ML052440190

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Attachment E, Crystal River Unit 3 - License Amendment Request #290, Revision 1 Probabilistic Methodology to Determine the Contribution to Main Steam Line Break Leakage Rates for the Once-Through Steam Generator from the Tube End Crack
ML052440190
Person / Time
Site: Crystal River Duke Energy icon.png
Issue date: 08/10/2005
From: Colgan K, Martin C
AREVA, Framatome ANP
To:
Office of Nuclear Reactor Regulation
References
3F0805-06 51-5053331-01
Download: ML052440190 (39)
v • d • e


Text

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PROGRESS ENERGY FLORIDA, INC.

CRYSTAL RIVER UNIT 3 DOCKET NUMBER 50-302/LICENSE NUMBER DPR-72 ATTACHMENT E LICENSE AMENDMENT REQUEST #290, REVISION 1 Addendum B Dated August 10, 2005 to Topical Report 2346P, Revision 0 Probabilistic Leakage Assessment of Crystal River Unit 3 Steam Generator (SG) Tube End Cracks Non-proprietary

20440-11 (3/30/2004)

A AREVA ENGINEERING INFORMATION RECORD Document Identifier 51 - 5053331 - 01 Title Probabilistic Leakage Assessment of Crystal River Unit 3 SG Tube End Cracks PREPARED BY: REVIEWED BY:

Name K.A.Colgan Name C.E.Martin Signature Date 8/10/2005 Signature Date 8/10/2005 Technical Manager Statement: Initials Reviewer is Independent.

Remarks:

This report documents a probabilistic methodology, developed for Crystal River Unit 3, to determine MSLB leakage rates for the OTSG tube end crack alternate repair criteria. This approach employs the same calculational methodology as that of the tube support plate alternate repair criteria (GL 95-05) incorporated in some PWR licenses. Regulator approval is expected to be required prior to implementation. The methodology is implemented in a MathCad spreadsheet entitled "Leak-TEC" which is described and benchmarked herein.

Revision 1 of this document incorporates comments provided by the Nuclear Regulatory Commission in response to Progress Energy's LAR #290. This document serves as Addendum B to Crystal River Unit 3 Topical Report BAW-2346P, Revision 0.

  • This document contains 38 pages including 13 in Appendix A (i.e., Al through A13).

Framatome ANP, Inc., an AREVA and Siemens Company Pace 1 of 38*

Record of Revisions Section Revision Description of Change Date All 00 Original Release 12/2004 5.1 01 Removed reference to Section 7.0 8/2005 5.2, Step 6 01 Changed "Steps 1 through 6 ... " to read "Steps 1 8/2005 through 5", clarified via footnote number 2 that the one-sided upper 95%/95% result is to be used.

5.3 01 Added footnote regarding POD value to be used, 8/2005 removed reference to Section 7.0 pertaining to new TECs.

6.0 01 Added description of extra benchmarking Tables 6-1 01 Modified Tables 6-1 and 6-2. Added additional 8/2005 and benchmarking runs to Tables 6-1 and 6-2. Added 6-2 footnotes 1 and 2 defining "known returned to service leakage" and "total returned to service leakage",

respectively.

Table 6-1 01 Changed LeakTEC result for SG A LTE as-found 8/2005 leakage from 0.00712 gpm to 0.00709 gpm to correct a typographical error Table 6-3 01 Added footnote 1 defining that the one-sided upper 8/2005 95%/ 95% result is to be used for TEC leakage evaluation. Added footnote 2 defining the POD value to be used. Clarified definition for POD value of 1.0.

7.1 01 Corrected the caution relating to voltage threshold, and 8/2005 clarified POD value to be used. Added clarification that the one-sided upper 95%/95% result is to be used for TEC leakage evaluation.

7.2 01 Deleted 8/2005 7.3 01 Renumbered as 7.2 8/2005 9.0 01 Added Reference 7 8/2005 Document Number 51-5053331-01 Page 2 of 25

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Table of Contents 1.0 Introduction ........................... 4 2.0 Background ........................... 4 3.0 Crystal River Unit 3 MSLB Conditions ............................ 5 4.0 Leakage Test Data ........................... 9 5.0 Probabilistic Leakage Evaluation ........................... 15 6.0 Benchmarking.19 7.0 Field Implementation ........................... 23 8.0 Summary and Conclusions ........................... 25 9.0 References ........................... 25 Appendix A: LeakTEC Listing .......... Al through A13 Document Number 51-5053331-01 Page 3 of 25

1.0 Introduction The NRC-approved bobbin voltage alternate repair criteria (ARC) described in Generic Letter 95-05 utilizes a probabilistic methodology to calculate total steam generator accident leakage at an upper 95% probability and 95% confidence level for axial ODSCC at tube support plates. This report documents an application of the same calculational approach to determine 95%195% accident leakage rates for Crystal River Unit 3 tube end cracks (TEC).

The probabilistic approach calculates bounding SG leakage at a high level of confidence, while reducing some of the conservatisms inherent in the current approach. The methodology is implemented in a MathCad spreadsheet entitled "LeakTEC" which is described and benchmarked within this report.

2.0 Background

Tube cracks have been identified within the roll expanded region near the primary tubesheet face in the Crystal River Unit 3 (CR-3) once through steam generators (OTSGs).

An ARC which allows certain tubes containing TECs to remain inservice has been implemented at CR-3 for several years (Ref. 1). The determination of primary to secondary leakage under main steam line break (MSLB) conditions is an important aspect of the ARC, and is the subject of this evaluation.

MSLB leakage must be evaluated following each tube inspection and the calculated leakage must remain below the limit specified in the ARC. The leakage rates currently used to implement the ARC are based on the results of a laboratory test program (Ref. 1).

The program applied simulated MSLB loads to a tube/tubesheet mockup and measured the resultant leakage though EDM notches within the tube under test. The testing demonstrated that expansion joint tightness is the key parameter which correlates with leakage rate. Joint tightness is quantified with a parameter called "delta dilation," a plant specific parameter which depends primarily upon axial tube load, tubesheet deformation, and primary pressure.

In the development of the ARC, the leakage test results were used with plant specific delta dilations to develop bounding leak rate estimates for various regions of the tubesheet. As currently implemented, these limiting leak rates are assigned to each identified TEC; a significant source of conservatism. Another significant source of conservatism lies in the use of delta dilation values which do not reflect the substantial difference between CR-3 axial tube loads and those employed in the leakage testing program. This is discussed in more detail in Section 3.0.

In recent years, the number of identified TECs has continued to increase and continued initiation is expected in both the hot and cold tube end regions. This, coupled with the conservatisms discussed above, may lead to significant increases in the number of tube repairs required. As a result, CR-3 initiated an effort to refine the method used to determine SG leakage associated with TECs. This report documents the results of that effort.

Document Number 51-5053331-01 Page 4 of 25

3.0 Crystal River Unit 3 MSLB Conditions Specific CR-3 MSLB conditions which relate to this evaluation are discussed in this section. A more detailed discussion of MSLB conditions and assumptions is provided in Ref. 2.

During a CR-3 MSLB, the SG which is unaffected by the line break is rapidly isolated from the break, effectively preventing any leakage from that SG from significantly impacting offsite radiation dose rates. Therefore, the SG loads most appropriate for evaluating leakage to the environment are those associated with the SG whose steam line breaks (i.e.,

the "affected" SG).

The parameters most relevant to this evaluation are axial tube load and delta dilation.

Table 3-1 summarizes CR-3 axial tube load and delta dilation values as a function of radial position within the tubesheet for the affected SG (Ref. 2). These values are based on the limiting assumption that 25% of the tubes are plugged when the MSLB occurs.

