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Determination of BWR minimum steam cooling reactor water level and associated steam flow using MAAP4 code
Nuclear Engineering and Design 240 (2010) 3791–3796
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Short communication
Determination of BWR minimum steam cooling reactor water level and associated steam flow using MAAP4 code Jyh-Jun Chen a , Shih-Jen Wang b,∗ , Chun-Sheng Chien b , Kuan-Shen Chiang b , Jyh-Tong Teng a a b
Department of Mechanical Engineering, Chung Yuan Christian University, 200 Chung-Pei Road, Chung-Li 32023, Taiwan Institute of Nuclear Energy Research (INER), 1000, Wunhua Rd., Jiaan Village, Longtan Township, Taoyuan County 32546, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 30 September 2009 Received in revised form 27 July 2010 Accepted 24 August 2010
a b s t r a c t The minimum steam cooling reactor pressure vessel (RPV) water level (MSCRWL) is defined to be the lowest RPV water level at which the covered portion of the core is capable of generating sufficient steam to preclude peak cladding temperature (PCT) in the uncovered portion of the core from exceeding 1500 ◦ F. The associated steam flow rate is called Wg-1500. Both MSCRWL and Wg-1500 are important parameters for safe operation of nuclear power plant. In the past, the calculations of MSCRWL and Wg-1500 were calculated by indirect way via simple model and provided by the vendor. It has to be revised quite often during the operation period of nuclear power plant. The process is time-consuming. To improve the situation, a direct and easy method of generating MSCRWL using MAAP4 code by the utilities in conjunction with the proportional and integral (PI) controller is developed in this study. The developed control loop with a PI controller is capable of generating the MSCRWL in a fast and precise manner. The MSCRWL and Wg-1500 are calculated simultaneously by controlling the PCT equal to 1500 ◦ F. Furthermore, the adjusting process is done automatically and readily with this methodology. The effect of feedwater inlet temperature is taken into account via thermal kits of the balance of plant system. The calculated MSCRWL is consistent with the calculated Wg-1500. The sensitivity study of power level and power shape are performed. For a given power shape, the MSCRWL is less sensitive to the power level. However, Wg-1500 is almost proportional to the power level. This information is helpful for the associated EOP application. This technique can be applied for other system codes. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Steam cooling (BWROG, 2001) is an important mechanism in the operation of boiling water reactor (BWR) as the core is uncovered. Adequate core cooling is required to be assured under this situation. Minimum steam cooling RPV water level (MSCRWL) plays an important role in the operation of BWR, especially in the case of the anticipated transient without scram (ATWS). It is the lowest reactor pressure vessel (RPV) water level for adequate core cooling. As the core is uncovered, metal–water reaction starts as the cladding temperature reaches 1500 ◦ F (1088 K). In this reaction, heat is generated in addition to fission power. The reaction rate depends on the cladding temperature. The metal–water reaction rate increases rapidly as the cladding temperature reaches 1800 ◦ F (1255 K). At this time, the fuel temperature increases rapidly and damages the fuel. One purpose of steam cooling is to maintain the peak cladding temperature (PCT) below 1500 ◦ F by steam cooling mechanism for the case of the anticipated transient without scram
∗ Corresponding author. E-mail address: [email protected] (S.-J. Wang). 0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.08.019
(ATWS). For the ATWS case, at least one of the make-up water systems is available. However, it is desired to reduce the fission power by reducing the RPV water level. By doing so, the fuel can be cooled properly, fuel damage is prevented, and a longer duration of time is available for the operator to scram the reactor. There is a low limit of the RPV water level control, named the minimum steam cooling RPV water level (MSCRWL). It is defined as the lowest RPV water level at which the covered portion of the core is capable of generating sufficient steam to preclude PCT in the uncovered portion of the core from exceeding 1500 ◦ F. The corresponding steam flow rate, named Wg-1500, is defined as the minimum bundle steam flow rate required to maintain PCT <1500 ◦ F. In BWROG Appendix C, Wg-1500, is defined as the minimum bundle steam flow rate required to maintain PCT <1500 ◦ F. It is used to determine the minimum steam cooling pressure (MSCP) which is used in Emergency Operating Procedure (EOP) for anticipated transient without scram (ATWS) case with RPV water level unknown. By controlling RPV pressure slightly above MSCP, adequate core cooling can be maintained. However, the Wg-1500 is calculated based on decay power of 2.2% rated power (10 min after shutdown) with core completely uncovered, which is nothing to do with MSCRWL. It is not suitable to be used in ATWS case. Instead, the proper value of the Wg-1500 is
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J.-J. Chen et al. / Nuclear Engineering and Design 240 (2010) 3791–3796 Table 1 Axial power shape used in MAAP4. Node number
Fig. 1. Conventional approach.
