Large thermal gradients on structural integrity of a reactor pressure vessel subjected to pressurized thermal shocks

International Journal of Pressure Vessels and Piping xxx (xxxx) xxxx

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Large thermal gradients on structural integrity of a reactor pressure vessel subjected to pressurized thermal shocks Pin-Chiun Huanga,∗, Hsoung-Wei Choub, Yuh-Ming Fernga, Chin-Hsiang Kanga a b

National Tsing-Hua University, Taiwan, ROC Mechanical and System Engineering Program, Institute of Nuclear Energy Research, Taiwan, ROC

ARTICLE INFO

ABSTRACT

Keywords: Pressurized thermal shock Computational fluid dynamics Probabilistic fracture mechanics Plume effect

Pressurized-thermal-shocks (PTSs) are the most severe accidents that impact the structural integrity of a pressurized water reactor pressure vessel (RPV). In general, the one-dimensional thermal-hydraulic analysis results for PTS transients were often used as the loading conditions for structural integrity evaluation of RPV, but may cause over-conservative results. This paper investigates the effects of the cold plume, which is the non-uniform temperature distribution caused by colder water injected separately into the RPV, on the fracture probability of a three loop pressurized water reactor (PWR) vessel subjected to PTS events. The three-dimensional computational fluid dynamics (CFD) technique associated with probabilistic fracture mechanics (PFM) analysis were employed to comprehensively evaluate the structural integrity of RPV under hypothetical PTS accidents. Firstly the model of a PWR pressure vessel in Taiwan was constructed to simulate the thermal-hydraulic phenomena by CFD methodology. Based on the Best Practice Guidelines (BPGs) and ASME V&V guidance, the estimation of mesh uncertainty has been conducted. Then the detailed thermal-hydraulic boundary conditions corresponding to various RPV shell regions were regarded as the loading conditions for PFM analysis. Present results are compared with those which consider the simplified thermal hydraulic analysis system code's results as boundary conditions.

1. Introduction The reactor pressure vessel (RPV) is the significant pressure boundary of nuclear power plant (NPP) which has to withstand high temperature and high pressure during operation. The vessel material may become brittle due to the severe radiation environment in the beltline region. Therefore, some regulations and industrial codes specify the fracture toughness requirements to prevent potential cracking in vessel materials [1–3] when the accident occurs. For pressurized water reactor (PWR), the pressurized thermal shocks (PTSs) induced by loss-of-coolant accident (LOCA) are the most critical and may impact the structural integrity of RPV [4]. The usual safety analysis is based on one-dimensional thermal hydraulic system codes such as RELAP5, MAAP, or TRACE, which included more conservative assumptions or margins to ensure the plant safety, but cannot reflect the complex mixing phenomena in the downcomer. For consideration of the effects, the sophisticated three-dimensional computational fluid dynamics (CFD) is able to provide detailed thermal hydraulic distributions of cold plume in RPV. For instance, Qian et al. [5] performed simplified threedimensional modeling of cracks at different locations under PTSs based

*

on CFD computations to discuss the plume effects on the vessel integrity. Furthermore, Kang et al. [6] investigated the methodology of combining three-dimensional CFD with probabilistic fracture mechanics (PFM) for PTS analysis. Therefore, the fracture toughness requirements of vessel materials under PTS events should be seriously investigated, especially when cold emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter primary water and/or steam. When ECC water flows into downcomer, it would cool down the RPV walls and cause sharp thermal gradients. Attention should be paid on the scenarios leading to flow stagnation which causes faster cool down rate and cold plumes in the downcomer. The IAEATECDOC-1627 report [7] also mentioned that it is important to consider non-uniform cooling of the RPV characterized by cold plumes and their interaction in the downcomer. For predicting the structural integrity of RPV, the thermal-hydraulic boundary conditions are necessary for the failure probability assessment. Advancements in understanding and knowledge of embrittlement mechanisms, the new model of 10 CFR 50.61a [8] includes not only the variables copper (Cu), nickel (Ni), and fluence that had been considered in Regulatory Guide 1.99 Rev.2, but also irradiation temperature,

Corresponding author.; E-mail address: [email protected] (P.-C. Huang).

https://doi.org/10.1016/j.ijpvp.2019.103942

0308-0161/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Pin-Chiun Huang, et al., International Journal of Pressure Vessels and Piping, https://doi.org/10.1016/j.ijpvp.2019.103942

International Journal of Pressure Vessels and Piping xxx (xxxx) xxxx

2. Computational fluid dynamics model

+ Gk

Yk + Sk

(1)

and the specific dissipation rate,

t

(

)+

xi

(

ui ) =

xj

xj

+G

Y +D +S

(2)

Table 1 Description of PTS transients.

