting the operation procedures mentioned above, using the latest knowledge mentioned above and in Chapter 2, is presented in Figure 3. The salient features of this event tree compared with the existing PRAs are

Figure 3. Main event tree of FEFPA.

1. more multiply-layered and various measures are provided for failed fuel pin detection and reactor shutdown,

2. more detailed event tree headings are explored and identified,

3. a possibility is included of fuel pin failures not to evolve to detectable scale even at the end of cycle,

4. removal of damaged FSAs is considered by refueling after reactor shutdown owing to the multiple detection systems for fuel pin failure and

5. a possibility is considered of decay heat removal failure after reactor shutdown even under coolable geometry.

Quantification of each branching probability is to be described below.

3.1. Phenomenological headings (headings (2), (4), (7), (9), (11) and (12))

The branching probabilities for phenomenological headings were quantified through engineering judgments based on the state-of-the-art knowledge on experiments and analyses [17]. The way of quantification was standardized as shown in Table 6 in order to keep this event tree analysis to be self-consistent.

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.

Following four possible mechanisms of FEFPA were identified in the text book on FBRs [5] and a recent paper [17]. Such possibilities have been one of the major concerns in SFR safety assessments for a long time. The recent deterministic assessments and experimental studies, however, revealed that FEFPA including thermal, mechanical and chemical propagation mechanisms was highly unlikely [5, 17–19].

1. Thermal transient due to FP gas impingement from adjacent failed fuel pin [5].

2. Mechanical load due to FP gas impingement from adjacent failed fuel pin [5].

3. Solid fuel release into the coolant channel due to sodium boiling cycle erosion [17].

4. Fuel melting due to fuel-sodium reaction product formation and subsequent molten fuel ejection into the coolant channel [17].

Table 7 shows quantified branching probabilities of each phenomenological heading on the basis of engineering judgments [17,20,21].

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

3.2. Fault tree analysis for other headings (headings (3), (5), (6), (8), and (10))

The other headings (3), (5), (6), (8), and (10) in Figure 3 are defined as a functional failure of the frontline systems (e.g., reactor shutdown system) which are required to prevent core damage against the initiating event. Correlation due to functional dependency exists among these frontline systems because they share common sub-systems (e.g., common detectors) or common support systems (e.g., common power supply system) with each other. These shared systems, therefore, were identified at first as shown in Table 8 in order to consider explicitly this correlation in quantifying the branching probabilities. Since these shared systems can fail independently from each other, combinations of success and/or failure of the shared systems were then developed in a supporting event tree. On one hand, a failure in these shared systems can cause dependent and correlated common mode failures in some of the frontline systems: e.g., failure in the heading “X” shown in Table 8 can cause failure in all the headings listed in Table 9. This relationship is summarized in Table 9 as prerequisites for quantification of the branching probability in the main event tree, and this is taken into account to combine the main and supporting event trees according to the event tree linking (ETL) method embedded in the RISKMAN® code.

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.

Details of the prerequisites in Table 9 are as follows for quantification of the branching probability of heading (3), for example. This heading (3) will be completely and dependently in failure, if the heading “X”, in Table 8, fails. Its failure probability is, therefore, 1.0 in this case. In a similar way, its failure probability is also 1.0, in case either one of the headings “I”, “II”, “III”, “IV”, “V” or “IX” fails. Furthermore, the same will be applied when assuming simultaneous failures of either two of the headings “VI” and “VII”, “VI” and “VIII” or “VII” and “VIII”. The remained situations can be classified into two cases: one is a combination of the simultaneous successes in the headings “I”, “II”, “III”, “IV”, “V”, “VI”, “IX” and “X”, and a success in either one of the heading “VII” or “VIII”, and the other is a combination of the simultaneous successes in the headings “I”, “II”, “III”, “IV”, “V”, “VII”, “VIII”, “IX” and “X”, and a failure in the heading “VI”. The failure probabilities of heading (3) were then evaluated to be 4.26 × 10⁻⁴ and 4.27 × 10⁻⁴, respectively, corresponding to the situations mentioned above. These entire results are briefly summarized as shown in Table 9.

A fault tree analysis was performed in addition to the consideration in Section 3.1, in order to obtain the branching probability in these event trees.

The common systems listed in Table 8 are kept in a standby state at a normal reactor operation. The failure probability of these systems per actuation demand was evaluated by using the standard PRA method [22]. The failure rate of the components specific to SFRs was estimated by using the CORDS database, which contains the component reliability data obtained from Japanese SFRs, “Monju” and “Joyo”, and US ones, “EBR-II” and “FFTF” [23]. In particular, the probability of failure in control rod insertion was estimated based on the data which was obtained in the control rod insertion tests using the control rod drive mechanism mockup test facility. The failure rate of the other components was estimated from the component reliability data of Japanese LWRs, compiled as the Nuclear Information Archives [24]. The conditional probability of common cause failure was then set by referring to the previous studies on this issue [25,26].

