Text

Suppl 1 to Pdq Two-Zone Model
	ML18152A041
Person / Time
Site:	Surry, North Anna
Issue date:	11/30/1992
From:	Berryman R, Dziadosz D, Randy Hall; VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
To:	;
Shared Package
ML18152A042	List: ML18152A041; ML18153D251;
References
	VEP-NAF-1, VEP-NAF-1-S01, VEP-NAF-1-S1, NUDOCS 9303040017
	Download: ML18152A041 (70)
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The PDQ Two Zone Model

. Nuclear Analysis and Fuel Department Nuclear Engineering Services VEP-NAF-1 Supplement l, November,* 1992 VIRGINIA POWER

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I THE PDQ TWO ZONE MODEL BY R. A. HALL W. A. PETERSON VEP-NAF-1-SUPPLEMENT 1 NUCLEAR ANALYSIS AND FUEL DEPARTMENT NUCLEAR ENGINEERING SERVICES VIRGINIA ELECTRIC AND POWER COMPANY RICHMONDt VIRGINIA November, 1992 Approval:

Supervisor, Nuclear Core Design Approved:

~..rr-,.-4-e..i.. 1-.J ~

I R. M. Berryman Manager, Nuclear Analysis and Fuel

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I CLASSIFICATION/DISCLAIMER The data and analytical techniques described in this report have been prepared specifically for application by the Virginia Electric and Power Company.

The Virginia Electric and Power Company makes no claim as to the accuracy of the data or techniques contained in this report if used by other organizations.

Any use of this report or any part thereof must have the prior written approval of the Virginia Electric and Power Company.

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ABSTRACT The Virginia Electric and Power Company (Virginia Power) has developed a coarse mesh (i.e., five non-uniform mesh per assembly), two dimensional, two neutron energy group diffusion-depletion calculational model designated as the PDQ Two Zone model.

The 3-D version of the PDQ Two Zone model has been previously documented in Topical Report VEP-NAF-1, entitled "The PDQ Two Zone Model" 1

The objective of this Supplement to Topical Report VEP-NAF-1, is to present results and conclusions for a 2-D collapsed version of the 3-D Two Zone model.

The 2-D computational model is identical in X-Y mesh structure, cross section modeling and calculational techniques to the 3-D model.

The primary difference is that the axial mesh structure has been reduced to a

single reflected plane.

A 3-D normalized axial buckling model approximates the effect of non-uniform axial burnup distribution, axial neutron leakage, and flux redistribution.

The purpose of the model is to provide power distribution data for core follow calculations and to predict physics characteristics of the Virginia Power Surry and North Anna nuclear reactors.

The accuracy of the 2-D Two Zone model is demonstrated through comparisons with the PDQ 3-D Two Zone model and measurements taken at the Surry and North Anna Nuclear Power Stations.

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CLASSIFICATION/DISCLAIMER ABSTRACT TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES TABLE OF CONTENTS SECTION 1 - INTRODUCTION SECTION 2 - MODEL DESCRIPTION SECTION 3 - RESULTS...

3.1 3.2 3.3 3.4 3.5 3.6 3.7 Introduction Relative Power Distribution Control Bank Worths Critical ~oron Calculations Isothermal Temperature Coefficients Boron Worth Coefficients......

Estimated Critical Position Calculations 3.8 Hot to Cold Defect Calculations SECTION 4 -

SUMMARY

AND CONCLUSIONS SECTION 5 - REFERENCES Page i

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1-1 2-1 3-1 3-1 3-1 3-27 3-32 3-43 3-44 3-45 3-49 4-1 5-1 iii

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I LIST OF FIGURES Figure Title Page 3-1 PDQ3D Versus PDQ2D Two Zone RPD Comparison (NlC8 1000)...... 3-4 3-2 PDQ3D Versus PDQ2D Two Zone RPD Comparison (NlC8 7000)...... 3-5 3-3 PDQ3D Versus PDQ2D Two Zone RPD Comparison (NlC8 15000)...... 3-6 3-4 PDQ3D Versus PDQ2D Two Zone RPD Comparison (NlC9 1000)...... 3-7 3-5 PDQ3D Versus PDQ2D Two Zone RPD Comparison (NlC9 7000)...... 3-8 3-6 PDQ3D Versus PDQ2D Two Zone RPD Comparison (NlC9 10095)...... 3-9 3-7 PDQ3D Versus PDQ2D Two Zone RPD Comparison (N2C7 1000)...... 3-10 3-8 PDQ3D Versus PDQ2D Two Zone RPD Comparison (N2C7 7000)...... 3-11 3-9 PDQ3D Versus PDQ2D Two Zone RPD Comparison (N2C7 15000)..... 3-12 3-10 PDQ3D Versus PDQ2D Two Zone RPD Comparison (N2C8 1000)...... 3-13 3-11 PDQ3D Versus PDQ2D Two Zone RPD Comparison (N2C8 7000)...... 3-14 3-12 PDQ3D Versus PDQ2D Two Zone RPD Comparison (N2C8 15000)...... 3-15 3-13 PDQ3D Versus PDQ2D Two Zone RPD Comparison (SICA 1000)...... 3-16 3-14 PDQ3D Versus PDQ2D Two Zone RPD Comparison (SICA 7000)...... 3-17 3-15 PDQ3D Versus PDQ2D Two Zone RPD Comparison (SlCA 13000)...... 3-18 3-16 PDQ3D Versus PDQ2D Two Zone RPD Comparison (SlCB 150)....... 3-19 3-17 PDQ3D Versus PDQ2D Two Zone RPD Comparison (SlCB 7000)...... 3-20 3-18 PDQ3D Versus PDQ2D Two Zone RPD Comparison (SlCB 13000)...... 3-21 3-19 PDQ3D Versus PDQ2D Two Zone RPD Comparison (S2CA 5000)...... 3-22 3-20 PDQ3D Versus PDQ2D Two Zone RPD Comparison (S2CA 11164)...... 3-23 3-21 PDQ3D Versus PDQ2D Two Zone RPD Comparison (S2CB 1000)...... 3-24 3-22 PDQ3D Versus PDQ2D Two Zone RPD Comparison (S2CB 7000)...... 3-25 3-23 PDQ3D Versus PDQ2D Two Zone RPD Comparison (S2CB 16500)...... 3-26 3-24 NlC8 Boron Letdown Curve.................................... 3-35 3-25 NlC9 Boron Letdown Curve.................................... 3-36 3-26 N2C7 Boron Letdown Curve..................................... 3-37 3-27 N2C8 Boron Letdown Curve..................................... 3-38 3-28 SlClO-lOA Boron Letdown Curve................................ 3-39 3-29 SlCll Boron Letdown Curve....................................... 3-40 3-30 S2C10 Boron Letdown Curve..................................... 3-41 3-31 S2Cll Boron Letdown Curve..................................... 3-42 iv