The turbulence model was adopted in this study and the transport equations for the model are listed in equation (1) and equation (2). Where Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients and G represents the generation of specific dissipation rate. Sk and S are user-defined source terms. D represents the cross-diusion term. k and represent the effective diffusivity of k and , respectively. Yk and Y represent the dissipation of k and due to turbulence. To calculate the pressure velocity coupling, the SIMPLE-C (SemiImplicit Method for Pressure-Linked Equations-Consistent) algorithm was taken into account in this study. Then, the algebraic multi grid (AMG) linear solver was adopted for all the finite differencing 2

1.17 × 10

−5

8.74 × 10−4 110

k xj

Main steam line break with AFW continuing to feed affected generator for 30 min. Small steam line break (simulated by sticking open all SG-A SRVs) with AFW continuing to feed affected generator for 30 min

k

103

xj

Main steam line break with AFW continuing to feed affected generator

( kui) =

74

xi

Transient Description

( k) +

Case No.

t

Operator Action

The three dimensional CFD model was used to simulate the thermalhydraulic characteristics in the downcomer of PWR vessel in this study. The CFD code is based on the governing equations of fluid dynamics including the conservation laws of mass, momentum and energy. In fact, most engineering applications are turbulent. To predict the effects of turbulence, the turbulence model must take into consideration. Based on previous study, the traditional turbulence model such as Shear-Stress Transport (SST) k-ω [14] should be applied to the complex flow field with uniform heating type. The turbulence kinetic energy, k

None

2.1. Mathematical models

Operator controls HHSI 30 min after allowed. Break is assumed to occur inside containment so that the operator trips the RCPs due to adverse containment conditions. Operator controls HHSI 60 min after allowed.

2.40 × 10

Transient Class Mean Frequency (/yr)

−6

neutron flux level, contents of phosphorus (P) and manganese (Mn), effective copper parameter, etc. In the consideration of uncertainty, 10 CFR 50.61a omits the margin term that used in Regulatory Guide 1.99 Rev.2. Thus, the alternative PTS rule of 10 CFR 50.61a can be more reasonable for regulating the structural integrity of RPV. In the alternative PTS rule, the plant-specific through wall crack frequency (TWCF) analysis is required. The probabilistic fracture mechanics code, FAVOR [9], which was developed by the Oak Ridge National Laboratory (ORNL) in the United States, was used for TWCF analysis to derive the alternate PTS rule. The thermal hydraulic data of transients, beltline region geometry, radiation embrittlement properties of vessel materials, and flaw distributions generated by PNNL's VFLAW code [10] were used as input parameters of FAVOR analysis. In addition, CFD and FAVOR can be used to consider the phenomenon of cold plumes cause by ECC water injection on the fracture probability of RPV subjected to PTS events. In the present work, the effects of cold plume which influence the fracture probability of a three loop PWR vessel subjected to PTS events were investigated. When one of the loops of the secondary side breaks, the pressure of feed water becomes lower and thus the steam generator could own more capacity of heat transfer, which would cause the nonuniform temperature distribution. Finally, the colder water from the disabled loop may cause large thermal gradient in the downcomer. Here, three serious PTS transients induced by secondary side break analyzed from Beaver Valley were chosen as the loading condition based on the ORNL's former PFM analysis [11]. Table 1 summarizes the transient descriptions of these PTS events [11–13], and the corresponding pressure and temperature histories are shown in Fig. 1. In addition, we assumed that the heat transfer coefficient remains constant and the water from cold leg is totally mixed when it is injected into the RPV.

MSLB (main steam line break) MSLB (main steam line break) SO-2 (secondary stuck-open valve)

P.-C. Huang, et al.