This fault tree analysis also includes the quantification of human error probability on the basis of allowable time estimation for operators. These probabilities during the allowable time are estimated based on time-reliability curves derived by the technique for human error rate prediction [27]. The results of this fault tree analysis are shown in Tables 8 and 9, and they were applied to calculate the occurrence probability of accident sequences leading to core damage using the ETL method.

4. Results and discussions

Table 10 presents the results of event tree analysis for FEFPA compared with those in the existing PRAs. The frequency of damage propagation to the neighboring FSAs was estimated to be 1.7 × 10⁻¹²/ry. It should be noted that the probability of whole core damage is extremely low because there are following multiply-layered detection and reactor shutdown systems against events subsequent to damage propagation mentioned above:

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	−	−	−

1. manual reactor shutdown owing to an alert from primary argon gas monitor and

2. automatic reactor shutdown triggered by a high-neutron flux level.

The frequency of AFPF in this study is much lower than that in the existing PRAs due to the following reasons:

1. the frequency of AFPF was derived from experiences not only before 1985 which were used in the existing PRAs but also after 1985 and

2. AFPF experiences in small-sized experimental reactors were excluded for applying to a mid-sized prototype reactor, Monju, because the cladding materials of these reactors were under development phase, not in practical use.

The frequency of damage propagation to the neighboring FSAs was also much lower than that in the existing PRAs because of the following reasons:

1. frequency of AFPF itself was lower in this study,

2. more multiply-layered and various detection and reactor shutdown systems were taken into account and

3. frequency of damage propagation within an FSA was reduced reflecting the latest experimental and analytical knowledge [17].

Table 11 shows the CDF of anticipated transient without scram (ATWS) and protected loss of heat sink (PLOHS) events in Monju [28].

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

The probability of damage propagation to the neighboring FSAs with or without scram is lower than the CDFs for PLOHS and ATWS events. Furthermore, the consequence of whole core accident induced by AFPF with or without scram is not greater than that of these events where almost all the FSAs in the core will be damaged. Therefore, the CDF induced by FEFPA can be comprised in either of these events from both the viewpoint of occurrence probability and consequences.

5. Conclusions

An event tree analysis on damage propagation from adventitious fuel pin failure in Monju was performed using the latest knowledge on experimental and analytical studies, reflecting the most recent operation manuals under off-normal conditions. As a result, the frequency of damage propagation to the neighboring FSAs was quantified to be 1.7 × 10⁻¹²/ry. The probability of whole core damage is evaluated to be much lower than this value due to multiply-layered detection and reactor shutdown systems against events subsequent to damage propagation mentioned above. It was concluded that the CDF of this phenomenon in Monju can be comprised in that of ATWS or PLOHS events from both the viewpoint of occurrence probability and consequences.

Nomenclature

An:	=	Total number of irradiated (driver) fuel pins in a reactor n (−)
Bn:	=	Total number of failed (driver) fuel pins in a reactor n (−)
BUm:	=	Average burnup in Monju (GWd/t)
Cn:	=	Mean residence time of fuel pins in a reactor n (years)
Dn:	=	Cumulative equivalent full power years in a reactor n (years)
En:	=	Number of fuel pins in equilibrium core in a reactor n (−)
Fn:	=	Average achieved burnup in a reactor n (GWd/t)
Gn:	=	Nominal full power in a reactor n (MWth)
LFm:	=	Mean load factor of Monju (−)
ln:	=	Mean residence time for inner core subassemblies in a reactor n (days)
mn:	=	Mean residence time for outer core subassemblies in a reactor n (days)
NSA:	=	Number of FSAs in the core (−)
Npin:	=	Number of fuel pins in one FSA (−)
NFPm:	=	Nominal full power of Monju (MWth)
on:	=	Number of inner core subassemblies in equilibrium core in a reactor n (−)
P1:	=	Frequency of AFPF in method 1 (/y/pin)
P2:	=	Frequency of AFPF in method 2 (/EFPY/pin)
P3:	=	Frequency of AFPF in method 3 (/EFPY/pin/(GWd/t))
P4:	=	Frequency of AFPF in method 4 (/EFPY/pin/MWth)
PM1:	=	Frequency of AFPF in Monju by method 1 (/ry)
PM2:	=	Frequency of AFPF in Monju by method 2 (/ry)
PM3:	=	Frequency of AFPF in Monju by method 3 (/ry)
PM4:	=	Frequency of AFPF in Monju by method 4 (/ry)
pn:	=	Number of outer core subassemblies in equilibrium core in a reactor n (−)
qn:	=	Number of fuel pins per subassembly in a reactor n (−)

Acknowledgements

The authors are grateful to H. Nishi, M. Sotsu, Y. Morohashi and S. Suzuki of JAEA for their useful suggestions and comments on this study.