MAAP5程式為核能工業界廣泛使用之整合嚴重事故分析程式，用於嚴重事故案例分析、嚴重事故現象研究、核電廠嚴重事故處理導則發展、核安演習劇本模擬、核電廠安全度評估二階層分析、及輻射源項計算等應用。MAAP5程式輸入模式參數有許多不準度，造成程式輸出參數的不準度。本研究針對MAAP5程式進行不準度研究，以龍門電廠為參考廠，以電廠全黑事故為範例，量化反應爐壓力槽內氫氣產生量不準度；找出其95%/95th機率及信心水準之上限值。
首先進行靈敏度分析，篩選對壓力槽內氫氣產生量有重大影響之輸入參數，確認其範圍與機率分不函數，使用拉丁超方體取樣( Latin Hypercube Sampling；LHS )方法，獲得59 組參數輸入組合向量，進行59次MAAP5計算，得到59個壓力槽內氫氣產生量。本研究採用統計方法分為參數法 (parametric)與非參數法(Nnon-parametric)。若輸出分佈經由卡方檢定(Chi-square Test)確認其分佈為常態分佈(Normal Distribution)，即計算氫氣產生量之母體平均值(Mean)、標準差(Standard Deviation) 及95%/95th機率及信心水準之上限值。若輸出量的分佈並非常態，則依非參數統計方法Wilks Formula，59組氫氣產生量之最大值極為95%/95th機率/信心水準之上限值。
MAAP5程式的氫氣產生量計算有兩個模式選項，包括4個鋯水反應計算模式的選擇 (IOXIDE)，以及爐心內流道是否會被熔融爐渣阻塞兩個選擇(FGBYPA)，因此共有8個組合。以(IOXIDE=0 FGBYPA=0)說明重要結果，量化結果顯示，59組數據輸出分佈並非常態。針對此模式組合，進行100, 200, 500, 1000, 2000, 2500組等樣本數不準度分析，當樣本數增加，會越偏離常態分佈，當樣本數超過500時，除極大與極小值外，其他百分位數都會快速的收斂。
8種不同模式組合各59組MH2GEN(1)及MH2GEN(2)之不準度量化結果，預設模式(IOXIDE=0及FGBYPA=0)數據較集中且符合常態分布，且95th與5th百分位數比值較其他組別小(亦即較收歛)，因此建議使用預設模式(IOXIDE=0 FGBYPA=0)計算爐心氫氣產生量。預設模式59組爐心氫氣累積產生量(MH2GEN(1))介於789.6 kg到1205 kg之間，59組下底部區間氫氣累積產生量(MH2GEN(2))介於6.4 kg到57 kg之間。皮爾森相關係數(PCC)分析顯示，TCLMAX、FCO、FOXBJ三個參數與RPV氫氣產生量的預測相關，三個參數的建議值分別為 2700 K, 2.0, 與1.0。
以預設模式選項量化樣本數增加對不準度的影響，分別進行100, 200, 500, 1000, 2000, 2500組樣本數不準度分析。當樣本數增加，氫氣產生分佈統計量會收斂，但也越偏離常態分佈；當樣本數超過500時，各分布統計量，除極大值與極小值都會收斂，且59組 MH2GEN(1) 95th百分位數(1188.6 kg)接近於2500組統計分佈的95th百分位數(1189.9 kg)，MH2GEN(2) 95th百分位數(50.97 kg)也接近於2500組統計分佈的95th百分位數(54.26 kg)，證明59 組數據統計結果是可以接受的，59組量化分析可節省使用者不準度分析時間與後續龐大的資料的處理。未來可將此方法應用於反應爐壓力槽失效時間、熔融爐心與混凝土作用等其他嚴重事故現象或其他電腦程式(如MELCOR)上。
另外爐外熔渣是否可被冷卻是嚴重事故一個重要的物理現象，對事故演進與後果影響很大，本研究也使用MAAP5程式，進行爐外熔渣冷卻的靈敏度分析。研究方法是先確認MAAP5程式對爐外熔渣冷卻有關的參數，並進行參數的靈敏度分析。主要影響爐外熔渣冷卻的參數有熔渣向上、向下及側向的熱傳係數，另外就是臨界熱通量(CHF) Kutateladze number (Ku)，即MAAP5程式FCHF值，分析結果發現增加熱傳係數會增加向下侵蝕厚度(約0.3 m)，但仍小於下乾井水泥地板的厚度(1.6 m)，但不會造成側向的侵蝕，被動式淹灌器(Passive Flooder)開啟後，熔渣即可被水冷卻。FCHF對爐外熔渣冷卻則有顯著的影響，較大的FCHF(大於0.036)可讓冷卻水滲入熔渣並進而冷卻熔渣，只會造成向下些許的侵蝕(低於0.6 m)，並不會造成側向侵蝕。反之較小之FCHF(小於0.01)無法完全讓冷卻水滲入熔渣進行冷卻，當FCHF值等於0.01，被動式淹灌器開啟後，雖然熔渣溫度緩慢下降，但仍高於1000 K，使得水泥地板與基座(Pedestal)持續侵蝕，在計算結束時(250,000 秒)，向下侵蝕會超過地板水泥的厚度，但側向侵蝕並未超過基座厚度(1.7 m)。當FCHF值等於0.0036，在250,000秒時，側向與向下侵蝕都超過基座與地板水泥的厚度。因此FCHF對爐外熔渣冷卻是一個很重要的參數。

MAAP5 is an integral severe accident analysis program which is widely used in the utilities. The program has been used intensively in the framework of probabilistic safety assessment, verification and validation of mitigation actions specified in the severe accident management guidelines (SAMG), and source term quantification in Taiwan. However, the uncertainties of the phenomenological models and the modeling parameters affect MAAP5 results. In the present