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Fig. 1. Pressure and temperature histories of Beaver Valley PTS transients (a)case 74；(b) case 103；(c) case 110.

equations. Furthermore, the reserved method with the second-order temporal discretization scheme was employed for the present transient simulations. In order to minimize the spatial discretization errors required by the Best Practice Guidelines (BPGs) [15], the second order upwind discretization scheme was adopted in the numerical simulation. All the simulation works presented in this paper were performed using the ANSYS FLUENT [16], which took around 210 hours on a standard desktop quad core CPU (Intel i7-3820, 3.6 GHz) for the Medium grid of a typical PTS transient.

p=

q (p) = ln

N i=1

(3)

21 GCI fine =

1/3

Vi / N

(Unstructured)

hcoarse > 1.3 hfine

2

2

1

+ q (p )

(6)

r21p r21p

s , s = sign s

3

2

2

1

r21p

Fs

2

1

1 1

unum = Unum/ k, k = 1.15

(7)

Under the boundary conditions, Reynolds Number of a fully-developed turbulent flow was set as 450,000 and the no-slip conditions were adopted for CFD calculation. Table 2 shows three types of mesh size: coarse (2,925,718 cells); medium, (4,452,608 cells); fine (7,538,839 cells). Due to the importance of structural integrity of the RPV, the gradient scalars, such as shear stress and heat flux, need to be seriously considered. The circumferential velocities demonstrate the similar trend in three types of mesh sizes as illustrated in Table 2. However,

(4)

Grid Refinement Factor, r :

h=

3

Next, according to the standard, the grid refinement factor should be larger than 1.3 as shown in equation (5), to select three different sizes of grids: coarse, medium, fine, as h3, h2 , h1. It should be noticed that the value of 1.3 is based on experience and not on formal derivation. Then, calculate the apparent order p of the method using equation (6), where r21 = h2/h1 , r32 = h3/ h2 , and h3 > h2 > h1. Where k denotes the simulation value of the variable on the k th grid. Grid Convergence Index (GCI) is a measure of the relative discretization error of the computed solution. Roache et al. [20] suggested a GCI to provide a consistent manner in reporting the results of grid convergence studies and recommended three levels to accurately estimate the order of convergence. The formula is shown in below. This approach used a expansion factor of k = 1.15 and assumed that the fine grid can be represented by Gaussian distribution with 95% confidence. Note that the factor of safety, Fs , was assigned a value of 1.25 for only at least three grid solutions.

The real-size RPV model was constructed based on the BPGs of the U.S. Nuclear Regulatory Commission (NRC) [17,18]. The uncertainties of the variables with monotonic convergence were analyzed based on Richardson's extrapolation as outline from ASME V&V 20-2009 [19] and accomplished through the following procedures. Firstly, calculate the representative grid size, h, for Structured and Unstructured as shown in below, respectively. In these two equations, V represents the volume, and Vi represents the volume of the ith cell. N represents the total number of cells used for the computations. Representative Grid size, h :

(Structured)

ln

where

2.2. Mesh uncertainty

h = [( x max )( ymax )( zmax )]1/3

1 ln(r21)

(5)

Order of Accuracy, p : 3

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Table 2 The parameters of three different mesh sizes. Grid

Coarse

Medium

Fine

Number of cells Representative grid size Mesh pattern

2925718 0.021874

4452608 0.016584

7538839 0.01233

Circumferential velocity

there are still some small differences identified in the region of relatively high velocity. The results of medium and fine mesh seem smoother. According to ASME V&V report for GCI , the mesh uncertainty in this study had been calculated and the value of GCI was 0.03%. It means that the difference between each mesh size could be ignored in following analysis. Further, it is important in turbulence modeling to determine the proper size of the cells near domain walls. The wall Y +, a non-dimensional number and similar to local Reynolds number, is regarded as an index for estimation. It is often used to describe how coarse or fine a mesh is for a particular flow pattern.

Y+ =

u×y v

seen that the wall Y + of different mesh sizes are all less than 2 and meet the requirement. As a result, the three dimensional RPV model was built by medium size meshes with 4,500,000 cells. Fig. 3 shows the 3-D model with enlarged views of the mesh distribution. 3. Probability fracture mechanics analysis and boundary conditions Updated computational technologies have impacted the fracture mechanics and risk-informed evaluations over the past two decades. The updated methodologies have been developed through interactions between various fields, such as fracture mechanics, materials embrittlement, probabilistic risk assessment, and thermal hydraulics, etc. The developers of these methodologies include the U.S. NRC staff and their contractors, and the representatives from the nuclear industry [21]. Recently, these methodologies have been used to update regulations which can ensure the structural integrity of RPVs. The probabilistic fracture mechanics code, FAVOR, which combines the updated methodologies, was used in the study. Two computational modules of the

(8)