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Table 1-1 LIST OF TABLES Title TWO ZONE 2-D PDQ COMPARISONS Page 1-4 1-2 SURRY NUCLEAR POWER STATION OPERATING HISTORY............... 1-5 1-3 NORTH ANNA NUCLEAR POWER STATION OPERATING HISTORY.......... 1-6 3-1 PDQ TWO ZONE QUARTER CORE 2-D VERSUS 3-D RPD COMPARISON (North Anna and Surry RPD'S > 0.9, 1.1, 1.2, & 1.3)......... 3-3 3-2 HZP INTEGRAL CONTROL ROD BANK WORTH COMPARISON (PDQ Two Zone 2-D Versus 3-D Data).......................... 3-28 3-3 CZP ARI INTEGRAL CONTROL ROD BANK WORTH COMPARISON (PDQ Two Zone 2-D Versus 3-D Data).......................... 3-30 3-4 PDQ TWO ZONE CONTROL ROD BANK WORTHS (Integral Bank Worths for D, C, B, A, SB, SA)..................................... 3-31 3-5 PDQ TWO ZONE CONTROL ROD BANK WORTHS (CZP ARI Integral Bank Worths)..................................................... 3-31 3-6 PDQ TWO ZONE CRITICAL BORON CONCENTRATIONS (PPM Difference 2-D Versus 3-D).............................................. 3-34 3-7 PDQ TWO ZONE CRITICAL BORON CONCENTRATIONS FOR HZP STARTUPS (PPM Difference 2-D and 3-D Versus Measured Data)............ 3-34 3-8 PDQ TWO ZONE ISOTHERMAL TEMPERATURE COEFFICIENTS (PCM/°F Difference 2-D Versus 3-D and Measured).............. 3-43 3-9 PDQ TWO ZONE BORON WORTHS(% Difference 2-D Versus 3-D)...... 3-44 3-10 ECP COMPARISON

SUMMARY

TABLE 3-47 3-11 ECP COMPARISON STATISTICS.................................... 3-48 3-12 PDQ TWO ZONE K-EFFECTIVE COMPARISON (PCM Difference 2-D Versus 3-D Model Data)....................................... 3-51 3-13 PDQ TWO ZONE TEMPERATURE DEFECT COMPARISON (PCM Difference 2-D Versus 3-D Model Data)................................... 3-51 4-1

SUMMARY

COMPARISONS OF TWO ZONE 2-D PDQ CALCULATIONS TO 3-D TWO ZONE PDQ CALCULATIONS.................................... 4-3 4-2

SUMMARY

COMPARISONS OF TWO ZONE 2-D PDQ CALCULATIONS TO MEASURED DATA................................................ 4-4 V

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SECTION 1 - INTRODUCTION The objective of this Supplement to Topical Report VEP-NAF-1, entitled "The PDQ Two Zone Model" 1, is-to present results and conclusions for a 2-D collapsed version of the 3-D Two Zone model.

The 2-D Two Zone model has been developed to replace the Virginia Power PDQ 2-D One-Zone model 2

The 2-D Two Zone model has an improved mesh structure, more detailed cross section representation, improved cross section data, Monte-Carlo benchmarking, and verified axial buckling inputs by direct comparison with 3-D model results.

Future enhancements will include pin power reconstruction capability for calculation of peaking factors and for use in core follow (i.e, flux map analysis) calculations.

The 2-D computational model is identical in X-Y mesh structure, cross section modeling and calculational techniques to the 3-D model.

The primary difference is that the axial mesh structure has been reduced to a

single reflected plane.

A 3-D normalized axial buckling model approximates the effect of non-uniform axial burnup distribution, axial neutron leakage, and flux redistribution.

The model uses the Virginia Power computer codes SHUFL and PDQV2, codes, as well as input from the EPRI ARMP-02 CELL2 and NUPUNCHER codes, the EPRI ESCORE code, and the SCALE3 package from ORNL.

The types of calculations that can be performed by the Two Zone 2-D model include:

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Reactor Physics and Core Follow Analysis

a.

Two-dimensional assembly average radial power distributions.

b.

Critical soluble boron concentrations 1-1

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Nuclide concentrations

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Integral control rod bank worths

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Hot-Zero-Power (HZP) temperature coefficients and defects

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Total power defects

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Boron worths

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Xenon parameters

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Shutdown margin calculations

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Fuel Management Analysis

a.

Batch power and burnup sharing

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Fuel isotopics as a function of burnup

c.

Scoping studies for the evaluation of alternative future cycle designs and fuel loadings Cal cu lat ion of enthalpy rise hot channel factors (F t.H(X, Y)) is planned using the same pin power reconstruction techniques 4 described in VEP-NAF-1.

This will also enable the 2-D model to calculate flux map analysis input data.

The reactor physics, core follow and fuel management calculations listed above are currently performed with other core models.

However, the benchmarking data presented in this supplement show that the 2-D PDQ Two Zone model is a capable alternative.

Calculational results are compared to both 3-D PDQ Two Zone predictions and measured data for the last two reload cycles for each North Anna and Surry unit. The comparisons provided include HZP isothermal temperature coefficents (ITC), HZP integral rod worths, HZP boron worths, HZP & Hot-Full-Power (HFP) critical boron calculations, and relative power distribution results.

Estimated critical position (ECP) calculations which require accurate calculation of power defect, xenon worths, boron worths, isotope 1-2

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I decay reactivity, and control rod worth, are presented for 32 of the most recent reactor restarts for North Anna and Surry. Table 1-1 lists the comparisons made to PDQ 3-D model calculations and to measured data..

Tables 1-2 and 1-3 list the Nuclear Power Station Operation History for Surry and North Anna obtained from Reference 5.

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Table 1-1 TWO ZONE 2-D PDQ COMPARISONS TWO ZONE 2-D PDQ CALCULATIONS COMPARED TO TWO ZONE 3-D PDQ

1) HFP RPD'S

2) ROD WORTH (HZP & CZP)

3) K-EFFECTIVE (HZP & CZP)

4) CRITICAL BORON

5) TEMPERATURE DEFECT (HZP-CZP)

6) ITC (HZP)

7) BORON WORTH 8 cycles@ BOC, MOC, and EOC 8 cycles@ BOC, MOC, and EOC, HZP individual banks and CZP all rods in cases 8 cycles@ BOC, MOC, and EOC 8 cycles of boron letdown data@ HFP 8 cycles@ BOC, MOC, and EOC (HZP & HFP) 8 cycles@ BOC, MOC, and EOC 8 cycles@ BOC, HZP CONDITIONS 8 cycles@ BOC, HZP CONDITIONS TWO ZONE 2-D PDQ CALCULATIONS COMPARED TO MEASURED DATA

1) REACTIVITY (ECP DATA)

2) REACTIVITY (HFP LETDOWN)

3) ITC (HZP)

4) BORON WORTH

5) REACTIVITY (HZP BOC STARTUP)

Note:

Latest 32 reactor restarts for 12 cycles

-ECP method (normalized to previous measured critical)

-Direct criticality predictions 8 cycle of boron letdown data@ HFP 8 cycles@ BOC, HZP Conditions 7 cycles@ BOC, HZP Conditions (See note 1) 8 cycles@ BOC, HZP Conditions

1) Only 7 cycles of measured data are available for comparison, due to the presence of a stuck control rod (F6) during S2Cll startup testing. For ITC and BOC critical borons, the SlClOA (second startup following replacement of one fuel assembly) data have been included.