steam flow rate associated with the MSCRWL. Therefore the revised Wg-1500 which is associated with MSCRWL is suggested in this study. MAAP4 (FAI, 1994) is a severe accident analysis code, developed by Electrical Power Research Institute. It has been used in developing the severe accident management strategy of nuclear power plants in Taiwan (Chien et al., 2008; Chuang et al., 2009; Su et al., 2006; Wang et al., 2004, 2005, 2006a,b). This study is intended to demonstrate another approach of generating these two parameters by using MAAP4 code. The Kuosheng (Final Safety Analysis Report, 1988) nuclear power plant (NPP) is taken as a reference plant for this study. A control loop of PCT with proportional and integral (PI) controller is developed and coupled with MAAP4 code without recompiling. With this algorithm, the MSCRWL and Wg-1500 can be generated at the same time automatically using MAAP4 code. Sensitivity study is performed of these two parameters with reactor power. 2. Description of conventional approach In the conventional approach, for a given reactor power, feedwater inlet temperature, and power shape, the determination of MSCRWL and Wg-1500 were provided by the vendor and calculated via indirect way as shown in Fig. 1. Curve A represents the steam flow rate required to maintain the PCT below 1500 ◦ F for each RPV water level. It is obtained from the heat balance of fuel cladding. Curve B represents the actual steam flow rate generated in the core for each RPV water level. It is obtained from the heat balance of the RPV. The intersection of curve A and B in the Xaxis is the MSCRWL. The corresponding intersection in the Y-axis is the minimum steam flow rate required to maintain the PCT below 1500 ◦ F (Wg-1500). Generally for a given power level, a RPV water level is guessed. The associated PCT is calculated and checked with 1500 ◦ F. Eventually, MSCRWL and Wg-1500 are calculated via trialand-error approach. The heat generation rate due to metal–water reaction is not included. Furthermore, the utility does not have this calculation tool and has to rely on the vendor. 3. Description of MAAP4 code MAAP4 code is an integrated severe accident analysis code, widely used in the nuclear industry. It can simulate the response of light water reactor power plants during a variety of severe accident sequences, including mitigations actions for accident management. The code provides a flexible, efficient, and integrated tool for evaluating the in-plant effects of a wide range of postulated accidents
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 SUM
Value 0.229 0.3585 0.4383 0.4882 0.5481 0.5981 0.6382 0.6781 0.7382 0.7882 0.8583 0.9583 1.0584 1.2085 1.4186 1.6288 1.8091 1.9195 2 1.8192 1.4866 1.1586 0.7987 0.3892
Remark Bottom node
Top node
24.015
and for examining the impact of operator actions on accident progressions. The entire spectrum of severe accident phenomena, including core heat-up, degradation and relocation, lower plenum phenomenology, corium–concrete interactions, containment hydraulics, hydrogen combustion, and radionuclide release and transport, are treated in MAAP4. All the control volumes of the plant, including reactor vessel, containment, and emergency core cooling system and its associated control logic are provided. Users only need to provide the plant data in performing calculations using the code. In this work, the MAAP4 parameter file and input file of the Kuosheng NPP were prepared. The default values associated with the severe accident phenomena were used with no modification. Since the MAAP4 code has been used extensively by the nuclear industry, the MAAP4 is selected as an analytical tool in this study. A function of determining PCT of the core is written and implemented in MAAP4 code. The heat generation rate for the metal–water reaction is included. A control loop with PI controller is developed and coupled with MAAP4 code. With this algorithm, the MSCRWL and Wg-1500 can be generated automatically using MAAP4 code. 4. Generation of MSCRWL and WG-1500 using MAAP4 Three parameters are required for the generation of MSCRWL using MAAP4. They are the axial power shape, reactor power and feedwater temperature. The typical conservative axial power shape as shown in Table 1 is used in this study. Flat radial power shape is used in this analysis as general approach. The feedwater temperature is function of reactor power which is obtained from the thermal kits. In this simulation, the reactor power is manually input with 10% full power. The inlet temperature of the injection flow is set to the feedwater temperature that obtained from the thermal kits (WEC, 1978) as shown in Table 2. The MSCRWL is generated through the following process. 4.1. Develop PCT control loop In order to find the MSCRWL associated with PCT equal 1500 ◦ F, a control loop for PCT is developed as shown in Fig. 2. The PCT
J.-J. Chen et al. / Nuclear Engineering and Design 240 (2010) 3791–3796
3793
Table 2 Relationship between reactor power and feedwater inlet temperature. Reactor power (%)
Feedwater temperature (K)
100 75 50 25 15 10 7
489 471 452 442 438 435 434
Fig. 2. Control block diagram of MSCRWL.
is obtained from the MAAP4 calculation. It is compared with the setpoint of 1500 ◦ F. The error signal passed through a proportional and integral (PI) controller to regulate the injection (feedwater) flow rate. The RPV water level is varied in response to the injection flow. And so is the PCT. Due to the feature of PI controller, the steady state error will be zero eventually in the controlled response. That is the PCT would equal 1500 ◦ F. Eventually, the MSCRWL is generated automatically with this algorithm. The PI controller is expressed by: PI = C[Kp × error + Ki × (integration of error)] where C is the gain coefficient to avoid overshoot in the process of numerical analysis and the Kp and Ki are the coefficients of the proportional and integral controller. The PI controller is implemented and coupled with MAAP4 code via parameter change as shown in Appendix A.
Fig. 3. Response of RPV water level.