The unadjusted delta dilation values in Table 3-1 reflect tubesheet distortion, tube/tubesheet thermal deformation, and free (non-end capped) pressure tube dilation effects. However, they do not reflect the affect of axial load on tube dilation (Ref. 3). For the ARC as it is currently implemented, this approach is appropriate because leakage test results are applied in a similar manner. Specifically, even though a bounding axial load was imposed during the leak testing, the calculated delta dilations for the leak tests did not reflect that effect; therefore, the tested joint was actually looser (i.e., greater tube-to-tubesheet delta dilation) than indicated by the calculated delta dilation values. Because the CR-3 MSLB tube loads (663 Wbf. max) are substantially lower than the tube load employed during the leak tests (3,060 lbf.), exclusion of this effect imposes an excessive level of conservatism on the estimated CR-3 MSLB leakage rate.

For this evaluation, CR-3 MSLB delta dilation values are adjusted to reflect the affect of axial tube load on joint tightness. This adjustment is discussed below. The leakage data, also adjusted for this effect, is discussed in Section 4.0.

Figure 3-1 illustrates that the axial tube load varies with tubesheet radius. Tubes located near the center of the tubesheet will experience compressive axial loads during an MSLB therefore no dilation adjustment is applied for these tubes. The tube diameter reduction resulting from an axial tensile load is calculated with the following equation:

ADiaineter -_- PRov nfRmidEt where:

P = axial load from Table 3-1 (Ibf)

Ro= outer radius within roll expansion (inch) v = Poisson's ratio Document Number 51-5053331-01 Page 5 of 25

Rmid' mid wall radius within roll expansion (inch)

E = modulus of elasticity at MSLB tube temperature (psi) t = tube wall thickness within roll expansion (inch)

This calculation is documented in Ref. 4 and the resulting adjusted delta dilations are provided in Table 3-1. Figures 3-2 and 3-3 illustrate that because of the relatively low loads, the adjustment causes very little change in the delta dilation values.

Figure 3-1, CR-3 MSLB Axial Tube Load 700 I I I g I I I I I I I I I I I I I I I r I I I I I I I I I I IS 600- . - - - -- -- r--I------ I--I I--/ -------- - - -- {-

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Document Number 51-5053331-01 Page 6 of 25

Figure 3-2, CR-3 Upper Tube End Delta Dilation 1.25 1.00 0.75 0.50 ------------L-----

E 0.25 C

0 I I- - - - - - - - - r

= 0.00 X -0.25 0

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- - -

  • Before Adjustnent - After AdjustnTnt Figure 3-3, CR-3 Lower Tube End Delta Dilation 1.25 I 1.00 - - - - - - - - - - - - - -T-4 - - - - - - - - -- - - - - - - - - - -4 I I I I I I I I 0.75

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- - - . Before Adjustment - After Adjustment Document Number 51-5053331-01 Page 7 of 25

Table 3-1, CR-3 MSLB Delta Dilations and Tube Loads (Affected SG, 25% tube plugging)

Delta Dilation (mils)

Tubesheet Radius Before Adjusting for Axial Load After Adjusting for Axial Load (in.) Axial Load (Ibf)

(in.) . Upper Tube End Lower Tube End Upper Tube End Lower Tube End 3 -159 -0.75 -0.83 -0.75 -0.83 4 -159 -0.82 -0.91 -0.82 -0.91 5 -157 -0.86 -0.95 -0.86 -0.95 6 -155 -0.88 -0.98 -0.88 -0.98 7 -152 -0.90 -0.99 -0.90 -0.99 8 -149 -0.91 -1.00 -0.91 -1.00 9 -144 -0.92 -1.01 -0.92 -1.01 10 -139 .0.92 -1.02 -0.92 -1.02 11 -134 -0.93 -1.02 -0.93 -1.02 12 -127 -0.93 -1.02 -0.93 -1.02 13 -120 -0.93 -1.02 -0.93 -1.02 14 -112 -0.92 -1.01 -0.92 -1.01 15 -104 -0.90 -0.99 -0.90 -0.99 16 -95 -0.89 -0.98 -0.89 -0.98 17 -85 -0.87 -0.96 -0.87 -0.96 18 -75 -0.85 -0.95 -0.85 -0.95 19 -65 -0.84 -0.93 -0.84 -0.93 20 -53 -0.82 -0.92 -0.82 -0.92 21 -42 -0.80 -0.90 -0.80 -0.90 22 -29 -0.78 -0.88 -0.78 -0.88 23 -17 -0.76 -0.86 -0.76 -0.86 24 -3 -0.74 -0.84 -0.74 -0.84 25 10 -0.72 -0.82 -0.72 -0.82 26 25 -0.70 -0.80 -0.70 -0.80 27 39 -0.68 -0.78 -0.68 -0.78 28 54 -0.66 -0.76 -0.66 -0.76 29 70 -0.64 -0.73 -0.63 -0.72 30 85 -0.62 -0.71 -0.61 -0.70 31 101 -0.59 -0.69 -0.58 -0.68 32 118 -0.57 -0.66 -0.56 -0.65 33 135 -0.54 -0.64 -0.53 -0.63 34 152 -0.52 -0.61 -0.51 -0.60 35 169 -0.50 -0.59 -0.48 -0.57 36 187 -0.47 -0.56 -0.45 -0.54 37 205 -0.45 -0.53 -0.43 -0.51 38 223 -0.43 -0.51 -0.41 -0.49 39 242 -0.40 -0.48 -0.38 -0.46 40 260 -0.38 -0.45 -0.36 -0.43 41 279 -0.36 -0.43 -0.33 -0.40 42 298 -0.34 -0.40 -0.31 -0.37 43 318 -0.32 -0.38 -0.29 -0.35 44 337 -0.30 -0.35 -0.27 -0.32 45 357 -0.28 -0.32 -0.25 -0.29 46 377 -0.26 -0.30 -0.23 -0.27 47 398 -0.25 -0.27 -0.21 -0.23 48 419 -0.23 -0.24 -0.19 -0.20 49 440 -0.21 -0.21 -0.17 -0.17 50 462 -0.19 -0.18 -0.15 -0.14 51 485 -0.16 -0.14 -0.12 -0.10 52 509 -0.12 -0.10 -0.07 -0.05 53 534 -0.07 -0.04 -0.02 0.01 54 561 0.01 0.04 0.06 0.09 55 591 0.14 0.17 0.19 0.22 56 624 0.44 0.44 0.50 0.50 57 663 1.01 0.93 1.07 0.99 57.72 663 0.92 0.81 0.98 0.87 Document Number 51-5053331-01 Page 8 of 25

4.0 Leakage Test Data In a manner similar to that described above for the CR-3 delta dilations, the leakage test results documented in Ref. 1 were adjusted to account for tube dilation under the applied test conditions.

During the tests the tubesheet mockup was loaded bilaterally to vary the extent of bore hole dilation while the tube was internally pressurized and axially loaded in tension. Positive bore hole dilation and the axial tensile load work to reduce joint tightness (i.e., a more positive delta dilation) while the internal tube pressure works to increase joint tightness.

As discussed in Section 3.0, the ARC as it is currently applied is based upon leak test results which do not account for the affect of axial load on delta dilation. However, for this evaluation, axial loading is taken into account. Under the limiting MSLB conditions tested (axial load 3060 lbf; pressure 2640 psi), the net tube dilation was determined to be +0.13 mils (Ref. 4)'. This value was subtracted from the tubesheet mockup bore dilations to arrive at the appropriate delta dilation values. The mockup bore dilations and resulting delta dilations, along with measured leakage rates, are provided in Table 4-2.

One test point (X bore dilation: 0.2 mils; Y bore dilation 1.5 mils; log(leakage): -6.69) had an indicated leakage that was several orders of magnitude lower than all other tests with the same delta dilation value and was therefore omitted from the evaluation.