study, the uncertainty of the in-vessel hydrogen generation as predicted by the MAAP5 code is quantified. The surrogate plant analyzed is Lungmen Nuclear Power Station of Taiwan Power Company. The plant employs Advanced Boiling Water Reactor (ABWR). First, define the input parameters of MAAP5 code that affect the prediction of in-vessel hydrogen generation. Then, use Latin Hypercube Sampling (LHS) to generate input value combinations. Multiple input value combinations were calculated by MAAP5 code. The calculation results were analyzed with Chi-square test to determine the 95th percentile with the 95% confidence level value(95%/95th) of the amount of in-vessel hydrogen generation. For the cases that pass the Chi-square test, the population mean and population standard deviation are calculated, and the 95%/95th value is estimated. For the cases that fail Chi-square test, the maximum value of the sample calculations is the 95%/95th value. The calculations show that the default model options (IOXIDE=0 and FGBYPA=0) are recommended. The Pearson Correlation Coefficient (PCC) was used to determine the impact of model parameters on the target output parameters. Through PCC analysis, three parameters, TCLMAX, FCO, FOXBJ, are highly depended on the in-vessel hydrogen generation, and provide suggested values of these three parameters. In order to further investigate the output distribution, uncertainty calculations are performed for 100, 200, 500, 1000, 2000, and 2500 samples based on the default model options (Baker-Just model and gas flow will reappear above the blocked channels). The deviation of the output distributions from a normal distribution is even more obvious when the number of samples increases. The distributions are not normal because there is a long tail when the amount of hydrogen generated is low. All major distribution parameters converge when the number of samples is greater than 500. The 95th value of 59 samples (1188.6 kg) of hydrogen generation in the core (MH2GEN(1)) is close to the 95th value of 2500 samples (1189.9 kg) of MH2GEN(1). The 95th value of 59 samples (50.97 kg) of hydrogen generation in the lower plenum (MH2GEN(2)) is also close to the 95th value of 2500 samples (54.26 kg) of MH2GEN(2). Therefore, 59 samples of uncertainty studies are acceptable. The reduced samples (59 samples) can save time and follow-up data processing in the uncertainty study. This methodology can apply for other severe accident phenomena, like molten corium concrete interaction and RPV failure, and other computer codes (MELCOR).