In the Kuosheng NPP, the BAF is at 5.30 m and TAF is at 9.11 m. The active fuel length is 3.81 m, obtained from the difference between these two values. Thus, these water levels can be expressed in terms of fractions of the active fuel length as shown in Table 4. The entire height of the active core between TAF and BAF is equally divided into 24 notches and the MSCRWL is calculated to be at the 19th notch, as shown in Table 4. The peak cladding temperature is controlled to 1500 ◦ F (1088 K) as shown in Fig. 4. In Fig. 5, the RPV pressure is kept at 7.284 MPa and the constant-pressure assumption satisfies the requirement needed for the evaluation of MSCRWL. The resultant steam flow rate is shown in Fig. 6. From Fig. 7, it is clearly shown that the injection flow rate is equal to the steam flow rate.
4.2. RPV pressure control The MSCRWL is associated with rated RPV pressure. In this approach, the RPV pressure is controlled against the setpoint (7.284 MPa) by regulating the control valve. A FUNCTION is used to provide this control action. 4.3. MSCRWL result With the modification implemented in MAAP4, the user can easily obtain the values of MSCRWL and Wg-1500 at the same time. The associated parameters used in the PI controller are shown in Table 3. For the cases of 10% full power, the responses of the five main state variables, RPV water level, peak cladding temperature, RPV pressure, steam flow rate, and injection flow rate, are shown in Figs. 3–7, respectively. The response of RPV water level is shown in Fig. 4. It is clear that a steady state RPV water level is observed. Table 3 Controller setpoints. Variables
Values
Proportional gain (Kp ) Integral gain (Ki ) Constant
1.0 × 10−2 1.0 × 10−3 0.1
Fig. 4. Response of peak cladding temperature.
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Fig. 5. Response of RPV pressure. Fig. 7. Response of injection flow.
The result of MSCRWL obtained in this study by using the MAAP4 code with PI controller indicates that the MSCRWL is at the 19th notch out of 24 notches for the entire active core; this elevation for MSCRWL is consistent with that obtained from the EPG using the evaluation method provided by the vendor. It should be noted that all conditions and assumptions used in this study are consistent with those specified by the EPG to make a meaningful comparison between the MSCRWL result obtained from this study and those from the method provided by the EPG. This demonstrates that the MAAP4 code with PI controller is adequate to determine the MSCRWL and Wg-1500 at the same time. It is not intended to compare the Wg-1500 with that given by the vendor due to lack of detailed information. A study is performed to demonstrate the reasonable results. The steam generation associated with RPV water level above TAF is 138 kg/s as shown in Table 4. Wg-1500 is about 0.71 of that flow rate. That mean 0.71 fraction of the power is used to generate steam for cooling the fuel above the MSCRWL. From MAAP4 results, total heat transfer rate from core to water at 10% full power (2.894 × 108 W) is 2.0414 × 108 W. The fraction of power below MSCRWL is about 0.71, which is consistent with Wg-1500/Wg. This demonstrates that the calculated Wg-1500 is consistent MSCRWL and reasonable. In a word, the work provides a direct and easy way of generating the MSCRWL and Wg-1500 using MAAP4. Once the axial power shape, reactor power, and feedwater temperature are given, the MSCRWL and Wg-1500 can be obtained automatically.
Fig. 6. Response of total core steam flow rate.
5. Sensitivity study
Table 4 Results with 10% full power. Variables
Value
Reactor power (%) RPV pressure (Pa) Feedwater temperature (K) MSCRWL (fraction) Wg-1500 (kg/s) Steam flow (kg/s) with level above TAF (Wg) Wg-1500/Wg
10 7,284,000 435 0.76 99 138 0.71
In this section, the effects of power level and power shape on MSCRWL and Wg-1500 are discussed. 5.1. Power level Four power levels (including 7% full power, 10% full power, 13% full power, and 16% full power) are used and the associated MSCRWL and Wg-1500 are shown in Table 5 and Fig. 8. The MSCRWL is shown to be less sensitive to the power level. How-
J.-J. Chen et al. / Nuclear Engineering and Design 240 (2010) 3791–3796 Table 7 List of abbreviations and parameter notations.
Table 5 Sensitivity results of power level. Variables
Case 1
Reactor power (%) RPV pressure (Pa) Feedwater temperature (K) MSCRWL (fraction) Wg-1500 (kg/s)
3795
Case 2
Case 3
Case 4
7
10
13
16
7,284,000
7,284,000
7,284,000
7,284,000
434
435
436
438
0.736
0.76
65.9
99
0.78 133
0.79 184
ATWS BAF BOC BWR BWROG EPG/SAGs EOP MSCP MSCRWL MAAP NPP PCT PI RPV TAF TPC Wg-1500
Anticipate transient without scram Bottom of active fuel Beginning of cycle Boiling water reactor BWR owners’ group Emergency procedure guidelines and severe accident guidelines Emergency operating procedure Minimum steam cooling pressure Minimum steam cooling reactor water level Modular accident analysis program Nuclear power plant Peak cladding temperature Proportional and integral Reactor pressure vessel Top of active fuel Taiwan power company The steam flow rate associate with the MSCRWL
6. Conclusion
Fig. 8. Power levels relative to Wg-1500 and MSCRWL.
ever, Wg-1500 is nearly proportional to the power level. MSCRWL can be assumed as a constant value for simplicity. However, Wg1500 is very sensitive to the reactor power. It cannot be treated as a constant and must be associated with its reactor power. 5.2. Power shape At beginning of cycle (BOC), it is associated with top peak power shape. At the end of cycle, it is associated with bottom peak profile. These two typical power shapes are used with same power level of 10% full power and the associated MSCRWL and Wg-1500 are shown in Table 6. The results indicate that both MSCRWL and Wg1500 are sensitive to the power shape. The MSCRWL is high with top peak power shape. The associated Wg-1500 is also high (Table 7). In a word, the MSCRWL and its associated Wg-1500 are varying during power operation. However, given the power shape and power level, the MSCRWL and MSCP (function of Wg-1500) can be obtained easily for operation use.