Figure 4-1 illustrates the linear relationship between delta dilation and the logarithm of leakage. Table 4-1 provides the sample estimates of regression parameters for this relationship:

Table 4-1, Leakage Regression Sample Parameters Regression Line Variance-Covariance Matrix Number of Data Points (N) 119 Intercept l Slope Intercept (B) -4.7493 0.011564 (V,) -0.0090940 (V12)

Slope (M) l 1.0063 -0.0090940 (V2 1) 0.013193 (V22)

Standard Error of Regression (S) 0.79382 In order to employ the probabilistic techniques as described in this report, it is necessary to confirm that the variation of log(leakage) about the regression line is normally distributed, and that no systematic variation of residuals exists with respect to delta dilation. Figure 4-2 illustrates that the regression residuals closely follow a normal distribution. An examination of Figure 4-3 confirms that there is no significant systematic relationship between the magnitude of regression residual and delta dilation. This validates the underlying assumptions required to implement the probabilistic evaluation described in the next section.

. The tube dilation associated with test pressure alone is +0.41mils, the value used to determine delta dilation in Reference 1.

Document Number 51-5053331-01 Page 9 of 25

Figure 4-1, OTSG Tube End Leakage vs Delta Dilation 0

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-2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 12 1.6 2.0 Residual

- - -- Norrral Dstrbution - Actual Residual Dstribution Document Number 51-5053331-01 Page 10 of 25

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Document Number 51-5053331-01 Page I11 of 25

Table 4-2, Leakage Test Results (Total axial load: 3,060 lbf; Pressure: 2,640 psi)

Diametral Dilation (mils) Leakage (gpm)

Tubesheet Mockup Bore / Tube Limiting (Ref. 1, Table B-1)

Bore Dilation Delta Dilation Delta X Y X y Dilation Measured Log 10 0 0 -0.13 -0.13 -0.13 1.41E-04 -3.851 0 0 -0.13 -0.13 -0.13 5.24E-05 -4.281 0 0 -0.13 -0.13 -0.13 1.09E-06 -5.963 0 0 -0.13 -0.13 -0.13 3.87E-06 -5.412 0 0 -0.13 -0.13 -0.13 2.66E-06 -5.575 0 0.2 -0.13 0.07 0.07 1.91 E-04 -3.719 0 0.2 -0.13 0.07 0.07 4.92E-05 -4.308 0 0.2 -0.13 0.07 0.07 1.33E-06 -5.876 0 0.2 -0.13 0.07 0.07 3.75E-06 -5.426 0 0.2 -0.13 0.07 0.07 3.51 E-06 -5.455 0 0.4 -0.13 0.27 0.27 1.47E-03 -2.833 0 0.4 -0.13 0.27 0.27 4.78E-05 -4.321 0 0.4 -0.13 0.27 0.27 2.54E-06 -5.595 0 0.4 -0.13 0.27 0.27 8.60E-06 -5.066 0 0.4 -0.13 0.27 0.27 5.69E-05 -4.245 0 0.6 -0.13 0.47 0.47 1.82E-03 -2.740 0 0.6 -0.13 0.47 0.47 1.84E-05 -4.735 0 0.6 -0.13 0.47 0.47 2.42E-06 -5.616 0 0.6 -0.13 0.47 0.47 2.30E-05 -4.638 0 0.6 -0.13 0.47 0.47 3.74E-05 -4.427 0 0.8 -0.13 0.67 0.67 2.09E-03 -2.680 0 0.8 -0.13 0.67 0.67 1.96E-05 -4.708 0 0.8 -0.13 0.67 0.67 2.03E-05 -4.693 0 0.8 -0.13 0.67 0.67 6.76E-05 -4.170 0 0.8 -0.13 0.67 0.67 2.23E-05 -4.652 0 1.1 -0.13 0.97 0.97 3.70E-03 -2.432 0 1.1 _ -0.13 0.97 0.97 1.65E-04 -3.783 0 1.1 -0.13 0.97 0.97 7.99E-06 -5.097 0 1.1 -0.13 0.97 0.97 3.75E-05 -4.426 0 1.1 -0.13 0.97 0.97 6.73E-05 -4.172 0.2 1.5 0.07 1.37 1.37 1.20E-02 -1.921 0.2 1.5 0.07 1.37 1.37 1.20E-04 -3.921 0.2 1.5 0.07 1.37 1.37 2.80E-05 -4.553 0.2 1.5 0.07 1.37 1.37 1.57E-04 -3.804 0.2 1.5 0.07 1.37 1.37 3.03E-04 -3.519 0.3 2 0.17 1.87 1.87 1.19E-02 -1.924 0.3 2 0.17 1.87 1.87 6.50E-04 -3.187 0.3 2 0.17 1.87 1.87 2.71 E-05 -4.567 0.3 2 0.17 1.87 1.87 1.95E-03 -2.710 0.3 2 0.17 1.87 1.87 7.48E-03 -2.126 0 0 -0.13 -0.13 -0.13 8.04E-06 -5.095 0 0 -0.13 -0.13 -0.13 4.50E-05 -4.347 0 0 -0.13 -0.13 -0.13 5.25E-06 -5.280 0 0 -0.13 -0.13 -0.13 1.08E-05 -4.967 0 0 -0.13 -0.13 -0.13 2.93E-05 -4.533 Document Number 51-5053331-01 Page 12 of 25

Table 4-2, Continued Diametral Dilation (mils) Leakage (gpm)

Tubesheet Mockup Bore / Tube Limiting (Ref. 1, Table B-i)

Bore Dilation Delta Dilation Delta _ -

x y x y Dilation Measured Log 10 o 0.2 -0.13 0.07 0.07 4.98E-05 -4.303 0 0.2 -0.13 0.07 0.07 1.13E-04 -3.947 0 0.2 -0.13 0.07 0.07 1.56E-05 -4.807 0 0.2 -0.13 0.07 0.07 3.93E-05 -4.406 0 0.2 -0.13 0.07 0.07 1.20E-04 -3.921 0 0.4 -0.13 0.27 0.27 3.15E-05 -4.502 0 0.4 -0.13 0.27 0.27 1.17E-04 -3.932 0 0.4 -0.13 0.27 0.27 2.17E-05 -4.664 0 0.4 -0.13 0.27 0.27 5.14E-05 -4.289 0 0.4 -0.13 0.27 0.27 7.54E-05 -4.123 0 0.6 -0.13 0.47 0.47 2.98E-05 -4.526 0 0.6 -0.13 0.47 0.47 1.13E-04 -3.947 0 0.6 -0.13 0.47 0.47 2.96E-05 -4.529 0 0.6 -0.13 0.47 0.47 3.48E-05 -4.458 0 0.6 -0.13 0.47 0.47 5.41 E-04 -3.267 0 0.8 -0.13 0.67 0.67 4.13E-05 -4.384 0 0.8 -0.13 0.67 0.67 1.20E-04 -3.921 0 0.8 -0.13 0.67 0.67 3.46E-05 -4.461 0 0.8 -0.13 0.67 0.67 3.71 E-05 -4.431 0 0.8 -0.13 0.67 0.67 5.61 E-04 -3.251 0 1.1 -0.13 0.97 0.97 6.88E-05 -4.162 0 1.1 -0.13 0.97 0.97 1.28E-04 -3.893 0 1.1 -0.13 0.97 0.97 2.44E-05 -4.613 0 1.1 -0.13 0.97 0.97 5.11 E-05 -4.292 0 1.1 -0.13 0.97 0.97 7.96E-04 -3.099 0.2 1.5 0.07 1.37 1.37 1.19E-04 -3.924 0.2 1.5 0.07 1.37 1.37 4.03E-04 -3.395 0.2 1.5 0.07 1.37 1.37 1.72E-03 -2.764 0.2 1.5 0.07 1.37 1.37 3.38E-03 -2.471 0.3 2 0.17 1.87 1.87 1.95E-03 -2.710 0.3 2 0.17 1.87 1.87 1.64E-03 -2.785 0.3 2 0.17 1.87 1.87 6.95E-05 -4.158 0.3 2 0.17 1.87 1.87 4.69E-03 -2.329 0.3 2 0.17 1.87 1.87 7.53E-03 -2.123 0 0 -0.13 -0.13 -0.13 3.73E-05 -4.428 0 0 -0.13 -0.13 -0.13 2.84E-05 -4.547 0 0 -0.13 -0.13 -0.13 3.02E-05 -4.520 0 0 -0.13 -0.13 -0.13 2.04E-06 -5.690 0 0 -0.13 -0.13 -0.13 4.44E-05 -4.353 0 0.2 -0.13 0.07 0.07 3.07E-05 -4.513 0 0.2 -0.13 0.07 0.07 7.61 E-04 -3.119 0 0.2 -0.13 0.07 0.07 2.17E-05 -4.664 0 0.2 -0.13 0.07 0.07 2.04E-06 -5.690 0 0.2 -0.13 0.07 0.07 1.57E-06 -5.804 0 0.4 -0.13 0.27 0.27 5.13E-05 -4.290 Document Number 51-5053331-01 Page 13 of 25