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TABLE 1-2 SURRY NUCLEAR POWER STATION OPERATING HISTORY UNIT/CYCLE ON LINE OFF LINE CYCLE BURNUP CORE RATING DATE DATE (MWD/MTU)

(MWT)

SlCl 09/12/1972 10/24/1974 13547 2441 S1C2 02/03/1975 09/26/1975 6915 2441 S1C3 12/08/1975 10/17/1976 8944 2441 S1C4 01/24/1977 04/22/1978 13107 2441 S1C5 07/09/1978 09/14/1980 14390 2441 S1C6 07/06/1981 02/07/1983 16491 2441 S1C7 05/30/1983 09/26/1984 11984 2441 S1C8 12/26/1984 05/10/1986 14040 2441 S1C9 07 I 12/1986 04/09/1988 16073 2441 S1Cl0 07/14/1988 09/14/1988 1789 2441 S1Cl0A 07/05/1989 10/06/1990 14073 2441 S1Cll 12/17/1990 02/29/1992 13956 2441 S1C12 05/01/1992 02/01/1994*

2441 S2Cl 03/19/1973 04/26/1975 14870 2441 S2C2 06/19/1975 04/22/1976 9054 2441 S2C3 06/10/1976 09/10/1977 9422 2441 S2C4 10/12/1977 02/04/1979 13678 2441 S2C5 08/19/1980 11/07/1981 13971 2441 S2C6 12/31/1981 06/30/1983 16006 2441 S2C7 09/25/1983 03/20/1985 14802 2441 S2C8 06/27/1985 10/04/1986 13359 2441 S2C9 11/30/1986 9/10/1988 15710 2441 S2Cl0 09/16/1989 03/30/1991 14941 2441 S2Cll 06/05/1991 03/06/1993*

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TABLE 1-3 NORTH ANNA NUCLEAR POWER STATION OPERATING HISTORY UNIT/CYCLE ON LINE OFF LINE CYCLE BURNUP CORE RATING DATE DATE (MWD/MTU)

(MWT)

NICI 04/23/1978 09/25/1979 15590 2775 NIC2 01/24/1980 12/28/1980 10711 2775 NIC3 04/10/1981 05/17/1982 13335 2775.

N1C4 11/18/1982 05/12/1984 13478 2775 N1C5 09/25/1984 11/04/1985 13398 2775 N1C6 12/23/1985 04/19/1987 15705 2775/2893 N1C7 06/29/1987 02/25/1989 16891

_2893 N1C8 07/15/1989 01/12/1991 19289 2893 N1C9 03/07/1991 01/02/1993*

2893 N2Cl 10/23/1980 03/07/1982 14494 2775 N2C2 06/02/1982 04/02/1983 8436 2775 N2C3 05/29/1983 08/02/1984 14717 2775 N2C4 11/02/1984 02/20/1986 15934 2775 N2C5 04/01/1986 08/24/1987 17467 2775/2893 N2C6 11/03/1987 02/20/1989 17844 2893 N2C7 05/07/1989 08/21/1990 18034 2893 N2C8 11/01/1990 02/26/1992 18253 2893 N2C9 04/22/1992 09/04/1993*

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I SECTION 2 -

PDQ TWO ZONE 2D HODEL DESCRIPTION The PDQ Two Zone model is essentially the same as the 3-D model presented in the model description section of VEP-NAF-1, with the exception of the representation of the axial dimension.

It incorporates a

few-group, diffusion-depletion theory model, with thermal-hydraulic feedback, to perform spatial neutron flux and nuclide concentration calculations in two dimensions throughout the reactor core. The 2-D model is derived from 3-D model and uses the same cross sections and cross section dependences as the 3-D model. To approximate axial dimension effects, an axial buckling model was developed for the 2-D model which gives good agreement with the 3-D model results over a

range of conditions.

Future enhancements of the 2-D model will include applying the same pin power reconstruction strategy described in Sectibn 2.5 of VEP-NAF-1 for the 3-D model.

The pin power reconstruction is not yet available for the 2-D model.

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I SECTION 3 - RESULTS

3.1 INTRODUCTION

The purpose of thi.s section is to present a co.*parison of analytical predictions from the PDQ Two Zone 2-D model with PDQ Two Zone 3-D model predictions and with measured data obtained from the latest Surry and North Anna cycles.

These.comparisons include the last two reload cycles of operation for each North Anna and Surry unit.

In addition, Estimated Critical Position (ECP) calculations have been performed for the 32 most recent reactor re-starts. Data from these ECP calculations will be presented in two forms: 1) Reactivity difference from measured critical conditions based on normalization to a known previous critical condition (PCC) and 2) direct model criticality prediction ~omparisons to actual critical conditions.

3.2 RADIAL POWER DISTRIBUTIONS Twenty-three 2-D versus 3-D Radial Power Distribution (RPO) quarter core comparison maps are presented as Figures 3-1 through 3-23 of this section.

The 2-D versus 3-D RPD comparisons included HFP cases near the beginning, middle and end of each cycle (BOC, MOC, EOC) for recent North Anna and Surry cycles.

Each of the 23 quarter core maps presented give 2-D and 3-D RPD's, the percent difference for each quarter core location, the root mean square (RMS) of the power distribution differences for each map, the maximum 2-D versus 3-D percent difference, and the maximum 2-D versus 3-D percent difference for RPD's greater than 0.9. Table 3-1 gives radial power distribution comparison statistics for all maps presented 3-1

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in quarter core locations with RPD's greater than 0.9, 1.1, 1.2, and 1.3.

These statistics show good agreement over the range of powers analyzed.

The largest RPD underprediction for all the cases is -1.2% and largest*

overprediction is 1.4i..

Table 3-2 of VEP-NAF-1 presents nuclear reliability factors (NRF) and nuclear uncertainty factor (NUF) applicable to the 3-D model.

There is no nuclear reliability factor (NRF) for RPO, but a closely related parameter is F-delta-H, and the 3-D model nuclear uncertainty factor (NUF) for F-delta-H is within the 1.05 NRF.

Currently the 2-D model does not have the capability to predict F-delta-H data, but accurate RPO predictions are the first requirement for accurate peaking factor calculation. Considering both the low mean and *standard deviation of the RPO differences (2-D versus 3-D) and the 3-D F-delta-H NUF indicate that meeting the 1. 05 F-delta-H NRF with the 2-D model is certainly possible.

A very conservative estimate of the 2-D RPO NUF may be determined by adding the bounding RPO underprediction to the 30 PDQ RPO NUF.

This results in an estimated bounding 2-D model RPO NUF of 1.040 which is further evidence of the accuracy of the 2-D model RPD predictions and is indirect verification of the accuracy of the buckling model.

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I TABLE 3-1 PDQ TWO ZONE QUARTER CORE 2-D VERSUS 3-D RPD COMPARISON NORTH ANNA AND SURRY RPD'S > 0.9, 1.1, 1.2, AND 1.3 NUMBER STANDARD DESCRIPTION OF PTS.

MEAN DEVIATION MAX.

MIN.

HFP RPD 1 S

> 0.9 815

-0.09 i.

0.37 i.

1. 4 i.

-1.2 i.

HFP RPD'S

> 1.1 639

-o. 15 i.

0.32 i.

