E-Journal of Advanced Maintenance Vol. 6 (2014) 57-70
Japan Society of Maintenology

Plant Transients under Small Abnormalities of FBR “Monju” Calculated
by a Plant System CodeHiroyasu MOCHIZUKI1,*
1

Research Institute of Nuclear Engineering, University of Fukui, 1-2-4 Kanawa-cho, Tsuruga, Fukui
914-0055, Japan
ABSTRACTThe objectives of the present study are to analyze plant transients caused by small abnormalities and to findplant parameters by which operators can recognize these small abnormalities. In order to evaluate the planttransient during an abnormal situation in the water system using the plant system code NETFLOW++, theturbine and feedwater (FW) systems should be analyzed with good precision. The code is validated using themeasured data at “Monju”. Several abnormalities in the water system are candidates of the present study, e.g.,
FW control valve degradation, FW pump degradation, heat transfer degradation due to fouling on heat transfer
tubes of the evaporator, loss-of-feedwater-heating, etc. All major components in the tertiary system areincluded in the calculation model such as the steam generators, the high-pressure turbine, the deaerator, the FW
pump, the FW heaters, the FW control valves, the steam control valve, extraction lines and drainpipes. In caseof a malfunction of a FW control valve resulting in low flow rate, a large temperature increase at the outlet ofthe evaporator is observed. On the other hand, a temperature decrease at the outlet of the evaporator occurs ifheat transfer tubes in the evaporator have fouling. As a result of the calculations, it was determined thattemperature at the outlet of the evaporator is a good indicator to detect abnormal situations.
KEYWORDS

ARTICLE INFORMATION

Monju, FBR, Plant system analysis, Water system, Slight abnormality,
Abnormality indicators

Article history:
Received 15 January 2014
Accepted 20 October 2014

1.

Introduction

When a large transient like a main pump trip occurs in a Fast Breeder Reactor (FBR), the reactor
should be scrammed within a couple of seconds. However, if the pump undergoes a small
degradation, plant parameters will change gradually and may reach the scram level in some cases.
The objectives of the present study are to analyze plant transients caused by small abnormalities andto deliver the results to the group members who are studying the detection of the plant abnormality.
The other objective of the present study is to find plant parameters which operators can use torecognize these abnormalities. In case of the FBR “Monju”, the fluctuation of the process data in the
primary system at 45% thermal power (40% electric power) were studied by Udagawa et al. [1].
However, since the operation analyzed in reference [1] was steady state, meaningful results
concerning off-normal situations were not obtained. Santhosh et al. [2] studied process data in orderto develop a system that would assist the operator to identify abnormal transients at the earliest stagesof their development. They focused on a large break LOCA. The present study is focusing on
abnormal predictors which operators can use to mitigate the conditions.
There are few studies related to the water loop for FBRs. Therefore, the present paper focuses
mainly on the abnormalities in the water loop consisting of turbine and feedwater (FW) systems. In
order to evaluate the plant transient under an abnormal transient in the water system using a plantsystem code, the turbine and FW systems should be analyzed with good precision. Mochizuki [3]developed the system code NETFLOW++ which can be applied to the above situation and Mochizuki
and Tsukamoto [4] analyzed the turbine and FW systems of the “Fugen” reactor which was a
prototype heavy-water-moderated, light-water-cooled pressure-tube-type reactor in Japan. The
following abnormalities in the water system are candidates of the present study: 1) FW control valve*

Corresponding author, E-mail: mochizki@u-fukui.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

57

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Codedegradation, 2) FW pump degradation, 3) steam control valve degradation, 4) heat transfer
degradation due to fouling on heat transfer tubes of the evaporator, 5) degradation of FW heating.
Relating the sodium system, a main pump abnormality is simulated.

2.

Calculation Code and Model

2.1

Brief code description

The system analysis 1D code NETFLOW++ (Mochizuki [3]) can calculate single-phase andtwo-phase flows of water. For liquid sodium, one-dimensional single-phase incompressible flow isassumed. The followings are momentum and continuity equations for flow segment i. The
following is the brief introduction of the basic equations to calculate the flow in the plant system.
Please refer to the above paper in order to understand the code precisely.
2.1.1

Momentum equation

Because of non-compressible flow, the momentum equation is simplified as follows.

dWi
ll W W= ( pu ,i − pd ,i ) −  ζ i + i i  i i2 − ρ i gH i + ρ i gH P
dt
Dei  2 ρ i Ai


Li

(1),

If there is no pump in the interested segment, the last term should be omitted. The pumpcharacteristics such as rotation speed, head and flow rate under steady state and transient conditions
are solved by a pump kinetic equation with inertia, the torque of the motor and frictional torque using
a characteristic curve between flow rate and head and an efficiency curve.
2.1.2

Continuity equation

Mass flow rate should be preserved at each main joint (junction) j.