Table 4-2, Continued Diametral Dilation (mils) Leakage (gpm)

Tubesheet Mockup Bore / Tube Limiting (Ref. 1, Table B-1)

Bore Dilation Delta Dilation Delta x Y x y Dilation Measured Log 10 0 0.4 -0.13 0.27 0.27 7.66E-04 -3.116 0 0.4 -0.13 0.27 0.27 3.04E-05 -4.517 0 0.4 -0.13 0.27 0.27 9.13E-06 -5.040 0 0.4 -0.13 0.27 0.27 1.33E-06 -5.876 0 0.6 -0.13 0.47 0.47 6.99E-05 -4.156 0 0.6 -0.13 0.47 0.47 1.77E-03 -2.752 0 0.6 -0.13 0.47 0.47 6.88E-05 -4.162 0 0.6 -0.13 0.47 0.47 2.35E-05 -4.629 0 0.6 -0.13 0.47 0.47 1.94E-06 -5.712 0 0.8 -0.13 0.67 0.67 4.99E-05 -4.302 0 0.8 -0.13 0.67 0.67 3.91 E-03 -2.408 0 0.8 -0.13 0.67 0.67 8.56E-05 -4.068 0 0.8 -0.13 0.67 0.67 5.30E-05 -4.276 0 0.8 -0.13 0.67 0.67 7.02E-06 -5.154 0 1.1 -0.13 0.97 0.97 9.74E-05 -4.011 0 1.1 -0.13 0.97 0.97 5.35E-03 -2.272 0 1.1 -0.13 0.97 0.97 1.71E-04 -3.767 0 1.1 -0.13 0.97 0.97 1.71 E-04 -3.767 0 1.1 -0.13 0.97 0.97 2.30E-05 -4.638 0.2 1.5 0.07 1.37 1.37 1.32E-03 -2.879 0.2 1.5 0.07 1.37 1.37 8.98E-03 -2.047 0.2 1.5 0.07 1.37 1.37 6.47E-04 -3.189 0.2 1.5 0.07 1.37 1.37 3.01 E-05 -4.521 0.2 1.5 0.07 1.37 1.37 5.96E-05 -4.225 0.3 2 0.17 1.87 1.87 2.99E-02 -1.524 0.3 2 0.17 1.87 1.87 1.24E-02 -1.907 0.3 2 0.17 1.87 1.87 7.57E-03 -2.121 0.3 2 0.17 1.87 1.87 2.55E-04 -3.593 0.3 2 0.17 1.87 1.87 5.72E-05 -4.243 Document Number 51-5053331-01 Page 14 of 25

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5.0 Probabilistic Leakage Evaluation The probabilistic calculation of CR-3 TEC leakage is implemented in MathCad spreadsheet "LeakTEC" (Appendix A). LeakTEC uses the delta dilation values from Section 3.0, the regression parameters developed in Section 4.0, and specific ECT inspection results to determine total SG leakage at various probability and confidence levels. This section describes the methodology employed within LeakTEC to accomplish this task. A complete validation of LeakTEC is documented in Ref. 4.

5.1 Overview For each TEC identified during an inspection, a leakage value corresponding to the crack's delta dilation is obtained by sampling from the leakage regression. These probabilistic leakage values reflect the uncertainty that is inherent in the regression. The sum of the leakage samples from all identified cracks represents one probabilistic estimate - or one Monte Carlo trial - of total SG leakage. Repeated many times, this process generates a collection of probabilistic estimates of total SG leakage. This collection is the simulated distribution of total SG leakage from which values at a desired probability and confidence level can be directly obtained.

Leakage may be evaluated for either condition monitoring (CM) or operational assessment (OA) purposes. This is the only option required to be specified by the LeakTEC user. The CM evaluation estimates MSLB leakage for all cracks as found, while the OA evaluation accounts for the inspection technique's probability of detection (POD) and any tube repairs performed to address TECs. The leakage associated with new cracks which develop during the next operating interval must also be accounted for in the OA; however, this aspect of the evaluation is beyond the scope of this document. Progress Energy has developed an analytical means of accounting for this source of leakage.

LeakTEC accepts as an input, a list of tubes which contain TECs, identified by row and column. For each tube the following additional information must also be provided: the affected tube end, the number of cracks, maximum crack voltage, and an indicator as to whether the tube will be repaired. The spreadsheet determines each tube's radial position within the tubesheet matrix based on the row and column values. In turn, the CR-3 MSLB delta dilation is determined for each tube based on its radial position within the tubesheet.

5.2 Condition Monitoring Leakage Determination At the heart of LeakTEC lies the Monte Carlo simulation which generates probabilistic leakage estimates for each crack and determines total leakage at desired probability and confidence levels. The approach employed is closely modeled on the process used in the TSP ODSCC ARC (Ref. 5). Probabilistic slope, intercept, and regression error values are generated for each Monte Carlo trial. For each crack, these values are used along with a random normal deviate applied to the regression error, to generate a probabilistic leak rate estimate. These estimates are summed to generate a probabilistic estimate of total SG Document Number 51-5053331-01 Page 15 of 25

leakage; a process that is repeated thousands of times. This process as applied to condition monitoring is described in more detail below.

Step 1: The X2distribution is used to model the uncertainty which is inherent in the sample estimate of standard error of regression provided in Section 4.0. In the equations below a random X2 deviate for N-2, or 117 degrees of freedom is used to generate a probabilistic value of the standard error of regression:

(N-2)

JV e2

({V-21PAVW RnS = SJ where:

N = number of data pairs used to calculate the regression coefficients N= 119 S = sample estimate of the standard error of regression S = 0.79382 RnS = probabilistic standard error of regression Step 2: The same approach is used to generate probabilistic estimates of the variance-covariance values for slope and intercept:

RnVII = fVv RnV1 2 = fV12 RnV 2 2, fVV2 where:

VII = sample estimate of the variance of the intercept V12 = sample estimate of the covariance of intercept and slope V22 = sample estimate of the variance of the slope RnVVx, = probabilistic value Step 3: A probabilistic intercept value is then generated as follows:

Rn/33 = B + Z a/J;I where:

B = sample estimate of the intercept B=-4.7493 Z, = a random normal deviate Document Number 51-5053331-01 Page 16 of 25

Rnfl3 = probabilistic intercept Step 4: A probabilistic value for slope must also be generated. While the slope and intercept are individually normally distributed, they are not independent of each other.