0.8 %

-0.9 i.

HFP RPD'S

> 1. 2 396

-o. 15 %

0.30 i.

0.8 %

-0.9 i.

HFP RPD'S

> 1. 3 140

-0.31 %

0.25 %

0.3 %

-0.9 i.

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I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~NlC8 FOl (1000 HWD/HTU) HFP HAP I

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1.159 1.157

-0.173

l. 278 1.270

-0.626 1.247 1.242

-0.401 1.229 1.226

-0.244 1.196 1.197 0.084 1.279 1.279 0.000 0.858 0.862 0.466 0.308 0.310 0.649 G

1.276 1.268

-0.627 i 1.032 1.029

-0.291 1.309 1.302

-0.535 1.198 1.197

-0.083 1.329 1.327

-0.150 1.170 1.173 0.256 1.025 1.028 0.293 0.283 0.286 1.060 F

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1.244 1.223 1.151 1.239 1.218 1.149

-0.402

-0.409

-0.174 1.306 1.195 1.321 1.299 1.193 1.317

-0.536

-0.167

-0.303 1.203 1.280 1.233 1.202 1.274 1.236

-0.083

-0.469 0.243 1.280 1.211 1.238 1.275 1.212 1.236

-0.391 0.083

-0.162 1.234 1.235 0.816 1.237 1.234 0.818 0.243

-0.081 0.245 1.234 1.050 0.368 1.235 1.051 0.371 0.081 0.095 0.815 0.633 0.341 0.635 0.343 0.316 0.587 Figure 3-1 C

B A

1.266 0.852 0.306 1.264 0.857 0.309

-0.158 0.587 0.980 1.163 1.020 0.282 1.166 1.023 0.285

o. 258 0.294 1.064 1.230 0.628 1.231 0.631 0.081 0.478 1.048 0.340 1.049 0.343 0.095 0.882 0.369 0.372 0.813 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RHS DIFFERENCE:

0 HAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-4

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.464 1.06

-0.63

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I PDQ3D VERSUS PDQ2D TWO ZONE RPD COMPARISION

~1C8 F07 (7000 MWD/HTU) HFP HAP I

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G 1.170 1.327 1.162 1.316

-0.684

-0.829 1.327 1.054 1.317 1.045

-0.754

-0.854 1.222 1.338 1.214 1.330

-0.655

-0.598 1.186 1.170 1.182 1.166

-0.337

-0.342 1.148 1.326 1.147 1.323

-0.087

-0.226 1.265 1.120 1.266 1.122 0.079 0.179 0.839 0.992 0.84&

0.998 0.834 0.605 0.329 0.299 0.332 0.303 0.912 1.338 F

E D

1.223 1.190 1.132 1.216 1.186 1.133

-0.572

-0.336 0.088 1.339 1.174 1.329 1.330 1.171 1.328

-0.672

-0.256

-0.075 1.199 1.333 1.204 1.194 1.327 1.205

-0.417

-0.450 0.083 1.330 1.202 1.259 1.324 1.200 1.258

-0.451

-0.166

-0.079 1.200 1.255 0.834 1.201 1.254 0.837 0.083

-0.080 0.360 1.218 1.032 0.394 1.220 1.036 0.397 0.164 0.388 0.761 0.631 0.361 0.635 0.364 0.634 0.831 Figure 3-2 C

B A

1.267 0.841 0.330 1.269 0.848 0.334 0.158 0.832 1.212 1.123 0.994 0.300 1.126 1.001 0.304 0.267 0.704 1.333 1.220 0.630 1.222 0.635 0.164 0.794 1.033 0.3&0 1.037 0.364 0.387 1.111 0.394 0.398 1.015 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 HAX DIFFERENCE:

HAX DIFF CRPD>0.9) 3-5

)

.620 1.34

-0.85

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I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~1C8 FOF (15000 HWD/HTU) HFP HAP I

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9 10 11 12 13 14 15 H

G 1.136 1.301 1.128 1.294

-0.704

-0.538 1.301 1.039 1.295 1.029

-0.461

-0.962 1.170 1.304 1.160 1.298

-0.855

-0.460 1.140 1.131 1.131 1.124

-0.789

-0.619 1.116 1.300 1.111 1.299

-0.448

-0.077 1.267 1.105 1.269 1.104 0.158

-0.090 0.879 1.017 0.884 1.023 0.569 0.590 0.392 0.351 0.397 0.356 1.276 1.425 F

E D

1.170 1.142 1.103 1.161 1.133 1.099

-0.769

-0.788

-0.363 1.304 1.133 1.301 1.298 1.126 1.300

-0.460

-0.618

-0.077 1.160 1.320 1.170 1.154 1.317 1.167

-0.517

-0.227

-0.256 1.319 1.174 1.259 1.316 1.170 1.262

-0.227

-0.341 0.238 1.168 1.257 0.869 1.166 1.260 0.872

-0.171 0.239 0.345

1. 217

l. 041 0.441 1.221 1.046 0.445 0.329 0.480 0.907 0.673 0.408 0.677 0.413 0.594 1.225 Figure 3-3 C

B A

1.267 0.880 0.393 1.269 0.884 0.397 0.158 0.455 1.018 1.106 1.017 0.351 1.105 1.023 0.356

-0.090 0.590 1.425 1.216 0.670 1.220 0.675 0.329 0.746 1.039 0.406 1.044 0.410 0.481 0.985 0.441 0.445 0.907 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-6

)

.655 1.42

-0.96

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~1C9 FOl (1000 HWD/HTU) HFP HAP I

I I

I

, I I

I I

I 8

9 10 11 12 13 14 15 I

H G

1.268 1.326 1.273 1.324 0.394

-0.151 1.326 1.163 1.324 1.166

-0.151 0.258 1.152 1.314 1.154 1.311 0.174

-0.228 1.310 1.161 1.308 1.163

-0.153 0.172 1.200 1.302 1.202 1.299 0.167

-0.230 1.301 1.137 1.300 1.139

-0.077 0.176 0.935 1.096 0.937 1.097 0.214 0.091 0.389 0.303 0.390 0.304 0.257 0.330 F

E D

1.152 1.310 1.196 1.154 1.307 1.198 0.174

-0.229 0.167 1.315 1.160 1.298 1.312 1.162 1.295

-0.228 0.172

-0.231 1.207 1.304 1.169

1. 209 1.301 1.172 0.16&

-0.230 0.257 1.305 1.151 1.208 1.302 1.152 1.205

-0.230 0.087

-0.248 1.173 1.215 0.790 1.175 1.211 0.789 0.171

-0.329

-0.127 1.202 1.059 0.347 1.200 1.057 0.347

-0.16&

-0.189 0.000 0.60&

0.317 0.607 0.317 0.165 0.000 Figure 3-4 C

B A

1.290 0.926 0.389 1.289 0.928 0.390

-0.078 0.216 0.257 1.130 1.090 0.302 1.133 1.091 0.303 0.265 0.092 0.331 1.196 0.603 1.194 0.603

-0.167 0.000 1.052 0.315 1.050 0.315

-0.190 0.000 0.344 0.344 0.000 RPD C TZ3D RPD C TZ2D

/oDIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-7

.197 0.33 0.39

~-----

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~1C9 F07 (7000 MWD/HTU) HFP HAP I