∑W = 0

(2),

i

i∈C j

i ∈ C j : a set of flow passage i linked to junction j

2.1.3

Energy equation of the secondary fluid in heat exchanger∂Ts Cs∂T∂ 2T
K+ Ws s = s (Tt − Ts ) + kl 2s∂t As′∂z∂zAs′

ρ s Cs(3),

In case of flow in a pipe, this equation is neglected.
2.1.4

ρt Ct

Energy equation of heat transfer tube

∂Tt K pK(=
Tp − Tt ) + s (Ts − Tt )
At′
At′
∂t

(4),

pN tube

(5),

Kp =

1
1  2d p 
1
+
ln
+


d p h p 2kt  d p + d s  d p h f , p

58

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System CodepN tube

Ks =

(6),

1
1  d p + ds 
1
 +
ln
+
d s hs 2kt  2d s  d s h f ,sAs′ = As secθ t
At′ = At secθ t(7),

Temperatures are calculated at the half thickness of the shell or pipe. In case of flow in a pipe, theabove equation should be transformed to the following equation taking into account the heat loss fromthe pipe.

ρt Ct∂Tt K p(Tp − Tt ) − q′
=
∂t
At
At

(8),

q′ = U Loss (Tt − Ta )(9).

The second term of the right hand side represents heat loss from the pipe to the environment.
The equation for the shell of the heat exchanger is the same. An overall heat transfer coefficient
ULoss should be calculated from the pipe to the environment through insulator in the similar way as Eq.
(5).
2.1.5

Energy equation of the primary fluidρ pC p

∂Tp
∂t

+

Cp
Ap

Wp

∂Tp
∂z

=

Kp
Ap

2

(T − T ) + k ∂ T
t

p

l

∂z

p
2

(10),

The second term expresses heat conduction in flow direction (similar to Eq. (3)). Theseequations are discretized using the implicit method. Models in the code are verified using test resultsof mock-ups of a boiling water reactor. Thermal-hydraulics and neutronics of the coupled system of
the core, heat transport systems and the turbine system can be calculated by this code. The models
in the code have been developed further in order to simulate characteristics specific to liquid metal
cooled fast reactors.
These models include inter-subassembly heat transfer that becomes
non-negligible under natural circulation conditions, the heat transfer and heat transfer models for air
coolers, the heat transfer model for the IHX, the model of the upper plenum, etc.
2.2

Calculation Model of “Monju”

The individual models incorporated in the NETFLOW++ code have been verified through theexperimental results and validated using data from nuclear plants like “Joyo”, “Monju”, “Phenix” and“EBR-II”. Therefore, it is confirmed that this code can be applied to both the loop-type andpool-type FBRs. The latest validation has been conducted through the IAEA benchmark (Mochizuki
et al. [5]). In the present study, the heat transport systems of the “Monju” prototype FBR aremodelled and analyzed. A schematic diagram of the reactor heat transport systems is
illustrated in Fig. 1. It is a loop type reactor which consists of the primary, secondary andtertiary systems. It has three loops in the primary and secondary heat transport systems(HTSs), respectively. Heat generated in the reactor core is transferred to the secondary HTS
via three intermediate heat exchangers (IHXs). Each secondary HTS has a steam generator
consisting of an evaporator (EV) and a super-heater (SH). Hot sodium from the core enters
59

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Codeinto the SH, then flows into the EV. The tertiary system consists of a high-pressure turbine,
low-pressure turbines, a condenser, a series of feedwater heaters (FWHs), a deaerator, FW
pumps, flow control valves, etc. FW is heated by a bank of FW heaters, controlled by theflow rate control valve, and is supplied to the EV, then flows into the SH. The dryout ofwater occurs near the outlet of the EV. A steam separator is installed at the outlet of the EV
to prevent liquid droplets from flowing into the SH. Dried steam at around 13MPa is
supplied to the high pressure turbine through a steam control valve. Exhausted low-pressure
steam is supplied to the low pressure turbines and condensed by the condenser situatedbeneath the low pressure turbines.