Taken together they are bivariate normally distributed. The probabilistic value of slope is constrained by the probabilistic value of intercept developed in Step 3. This co-dependence is quantified by parameter V12, the covariance of intercept and slope. The probabilistic slope value is calculated as follows:

Rn34=M +Z1 iVr RnV7_ (Rn V,2)2 where:

M = sample estimate of the slope M = 1.0063 Z2 = a random normal deviate Rn/84 = probabilistic slope Step 5: Using the probabilistic values of slope, intercept, and regression error a probabilistic estimate of leakage is obtained for each crack. The sum of the leakage for all cracks represents one probabilistic estimate of total SG leakage:

Leakage, = InvLoglo (Rn /3 + DD1 Rn/34 + Z3 RnS)

NumCracks SGLeakk = E Leakage, i=1 where:

DD, = delta dilation for crack i Z3 = a random normal deviate Leakages = leakage rate for crack i SGLeakk = total SG leakage rate for trial k Step 6: Steps 1 through 5 are repeated, generating thousands of SGLeakk values. Together these values represent the simulated distribution of expected total SG leakage. Once ordered from smallest to largest, leakage values at desired probability and confidence levels can be taken directly from the distribution using an appropriate index value. For example, the one-sided upper 95% probability / 95% confidence 2 value of leakage in an ordered distribution of 10,000 values would be the 9,537h value. This index is the smallest value of n for which the following relationship is true (Ref. 5):

2 The statistical figure of merit to be used to evaluate TEC leakage against the accident leakage performance criteria is the one-sided upper 95% probability / 95% confidence value.

Document Number 51-5053331-01 Page 17 of 25

N-n+21 1 + N-n Fl-,2(N-n+1),2n where:

P = probability (fractional) 1-a = confidence (fractional)

N = number of trials F = critical value from the F-distribution n = the index corresponding to the specified probability and confidence 5.3 Operational Assessment Leakage Determination The OA calculation is identical to the process described above except for one additional step. That step adjusts the number of cracks in each tube to reflect the inspection POD and to reflect any tube repairs to be performed prior to returning the SG to service. Within LeakTEC this step is performed for all imported tubes prior to each Monte Carlo trial. It is applied probabilistically such that "fractional cracks" are appropriately represented in the results.

As illustrated by the following equation, a POD value of less than one increases the number of inservice cracks expected during the next operating cycle, while tube repairs reduce the number of inservice cracks:

NumCracks(n+l) = NumCracksn _NwnRepaired, POD where:

NumCracksn = the number of TECs identified in a particular tube during the current outage Nu=Repairedn = of the TECs above, the number removed from service during the current outage NumCracks(.+l) = the number of TECs expected at the next outage in a tube having the same delta dilation value For example if POD is 0.843, a tube with two cracks identified and repaired during the current outage would yield 0.381 cracks for OA evaluation purposes. To account for the fractional crack, prior to each Monte Carlo trial the fraction is compared with a random number between zero and one. If the random number is greater than the fraction, the number of cracks is rounded down to the nearest integer. Otherwise it is rounded up to the nearest integer. For this example, in a large number of trials the number of cracks 3The NRC approved value of POD for estimating the quantity of undetected TEC leakage is 0.84.

Document Number 51-5053331-01 Page 18 of 25

evaluated for this tube will equal one in 38.1% of the trials (i.e., 0.381 x 100%) and will equal zero in 61.9% of the trials.

6.0 Benchmarking It is desirable to benchmark the probabilistic approach described in this report against the deterministic approach described in Ref. 1. To accomplish this, October 2003 (EOC13)

CR-3 inspection results were evaluated using LeakTEC and the results were compared with those documented in the post-inspection CMOA (Ref. 6).

Additional deterministic estimates for EOC13 were also developed (Ref. 7) for benchmarking purposes in response to comments received from the NRC. These estimates are based on a methodology similar to that of Ref. 6; however, a continuous leakage vs.

delta dilation relationship was used in lieu of tubesheet zones. Estimates were generated with and without consideration for the affect of tube load on delta dilation values from the leakage test program (i.e., Poisson Effect). Note that these additional deterministic estimates are provided for benchmarking purposes only.

Tables 6-1 and 6-2 summarize the leakage values determined using the various approaches, while detailed LeakTEC results are provided in Table 6-3. As expected, the probabilistic approach yields lower leakage estimates than the Ref. 6 deterministic approach. Tables 6-1 and 6-2 illustrate that LeakTEC reduces the estimated MSLB leakage by a factor of up to 3.3.

The elimination of tubesheet zones in the deterministic evaluation produced a 12% to 15%

reduction in the estimates of total SG leakage returned to service as compared with the Ref.

6 approach. Accounting for the Poisson Effect further reduced the estimates by an additional 45%. In a number of cases, these deterministic estimates fall below the probabilistic values.

Document Number 51-5053331-01 Page 19 of 25

Table 6-1, SG A EOC13 MSLB Leakage Comparison Leak Rate Estimnates(GPM)

Known Returned to Total Returned to As-Found Service] Service2

. CMOA 0.932 0.266

> Deterministic,No Zones, 0.783 0.239 0.388 t iv/o Poisson Effect w

,i Deterministic,No Zones, 0.370 0.113 0.183 N With Poisson Effect

_ LeakTEC (95195) 0.296 0.127 0.186 CMOA 0.0130 0.0130 --

> Deterministic, No Zones, 0.0114 0.0114 0.0136 U qu Wo PoissonEffect R Deterministic, No Zones, 0.00541 0.00541 0.00644 With, Poisson Effect__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

LeakTEC (95/95) 0.00709 0.00726 0.00848 i CMOA 0.945 0.279 0.459

.a t Deterministic, No Zones, 0.794 0.250 0.402 w/o Poisson Effect L Deterministic, No Zones, 0.375 0.118 0.189 With Poisson Effect 0_3_75_______0_18

_ LeakTEC (95/95) 0.298 0.132 0.188 I. -Knownxeturnea to service is tme leaKage trom INurE-lUentifiea lE.s that were not repaireu dunng tme outage.

2. 'Total Returned to Service' includes leakage 'Known Returned to Service' plus leakage from TECs not identified by NDE but expected to be present based on a POD of 0.84.

Document Number 51-5053331-01 Page 20 of 25

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Table 6-2, SG B EOC13 MSLB Leakage Comparison Leak Rate Estitnates (GPM)

Known Returned to Total Returned to As-Found Servicel Service2 G CMOA 1.102 0.278 k 3 Detenninistic, No Zones, 0.985 0.242 0.430 S^ w/o Poisson Effect rpM Deterministic, No Zones, 0.466 0.115 0.203 With Poisson Effect .

_ LeakTEC(95195) 0.344 0.123 0.191 CMOA 0.124 0.107 --

l Detenninistic,No Zones, 0.0884 0.0796 0.0964 s a w/o Poisson Effect R Deterministic, No Zones, 0.018 0.0376 0.056 k With PoissonEffect 001 .36005 LeakTEC (95195) 0.0418 0.0388 0.0455 s CMOA 1.226 0.385 0.619 z: Detenninistic,No Zones, 1.073 0.322 0.526

w/o Poisson Effect 1_073_0_322_0_526 2% Detenninistic, No Zones, 0.508 0.153 0.249 Wit/h Poisson Effect ___ __ __ __ __ _0__ _ 153__ __ _ _ 0__ _249 __

_ LeakTEC (95/95) 0.376 0.156 0.228

1. 'Known Returned to Service' is the leakage from NDE-identified TECs that were not repaired during the outage.
2. 'Total Returned to Service' includes leakage 'Known Returned to Service' plus leakage from TECs not identified by NDE but expected to be present based on a POD of 0.84.