In equation (8), u is the friction velocity at the first cell centred near the wall, y is the distance from the first cell centred to the nearest wall, and v is the local kinematic viscosity of the fluid. The turbulence model wall laws have restrictions on the Y + value at the wall. It requires a wall Y + value between approximately 30 and 100, or less than 5. The wall Y + of different mesh sizes in the downcomer are shown in Fig. 2. It can be

Fig. 2. The wall Y+ in downcomer: (a) Coarse (b) Medium (c) Fine. 4

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a KIC (T RTNDT ) = 19.35 + 8.335 exp[0.02254(T RTNDT )] b KIC (T RTNDT ) = 15.61 + 50.132 exp[0.008(T RTNDT )] c KIC = 4 It's a three-parameter Weibull distribution, W (a , b , c ) , as a lowerbounded continuous statistical distribution, has a lower limit (referred to as the location parameter, a KIC ). The location parameter has a zero probability of initiation, if the value of KI below a KIC .b KIC and c KIC represent the parameter of the Weibull distribution as scale parameter and the shape parameter respectively. The definition of conditional probability of initiation (CPI) of each simulated flaw during the transient is the maximum value of cpi ( ) . Meanwhile, the RPV would be defined as failure when the simulated flaw propagates to 90% of vessel wall thickness to determine the conditional probability of failure (CPF). The warm-prestress (WPS) effect, which is characterized as an apparent increase of fracture toughness of ferritic steels after first being “prestressed” at an elevated temperature, was considered in the study [22]. Although some researchers also investigated the fracture behavior of the RPV material in the ductile-to-brittle transition regime and the transferability of the material toughness for the postulated flaws under pressurized thermal shocks [23–25], it has been demonstrated that the baseline WPS model of FAVOR produces more conservative results of PFM analysis [26]. The flaw files of VFLAW are generated by the vessel geometry and some generic values of flaw characteristics, including flaw density, through-wall depth and flaw length (aspect ratio), which are based on data sets from either the PVRUF or SHOREHAM vessels. The flaw depth category and the weld process, such as SAW, SMAW and repair weld are also taken into consideration. Overall, VFLAW will perform 1000 times of Monte Carlo simulation to generate 1000 flaw distribution sets output into the flaw files for FAVOR, based on these parameters. There are total three flaw files which describe the flaw characteristics as the loading boundary conditions of FAVPFM, including surface breaking flaw in S.dat, embedded weld flaw in W.dat, and embedded plate flaw in P.dat generated by VFLAW code [27]. FAVOR assumes all pre-existing internal surface breaking flaws are circumferentially oriented due to inner cladding of the vessel fabrication. At the same time, embedded weld flaws are oriented axially for axial welds, and oriented circumferentially for circumferentially welds. For embedded flaws in plates, 50% of both axially and circumferentially oriented flaws are assigned [27,28]. Analysis of flaws should consider different vessel regions and welding types. Fig. 4 shows the configuration of welds and plates within the beltline region of Beaver Valley 2 RPV, including the corresponding sizes [11]. The inner radius and wall thickness of the RPV beltline region are 78.5 inches and 8.04 inches which includes

Fig. 3. PWR mesh distribution with complete view.

latest version of FAVOR code v16.1 were applied in this study to compare the effects of the thermal gradient on the fracture probability of RPV: (1) the deterministic load generator (FAVLoad), and (2) the Monte Carlo PFM module (FAVPFM). The detailed thermal hydraulic boundary conditions analyzed by CFD were used as the input file for FAVLoad, which also contains the RPV geometry and material properties. First, it calculates and then outputs the histories of stress, temperature and stress intensity factor, KI , with various depth and aspect ratio along the wall thickness of the RPV under each transient. Based on the output of FAVLoad, the instantaneous conditional probability of initiation (cpi) of each simulated flaw tip at each time step, τ, during the transient is calculated according to the Weibull probability function by FAVPFM, given by Ref. [21]:

0, cpi ( ) =

1

exp

(

(KI ( ) b KIC

)

a KIC ) c KIC

KI ( )

a KIC

, KI ( ) > a KIC

(9)

where

Fig. 4. The configuration of welds and plates in the RPV beltline region. 5

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Table 3 Embrittlement-related properties of beltline region materials and corresponding neutron fluence. Material ID

Axial weld

Cir. Weld Plate

305414A 305414B 305424A 305424B 90136 C6317-1 C6293-2 C4381-2 C4381-1

Major Region

Cu (%)