Ex-vessel debris cooling has been categorized as a dominant uncertainty with respect to severe accident phenomena. MAAP5 analyses have been performed to investigate the phenomena uncertainties of ex-vessel debris cooling. This study presented key parameters associated with ex-vessel debris cooling in MAAP5. For the MAAP5 uncertainty studies on ex-vessel debris cooling, heat transfer coefficients and critical heat flux Kutateladze number (Ku), i.e. MAAP5 parameter FCHF, are investigated. Increase heat transfer coefficient will increase erosion distances. Maximizing the heat transfer coefficients can increase erosion distances in downward directions (about 0.3 m). But the erosion distances are less than the depth of lower drywell concrete floor (1.6 m). No sideward erosions predict for the different heat transfer coefficients. But corium can be cooled down after passive flooder opens. For FCHF is greater than 0.036, water can ingress into the debris, thus cool down the debris. Little erosions (below 0.6 m) happen in downward directions. No sideward erosions predict for FCHF greater than 0.036. However, corium can’t be cool down for the small value of FCHF. Small value of FCHF represents impermeable debris. When FCHF is smaller than 0.01, that results in higher corium temperature and continuous erosion on the lower drywell floor and pedestal. At the end time of calculation (250,000 s), erosion distances in both downward and sideward directions exceed the thickness of lower drywell floor and pedestal when FCHF is equal to 0.0036. Therefore, FCHF is a very important parameter to affect ex-vessel debris cooling.

1.Randall O. Gauntt et al., “MELCOR Computer Code Manuals,” SAND 2017-0455 O, Sandia National Laboratories, January 2017.
2.R. E. Henry, C. Y. Paik, C. E. Henry, "MAAP5-Modular Accident Analysis Program for LWR Power Plants," Fauske & Associates, Inc., 2008.
3.Sandia National Laboratories, “Dakota Users’ Manual Version 1.8.5,”, 2000.
4.K. Nagashima et al., “Application of Uncertainty Analyses with the MAAP4,” Uncertainty Working Group of the MAAP Users’ Group, 1995.
5.Randall O. Gauntt, “Uncertainty Analysis Using the MELCOR Severe Accident Analysis Code,” SNL, OECD workshop Proceeding, Aix-en-Provence, November 2005.
6.S.Y. Park et al., “Uncertainty Analysis of the fission Product Behaviors during Severe Accidents for a Typical PWR,” Progress in Nuclear Science and Technology, 2011.
7.S.Y. Park et al., “Phenomenological Uncertainty Analysis of Containment Building Pressure Load Caused by Severe Accident Sequences,” Annals of Nuclear Energy, 2014.
8.K. Nagashima et al., “MAAP4 Uncertainty and Sensitivity Analysis” Annual Meeting of the Amercian Nuclear Society (ANS), Reno, NV, USA. Jun. 1996.
9.Farmer, M. T., Spencer, B.W. and Sehgal, B. R., 1992, “MACE Core Coolability Test M1B,” 20th Water Reactor Safety Meeting, Bethesda, MD, October 21-23.
10.Farmer, M.T., Lomperski, S., Kilsdonk, K., Aeschlimann, R.W., Basu, S., “OECD
MCCI Project 2-D Core Concrete Interaction (CCI) Tests: Final Report, OECD/
MCCI-2005-TR05” 2006.
11.Nagashima (NUPEC), K., Alammar (GPU), M., Da Silva (TU), H.C., Henry (FAI), R.E.,
Kenton (D&M), M., Kuhtenia (TE), D., et al., “MAAP4 Uncertainty and
Sensitivity Analysis. Uncertainty Working Group of the MAAP User’s Group, 2012.