I I

8 9

10 11 12 13 14 15 I

H 1.251 1.244

-0.560 1.377 1.367

-0.726 1.150 1.143

-0.609 1.351 1.343

-0.592 1.172 1.170

-0.171

_l. 280 1.283 0.234 0.872 0.878 0.688 0.381 0.386 1.312 G

F E

D 1.377 1.151 1.352 1.171 1.367 1.144 1.344 1.169

-0.726

-0.608

-0.592

-0.171 1.161 1.362 1.155 1.337 1.154 1.353 1.151 1.335

-0.603

-0.661

-0.346

-0.150 1.361

l. 202 1.361 1.151 1.352 1.196 1.356 1.151

-0.661

-0.499

-0.367 0.000 1.155 1.361 1.145 1.238 1.150 1.356 1.143 1.238

-0.433

-0.367

-0.175 0.000 1.338 1.152 1.243 0.805 1.336 1.152 1.243 0.806

-0.149 0.000 0.000 0.124 1.082 1.201 1.041 0.365 1.085 1.206 1.046 0.366 0.277 0.416 0.480 0.274 1.011 0.594 0.329 1.020 0.598 0.331 0.890 0.673 0.608 0.298 0.302 1.342 Figure 3-5 C

B A

1.275 0.868 0.383 1.278 0.874 0.388 0.235 0.691 1.305 1.080

l. 010 0.299 1.083 1.019 0.303 0.278 0.891 1.338 1.200 0.593 1.204 0.597 0.333 0.675 1.037 0.328 1.042 0.330 0.482

o. 610 0.363 0.364 0.275 RPD C TZ3D RPD C TZ2D 4DIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-8

)

.589 1.34 0.89

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~C9 FOAl (10095 HWD/HTU) HFP HAP I 8 I

9 I

I I

10 11 12 13 14 15 1*

H G

1.237 1.380 1.230 1.374

-0.566

-0.435 1.380 1.156 1.374 1.149

-0.435

-0.606 1.147 1.369 1.140 1.364

-0.610

-0.365 1.359 1.148 1.354 1.144 0.368

-0.348 1.162 1.337 1.159 1.337

-0.258 0.000 1.279 1.069 1.281 1.070 0.156 0.094 0.871 1.001 0.874 1.007 0.344 0.599 0.395 0.309 0.398 0.311 0.759 0.647 F

E D

1.148 1.360 1.162 1.141 1.356 1.159

-0.610

-0.294

-0.258 1.371 1.149 1.337 1.365 1.144 1.337

-0.438

-0.435 0.000 1.193 1.361 1.139 1.187 1.361 1.139

-0.503 0.000 0.000 1.361 1.138 1.245 1.360 1.136 1.247

-0.073

-0.176 0.161 1.139 1.248 0.816 1.139 1.251 0.817 0.000 0.240 0.123 1.192 1.035 0.377 1.197 1.039 0.378 0.419 0.386 0.265 0.600 0.339 0.603 0.341 0.500 0.590 Figure 3-6 C

B A

1.276 0.869 0.397 1.278

0. 8-72 0.400 0.157 0.345 0.756 1.069

1. 001 0.310 1.069 1.007 0.312 0.000 0.599 0.645 1.191 0.599 1.196 0.602 0.420 0.501 1.032 0.339 1.037 0.340 0.484 0.295 0.375 0.376 0.267 RPD

( TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RHS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF (RPD>0.9) 3-9

)

).

)

.401 0.76

-0.61

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~N2C7 FOl (1000 HWD/HTU) HFP HAP I 8 I

9 I

10 I

11

I I

I I

12 13 14 15 H

G 0.960 l.181 0.963 1.178 0.312

-0.254 l.182 1.146 1.179 1.147

-0.254 0.087 1.129 1.240 1.129 1.236 0.000

-0.323 1.207

1. 217 1.206 l.217

-0.083 0.000 1.249 1.351 l.250 1.348 0.080

-0.222 1.311 1.180 1.308 l.181

-0.229 0.085 0.952 l.063 0.952 1.063 0.000 0.000 0.353 0.295 0.354 0.296 0.283 0.339 F

E D

1.128 1.206 1.248 l.129 1.206 1.250 0.089 0.000 0.160 1.239 1.216 1.350 1.235 1.217 1.348

-0.323 0.082

-0.148 1.179 1.282 1.226 1.181 1.278 1.229 0.170

-0.312 0.245 1.283 1.185 1.267 1.279 1.188 1.267

-0.312 0.253 0.000 1.227 l.267 0.796 1.229 1.266 0.798 0.163

-0.079 0.251 l.194 1.062 0.369 1.192 l.062 0.369

-0.168 0.000 0.000 0.604 0.311 0.605 0.312 0.166 0.322 Figure 3~7 C

B A

1.311 0.952 0.354 1.308 0.953 0.354

-0.229 0.105 0.000 1.179 1.063 0.295 1.181 1.063 0.296 0.170 0.000 0.339 1.194 0.604 1.192 0.605

-0.168 0.166 1.063 0.311 1.063 0.312 0.000 0.322 0.371 0.372 0.270 RPD

( TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-10

)

.202 0.34

-0.32

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~2C7 F07 (7000 HWD/HTU) HFP HAP I

I I

8 9

10 11 12 13 14 15 I

H 1.066 1.059

-0.657 1.326 1.315

-0.830 1.165 1.159

-0.515 1.187 1.182

-0.421 1.189 1.189 0.000 1.276 1.278 0.157 0.905 0.910 0.552 0.364 0.368 1.099 G

F E

D 1.325 1.165 1.187 1.189 1.315 1.159 1.182 1.188

-0.755

-0.515

-0.421

-0.084 1.211 1.336 1.203 1.340 1.204 1.327 1.200 1.339

-0.578

-0.674

-0.249

-0.075 1.336 1.203 1.339 1.188 1.328 1.199 1.334 1.188

-0.599

-0.333

-0.373 0.000 1.203 1.339 1.172 1.257 1.200 1.334 1.171 1.258

-0.249

-0.373

-0.085 0.080 1.341 1.188 1.257 0.791 1.339 1.189 1.258 0.794

-0.149 0.084 0.080 0.379 1.117 1.181 1.024 0.380 1.119 1.183 1.028 0.382 0.179 0.169 0.391 0.526

1. 007 0.600 0.322 1.013 0.604 0.324 0.596 0.667 0.621 0.302 0.305 0.993 Figure 3-8 C

B A

1.276 0.905 0.365 1.277 0.910 0.368 0.078 0.552 0.822 1.117 1.007 0.302 1.119 1.013 0.305 0.179 0.596 0.993 1.181 0.600 1.183 0.604 0.169 0.667 1.024 0.322 1.029 0.324 0.488 0.621 0.382 0.385 0.785 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RHS DIFFERENCE:

0 HAX DIFFERENCE:

HAX DIFF CRPD>0.9) 3-11

.506 1.10

-0.83

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~N2C7 FOF (15000 MWD/HTU) HFP HAP I