Super-heater(SH)
TurbinePrimary pump

Air cooler

Generator

Condenser
Secondarypump
Evaporator
(EV)

Core

Seawaterpump
Feedwater
pump

IHX
Secondary HTS

Primary heat transport system

Turbine andfeedwater system

Fig. 1. Schematic diagram of heat transport systems of “Monju” FBR reactor

In order to analyze the turbine and FW systems together with the primary and secondary HTSs,
the calculation models illustrated in Fig. 2 and Fig. 3 are used. Figure 2 shows the whole plantmodel and Fig. 3 shows the detailed model of the turbine and FW systems. Although condensed
water is heated by three low-pressure FWHs, these are omitted in the main analysis because the effecton the FW temperature by these heaters is small. Thus, the flow rate and temperature at the inlet ofthe deaerator are provided as constant boundary conditions. The outlet pressure at the high-pressure
turbine is taken as a boundary condition. These simplifications are justified by taking into accountthe low-pressure turbine and a bank of the low-pressure FWHs. The calculation model connecting
the sodium systems and whole water systems is unusual and challengeable one.
A number in circle in Fig. 2 indicates “joint” where a flow path may branch. The joint has novolume. Piping, indicated as a line called as a “link” in the model, connects these joints. The linkhas a cross-section and length which can be divided into several nodes. Small circles indicate
sub-joints, where the diameter of the piping may change. The reactor core is modelled with ten
different hydraulic channels and a bypass channel.
The turbine and FW systems are modelled in detail as shown in Fig. 3. All major components
in the systems are included in the model such as the steam generators consisting of the EVs and SHs,
the high-pressure turbine, the deaerator, the FW pump, the FWHs, the FW control valves, the steam
control valve, extraction lines and drainpipes. The shell-side of the FWH is divided into three
regions in order to have stable calculation. Nevertheless, the calculation in the water system issometimes unstable dependent on the input conditions because of condensation on the shell-side andflashing in drainpipes connecting the higher and lower pressure FWHs. When the low-pressure
system is connected, the calculation is much difficult compared to the case of high-pressurecomponents because the pressure in the drainpipe of the FWH #1 is only 0.004 MPa. The pressure
range in the water system is enormous. Therefore, the low-pressure side is neglected in the most
calculations and constant FW flow rate from the low-pressure FWH is assumed. The pressure
boundary condition is provided at the exhaust line to the low pressure turbines.

60

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Code
[37]

15
[20]

[36]

14

B-loop

13

[38]
[48]

16

16

18

[19]

Link 1-Link 6: 1st to 6th layer (Inner driver)
Link 7: 7th & 8th layer (Outer driver)A-loop
Link 8: 9th to 11th layer (Blanket)
Link 9: Center CR
Air cooler
Link 10: CRs[14]
Link 11: Bypass
-1

-3

14

[46]
6 1
[30]

1

3

18
[40]
[39]
17

[21]

[42]
20

21
[25]

[41]

22

19

to
turbine

15

[17]

[28]

12
[35]

[8]
[9] [10]High[1]～[7]４pressure2[12] Low-pressure
plenum[34]
11

to B-loop

plenumSuperheater

Evaporator

[16]

IHX

From B&C loops

14

Low-pressure
side

16

to C-loop

[24]
[49]

16

[47] 10

Pump
[13]

Pump

[43]

[15]

[33]
-2

[11]

C-loop

19

9

8

[31]

Upper plenum

[29]
5

[18]

[22]

[32]
7

Low-pressure turbine

[23]

-4

14

1
[27]

24

13

23

[26]

-1

Deaerator

[45]

[44]

#5

Condenser#4#3High-pressure f eedwater heaters

#1

#2

11

2

25

20

Feedwaterpump

30

Low-pressure f eedwater heaters

Fig. 2. Whole plant calculation model of the “Monju” reactor system
Low-pressure side

19

Steam control valve
High-pressure 17 9 10 11 12
turbine20 9 10 11
Loss

Sodiumflow

16

Low-pressure
turbine

12

35 24
42

Super-heater

29

43

34 35
44

45

46
21
25

23

13

Deaerator

14

Flow
control
valve

15 17

14

#5

Turbine for

6

3

6

7

8

2

3

3

2

2

32 feedwater

27

pump

5

#4

#3

16
4

28

3

4

5 1

2

3

3

8

1

2
Feedwater pump

3

37
41

#2

29

3

20

#1
38

34

33

21 22 23 26

High-pressure feedwater heaters

-1

49

48

13

Evaporator

24

Condenser

47

36 37

19 18 15

22

15

18

26

27 28 31

2

3

30

3

25

39

31

32 33 36

2

3

35

3

30
40

Low-pressure feedwater heaters

Fig. 3. Detailed model of turbine and FW systems

3.