Table 6 Sensitivity results of power shape. Variables
Top peak
Bottom peak
MSCRWL (fraction) Wg-1500 (kg/s)
0.76 99
0.67 91
MSCRWL and Wg-1500 are important parameters for safe operation of NPP when the EOP are demanded. It can keep the reactor core in appropriate cooling condition if the water level can be maintained above this water level. In conventional approach, both MSCRWL and Wg-1500 are calculated by iteration via simple models and provided by the vendor. In this study, a direct and easy method of generating MSCRWL and Wg-1500 using MAAP4 is developed. The PI controller developed is capable of generating the MSCRWL and Wg-1500 at the same time. The calculated MSCRWL is consistent with the calculated Wg-1500. The effect of feedwater inlet temperature is taken into account via thermal kits of the balance of plant system. This technique can be applied for other system codes. The MSCRWL and Wg-1500 under different conditions can be obtained easily using this approach. The effects of power level and power shape on the MSCRWL and Wg-1500 is investigated in this study. For a given power shape, the value of MSCRWL is found to be less sensitive to the power level. But the value of Wg-1500 is found to be almost proportional to the power level. This information is helpful for the associated EOP application. Acknowledgements The authors would like to appreciate the technical support of the personnel at Kuosheng NPP and at Taiwan Power Company. This work is partially supported financially by Institute of Nuclear Energy Research and by Chung Yuan Christian University through a grant (grant no. CYCU-98-CR-ME). Appendix A. Appendix A PARAMETER CHANGE ALIAS TIMER 1 AS PICONTROL END IF TIM >1000.0 error = (TCLMX − 1500.0)/1500.0 Lterm=KP*error adjust=Lterm + Rterm WFWCD(7) = FWini * adjust WFWCD(8) = WFWCD(7) SET PICONTROL
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REPEAT END IF PICONTROL >0.0 KInew = KIold + KI * err * gain Rterm = KInew KIold = KInew REPEAT END References BWROG EPGs/SAGs Rev. 2. General Electric Company, 2001. Chien, C.S., Wang, S.J., Chiang, S.C., 2008. Development of parameter identification capability for MAAP4 code. Nucl. Technol. 161 (3), 203–209. Chuang, M.J., Wang, S.J., Fann, S.Y., Chiang, S.C., 2009. Simplification of the severe accident management guideline for the containment flooding in a Mark-III containment. Nucl. Technol. 167 (2), 247–253. FAI, 1994. MAAP4-Modular accident analysis program for LWR power plants. General Electric Company, 1981. Additional Information Required for NRC Staff General Report on Boiling Water Reactors, NEDO-24708A. Final Safety Analysis Report of Kuosheng Nuclear Power Station. Taiwan Power Company, 1988. Su, W.-N., Wang, S.-J., Chiang, S.-C., 2006. Development of drywell water level computational aid and application on containment flooding strategy of Mark-III system. Nucl. Technol. 155, 253.
Wang, S.-J., Chiang, K.-S., Chiang, S.-C., 2004. Analysis of PWR RCS injection strategy during severe accident. Nucl. Technol. 146, 199. Wang, S.-J., Chien, C.-S., Chiang, S.-C., 2006a. Development of accumulator calculation aid for determining RCS injection volume. Nucl. Eng. Des. 236, 1330. Wang, T.-C., Wang, S.-J., Teng, J.-T., 2005. Analysis of severe accident management strategy for a BWR-4 nuclear power plant. Nucl. Technol. 152, 253. Wang, T.-C., Wang, S.-J., Teng, J.T., 2006b. Analysis of the Chinshan raw water system performance for severe accident. Nucl. Technol. 156, 347. Westinghouse Electric Corporation, 1978. Thermal Performance Data For Taiwan Power Company, Kuosheng 1 & 2, AJ405-0151. Jyh-Jun Chen (BS, mechanical engineering, Chung Yuan Christian University, Taiwan, 2002; MS, mechanical engineering, Chung Yuan Christian University, Taiwan, 2004) is an Ph.D. student at Chung Yuan Christian University. His interests include severe accident analysis, transient analysis, and nuclear power plant simulation. Shih-Jen Wang (MS, nuclear engineering, NTHU, Taiwan, 1976; Ph.D., nuclear engineering, University of Tennessee, 1983) is an researcher at INER. His interests include modeling and simulation of nuclear power plants, transient analysis, severe accident analysis, and the related optimization research in nuclear industry. Chun-Sheng Chien (BS, physics, Tang-Kung University, Taiwan, 1970) is an assistant researcher at INER. His interests include severe accident analysis, nuclear power plant simulation, and computer systems. Kuan-Shen Chiang (BS, mechanical engineering, Feng-Chia University, Taiwan, 1996; MS, marine and mechanical engineering, National Taiwan Ocean University (NTOU), 1998) was an associate researcher at the Institute of Nuclear Energy Research (INER) during 1998–2007. His interests include severe accident analysis and nuclear power plant simulation.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Short communication
Determination of BWR minimum steam cooling reactor water level and associated steam flow using MAAP4 code Jyh-Jun Chen a , Shih-Jen Wang b,∗ , Chun-Sheng Chien b , Kuan-Shen Chiang b , Jyh-Tong Teng a a b