Ni (%)

P (%)

Mn (%)

Initial RTNDT (°F)

Neutron fluence for 36 EFPY (1019n/ cm2)

Neutron fluence for 60 EFPY (1019n/ cm2)

Neutron fluence for 100 EFPY (1019n/ cm2)

Neutron fluence for 200 EFPY (1019n/ cm2)

1 2 3 4 5 6 7 8 9

0.337 0.337 0.273 0.273 0.269 0.200 0.140 0.140 0.140

0.609 0.609 0.609 0.609 0.070 0.540 0.570 0.620 0.620

0.012 0.012 0.013 0.013 0.013 0.010 0.015 0.015 0.015

1.440

−56.0

0.8428

1.5738

2.6182

5.2292

0.964 1.310 1.300 1.400 1.400

−56.0 27.0 20.0 73.0 43.0

4.2523 4.3218

8.1256 8.2642

13.6589 13.8962

27.4923 27.9761

Fig. 5 depict the temperature distribution with the configuration of welds and plates in the RPV beltline region when the PTS transients induced by secondary side break occurs. Three regions can be roughly classified regarding to the different temperature. It can be seen that the axial weld number 305414B is entirely under the cold temperature region; part of plates are in the cold region, especially plate C4381-2, which has the largest cold region. As for the circumferential weld, around 1/3 range is under the cold region caused by the ECC water. Further, the temperature histories of the three regions are shown in Fig. 6. Due to the cold region is directly below the cold leg of the RPV, the temperature histories is similar to the boundary conditions calculated by RELAP. On the contrary, the high temperature regions stay the same temperature condition as the normal operation condition. Therefore, the FAVOR analysis excluded the high temperature region of the RPV beltline region. Based on the above assumptions, the FAVOR analysis results sorted by different temperature regions under various type of PTS transients are listed in Table 6, respectively. It can be seen that the cold region dominates the whole fracture behavior of RPV. Need to be noticed that the presentation of 0.00E+00 in Table 6 is cause by KI < a KIC , as the location parameter has a zero probability of initiation. Furthermore, Fig. 7 shows comparisons of the CPI and CPF of each temperature region under PTS transients with the results that consider the temperature histories calculated from RELAP being applied on the whole beltline region. Approximately one time smaller results are presented. It can be attributed to the less flaws simulated considering different temperature regions than the whole region, as shown in Table 5. Generally speaking, whether or not considering the different temperature regions when performing PFM analysis may cause

Table 4 Boundary conditions of CFD model in normal operation. Boundary conditions

Values

Loop Density (kg/m3) Mass flow rate (kg/s) Normal Operation Temperature (K)

3 740 4410.18 Cold leg: 564.14 Hot leg: 599.45 15258204

Normal Operation Pressure (pa)

0.16 inch stainless-steel cladding, respectively. Table 3 lists the embrittlement-related properties including the weight percentage of the chemical contents and the initial RTNDT of weld and plate materials in the beltline region. The boundary conditions of normal operation for CFD analysis are based on the operating data and listed in Table 4. 4. Analysis results and discussions In order to more clearly distinguish the effects of thermal gradient on vessel intensity against the embrittlement level, 36 to 200 EFPY radiation embrittlement conditions of Beaver Valley 2 have been taken into consideration in this study [11]. Some of the extrapolations used in these analyses are far beyond the range of EFPY for which plants would ever actually operate, the operating life of the RPV later than 40 EFPY were obtained by linear extrapolation from the 32 and 40 EFPY. It should be notice that 100,000 Monte Carlo simulations were performed and more than 1.2 billion flaws were simulated to seek the appropriate solution for each case of FAVPFM analysis.

Fig. 5. The distribution of temperature of RPV beltline region under the MSLB transient. 6

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Fig. 6. Temperature histories of each temperature region of Beaver Valley PTS transients (a)case 74；(b) case 103；(c) case 110.

Fig. 7. The PFM Analysis results of considering thermal gradient of Beaver Valley PTS transients (a)case 74；(b) case 103；(c) case 110.