Validation of the Initial Conditions

In order to investigate the small disturbances in the FBR plant due to a small abnormality such as
the FW control valve degradation, the initial conditions of the plant should be calculated with goodprecision. The heat balance confirmation test was conducted at 45% thermal power (40% electrical
power) of “Monju” and the result was reported by Miyakawa et al. [6]. Although 40 % power is
described in their paper, that value is electrical power and electrical power does not make sense in theplant analysis. Therefore the above expression in thermal power is used in the present paper. The
operation mode of the FW pump is switched from an electric pump to a turbine driven pump at 45%

61

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Codethermal power. The test conditions are calculated by the NETFLOW++ code over a period of
20,000 seconds to get a good steady state condition. The calculated results are compared with thetest results in Table 1. Since all water is evaporated in the heat transfer tubes near the outlet of theEV, i.e., dryout, the outlet temperature is higher than the saturation temperature. The outlet
temperature cannot be predicted well if the dryout position is not predicted well. Other than thistemperature, the super-heater outlet temperature, are used as indicators of the scram inter-locks.
Therefore, the absolute values of these temperatures are important parameters. Major plantparameters are calculated within 2.25% error. The error is calculated as the fractional difference
between calculated and measured data. In the case of temperature, the error is dependent on unit
such as Celsius and Kelvin. Therefore, the value of the error is shown as a subtracted value from themelting point in order to be independent from the unit. Since “Monju” has never been operated atfull power condition, there is no measurement data for plant parameters at full power. The
calculated conditions are compared with the design values as shown in Table 2. Good agreement isalso obtained for the 100% full power condition. Even in the case of a large transient such as theturbine trip event from 45% thermal power, the major parameters of the plant could be evaluated withgood precision [3]. Therefore, it is concluded that the small disturbances caused by the various
abnormalities can be calculated with good accuracy by the NETFLOW++ code.
Table 1 Comparison of plant parameters between measured data at “Monju” and calculation at 45%
thermal power
Item
Measured data
Calculated result
Error* (%)
Reactor vessel inlet temperature (ºC)
364
372.2
3.11
Reactor vessel outlet temperature (ºC)
486
491.3
1.37
IHX primary outlet temperature (ºC)
367
372.2
1.95
IHX secondary inlet temperature (ºC)
282
278.8
-1.76
IHX secondary outlet temperature (ºC)
486
491.0
1.29
B-loop primary flow rate (kg/s)
702.4
706.4
0.569
B-loop secondary flow rate (kg/s)
398.6
391.5
-1.53
Feedwater (FW) flow rate (kg/s)
43.33
42.20
-2.58
FW temperature (ºC)
196.9
194.2
-1.32
Evaporator outlet steam temperature (ºC)
370
365.9
-1.11
Super-heater outlet steam temperature (ºC)
483.1
486.9
0.787
*Error= (Calculation result - Measured data)/(Measured data) for flow rate, andError= (Calculation result - measured data)/(Measured data - melting point) for temperature
Table 2 Comparison of plant parameters between design data of “Monju” and calculation at 100%
thermal power
Item
Design data
Calculated result
Error* (%)
Reactor vessel inlet temperature (ºC)
397
391.4
-1.89
Reactor vessel outlet temperature (ºC)
529
523.0
-1.40
IHX primary outlet temperature (ºC)
397
391.4
-1.89
IHX secondary inlet temperature (ºC)
325
328.4
1.51
IHX secondary outlet temperature (ºC)
505
508.6
0.88
Primary loop flow rate (kg/s/loop)
1422.21425.80.25
Secondary loop flow rate (kg/s/loop)
1030.61035.1
0.44
FW flow rate (kg/s)
105.6
106.7
1.04
FW temperature (ºC)
240
238.2
-0.75
Evaporator outlet steam temperature (ºC)
369
368.8
-0.05
Super-heater outlet steam temperature (ºC)
487
485.0
-0.41
*Error= (Calculated result - Design data)/(Design data) for flow rate, andError= (Calculation result - Design data)/(Design data - melting point) for temperature

4.

Simulation

4.1

Decrease of FW flow rate
The plant is scrammed if the FW flow rate decreases to 20% of rated value. However, the62

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Codetemperatures around the steam generators may rise up to the trip level even if the flow rate is only
slightly degraded. Temperatures and FW flow rate for plant trip are listed in Table 3. Two directcauses for a decrease of the FW flow rate are discussed in the present chapter, although there arepossible causes, e.g., malfunction of a FW control valve, degradation of a FW pump, a blockage offlow passage by a loose part, etc.
Regarding the FW system, a FW control system is provided in order to keep the EV outlet
temperature at the set point temperature. This system controls the FW control valve directly under
the normal conditions. The other controlling is to keep the pressure difference of the FW control
valve at the set point pressure by changing the speed of revolution of the FW pump. However,
above mentioned control system does not work properly for the abnormalities of FW system.
Table 3
Items
Feed water (FW) flow rate
FW temperature
Evaporator outlet steam temperature
Evaporator outlet sodium temperature
Super-heater outlet sodium temperature