Department of Mechanical Engineering, Chung Yuan Christian University, 200 Chung-Pei Road, Chung-Li 32023, Taiwan Institute of Nuclear Energy Research (INER), 1000, Wunhua Rd., Jiaan Village, Longtan Township, Taoyuan County 32546, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 30 September 2009 Received in revised form 27 July 2010 Accepted 24 August 2010
a b s t r a c t The minimum steam cooling reactor pressure vessel (RPV) water level (MSCRWL) is defined to be the lowest RPV water level at which the covered portion of the core is capable of generating sufficient steam to preclude peak cladding temperature (PCT) in the uncovered portion of the core from exceeding 1500 ◦ F. The associated steam flow rate is called Wg-1500. Both MSCRWL and Wg-1500 are important parameters for safe operation of nuclear power plant. In the past, the calculations of MSCRWL and Wg-1500 were calculated by indirect way via simple model and provided by the vendor. It has to be revised quite often during the operation period of nuclear power plant. The process is time-consuming. To improve the situation, a direct and easy method of generating MSCRWL using MAAP4 code by the utilities in conjunction with the proportional and integral (PI) controller is developed in this study. The developed control loop with a PI controller is capable of generating the MSCRWL in a fast and precise manner. The MSCRWL and Wg-1500 are calculated simultaneously by controlling the PCT equal to 1500 ◦ F. Furthermore, the adjusting process is done automatically and readily with this methodology. The effect of feedwater inlet temperature is taken into account via thermal kits of the balance of plant system. The calculated MSCRWL is consistent with the calculated Wg-1500. The sensitivity study of power level and power shape are performed. For a given power shape, the MSCRWL is less sensitive to the power level. However, Wg-1500 is almost proportional to the power level. This information is helpful for the associated EOP application. This technique can be applied for other system codes. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Steam cooling (BWROG, 2001) is an important mechanism in the operation of boiling water reactor (BWR) as the core is uncovered. Adequate core cooling is required to be assured under this situation. Minimum steam cooling RPV water level (MSCRWL) plays an important role in the operation of BWR, especially in the case of the anticipated transient without scram (ATWS). It is the lowest reactor pressure vessel (RPV) water level for adequate core cooling. As the core is uncovered, metal–water reaction starts as the cladding temperature reaches 1500 ◦ F (1088 K). In this reaction, heat is generated in addition to fission power. The reaction rate depends on the cladding temperature. The metal–water reaction rate increases rapidly as the cladding temperature reaches 1800 ◦ F (1255 K). At this time, the fuel temperature increases rapidly and damages the fuel. One purpose of steam cooling is to maintain the peak cladding temperature (PCT) below 1500 ◦ F by steam cooling mechanism for the case of the anticipated transient without scram
∗ Corresponding author. E-mail address: [email protected] (S.-J. Wang). 0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.08.019
(ATWS). For the ATWS case, at least one of the make-up water systems is available. However, it is desired to reduce the fission power by reducing the RPV water level. By doing so, the fuel can be cooled properly, fuel damage is prevented, and a longer duration of time is available for the operator to scram the reactor. There is a low limit of the RPV water level control, named the minimum steam cooling RPV water level (MSCRWL). It is defined as the lowest RPV water level at which the covered portion of the core is capable of generating sufficient steam to preclude PCT in the uncovered portion of the core from exceeding 1500 ◦ F. The corresponding steam flow rate, named Wg-1500, is defined as the minimum bundle steam flow rate required to maintain PCT <1500 ◦ F. In BWROG Appendix C, Wg-1500, is defined as the minimum bundle steam flow rate required to maintain PCT <1500 ◦ F. It is used to determine the minimum steam cooling pressure (MSCP) which is used in Emergency Operating Procedure (EOP) for anticipated transient without scram (ATWS) case with RPV water level unknown. By controlling RPV pressure slightly above MSCP, adequate core cooling can be maintained. However, the Wg-1500 is calculated based on decay power of 2.2% rated power (10 min after shutdown) with core completely uncovered, which is nothing to do with MSCRWL. It is not suitable to be used in ATWS case. Instead, the proper value of the Wg-1500 is
3792
J.-J. Chen et al. / Nuclear Engineering and Design 240 (2010) 3791–3796 Table 1 Axial power shape used in MAAP4. Node number
Fig. 1. Conventional approach.