I I

8 9

10 l

I ae I

13 I

114 I 15 I

I I

I H

G 1.076 1.334 1.067 1.329

-0.836

-0.375 1.334 1.186 1.329 1.178

-0.375

-0.675 1.137 1.326 1.129 1.321

-0.704

-0.377 1.142 1.160 1.133 1.153

-0.788

-0.603 1.143 1.307 1.137 1.305

-0.525

-0.153 1.263 1.099 1.265 1.098 0.158

-0.091 0.929 1.023 0.932 1.029 0.323 0.587 0.423 0.348 0.427 0.352 0.946 1.149 F

E D

1.137 1.142 1.143 1.129 1.133 1.137

-0.704

-0.788

-0.525 1.326 1.160 1.307 1.321 1.153 1.305

-0.377

-0.603

-0.153 1.170 1.326 1.156 1.164 1.324 1.154

-0.513 -o.151

-0.173 1.326 1.146 1.249 1.324 1.144 1.253

-0.151

-0.175 0.320 1.157 1.249 0.818 1.154 1.252 0.821

-0.259 0.240 0.367 1.195 1.028 0.421 1.200 1.034 0.423 0.418 0.584 0.475 0.644 0.362 0.649 0.365

o. 776 0.829 Figure 3-9 C

B A

1.263 0.929 0.423 1.265 0.932 0.428 0.158 0.323 1.182 1.099 1.024 0.348 1.098 1.030 0.352

-0.091 0.586 1.149 1.195 0.644 1.200 0.649 0.418

o. 776 1.028 0.362 1.034 0.365 0.584 0.829 0.421 0.425 0.950 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RHS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-12

)

.582 1.18

-0.84

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~2C8 FOl (1000 HWD/HTUJ HFP HAP I 8 I

9 I

10 I

11 12 I

113 I

I I

14 15 I

H G

0.9&9 1.279 0.9&9 1.277 0.000

-0.15&

1.282 1.199 1.280 1.201

-0.15&

0.1&7 1.050 1.301 1.055 1.298 0.47&

-0.231 1.147 1.210 1.150 1.212 0.2&2 0.165 1.1&5 1.319 1.1&7 1.315 0.172

-0.303 1.305 1.210 1.302 1.212

-0.230 0.1&5 0.941 1.081 0.944 1.082 0.319 0.093 0.332 0.274 0.333 0.27&

0.301 0.730 F

E D

1.027 1.13&

1.1&3 1.030 1.137 1.1&4 0.292 0.088 0.08&

1.294 1.205 1.317 1.291 1.205 1.313

-0.232 0.000

-0.304 1.187 1.287 1.1&7 1.187 1.281 1.1&8 0.000

-0.4&&

0.08&

1.287 1.158 1.259 1.282 1.159 1.25&

-0.389 0.08&

-0.238 1.1&7 1.258 0.833 1.1&9 1.255 0.833 0.171

-0.238 0.000 1.243 1.0&4 0.351 1.242 1.0&2 0.352

-0.080

-0.188 0.285 0.&28 0.328 0.&29 0.329 0.159 0.305 Figure 3-10 C

B A

l.30S 0.942 0.332 1.302 0.945 0.333

-0.230 0.318 0.301 1.210 1.081 0.273 1.212 1.083 0.27&

0.1&5 0.185 1.099 1.243 0.&28 1.242 0.&30

-0.080 0.318 1.0&5 0.328

1. 063 0.329

-0.188 0.305 0.351 0.352 0.285 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-13

)

.309 1.10 0.48

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~2C8 F07 (7000 MWD/HTU) HFP HAP I

I I

I 8

9 10 11 12 13 14 15 H

G 1.012 1.350 1.001 1.338

-1. 087

-0.889 1.352 1.204 1.340 1.195

-0.888

-0.748 1.064 1.350 1.059 1.340

-0.470

-0.741 1.121 1.190 1.117 1.18&

-0.357

-0.336 1.132 1.349 1.131 1.346

-0.088

-0.222 1.305 1.148 1.307 1.152 0.153 0.348 0.895 1.021 0.901 1.029 0.670 0.784 0.336 0.279 0.340 0.283 1.190 1.434 F

E D

1.044 1.112 1.131 1.037 1.109 1.130

-0.670

-0.270

-0.088 1.345 1.186 1.348 1.334 1.182 1.344

-0.818

-0.337

-0.297 1.187 1.352 1.145 1.180 1.345 1.145

-0.590

-0.518 0.000 1.352 1.153 1.284 1.345 1.153 1.286

-0.518 0.000 0.156 1.145 1.284 0.843 1.145 1.285 0.846 0.000 0.078 0.356 1.224 1.053 0.368 1.228 1.058 0.370 0.327 0.475 0.543 0.615 0.338 0.620 0.341 0.813 0.888 Figure 3-11 C

B A

1.30&

0.89&

0.33&

1.308 0.902 0.340 0.153 0.&70 1.190 1.148 1.022 0.279 1.152 1.029 0.283 0.348 0.&85 1.434 1.225 0.&15 1.228 0.&20 0.245 0.813 1.053 0.338 1.058 0.341 0.475 0.888 0.368 0.371 0.815 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE=

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-14

)

.649 1.43

-1. 09

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COMPARISION

~2C8 FOF (15000 HWD/MTU) HFP MAP H

G F

E I 8 I 9 110 I

I I

I 11 13 14 15 1.024

1. 012

-1.172 1.351 1.345

-0.444

l. 0&5 1.05&

-0.845 1.100

1. 092

-0.727 1.109 1.104

-0.451 1.295 1.297 o.154 0.910 0.913 0.330 0.384 0.388

1. 042 1*

1.350 1.048 1.09&

1.343 1.039 1.088

-0.519

-0.859

-0.730 1.182 1.349 1.1&1 1.172 1.343 1.154

-0.846

-0.445

-0.603 1.352 1.1&5 1.351 1.34&

1.157 1.349

-0.444

-0.&87

-0.148 1.162 1.350 1.130 1.155 1.349 1.128

-0.602

-0.074

-0.177 1.342 1.118 1.2&9 1.342 1.115 1.274 0.000

-0.2&8 0.394 1.119 1.20&

1.04&

1.118 1.210 1.053

-0.089 0.332 0.&&9 1.022 0.643 0.372 1.028 o.&48 0.37&

0.587 0.778 1.075 0.318 0.323 1.572 D

1.109 1.104

-0.451 1.342 1.342 0.000 1.119 1.116

-0.268 1.270 1.274 0.315 0.864 0.867 0.347 0.404 0.407 0.743 Figure 3-12 C

B A

1.29&

0.910 0.384 1.298 0.913 0.387 0.154 0.330 0.781 1.119 1.023 0.318 1.118 1.028 0.322

-0.089 0.489

l. 258 1.20&

0.&43 1.211 0.648 0.415

o. 778 1.047 0.373 1.053 0.37&

0.573 0.804 0.405 0.408 0.741 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-15

.&33 1.57

-1.17

I I

PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION tlCA FOl (1000 HWD/HTUJ HFP HAP I