Relevant plant trip conditions
Conditions
Less than 20% of the rated condition
under
the
evaporator
steam
temperature more than 325 ºC
Less than 153 ºC
Higher than 417 ºC
Higher than 347 ºC
Higher than 497 ºC

Trip activation
Secondary pump trip
FW pump trip
Secondary pump trip
Scram
Secondary pump trip

4.1.1. Malfunction of the FW control valve
What will happen when the FW control valve in the A-loop undergoes a small malfunction?
One can easily imagine that the location where dryout occurs in the heat transfer tubes of the EV
moves upstream. The assumption is that the FW flow rate decreases to 90% of the rated value at
t=1,000 seconds and the plant is operating at 45% thermal power. The effect on important plantparameters on the water side and the sodium side are shown in Fig. 4. The system pressure of thesteam generator at the initial conditions is approximately 13MPa, and the saturation temperature is
330 ºC. Since two-phase flow causes dryout and is super-heated near the outlet of the EV, the steam
temperature at the outlet of the EV increases from 366 ºC of the initial temperature to the trip
temperature of the secondary main pump at 417ºC within 1,100 seconds. In the present study, thecalculation is continued without reactor trip. This time domain is shown as a shadowed area.
During this transient, the steam pressure at the outlet of the SH is almost constant. Similar trends are
obtained for the operation at 100 % thermal power. Although the sodium temperature at the outlet of
the SH increases due to a decrease of heat transfer from sodium to steam in the SH, sodium
temperatures at the SH outlet and the EV outlet do not reach the trip levels. It is concluded that the
EV outlet steam temperature is a good indicator to detect long-term flow degradation due tomalfunction of the FW control valve.

417 C trip temp. at 2100 sec.
400

100
SH outlet
EV-A outlet
EV-B outlet
EV-C outlet
Feedwater

300

200

100

50

A-loop flowrate
B-loop flowrate
SH outlet pressure

Degradation of feedwater
control valve A
0

500

1000

1500
Time (sec)

2000

2500

450
SH-A outlet
SH-B outlet
SH-C outlet
EV-A outlet
EV-B outlet
EV-C outlet

400
350
300

Trip level of evaporator
outlet sodium temperature

250
200

0
3000

Trip level of super-heater
outlet sodium temperature

500

o

o

550
Sodium temperature ( C)

Water temperature (oC)

500

0

600

150
Feedwater flow rate (kg/s/loop), Pressure (bar)

600

0

500

1000

1500

2000

2500

3000

Time (sec)Fig. 4. Evolution of plant parameters in the tertiary (left) and the secondary (right) heat transport system
during an A-loop FW control valve malfunction at 45% thermal power

63

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Code

4.1.2. Degradation of the FW pump

Water temperature (oC)

500

400

100
417oC trip temp. at 1373 sec.
SH outlet
EV outlet
Feedwater

300

200

50

100

0

Feedwater flowrate
SH outlet pressure

Degradation of
feedwater pump
0

500

1000

1500
Time (sec)

2000

2500

Upper plenum
IHX secondary outlet
SH outlet
IHX primary outlet
EV outlet

600
550
500

Trip level of super-heater
outlet sodium temperatureo150

Sodium temperature ( C)600

Feedwater flow rate (kg/s/loop), Pressure (bar)It is assumed that the plant operates at 45% thermal power. At t=1,000 s the pump head of theFW pump is degraded by 10% in a stepwise manner. This causes a reduction of the FW pump flow
rate. The flow rates in the three loops decrease by approximately 8% as shown in Fig. 5. All steam
temperatures at the outlet of the EV increase and reach the trip temperature of 417ºC at t=1373 s.
The steam pressure at the outlet of the SH decreases at the same time. In case of the periodic FW
flow rate fluctuation, the temperature at the EV outlet does not change. This is confirmed by the test
and calculation. Although the sodium temperature at the SH outlet increases, the temperature does
not reach the trip level before the reactor trip by the steam temperature at the EV outlet. It is
concluded that the EV steam and SH sodium outlet temperatures and the system pressure are good
indicators to detect long-term flow degradation due to degradation of the FW pump.
Similar trends are found in the case of the 100% rated power condition. The result is illustrated
in Fig. 6. The temperature at the outlet of the EV reaches the trip temperature at around t=1900 s.
As a result of these analyses, it is obvious that a small degradation of the FW pump causes plant trip
in a relatively short period. It will be difficult for operators to avoid this trip.

450
400
350

250
200

0
3000

Trip level of evaporator
outlet sodium temperature

300

0

500

1000

1500

2000

2500

3000

Time (sec)Fig. 5. Evolution of plant parameters in the tertiary (left) and sodium (right) heat transport system
during a FW pump degradation at 45% thermal power
150
417oC trip temp. at 1900 sec.