steam flow rate associated with the MSCRWL. Therefore the revised Wg-1500 which is associated with MSCRWL is suggested in this study. MAAP4 (FAI, 1994) is a severe accident analysis code, developed by Electrical Power Research Institute. It has been used in developing the severe accident management strategy of nuclear power plants in Taiwan (Chien et al., 2008; Chuang et al., 2009; Su et al., 2006; Wang et al., 2004, 2005, 2006a,b). This study is intended to demonstrate another approach of generating these two parameters by using MAAP4 code. The Kuosheng (Final Safety Analysis Report, 1988) nuclear power plant (NPP) is taken as a reference plant for this study. A control loop of PCT with proportional and integral (PI) controller is developed and coupled with MAAP4 code without recompiling. With this algorithm, the MSCRWL and Wg-1500 can be generated at the same time automatically using MAAP4 code. Sensitivity study is performed of these two parameters with reactor power. 2. Description of conventional approach In the conventional approach, for a given reactor power, feedwater inlet temperature, and power shape, the determination of MSCRWL and Wg-1500 were provided by the vendor and calculated via indirect way as shown in Fig. 1. Curve A represents the steam flow rate required to maintain the PCT below 1500 ◦ F for each RPV water level. It is obtained from the heat balance of fuel cladding. Curve B represents the actual steam flow rate generated in the core for each RPV water level. It is obtained from the heat balance of the RPV. The intersection of curve A and B in the Xaxis is the MSCRWL. The corresponding intersection in the Y-axis is the minimum steam flow rate required to maintain the PCT below 1500 ◦ F (Wg-1500). Generally for a given power level, a RPV water level is guessed. The associated PCT is calculated and checked with 1500 ◦ F. Eventually, MSCRWL and Wg-1500 are calculated via trialand-error approach. The heat generation rate due to metal–water reaction is not included. Furthermore, the utility does not have this calculation tool and has to rely on the vendor. 3. Description of MAAP4 code MAAP4 code is an integrated severe accident analysis code, widely used in the nuclear industry. It can simulate the response of light water reactor power plants during a variety of severe accident sequences, including mitigations actions for accident management. The code provides a flexible, efficient, and integrated tool for evaluating the in-plant effects of a wide range of postulated accidents
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 SUM
Value 0.229 0.3585 0.4383 0.4882 0.5481 0.5981 0.6382 0.6781 0.7382 0.7882 0.8583 0.9583 1.0584 1.2085 1.4186 1.6288 1.8091 1.9195 2 1.8192 1.4866 1.1586 0.7987 0.3892
Remark Bottom node
Top node
24.015
and for examining the impact of operator actions on accident progressions. The entire spectrum of severe accident phenomena, including core heat-up, degradation and relocation, lower plenum phenomenology, corium–concrete interactions, containment hydraulics, hydrogen combustion, and radionuclide release and transport, are treated in MAAP4. All the control volumes of the plant, including reactor vessel, containment, and emergency core cooling system and its associated control logic are provided. Users only need to provide the plant data in performing calculations using the code. In this work, the MAAP4 parameter file and input file of the Kuosheng NPP were prepared. The default values associated with the severe accident phenomena were used with no modification. Since the MAAP4 code has been used extensively by the nuclear industry, the MAAP4 is selected as an analytical tool in this study. A function of determining PCT of the core is written and implemented in MAAP4 code. The heat generation rate for the metal–water reaction is included. A control loop with PI controller is developed and coupled with MAAP4 code. With this algorithm, the MSCRWL and Wg-1500 can be generated automatically using MAAP4 code. 4. Generation of MSCRWL and WG-1500 using MAAP4 Three parameters are required for the generation of MSCRWL using MAAP4. They are the axial power shape, reactor power and feedwater temperature. The typical conservative axial power shape as shown in Table 1 is used in this study. Flat radial power shape is used in this analysis as general approach. The feedwater temperature is function of reactor power which is obtained from the thermal kits. In this simulation, the reactor power is manually input with 10% full power. The inlet temperature of the injection flow is set to the feedwater temperature that obtained from the thermal kits (WEC, 1978) as shown in Table 2. The MSCRWL is generated through the following process. 4.1. Develop PCT control loop In order to find the MSCRWL associated with PCT equal 1500 ◦ F, a control loop for PCT is developed as shown in Fig. 2. The PCT
J.-J. Chen et al. / Nuclear Engineering and Design 240 (2010) 3791–3796
3793
Table 2 Relationship between reactor power and feedwater inlet temperature. Reactor power (%)
Feedwater temperature (K)
100 75 50 25 15 10 7
489 471 452 442 438 435 434
Fig. 2. Control block diagram of MSCRWL.
is obtained from the MAAP4 calculation. It is compared with the setpoint of 1500 ◦ F. The error signal passed through a proportional and integral (PI) controller to regulate the injection (feedwater) flow rate. The RPV water level is varied in response to the injection flow. And so is the PCT. Due to the feature of PI controller, the steady state error will be zero eventually in the controlled response. That is the PCT would equal 1500 ◦ F. Eventually, the MSCRWL is generated automatically with this algorithm. The PI controller is expressed by: PI = C[Kp × error + Ki × (integration of error)] where C is the gain coefficient to avoid overshoot in the process of numerical analysis and the Kp and Ki are the coefficients of the proportional and integral controller. The PI controller is implemented and coupled with MAAP4 code via parameter change as shown in Appendix A.
Fig. 3. Response of RPV water level.
In the Kuosheng NPP, the BAF is at 5.30 m and TAF is at 9.11 m. The active fuel length is 3.81 m, obtained from the difference between these two values. Thus, these water levels can be expressed in terms of fractions of the active fuel length as shown in Table 4. The entire height of the active core between TAF and BAF is equally divided into 24 notches and the MSCRWL is calculated to be at the 19th notch, as shown in Table 4. The peak cladding temperature is controlled to 1500 ◦ F (1088 K) as shown in Fig. 4. In Fig. 5, the RPV pressure is kept at 7.284 MPa and the constant-pressure assumption satisfies the requirement needed for the evaluation of MSCRWL. The resultant steam flow rate is shown in Fig. 6. From Fig. 7, it is clearly shown that the injection flow rate is equal to the steam flow rate.