7

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Table 5 The characteristic of simulate flaw in each region. EFPY32 for MSLB103

Region1 Region2 Region3 Region4 Region5 Region6 Region7 Region8 Region9

Full region

Cold region

Border of the region

Simulate flaw

% of flaws

Initial RTNDT (°F)

Simulate flaw

% of flaws

Initial RTNDT (°F)

Simulate flaw

% of flaws

Initial RTNDT (°F)

1.81E+07 1.81E+07 1.30E+07 1.30E+07 9.75E+07 1.96E+08 1.95E+08 3.15E+08 3.15E+08

1.53 1.53 1.1 1.1 8.25 16.55 16.55 26.69 26.69

−56 −56 −56 −56 −56 27.0 20.0 73.0 43.0

0 1.81E+07 0 0 9.75E+07 5.78E+07 4.58E+07 1.67E+08 0

0 4.68 0 0 25.2 14.98 11.87 43.28 0

−56 −56 −56 −56 −56 27.0 20.0 73.0 43.0

0 0 0 0 9.75E+07 2.18E+07 2.18E+07 7.04E+07 0

0 0 0 0 46.04 10.33 10.33 33.3 0

−56 −56 −56 −56 −56 27.0 20.0 73.0 43.0

different prediction of fracture probability of RPV under PTSs caused by secondary breaks. The CPI and CPF of different temperature regions under MSLB 74 at 36 and 60 EFPY conditions are slightly higher. The reason for that can be attributed to the non-convergent results due to extreme low fracture probabilities at lower embrittlement levels that the sample of PFM analysis was still insufficient. Fig. 8 presents the trends of CPI under MSLB 74 transient at low embrittlement level of 60 EFPY condition to 80,000 Monte Carlo simulations against iteration times. It shows that the trends of iteration are slowly close to each other but not yet fully converged. CPI and CPF of the cold region should be lower than the whole region when it is totally converged. Technically, the more iteration times are performed under ideal condition, the more accurate the results will be. However, CPF against MSLB 74 and SO2110 at low embrittlement level have been approximately around 1 × 10 6 . That means the TWCF, which is the product of CPF and occurrence frequency of PTS transient, will be far below the value of 1 × 10−6/yr of new PTS requirement specified by the U.S. NRC's [29,30]. Accordingly, to reduce the analysis time and resource, the subtle inaccuracy of TWCF at low embrittlement level under secondary side of PTS transient can be ignored.

Fig. 8. The Monte Carlo iteration against CPI.

It is found that the temperature distribution can be mainly divided into three regions, and the cold region dominates the fracture behavior of RPV. Additionally, the cold region is directly below the cold leg of the RPV, where the temperature histories are similar to the RELAP results. Therefore, the fracture probabilities considering the beltline region divided into different temperature regions under PTS transients are approximately one time lower than which conservatively assumes that whole beltline region is under colder condition. Because the fracture mainly occurs in the colder region of beltline shell, the procedure of combining CFD with probability fracture mechanics can provide more reasonable results when the RPV subjects to PTSs caused by the secondary side break accidents.

5. Conclusions This paper presents the effects of non-uniform temperature distribution caused by colder water injected separately into RPV on the fracture probability of a three loop PWR vessel subjected to PTS events. The CFD model of RPV was built to calculate the three-dimensional thermal hydraulic conditions for PFM analysis. To establish the reliable model, the mesh uncertainty test has been performed, and SST k-ω was chosen as the turbulence model for complex geometry. Three typical PTS transients caused by secondary pipe break analyzed from Beaver Valley were investigated in the analysis as the loading condition. Moreover, we assume that the heat transfer coefficient remains constant and the water from cool leg is totally mixed when it is injected in the RPV.

Acknowledgement This work was supported by the Institute of Nuclear Energy Research of Taiwan ROC. The support is greatly acknowledged.

Table 6 The PFM analysis results of each temperature region under PTS transients. Temp. Region

PTS case

Cold temperature region

MSLB 74 MSLB 103 SO-2110

Parting of two regions

MSLB 74 MSLB 103 SO-2110

CPI CPF CPI CPF CPI CPF CPI CPF CPI CPF CPI CPF

32 EFPY

60 EFPY

100 EFPY

200 EFPY

1.54E-07 1.93E-08 1.62E-03 8.29E-04 2.49E-07 5.83E-09 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.96E-06 6.54E-07 1.09E-02 6.81E-03 4.53E-06 3.29E-07 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.18E-05 1.88E-05 5.03E-02 3.53E-02 6.13E-05 1.40E-05 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.77E-03 1.31E-04 3.00E-01 2.47E-01 2.98E-03 1.68E-03 0.00E+00 0.00E+00 5.43E-08 4.58E-09 0.00E+00 0.00E+00

8

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