Water temperature (oC)

500

100

400
Feedwater flowrate
SH outlet pressure

300

50

200
Degradation of feedwater pump
SH outlet
EV outlet
Feedwater

100

0

0

500

1000

1500
Time (sec)

2000

2500

Feedwater flow rate (kg/s/loop), Pressure (bar)

600

0
3000

Fig. 6. Evolution of plant parameters in the tertiary heat transport system during a FW pumpdegradation at 100% thermal power

4.2

Pressure increase due to steam control valve malfunction

The plant behavior is investigated when the steam control valve causes malfunction resulting inthe system pressure increase. The FW control system to keep the EV outlet temperature is assumed
to be out of order. Figure 7 shows the temperature behavior in the steam generator and the system

64

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Code

Water temperature (oC)

500

400

100
417oC trip temp. at 1607 sec.

300

SH outlet
EV outlet
Feedwater

200

50

100

0

Feedwater
SH outlet pressure
Degradation of steam control valve
0

500

1000

1500
Time (sec)

2000

2500

600

150

500

0
3000

400

100
SH outlet
EV outlet
Feedwater

300

Feedwater
SH outlet pressure

200

50

100
0

Degradation of fsteam control valve
0

1000

2000

3000
Time (sec)

4000

5000

0
6000

Feedwater flow rate (kg/s/loop), Steam pressure (bar)150

Watr temperature (oC)600

Feedwater flow rate (kg/s/loop), Pressure (bar)pressure, when the plant operates at 45% thermal power. Pressure loss at the steam flow control
valve is approximately 9MPa under the normal operating conditions (0 to 1,000 seconds). The left
figure shows an example when the system pressure increases by 0.5 MPa, for instance due to thevalve stick at a small throttling position without FW flow rate control. This event results in adecrease of the FW flow rate. The temperature at the EV outlet increases rapidly and reaches the trip
temperature at 417 ºC within approximately 10 minutes. Similar trends are found for the 100% rated
operation condition. However, the plant has a control system to keep the EV outlet temperature at aconstant value. As a result, the evolution of the plant parameters on the right figure is obtained. It
is seen that the malfunction, i.e., a slight closure of the steam control valve, can only be detected by
the increase of the system pressure.
When the feed water system is normal, the FW flow rate is increased in order to keep theconstant EV outlet temperature. As a result, all the plant parameters except the system pressure
show constant.

Fig. 7. Evolution of plant parameters in the tertiary heat transport system during a steam control valve
malfunction without (left) and with (right) FW flow control at 45% thermal power

4.3

Heat transfer degradation due to fouling on heat transfer tubes of evaporators

Water contains many impurities which cause fouling on the inside surface of heat transfer tubes.
The heat transfer tubes in the EVs are susceptible to catch fouling due to the boiling of water. Since
super-heated steam is supplied to the SH from the EV, it is assumed that the fouling will not depositon the inner surface of the heat transfer tubes of SH. The fouling causes a decrease of the overall
heat transfer coefficient. Every steam generator will encounter the above situation in the long run.
We assume a stepwise increase of the thermal resistance due to fouling (0.01 to 0.05 m2K/kW: inverse
value of the heat transfer coefficient) at t=1,000 s. The evolution of the plant parameters is shown in
Fig. 8.
The abnormality of the FW system is also assumed. In this event, the SH outlet sodium
temperature decreases. The EV outlet sodium temperature is almost constant. Regarding
temperatures in the tertiary system, only the EV outlet temperature decreases to the saturation
temperature corresponding to the system pressure which is not affected strongly by fouling. The
transient behavior is similar for the case under 100% power conditions. In this event, the two-phaseflow does not cause dryout near the outlet of the EV. As a result, lower energy steam and a large
amount of droplets will flow into the SH. Because of this, the heat transfer rate in the SH increases
and the sodium temperature at the outlet of the SH decreases. Therefore, the heat transfer
degradation event in the EV can be detected by the decrease of the steam temperature signals at theoutlet of the EV, as well as the decrease of the sodium temperatures at the outlet of the SH.
In practice, the FW control system acts to keep the EV outlet temperature at the set point.
Therefore, FW flow rate is decreased automatically by the system in a long period. Therefore,
operators may not aware of the heat transfer degradation because of the slow event.