Document Number 51-5053331-01 Page 21 of 25

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Table 6-3, LeakTEC Results based on EOC13 Inspection Data It Leakage (gpm) l Computation I Tvpe I POD l @ /50/50 @ 95/50 @ 95/95 l Time (min.)*

SGA Upper CM1T 2 0.151 0.293 0.296 7.0 1467 UTECs, 246 OA 0.84 0.0909 0.184 0.186 9.5 OA 1.00 0.0625 0.126 0.127 8.0 SG A Lower CM l lc 0.000863 l 0.00686 l 0.00709 0.05 0 Repaired, 7 RTS OA 0.84 0.00110 0.00815 0.00848 0.07 OA 1.00 0.000832 0.00702 0.00726 0.07 SG A Combined 1467 UTECs, CM 0.153 0.294 0.298 7.0 7 LTECs, 246 Repaired, OA 0.84 0.0932 0.185 0.188 10.0 1228 RTS OA 1.00 0.0641 0.130 0.132 8.5 SG B Upper CMI7 T 24 0.175 0.340 0.344 5.75 Repaired, 959 RTS OA 0.84 0.0949 0.189 0.191 8.5 OA 1.00 0.0609 0.122 0.123 6.5 SG B Lower l 115CM l l c 0.0156 0.0410 0.0418 0.5 3 Repaired, 112 RTS OA l 0.84 0.0175 l 0.0446 0.0455 1.0 OQA l 1.00 0.0142 1 0.0381 0.0388 0.75 SG B Combined l 1173 UTECs, CM J - l 0.193 J 0.372 0.376 6.25 115 LTECs, 217 OA l 0.84 0.114 j 0.225 l 0.228 8.75 Repaired, 1071 RTS OA l 1.00 0.0772 0.154 0.156 7.5 RTS = Returned to service UTEC = Upper Tube End Cracks LTEC = Lower Tube End Cracks Number of Trials = 20,000 in all cases

  • Witha 2.16 GHz Pentium 4 CPU
1. The statistical figure of merit to be used to evaluate TEC leakage against the accident leakage performance criteria is the one-sided upper 95% probability / 95% confidence value.
2. The NRC approved value of POD for estimating the quantity of undetected TEC leakage is 0.84.

The POD value of "1.0" is only a mathematical means of calculating the "known return to service" part of the total return to service leakage.

Document Number 51-5053331 -01 Page 22 of 25

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7.0 Field Implementation 7.1 User Instructions A typical implementation of LeakTEC involves the following steps:

1) Confirm that the spreadsheet to be used is the validated version by running it with input data from a documented case such as those discussed in Section 6.0. Confirm that the same results are generated. Note that due to the probabilistic nature of this calculation, the repeatability of results is dependent upon the number of trials used. If the number of trials specified is too low, the results will vary significantly from one run to another.
2) Within the "Options and Inputs" section of LeakTEC, perform the following:

a) Choose the type of leakage assessment to be performed (CM or OA).

b) If "Operational Assessment" was selected, specify the POD value. The NRC approved POD value for estimating the leakage from undetected TECs is 0.84.

To determine the known leakage returned to service - that is, leakage from TECs identified by NDE and not repaired - execute the "Operational Assessment" option with a POD value of 1.0.

c) Specify an appropriate voltage screening threshold. If no screening is to be applied, VThresh should equal zero.

CAUTION A non-zero value for voltage threshold may only be used if approved by the NRC.

d) Specify the Excel file which contains crack data to be imported. Do this by modifying the filename and data range within the properties of the "InCrkDat" source file. The following example illustrates the required Excel file format:

Number of Maximum Row Column Tube End Cracks Repair Flag Voltage 113 115 UTE 2 N 0.2 N = not to be repaired R = to be repaired

3) Occasionally it may be desirable to modify the number of Monte Carlo trials to be used. This parameter "NumTrials," is defined within the "Constants" section of LeakTEC. This parameter must be a positive integer and is constrained to be >100 Document Number 51-5053331-01 Page 23 of 25

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within the spreadsheet. However, in practice the value should be set to at least 10,000.

4) Press CTRL+F9 to recalculate the entire spreadsheet.
5) Once the evaluation is complete, calculated leakage rates are available in the "Results" section. The one-sided, upper 95% probability / 95% confidence leakage value is to be used to evaluate TEC leakage against the accident leakage performance criteria.

7.2 LeakTEC Usage Notes

1) MathCad's automatic calculation feature should be disabled (ToolsICalculate). This will prevent the spreadsheet from recalculating before all desired input changes have been made.
2) Two files which contain informa~tion imported within the "Constants" section must reside within the same file directory as the spreadsheet. The files are: "DeltaDilation w Axial Load.xls" and "TRvTID.xls." If it should become necessary to re-link these files within LeakTEC, the appropriate data ranges are as follows:

Filename Data Range DeltaDilation w Axial Load.xls CR3-Specific!k3:m58 TRvTID.xls Sheetl !a2:cl5532

3) A read-only master copy and backup of the spreadsheet and above files should be maintained.
4) For CM simulations, the following equation provides an order of magnitude estimate of computation time:

= (NwunTrials)(NumCracks)

(1.92E06)(P) where:

t = computation time (minutes)

NumTrials = number of Monte Carlo trials Num Cracks = number of cracks evaluated P = CPU clock speed (GHz)

5) The OA computation takes longer than the CM computation. The time depends upon the POD value and the number of cracks to be repaired, in addition to the number of cracks imported.

Document Number 51-5053331-01 Page 24 of 25

8.0 Summarv and Conclusions A refinement of the MSLB leakage calculation methodology which is applicable to the CR-3 ARC for SG tube end cracking has been described in this report. This methodology employs Monte Carlo techniques and is implemented in MathCad spreadsheet "LeakTEC."

Several benchmarking cases have demonstrated that, as expected, this approach yields lower leakage estimates than the deterministic approach currently in use. Instructions for field implementation of the spreadsheet have also been provided.

9.0 References

1) FANP, "ARC for Tube End Cracking in the Tube-to-Tubesheet Roll Joint of OTSGs,"

BAW-2346P, April 1999

2) FANP Calculation 32-5003879-03, "OTSG Tube End Crack Leak Rate vs. Tubesheet Radius," November 11, 1999
3) FANP Calculation 32-5002623-02, "OTSG Transient Analysis," May 1999
4) FANP Calculation 32-5053981-00, "Probabilistic Implementation of CR-3 TEC ARC -

Supporting Calculations"

5) WCAP-14277, "SLB Leak Rate and Tube Burst Probability Analysis Methods for ODSCC at TSP Intersections," Revision 1, December 1996
6) FANP Calculation 32-5035732-00, "CR3 RFO-13 TEC ARC Leakage Calculation,"

January 16, 2004

7) FANP Calculation 32-5070303-00, "Deterministic Leakage Assessment of Crystal River Unit 3 Steam Generator Tube End Cracks," August 2005 Document Number 51-5053331-01 Page 25 of 25

Appendix A - LeakTEC Listing Document Number 51-5053331-01 Page Al of A13

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[ INTRODUCTION. _ ... .. . . . ..

This spreadsheet calculates the total primary to secondary steam generator leak rate from tube end cracks (TEC) for Crystal River Unit 3 under limiting MSLB conditions. The spreadsheet employs Monte Carlo simulation techniques to generate leak rates at 50%1/50%, 95%/50%, and 95%/95% probability/confidence levels, and may be used for both Condition Monitoring and Operational Assessment purposes. The probabilistic aspects of this evaluation are similar to that of the tube support plate ODSCC alternate repair criteria currently employed by several PWRs.

Required inputs are identified in the "OPTIONS AND INPUT DATA" section below. Calculated leak rates are obtained from the "RESULTS" section further on in the spreadsheet.