12.Paik, C.Y., Reeves, R.W., Luangdilok, W., Henry, R.E., Zhou, Q., “Current Status
of MCCI Modelling in MAAP, MCCI-OECD Seminar, Cadarache, France, 2010.
13.S.S. Wilks, “Determination of Sample Sizes for Setting Tolerance Limits,” Annals of Mathematical Statistics, Vol.12, Page 9-96 (1941).
14.施聿懷、王德全，「龍門電廠MAAP5程式設計紀錄資料的建立」，INER-A23637，中華民國100年
15.Baker, L., Jr., and Just, L. C., “Studies of Metal-Water Reactions and High Temperatures, III. Experimental and Theoretical Studies of the Zirconium-Water Reaction,” ANL-6548, May 1962.
16.FAI and ANL, “Hydrogen Generation During Severe Core Damage Sequences,” Fauske & Associates, Inc.(FAI) and Argonne National Laboratory (ANL), Final Report for IDCOR Task 12.1, June 1983
17.NUREG, SCDAP/RELAP5/MOD2 Code Manual, Volume 4, “MATPRO - A Library of Material Properties for Light-Water-Reactor Accident Analysis,” NUREG/CR-5273, EG&G-2555, Rev. 3, February 1990.
18.Urbanic, V. F., and Heidrick, T. R., “High-Temperature Oxidation of Zircaloy-2 and Zircaloy-4 in Steam,” Journal of Nuclear Materials, Vol. 75, pp. 251-261, North Holland Publishing Co., 1978.
19.Prater, J. T., Courtright, E. L., “High Temperatures Oxidation of Zircaloy-4 in Steam-Hydrogen Environments”, Journal of Heat Transfer Paper NC2-8, Vol. 3, pp. 74-78., 1974.
20.FAI and EPRI, “MAAP5 Models Training Workshop,” Tokyo, Japan, May 17-20., 2016.
21.Ricou, F. B. and Spalding, D. B., “Measurements of Entrainment by Axisymmetrical Turbulent Jets,” Journal of Fluid Mechanics, Vol. 11, pp. 21-32., 1961.
22.Saito, M. et al., “Experimental Study on Penetration Behaviors of Water Jet into Freon-11 and Liquid Nitrogen,” ANS Proceedings 1988 Nat. Heat Transfer Conference, Houston, Texas, Vol. 3, pp. 173-183, July 24-27., 1988.
23.Meignen, R. and Berthoud, G., “Fragmentation of Molten Fuel Jets, Vapor Explosions and Explosive Eruptions,” Sendai, pp. 83-99, May 22-25., 1997.
24.Epstein, M., and Hauser, G.M., "Subcooled Forced Convection Film Boiling in the Forced Stagnation Region of a Sphere or Cylinder," Int. J. Heat & Mass Transfer, Vol.23, pp.179-189., 1980.
25.Chan Paik, Quan Zhou “MAAP5 Users’ Group Workshop,” Fauske & Associates, Inc. Taipei, Taiwan, 2012.
26.R. L. Iman, “Latin hypercube sampling (program user’s guide),” OSTI 5577631, 1980.
27.William Mendenhall, Robert J. Beaver, Barbara M. Beaver “Introduction to Probability and Statistics” 13th Edition, 2012.
28.J. C.Helton, F. J. Davis, and J. D. Johnson, “A Comparison of Uncertainty and Sensivity Analysis Results Obtained with Random and Latin Hypercube Sampling,” Reliability Engineering and System safety, Vol. 89, pp.305-330, 2005
29."Final Safety Analysis Report of Lungmen Nuclear Power Station," Taiwan Power Company, 2007.
30.Leung, J. C., “Overpressure During Emergency Relief Venting in Bubbly and Churn-Turbulent Flow,” AIChE Journal, Vol. 33, No. 6, June. (1987)
31.Henry, R. E. et al. , “Hydrogen Generation During Severe Core Damage Sequences,” FAI/82-33, Fauske & Associates, Inc., Burr Ridge, IL, June 1982.