65

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Code

100

300
Degradation ofheat transfer

200

50

100

0

Feedwater flowrate
SH outlet pressure

0

2000

4000
6000
Time (sec)

8000

1 10

SH-A outlet
SH-B outlet
SH-C outlet
EV-A outlet
EV-B outlet
EV-C outlet

550
500

o

SH outlet
EV outlet
Feedwater

400

600

Sodium temperature ( C)

Water temperature (oC)500

Feedwater flow rate (kg/s/loop), Pressure (bar)

150

600

450
400
350
300
250

0

200

4

0

2000

4000

6000

8000

1 10

4

Time (sec)Fig. 8. Evolution of plant parameters in the tertiary (left) and the secondary (right) heat transport system
when the thermal resistance increases to 0.05m2K/kW due to fouling at 45% thermal power

4.4

Degradation of FW heating

There are several reasons which cause degradation of FW heating. One is fouling on the insideand outside of the heat transfer tubes. Another reason is the loss of extracted steam flow from theturbine system. These events may cause a decrease of the temperature of the FW supplied to the EV.
Figure 9 shows the transient where a valve on the extraction line from the high-pressure turbine to thelast stage high-pressure FWH fails. As a result of the failure, the FW temperature decreases and the
EV outlet temperature decreases. The FW flow rate is decreased by the control system in order tomaintain the EV outlet temperature at the present level. Therefore, non-stationary signals are theFW temperature, FW flow rate and the system pressure. The temperatures in the secondary systemdecrease slightly as shown in the right side of figure of Fig. 9. These trends are almost same as theresults using a full scope simulator of the “Monju” reactor.
The effect of thermal resistance in the FWHs was also investigated. The thermal resistance is anorder of magnitude larger than in the case of fouling on the heat transfer tubes of the evaporators.
However, the effect on the FW temperature is very small and there is sufficient margin to the FW
pump trip due to low temperature. Therefore, detection of the fouling build-up on the inner andouter surfaces of the heat transfer tubes is rather difficult compared to the case of the evaporator.
150

400

100
Abnormarity of extraction valve
for #2 high-pressure feedwater heater

300
200

50

100
0

Feedwater flow rate
Main steam pressure (bar)
0

1000

2000

3000
Time (sec)

4000

5000

0
6000

Super-heater inlet
Super-heater outlet
Evaporator outlet

550
Sodium temperature ( C)

Temperature (oC)

500

600

500

o

Super-heater outlet
Evaporator-A outlet
Feedwater

Feed water flow rate (kg/s/loop), Pressure (bar)

600

450
400
350
300
250
200

0

1000

2000

3000

4000

5000

6000

Time (sec)Fig. 9. Evolution of plant parameters in the tertiary (left) and the secondary (right) heat transport system
when a valve on the extraction line fails at 45% thermal power

4.5

Degradation of Main pump

Even though there are not many active components in the primary system, the main pump is oneof the active components. Three heat transport systems are provided in the “Monju” reactor, andeach system is recirculated by one main pump. It is assumed that the pump in the A-loop causes

66

H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Codedegradation at 1000 seconds. The evolution of the temperature and flow rate in the primary heattransport system is illustrated in Fig. 10. When the flow rate in the A-loop decreases, the flow rates
in the other two loops increase as if to compensate the total flow rate. As a result, the outlet
temperatures in the primary system change slightly, and inlet temperatures stay almost constant. The
evolution of these plant parameters is quasi-static. This event can be detected by watching the flowrate difference between the loops.
700

1500

400
Temperature
IHX A inlet
IHX B inlet
IHX C inlet
IHX A outlet
IHX B outlet
IHX C outlet

300
200
100

0

1000

2000

Flowrate
A loopB loopC loop

3000
Time (sec)

4000

5000

500

Fow rate (kg/s/loop)

1000

500

o

Temperature ( C)

600

0
6000

Fig. 10. Evolution of plant parameters in the primary system during a degradation of a main pump in the
A-loop5.

Discussion

The above analyses are conducted with a model which neglects the low-pressure equipment suchas low-pressure turbines, low-pressure FWHs etc. Therefore, the differences of analytical results
using the simplified model and the detailed model should be discussed. In the simplified model,
three FW heaters and the low-pressure turbine are omitted from the calculation model as mentioned in
the previous section. The detailed model consists of whole plant system as shown in Fig. 2 and Fig.
3. Representative of the abnormalities, a degradation of the FW pump at 100% thermal power isdiscussed. A comparison of the analytical results between simplified and detailed models is shownin Fig. 11. There are minor differences of initial parameters between the two models. After theslight degradation of pump head, the plant parameters show similar trends between the two
calculation models. However, the pressure at the outlet of the super-heater is higher by 1 MPa andthe time to initiate the trip signal is earlier by 200 seconds for the detailed calculation model. The
temperature difference at the EV outlet between the two models is 6.5 ºC. The difference of pressure
between the simplified and detailed model may be caused by the inventory of vapor in the turbine
system.
The above plant transient is almost independent of conditions of FW control system because thecontrol system is inefficient due to the FW pump degradation. A malfunction of the steam control
valve without FW control under the rated condition is also calculated using the simplified and detailed
models as shown in Fig. 12. When the valve sticks at the small opening, the system pressure
increases and FW flow rate decreases.
Therefore, the evaporator outlet temperature increases to the trip temperature level quickly.
Results are very similar between the simplified and detailed models. The temperature difference atthe EV outlet between the two models is 4.5 ºC. The two calculation cases show that the simplified
model is adequate to calculate the effects due to minor abnormalities without large discrepancies
compared to an analysis with a detailed analysis model. The similar result could be calculated forthis event with the FW control system because the FW control system is inefficient due to the problem
downstream of the water system.