The master version of this spreadsheet is entitled "LeakTEC.mcd."

lZ NROUTO ET0OPTIONSANDINPUT.DATA._. . _. ....

Choose Leakage Assessment Type:

(- Condition Monitoring r Operational Assessment Specify Probability of Detection (for OA):

POD_ 1.0 This value has no affect on CM results Specify Crack Voltage Threshold:

Cracks with voltage below this value will be excluded from the evaluation. CAUTION: A Vrhresh _ 0 non-zero value for voltage threshold may only be used if approved by the NRC.

Specify Filename to Import Crack Locations. Quantities. and Repair Plans:

InCrkDat :=

Simulation will not run if the number of cracks to NC := CntCrks (InCrkDat) evaluate is zero.

_ .0 1 0 'Number of lines in the data file:' 1115 1 'Number of UTE cracks imported:' 1467 NrC - 2 'Number of LTE cracks imported:' 0

"'%. - I-+

3 'Number of cracks flagged for repair:" 246 4 "Number of cracks not flagged for repair:" 1221 5 'Total cracks imported:' 1467 6 'Number of cracks to evaluate:" 1467 Document Number 51-5053331-01 Page A2 of A 13

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0 1 2 3 4 5 0 1 7 OUTE' 2 OR" 100 1 1 8 'UTE' 3 WR 100 2 1 9 'UTE" 1 "R' 100 3 2 10 'UTE' 1 'R' 100 4 2 11 OUTE' 1 'R' 100 5 3 14 OUTE" 1 "R' 100 Row, column, tube end, 6 3 21 'UTE" 1 "R" 100 number ofcracks, repair InCrkDat= 7 3 31 'UTE' 1 "R" 100 flag, max crack voltage 8 4 17 'UTE' 2 OR" 100 (trncated listing Ifmore 9 4 26 'UTE" 2 "R' 100 than 16 lines) 10 4 37 'UTE' 1 "R' 100 11 5 1 "UTE" 2 NR" 100 12 5 3 "UTE' 1 "R" 100 13 5 20 'UTE' 2 "R" 100 14 5 21 'UTE" 1 "N" 100 15 5 23 "UTE" 1 'N' 100 RDATOPTONSADINPU HCONSTANTS- _, =. . ... - ._ ......

Number of Monte Carlo Trials:

NumTrials _ 20000 The number of Monte Carlo trials should should be as large as necessary to achieve repeatable run-to-run results.

Mode:= if(NumTrials < 100,-2, Mode)

Mode = 1 Log(Leak) v Delta Dilation Regression Parameters:

N -- 119 Number ofpoints S _ 0.79382 Standard error of regression RgV =S2 Regression error variance RgV = 0.63 M - 1.0063 Slope B = -4.7493 Intercept Vil E 0.011564 V12 _ -0.009094C Variance matrix V21 -- 0.009094C V22 = 0.01319^ Variance matrix Document Number 51-5053331-01 Page A3 of A13

Delta Dilation v Tubesheet Radius:

DDilation := Import accident delta dilation values rows (DDilation) = 56 Number of data fines imported 0 1 2 0 3 -0.75 -0.83 1 4 -0.82 -0.91 2 5 -0.86 -0.95 3 6 -0.88 -0.98 4 7 -0.9 -0.99 5 8 -0.91 -1 6 9 -0.92 -1.01 Tubesheet radius (in.), upper TS delta DDilation = 7 10 -0.92 -1.02 dilation (mils), lower TSdelta dilation 8 11 -0.93 -1.02 (mils) (truncated listing) 9 12 -0.93 -1.02 10 13 -0.93 -1.02 11 14 -0.92 -1.01 12 15 -0.9 -0.99 13 16 -0.89 -0.98 14 17 -0.87 -0.96 15 18 -0.85 -0.95 Tubesheet Radius v Tube Number:

TRvTID:= Import tubesheet radius vs tube number rows (TRvTID) = 15531 Number of data lines imported Document Number 51-5053331-01 Page A4 of A13

0 1 2 0 1 1 57.21 1 1 2 57.12 2 1 3 57.04 3 1 4 56.97 4 1 5 56.92 5 1 6 56.88 6 1 7 56.85 TRvTID = 7 1 8 56.84 Tubesheet radius vs tube number (truncated listing) 8 1 9 56.84 9 1 10 56.85 10 1 11 56.88 11 1 12 56.92 12 1 13 56.97 13 1 14 57.04 14 1 15 57.12 15 1 16 57.21 ORIGIN_ 0 CONSTANTS---a-HIPREPROCESSING ,. -

Check the Crack Innut File for Problems:

Mode:= if [(NC1, 1 + NC2 , 1

  • NCS, 1), -1, Mode]

Mode:= if[(NC3 , 1 + NC4 , 1

  • NCs, 1), -1, Mode]

Mode = 1 If mode is not 1or2, simulation will not run.

TCrks := NC 5, 1 Eliminate Cracks Not > or = to the Voltaae Threshold:

CrkDat:= ElimLoVolts (InCrkDat)

Add the Radius Value to the Crack Data Matrix:

i := 0.. rows (CrkDat) - 1 CrkDat(I, 5) := RadLookup[CrkDat(i, o) , CrkDat( i, 1) ,TRvTID]

Document Number 51-5053331-01 Page A5 of A 13

Add the Delta Dilation Value to the Crack Data Matrix:

CrkDat( i,6 ) := DDLookup[CrkDat(l, 5), CrkDatq ,2), DDilation]

This array contains: Row, Col, Leg, #Cracks, TS Radius, Delta Dilation. If simulation does not run, check this array for "Errr" entry caused by invalid tube row or column.

0 1 2 3 4 5 6 0 1 7 'UTE' 2 OR' 56.85 0.9841 1 1 8 'UTE' 3 OR" 56.84 0.9783 2 1 9 'UTE* 1 OR 56.84 0.9783 3 2 10 "UTE' 1 OR' 56.19 0.6055 4 2 11 "UTE' 1 OR 56.14 0.5769 5 3 14 "UTE" 1 PR" 55.4 0.3148 6 3 21 *UTE" 1 'R' 55.4 0.3148 CrkDat = 7 3 31 OUTE' 1 OR" 56.57 0.8235 8 4 17 "UTE' 2 'R" 54.67 0.1498 9 4 26 "UTE' 2 OR" 54.74 0.1591 10 4 37 'UTE" 1 'R 56.33 0.6858 11 5 1 "UTE" 2 'R' 57.29 1.0339 12 5 3 OUTE' 1 OR" 56.72 0.9095 13 5 20 'UTE" 2 'R' 53.89 0.0518 14 5 21 OUTE' 1 "N" 53.85 0.0485 15 5 23 'UTE" 1 ON" 53.81 0.0452 Calculate Index Values for 50/50, 95/50, and 95/95 Leakage:

Indx5O5OE round[(NumTrials.0.5) - 1] IndxO50= 9999 Indx9550-- round [(NumTrials-0.95) - 1] Indx9550= 18999 Indx9595- P - 0.95 no <- trunc(0.95-NumTrials) for n e no.. NumTrials 1

Crit +-

NumTrials - n + 1 1+ *qF [0.95, [2.(NumTrials - n + 1)], 2.n]

n return n-I if Crit2P n+- "error" Indx9595= 19050 lrPREPROCESSING Document Number 51-5053331-01 Page A6 of A13

El RESULTS _-

Press C77?L + F9 to calculate.