4.2. RPV pressure control The MSCRWL is associated with rated RPV pressure. In this approach, the RPV pressure is controlled against the setpoint (7.284 MPa) by regulating the control valve. A FUNCTION is used to provide this control action. 4.3. MSCRWL result With the modification implemented in MAAP4, the user can easily obtain the values of MSCRWL and Wg-1500 at the same time. The associated parameters used in the PI controller are shown in Table 3. For the cases of 10% full power, the responses of the five main state variables, RPV water level, peak cladding temperature, RPV pressure, steam flow rate, and injection flow rate, are shown in Figs. 3–7, respectively. The response of RPV water level is shown in Fig. 4. It is clear that a steady state RPV water level is observed. Table 3 Controller setpoints. Variables
Values
Proportional gain (Kp ) Integral gain (Ki ) Constant
1.0 × 10−2 1.0 × 10−3 0.1
Fig. 4. Response of peak cladding temperature.
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Fig. 5. Response of RPV pressure. Fig. 7. Response of injection flow.
The result of MSCRWL obtained in this study by using the MAAP4 code with PI controller indicates that the MSCRWL is at the 19th notch out of 24 notches for the entire active core; this elevation for MSCRWL is consistent with that obtained from the EPG using the evaluation method provided by the vendor. It should be noted that all conditions and assumptions used in this study are consistent with those specified by the EPG to make a meaningful comparison between the MSCRWL result obtained from this study and those from the method provided by the EPG. This demonstrates that the MAAP4 code with PI controller is adequate to determine the MSCRWL and Wg-1500 at the same time. It is not intended to compare the Wg-1500 with that given by the vendor due to lack of detailed information. A study is performed to demonstrate the reasonable results. The steam generation associated with RPV water level above TAF is 138 kg/s as shown in Table 4. Wg-1500 is about 0.71 of that flow rate. That mean 0.71 fraction of the power is used to generate steam for cooling the fuel above the MSCRWL. From MAAP4 results, total heat transfer rate from core to water at 10% full power (2.894 × 108 W) is 2.0414 × 108 W. The fraction of power below MSCRWL is about 0.71, which is consistent with Wg-1500/Wg. This demonstrates that the calculated Wg-1500 is consistent MSCRWL and reasonable. In a word, the work provides a direct and easy way of generating the MSCRWL and Wg-1500 using MAAP4. Once the axial power shape, reactor power, and feedwater temperature are given, the MSCRWL and Wg-1500 can be obtained automatically.
Fig. 6. Response of total core steam flow rate.
5. Sensitivity study
Table 4 Results with 10% full power. Variables
Value
Reactor power (%) RPV pressure (Pa) Feedwater temperature (K) MSCRWL (fraction) Wg-1500 (kg/s) Steam flow (kg/s) with level above TAF (Wg) Wg-1500/Wg
10 7,284,000 435 0.76 99 138 0.71
In this section, the effects of power level and power shape on MSCRWL and Wg-1500 are discussed. 5.1. Power level Four power levels (including 7% full power, 10% full power, 13% full power, and 16% full power) are used and the associated MSCRWL and Wg-1500 are shown in Table 5 and Fig. 8. The MSCRWL is shown to be less sensitive to the power level. How-
J.-J. Chen et al. / Nuclear Engineering and Design 240 (2010) 3791–3796 Table 7 List of abbreviations and parameter notations.
Table 5 Sensitivity results of power level. Variables
Case 1
Reactor power (%) RPV pressure (Pa) Feedwater temperature (K) MSCRWL (fraction) Wg-1500 (kg/s)
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Case 2
Case 3
Case 4
7
10
13
16
7,284,000
7,284,000
7,284,000
7,284,000
434
435
436
438
0.736
0.76
65.9
99
0.78 133
0.79 184
ATWS BAF BOC BWR BWROG EPG/SAGs EOP MSCP MSCRWL MAAP NPP PCT PI RPV TAF TPC Wg-1500
Anticipate transient without scram Bottom of active fuel Beginning of cycle Boiling water reactor BWR owners’ group Emergency procedure guidelines and severe accident guidelines Emergency operating procedure Minimum steam cooling pressure Minimum steam cooling reactor water level Modular accident analysis program Nuclear power plant Peak cladding temperature Proportional and integral Reactor pressure vessel Top of active fuel Taiwan power company The steam flow rate associate with the MSCRWL
6. Conclusion
Fig. 8. Power levels relative to Wg-1500 and MSCRWL.
ever, Wg-1500 is nearly proportional to the power level. MSCRWL can be assumed as a constant value for simplicity. However, Wg1500 is very sensitive to the reactor power. It cannot be treated as a constant and must be associated with its reactor power. 5.2. Power shape At beginning of cycle (BOC), it is associated with top peak power shape. At the end of cycle, it is associated with bottom peak profile. These two typical power shapes are used with same power level of 10% full power and the associated MSCRWL and Wg-1500 are shown in Table 6. The results indicate that both MSCRWL and Wg1500 are sensitive to the power shape. The MSCRWL is high with top peak power shape. The associated Wg-1500 is also high (Table 7). In a word, the MSCRWL and its associated Wg-1500 are varying during power operation. However, given the power shape and power level, the MSCRWL and MSCP (function of Wg-1500) can be obtained easily for operation use.