67

Feedwater flowrate (Simple)
SH outlet pressure (Simple)
Feedwater flowrate (Detailed)SH outlet prssure (Detailed)

600

150

Water temperature (oC)

500

400

100
417oC trip temp. at 1700 sec.
Degradation of
feedwater pump

300

200

100

0

50

SH outlet (Simple)
EV outlet (Simple)
Feedwater (Simple)
SH outlet (Detailed)EV outlet (Detailed)Feedwater (Detailed)
0

500

1000
1500
Time (sec)2000

Feedwater flow rate (kg/s/loop), Pressure (bar)H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Code0
2500

Feedwatr flowrate (Simple)
SH outlet pressure (Simple)
Feedwater flowrate (Detailed)SH outlet pressure (Detailed)

600

150

Water temperature (oC)

500

100

400
o

417 C trip temp. at 1437 sec.
Degradation of
feedwater pump

300

200

100

0

50

SH outlet (Simple)
EV outlet (Simple)
Feedwater (Simple)
SH outlet (Detailed)EV outlet (Detailed)Feedwater (Detailed)
0

500

1500
1000
Time (sec)2000

Feedwater flow rate (kg/s/loop), Pressure (bar)Fig. 11. Comparison of evolutions of plant parameters in the tertiary heat transport system during a FW
pump degradation at 100% thermal power between simplified and detailed turbine and FW systems

02500

Fig. 12. Comparison of evolutions of plant parameters in the tertiary heat transport system during asteam control valve malfunction at 100% thermal power between simplified and detailed turbine and FW
systems

6.

Conclusion

Minor abnormalities which do not cause a trip caused in the tertiary system of the prototype fast
reactor “Monju” are analyzed by the NETFLOW++ code using a whole plant model consisting of the
primary, the secondary and the tertiary systems. A malfunction of a feedwater control valve and adegradation of a feedwater pump are selected as events of decreasing feedwater flow rate. In these
events, the steam temperature at the outlet of the evaporator has a high sensitivity to the abnormalities.
Fouling on the heat transfer tubes of evaporators is selected as an abnormality due to heat transfer inthe EV. The EV outlet steam temperature has high sensitivity if the feedwater control system does
not work. However, since the EV outlet temperature is controlled in order to maintain a constanttemperature, detection of the heat transfer degradation of the EV is rather difficult. In the case of apressure increase due to steam control valve malfunction, only the system pressure undergoes

68H. Mochizuki / Plant Transients under Small Abnormalities of FBR “Monju”
Calculated by a Plant System Codesufficient change to detect the problem. Therefore, operators should pay attention to the pressure
signal to detect the malfunction of the steam control valve.

Nomenclature
A: cross sectional area or heat transfer area (m2)
C: specific heat (J/kg K)
De: equivalent diameter (m)d: diameter (m)g: gravitational acceleration (m/s2)
Hp: pump head if there is a pump in the interested link i.
h: heat transfer coefficient (W/m2K)
k: thermal conductivity (W/mK)
L: inertia li／Ai (1/m),
l: length (m),Ntube: number of tubes
p: pressure (Pa)q’: heat loss (W/m2)
T: temperature (K)t: time (s)U: overall heat transfer coefficient (W/m2K)
W: flow rate (kg/s)
z: coordinate (m)θ: angle of flow direction to the vertical direction (radian),
ζ: local loss coefficient (-)
l: pipe friction factor (-)ρ: density (kg/m3)
Subscripts
i; link number
j: junction number
f: fouling
p: primarys :secondary
t: tube.

Acknowledgement
The present study includes the result of “R&D of an anomaly detection system by the advanced
hybrid processing of plant data of “MONJU” entrusted to Okayama University by the Ministry of
Education, Culture, Sports, Science and Technology of Japan (MEXT), and re-commissioned to
University of Fukui. The authors would like to express their thanks to MEXT. The author would
like to express his thanks to Mr. T. Shimizu and Mr. D. Nakamura who helped the author to adjust
data of plant.

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