0 1 Leak(CrkDat, Mode) =0 "50/50 CM Accident Leakage' 0.1512575 1 "95/50 CM Accident Leakage' 0.2931619 GPM 2 "95/95 CM Accident Leakage" 0.2958761 rnRESULTS Given a Matrix of Crack Data, Keep only Those Exceeding the Voltage Threshold:

ElimLoVolts(InCrkDat) - jp--

for i E 0.. rows (InCrkDat) - 1 if InCrkDak j,5) 2 Vrhresh j4-j+l CrkDat(j,o) <- InCrkDat(I,o)

CrkDat(j,l) -InCrkDak i,)

CrkDat(j, 2 ) *InCrkDatk I,2)

CrkDat( j, 3) 4 InCrkDaki , 3)

CrkDaqj4)j4 InCrkDak i,4 )

CrkDat Given a Row and Col, Return the TS Radius:

RadLookup(Ro, Co, Tr) - Radius 4- "Error" rows -- rows (Tr) - 1 for re 0.. rows if [Tr(r,O) = Ro] A [Tr(r,1) = CO]

Radius + Tr(r,2) l break return Radius Document Number 51-5053331-01 Page A7 of A13

Given a Radius, Return the ApproDriate Delta Dilation Value:

DDLookup(Rad, Leg, DDilation) _ I return "Error" if Rad = "Error" j - 1 This function interpolates to j -2 if Leg= "LTE" obtain the delta dilation value.

Radc 3 if Rad < 3 RadFloor 4- floor(Rad)

RadCeil - ceil (Rad)

RadCeil - 57.72 if RadCeil > 57.72 RadDel - RadCeil - RadFloor RadInc - Rad - RadFloor DDFloor *- DDFloor 4- DDilation( RadFloor-3 ,j)

DDCeil <- DDCeil - DDilation(RadFloor-2,j)

DDDel - DDCeil - DDFloor RadInc.DDDel DeltaD - DDFloor + Rd RadDel DeltaD)

Document Number 51-5053331-01 Page A8 of A13

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Count Various Crack Classifiers:

CntCrks(CrkDat) - UCrks -0 LCrks 4- 0 RCrks +- 0 NCrks4-0 TCrks - 0 ECrkS - 0 Lines - rows (CrkDat) for i e O.. Lines - 1 UCrks - UCrks + CrkDat(i,3) if CrkDat( ,2):- :"UTE" LCrks +- LCrks + CrkDak j,3) if CrkDak i,2) = "LTE" RCrks - RCrks + CrkDatki, 3 ) if CrkDat(i, 4 ): "R" NCrks - NCrks+CrkDaki,3) if CrkDat(i, 4 )- "N" TCrks - TCrks + CrkDaki, 3)

ECrks +- ECrks + CrkDat(i, 3 ) if CrkDat(i,5) 2tVThresh "Number of lines in the data file:" Lines "Number of UTE cracks imported:" UCrks "Number of LTE cracks imported:" LCrks Out - "Number of cracks flagged for repair:" RCrks "Number of cracks not flagged for repair:" NCrks "Total cracks imported:" TCrks "Number of cracks to evaluate:" ECrks Document Number 51-5053331-01 Page A9 of A13

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CM Leakage Calculation: Total SG Leakage at 50/50, 95/50, and 95/95 Prob./Conf. Levels:

'CMLeaks' calculates acdident leakage valves for condition monitoring purposes (ie., calculates totalSGleakageforcracksas-found). Within thefunction, a vectorcontaining 'WumTrials" leakage values isgenerated Each value is a probablisticestimate oftotal SGleakage. 7he 50/50, 95/50, and 95/95 leakage values are taken directly from this (sorted) vector.

CMLeaks(CrkDat) NDatLimrn rows(CrkDat) - 1 for t 0.. NumTrials - 1 CumuL - 0 N - (N -2) rchisq(1, N - 2)0 RnS +-v RnV11 4 fv-V 11 RnV22 - fv-V 22 RnV12 - fv-V12 Z1 *morm(1,0,1)o on error Z1 -morm(1,0,1)O Z2 - morm(1,0, 1) on error Z2 rorm(1,0, m 1)0 RnP3 - B+ Z1 -fRii RnfK4 M+ Z1. RnV12 + Z2. RnV22 - (RnV12) 7 j RnV11 for rE 0.. NDatLim continue if CrkDakr,3) = 0 for ce 1.. CrkDatr,3)

DD - CrkDat r, 6)

Z3 4 morm(1,0,1)o on error Z3 mrnorm(1,0,1)Q LogL Rn03 + DD RnM4 + Z3-RnS CumuL +- (CumuL + 10LogL)

TotLeakTrialst +- CumuL LeakSorted 4- sort(TotLeakTrials)

L_5050 - Leak-SortedIndx5oso L_9550 Leak-Sortedlndx950o L_9595 Leak-sortedIndx9595 "50/50 CM Accident Leakage" L 5050)

Out +- "95/50 CM Accident Leakage" L_9550 "95/95 CM Accident Leakage" L_9595)

Document Number 51-5053331-01 Page A10 of A13

Alter the Number of Cracks to Account for Repairs and POD:

ApplyPODtoCrackData(CDat) - NDatUm +- rows (CDat) - 1 for re O..NDatLim NCrks - CDat( r, 3)

PODCrks NCrks POD PODCrks v PODCrks- NCrks if CDat(r,4) ="W Lo - floor(PODCrks)

Hi v- ceil(PODCrks)

Frac v- PODCrks - Lo PODCrks v- Lo Rndm v- md(1)

PODCrks v- Hi if Rndm < Frac CDat(r,3) +- PODCrks return CDat Document Number 51-5053331-01 Page Al I of A13

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OA Leakage Calculation: Total SG Leakage at 50/50, 95/50, and 95/95 Prob./Conf. Levels:

'OALeaks' calculates accident leakage values for operational assessment purposes (Ze., calculates total SG leakage for cracks projected at the next EOC). The function is very similar to 'CMLeaks, however, prior to each Monte Carlo trial, the number of cracks at each location is adjusted to account for those repaired, and to reflect the affect of POD.

OALeaks(CrkDat)-- NDatLim -rows(CrkDat) - 1 for t E O.. NumTrials - 1 AdCrkDat +- ApplyPODtoCrackData(CrkDat)

CumuL - 0 fV (N-2) rchisq(1, N-2)

RnS <- ~vWV RnV11 - fv-V11 RnV22 4- fv-V22 RnV12 4- fv-V12 Z1 r morm(1,0,1)o on error Z1 - morm(1,0,1)o Z2+-morm(1,0,1) 0 onerror Z2 -morm(1,0,1) 0 RnP3 +- B + Zl-i/R i~l RnM4 M + Z1. RnV12 + Z2. RnV 22 - (RnV12 )

for r e 0.. NDatLim continue if AdCrkDat(r,3) = 0 for c e 1.. AdCrkDakr,3)

DD 4- AdCrkDatk r, 6)

Z34-morm(1,0,)o onerror Z34-rnorm(1,0,)o LogL Rn133 + DD-Rn,4 + Z3-RnS CumuL 4- (CumuL + 10 LogL)

TotLeakTrialst 4- CumuL Leak_Sorted *- sort(TotLeakTria ls)

L_5050 4- Leak-SortedIndx5o50 L_9550 - Leak-sortedIndx9550 L_9595 - Leak-Sortedlndx9595 "50/50 OA Accident Leakage" L_5050 Out 4- "95/50 OA Accident Leakage" L_9550 "95/95 OA Accident Leakage" L_9595)

Document Number 51-5053331-01 Pa.-.,e A12 of A13

Process Errors and Execute Correct Function based on User Selection:

Leak(CrkDat, Mode) _ return "'NumTrials' is too small" if Mode = -2 return "Crack file contains improper characters" if Mode = -1 return "Must specify CM or OA" if Mode- 0 return CMLeaks(CrkDat) if Mode= 1 return OALeaks(CrkDat) if Mode=2 "Error" l F; 'I -

Document Number 51-5053331-01 Page A13 of A13

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