Table 6 Sensitivity results of power shape. Variables
Top peak
Bottom peak
MSCRWL (fraction) Wg-1500 (kg/s)
0.76 99
0.67 91
MSCRWL and Wg-1500 are important parameters for safe operation of NPP when the EOP are demanded. It can keep the reactor core in appropriate cooling condition if the water level can be maintained above this water level. In conventional approach, both MSCRWL and Wg-1500 are calculated by iteration via simple models and provided by the vendor. In this study, a direct and easy method of generating MSCRWL and Wg-1500 using MAAP4 is developed. The PI controller developed is capable of generating the MSCRWL and Wg-1500 at the same time. The calculated MSCRWL is consistent with the calculated Wg-1500. The effect of feedwater inlet temperature is taken into account via thermal kits of the balance of plant system. This technique can be applied for other system codes. The MSCRWL and Wg-1500 under different conditions can be obtained easily using this approach. The effects of power level and power shape on the MSCRWL and Wg-1500 is investigated in this study. For a given power shape, the value of MSCRWL is found to be less sensitive to the power level. But the value of Wg-1500 is found to be almost proportional to the power level. This information is helpful for the associated EOP application. Acknowledgements The authors would like to appreciate the technical support of the personnel at Kuosheng NPP and at Taiwan Power Company. This work is partially supported financially by Institute of Nuclear Energy Research and by Chung Yuan Christian University through a grant (grant no. CYCU-98-CR-ME). Appendix A. Appendix A PARAMETER CHANGE ALIAS TIMER 1 AS PICONTROL END IF TIM >1000.0 error = (TCLMX − 1500.0)/1500.0 Lterm=KP*error adjust=Lterm + Rterm WFWCD(7) = FWini * adjust WFWCD(8) = WFWCD(7) SET PICONTROL
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REPEAT END IF PICONTROL >0.0 KInew = KIold + KI * err * gain Rterm = KInew KIold = KInew REPEAT END References BWROG EPGs/SAGs Rev. 2. General Electric Company, 2001. Chien, C.S., Wang, S.J., Chiang, S.C., 2008. Development of parameter identification capability for MAAP4 code. Nucl. Technol. 161 (3), 203–209. Chuang, M.J., Wang, S.J., Fann, S.Y., Chiang, S.C., 2009. Simplification of the severe accident management guideline for the containment flooding in a Mark-III containment. Nucl. Technol. 167 (2), 247–253. FAI, 1994. MAAP4-Modular accident analysis program for LWR power plants. General Electric Company, 1981. Additional Information Required for NRC Staff General Report on Boiling Water Reactors, NEDO-24708A. Final Safety Analysis Report of Kuosheng Nuclear Power Station. Taiwan Power Company, 1988. Su, W.-N., Wang, S.-J., Chiang, S.-C., 2006. Development of drywell water level computational aid and application on containment flooding strategy of Mark-III system. Nucl. Technol. 155, 253.
Wang, S.-J., Chiang, K.-S., Chiang, S.-C., 2004. Analysis of PWR RCS injection strategy during severe accident. Nucl. Technol. 146, 199. Wang, S.-J., Chien, C.-S., Chiang, S.-C., 2006a. Development of accumulator calculation aid for determining RCS injection volume. Nucl. Eng. Des. 236, 1330. Wang, T.-C., Wang, S.-J., Teng, J.-T., 2005. Analysis of severe accident management strategy for a BWR-4 nuclear power plant. Nucl. Technol. 152, 253. Wang, T.-C., Wang, S.-J., Teng, J.T., 2006b. Analysis of the Chinshan raw water system performance for severe accident. Nucl. Technol. 156, 347. Westinghouse Electric Corporation, 1978. Thermal Performance Data For Taiwan Power Company, Kuosheng 1 & 2, AJ405-0151. Jyh-Jun Chen (BS, mechanical engineering, Chung Yuan Christian University, Taiwan, 2002; MS, mechanical engineering, Chung Yuan Christian University, Taiwan, 2004) is an Ph.D. student at Chung Yuan Christian University. His interests include severe accident analysis, transient analysis, and nuclear power plant simulation. Shih-Jen Wang (MS, nuclear engineering, NTHU, Taiwan, 1976; Ph.D., nuclear engineering, University of Tennessee, 1983) is an researcher at INER. His interests include modeling and simulation of nuclear power plants, transient analysis, severe accident analysis, and the related optimization research in nuclear industry. Chun-Sheng Chien (BS, physics, Tang-Kung University, Taiwan, 1970) is an assistant researcher at INER. His interests include severe accident analysis, nuclear power plant simulation, and computer systems. Kuan-Shen Chiang (BS, mechanical engineering, Feng-Chia University, Taiwan, 1996; MS, marine and mechanical engineering, National Taiwan Ocean University (NTOU), 1998) was an associate researcher at the Institute of Nuclear Energy Research (INER) during 1998–2007. His interests include severe accident analysis and nuclear power plant simulation.