I I

I 8

9 10 11 12 13 14 15 H

G 1.295 1.282 1.294 1.278

-0.077

-0.312 1.283 l.072 1.279

l. 070

-0.312

-0.187 1.237 1.269 1.235 1.261

-0.162

-0.630 1.287 1.295 1.286 1.293

-0.078

-0.154 1.287 1.251 1.288 1.245 0.078

-0.480 1.241 1.158 1.245 1.163 0.322 0.432 0.976 1.094 0.981 1.097 0.512 0.274 0.3&1 0.297 0.3&4 0.299 0.831 0.673 F

E D

l.235 1.286 1.289 1.234 1.286 1.290

-0.081 0.000 0.078 1.268 1.294 1.252 1.260 1.293 1.247

-o. 631

-0.077

-0.399 l.324 1.215 1.176 l.32S 1.213 1.177 0.076

-0.165 0.085 1.215 1.203 1.166" l.214 1.203 1.162

-0.082 0.000

-0.343 1.176 1.167 0.768 1.177 1.163

o. 771 0.085

-0.343 0.391 1.144

1. 018 0.359 1.141 1.017 0.361

-0.262

-0.098 0.557 0.655 0.340 0.658 0.342 0.458 0.588 Figure 3-13 C

B A

1.243 0.978 0.362 1.247 0.984 0.365 0.322 0.613 0.829 1.160 1.096 0.299 1.165 1.100 0.302 0.431 0.365 1.003 1.145 0.657 1.142 0.659

-0.262 0.304

1. 019 0.341 1.018 0.343

-0.098 0.587 0.360 0.362 0.556 RPD C TZ3D RPD C TZ2D 4DIFF C2D*3D/3D RHS DIFFERENCE:

0 MAX DIFFERENCE:

HAX DIFF (RPD>0.9) 3-16

)

.414 1.00

-0.&3

I I

.1 PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~lCA F07 (7000 HWD/HTU) HFP HAP I 8 I

9 I

10 I

11 12 I

I

13.

114 I

I I

15 H

G 1.147 1.167 1.145 1.163

-0.174

-0.343 1.168 1.019 1.1&4

1. 015

-0.342

-0.393 1.1&5 1.299 1.1&3 1.295

-0.172

-0.308 1.235 1.237 1.234 1.235

-0.081

-0.1&2 1.229 1.307 1.227 1.303

-0.1&3

-0.306 1.1&4 1.119 1.1&7 1.122 0.258 0.2&8 0.912 1.059 0.925 1.0&5 1.425 0.5&7 0.3&5 0.304 0.370 0.307 1.370 0.987 F

E D

1.164 1.235 1.230 1.162 1.234 1.229

-0.172

-0.081

-0.081 1.298 1.237 1.308 1.294 1.235 1.303

-0.308

-0.1&2

-0.382 1.250 1.190 1.177 1.2&0 1.190 1.175 0.800 0.000

-0.170 1.191 1.191 1.2&1 1.191 1.190 1.25&

0.000

-0.084

-0.397 1.177 1.2&2 0.829 1.175 1.257 0.829

-0.170

-0.396 0.000 1.222 1.082 0.402 1.219 1.079 0.402

-0.245

-0.277 0.000 0.&81 0.375 0.&83 0.375 0.294 0.000 Figure 3-14 C

B A

1.165 0.913 0.366 1.168 0.926 0.370 0.258 1.424 1.093 1.120 1.060 0.305 1.123 1.06&

0.308 0.2&8 0.5&&

0.984 1.223 0.682 1.219 o.&83

-0.327 0.147 1.082 0.375 1.079 0.37&

-0.277 0.2&7 0.402 0.403 0.249 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-17

.472 1.43 1.43

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION ISlCA FOD (13000 HWD/HTU) HFP HAP I 8 I

9 I

10 I

11

I I

I I

12 13 14 15 H

G 1.070 1.104 1.063 1.095

-0.654

-0.815 1.104 0.991 1.096 0.984

-0.725

-0.706 1.118 1.304 1.113 1.302

-0.447

-0.153 1.191 1.190 1.186 1.185

-0.420

-0.420 1.185 1.328 1.180 1.326

-0.422

-0.151 1.122 1.099 1.121 1.100

-0.089 0.091 0.899 1.054 0.911 1.060 1.335 0.569 0.391 0.326 0.395 0.330 1.023 1.227 F

E D

1.118 1.191 1.186 1.112 1.186 1.181

-0.537

-0.420

-0.422 1.304 1.189 1.328 1.301 1.184 1.326

-0.230

-0.421

-0.151 1.195 1.162 1.165 1.202 1.159 1.163 0.586

-0.258 -o.172 1.162 1.170 1.307 1.159 1.167 1.307

-0.258 -o. 256 0.000 1.165 1.307 0.867 1.163 1.308 0.868

-0.172 0.077 0.115 1.269 1.112 0.439 1.270 1.115 0.440 0.079 0.270 0.228 0.710 0.408 0.713 0.409 0.423 0.245 Figure 3-15 C

B A

1.122 0.900 0.392 1.121 0.911 0.396

-0.089 1.222 1.020 1.100 1.054 0.328 1.100 1.060 0.331 0.000 0.569 0.915 1.269

o. 710 1.270 0.713 0.079 0.423 1.112 0.408 1.115 0.410 0.270 0.490 0.439 0.441 0.456 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RHS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-18

.496 1.33 1.33

I I

I

~DQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~lCB FOZ (150 MWD/HTUl HFP HAP I 8 I 9 I

10 I

11 12 I

13 I

114 115 I

I I

I H

G 0.998 1.247 0.998 1.239 0.000

-0.642

1. 241 1.036 1.233 1.029

-0.645

-0.676 1.289

1. 271 1.284 1.263

-0.388

-0.629 1.291 1.010 1.284 l.006

-0.542

-0.396 1.277 1.288 1.276 1.289

-0.078 0.078 1.282 1.292 1.280 1.295

-0.156 0.232 1.098 1.190 1.102 1.192 0.364 0.168 0.388 0.337 0.388 0.338 0.000 0.297 F

E D

1.295 1.291 1.276 1.289 1.284 1.274

-0.463

-0.542

-0.157 1.272

1. 008 1.286 1.264 1.004 1.287

-0.629

-0.397 0.078 1.302 1.229 1.029 1.299 1.226 1.032

-0.230

-0.244 0.292 1.232 0.959 1.154 1.229 0.961 1.156

-0.244 0.209

. 0.173 1.032 1.158 0.620 1.036 1.161 0.624 0.388 0.259 0.645 1.210 1.097 0.375 1.211 1.102 0.377 0.083 0.456 0.533 0.782 0.353 0.785 0.355 0.384 0.567 Figure 3-16 C

B A

1.280 1.096 0.386 1.278 1.100 0.387

-0.156 0.365 0.259 1.289 1.187 0.336 1.292 1.190 0.337 0.233 0.253 0.298 1.205

o. 779 1.206 0.782 0.083 0.385 1.087 0.362 1.091 0.364 0.368 0.552 0.363 0.365 0.551 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RHS DIFFERENCE:

0 HAX DIFFERENCE: -

HAX DIFF (RPD>0.9) 3-19

.387 0.68

-0.68

I I

I PDQ3D llCB I 8 I 9 110 I

I I

11 l

13 14 15 I ae I

VERSUS PDQ2D TWO ZONE F07 (7000 MWD/MTU) HFP H

G F

1.028 1.309 1.219 1.026 1.302 1.216

-0.195

-0.535

-0.246 1.304

l. 012 1.212 1.298 1.006 1.208

-0.460

-0.593

-0.330 1.215 1.211 1.236 1.213 1.207 1.234

-0.165

-0.330

-0.162 1.336 0.988 1.305 1.332 0.983 1.301

-0.299

-0.506

-0.307 1.214 1.210 1.036 1.213 1.210

l. 035

-0.082 0.000

-0.097 1.316 1.205 1.260 1.315 1.207 1.260

-0.076 0.166 0.000 1.031 1.142

o. 770 1.035 1.148

o. 774 0.388 0.525 0.519 0.392 0.339 0.393 0.341 0.255 0.590 RPD COHPARISION HAP E

D 1.337 1.214 1.332 1.213

-0.374

-0.082 0.987 1.209 0.982 1.209

-0.507 0.000 1.303 1.034 1.298 1.034

-0.384 0.000 0.999 1.249 0.997 1.250

-0.200 0.080 1.252 0.682 1.253 0.683 0.080 0.147 1.129 0.415 1.133 0.416 0.354 0.241 0.376 0.377 0.266 Figure 3-17 C

B A

1.316 1.031 0.391 1.315 1.035 0.392

-0.076 0.388 0.256 1.204 1.142 0.339 1.207 1.147 0.341 0.249 0.438 0.590 1.257 0.769 1.258

o. 772 0.080 0.390 1.122 0.385 1.126 0.387 0.357 0.519 0.404 0.404 0.000 RPD

( TZ3D RPD C TZ2D

%DIFF (2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE: -

MAX DIFF (RPD>0.9) 3-20

.335 0.59

-0.59

~-~-----

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~lCB FOD (13000 HWD/HTU) HFP HAP I 8 I 9 I 10 I

11 12 I

13 I

114 I

I I

I 1*

15 H

G F

E D

1.045 1.335 1.180 1.339 1.178 1.041 l.331 1.174 1.336 l.175

-0.383

-0.300

-0.508

-0.224

-0.255 l.332 l.007 1.177 0.982 1.172 1.328 0.999 1.169 0.974 1.169

-0.300

-0.794

-0.680

-0.815

-0.256 l.178 l.176 1.203 1.333 1.038 l.172 1.169 1.198 l.332 1.036

-0.509

-0.595

-0.416

-0.075

-0.193 l.338 0.983 1.334 l.017 1.274 1.336 0.975 l.334 1.014 1.279

-0.149

-0.814 0.000

-0.295 0.392 l.178 l.172 1.039 1.276 0.720 1.174 l.169 1.037 1.281

o. 722

-0.340

-0.256

-0.192 0.392 0.278 l.326 l.165 1.281 1.127 0.446 l.329 l.166 1.287 1.134 0.447 0.226 0.086 0.468 0.621 0.224 l.008 1.113 0.775 0.399

l. 010 l.118 0.779 0.401 0.198 0.449 0.516 0.501 0.411 0.355 0.412 0.357 0.243 0.563 Figure 3-18 C

B A

1.326 1.008 0.411 1.330 1.010 0.412 0.302 0.198 0.243 1.165 1.113 0.355 1.165 1.119 0.357 0.000 0.539 0.563 1.280

o. 774 1.285

o. 778 0.391 0.517 1.122 0.408 l.129 0.410 0.624 0.490 0.434 0.436 0.461 RPD C TZ3D RPD C TZ2D

~DIFF (2D-3D/3D RHS DIFFERENCE:

0 MAX DIFFERENCE:

~

HAX DIFF CRPD>0.9) 3-21

)

.448 0.81

-0.81

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION IS2CA F05 (5000 HWD/HTU) HFP HAP I 8 I 9 I 10 I

11..,

I I

13 14 15 H

G L129 1.201 1.131 1.203 0.177 0.167 l.201 1.134 1.202 1.136 0.083 0.176 1.193 1.288 1.195 1.280 0.168

-0.621 1.206 1.028 1.205

1.025

-0.083

-0.292 1.168 1.312 1.166 1.304

-0.171

-0.610 1.303 1.167 1.297 1.170

-0.460 0.257 l.020 1.078 1.024 1.082 0.392 0.371 0.498 0.341 0.503 0.344 l.004 0.880 F

E D

1.193 l.206 1.168 1.194 1.205 1.166 0.084

-0.083

-0.171 1.288 l.028 1.312 1.280 l.026 1.304

-0.621

-0.195

-0.610 1.194 1.205 1.237 1.190 1.205 1.238

-0.335 0.000 0.081 1.204 l.198 1.233 1.204 l.200 1.227 0.000 0.167

-0.487 1.236 l.232 0.705 1.238 1.227 0.707 0.162

-0.406 0.284 1.226 1.034 0.401 1.222 1.035 0.405

-0.326 0.097 0.998 0.627 0.397 0.632 0.401 0.797 l.008 Figure 3-19 C

B A

1.304 1.020 0.4.98 1.298 1.025 0.503

-0.460 0.490 l.004 l.167 1.078 0.341 1.170 1.083 0.344 0.257 0.464 0.880 1.227 0.626 1.222 0.631

-0.407 0.799 1.034 0.397 1.035 0.401 0.097 1.008 0.401 0.405 0.998 RPD C TZ3D RPD C TZ2D

~DIFF C2D-3D/3D RMS DIFFERENCE:

0 HAX DIFFERENCE:

HAX DIFF CRPD>0.9) 3-22

)

.540 1.01

-0.62

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COMPARISION

~2CA FOB (11164 MWD/MTU) HFP MAP I

I I

I 8

9 10 11 12 13 14 15 H

G 1.063 1.121

l. 061 1.117

-0.188

-0.357 1.121 1.082 1.117 1.078

-0.357

-0.370 1.132 1.291 1.129 1.283

-0.265

-0.620 1.162 1.008 1.158 1.003

-0.344

-0.496 1.179 1.349 1.177 1.345

-0.170

-0.297 1.344 1.157 1.343 1.160

-0.074 0.259

l. 000 1.060 1.004 1.065 0.400 0.472 0.522 0.361 0.526 0.364 0.766 0.831 F

E D

1.132 1.161 1.178 1.129 1.158 1.177

-0.265

-0.258

-0.085 1.291 1.008 1.349 1.283 1.003 1.345

-0.620

-0.496

-0.297 1.140 1.150 1.209 1.135 1.147 1.209

-0.439

-0.261 0.000 1.149 1.159 1.275 1.14&

1.159 1.274

-0.261 0.000

-0.078 1.209 1.275 0.749 1.209 1.273 0.751 0.000

-0.157 0.267 1.273 1.047 0.436 1.273 1.051 0.440 0.000 0.382 0.917 0.655 0.428 0.659 0.433 0.611 1.168 Figure 3-20 C

B A

1.344 1.000 0.521 1.343 1.004 0.526

-0.074 0.400 0.960 1.157 1.059 0.361 1.159 1.064 0.364 0.173 0.472 0.831 1.273 0.654 1.273 0.659 0.000 0.765 1.047 0.428

1. 050 0.433 0.287 1.168 0.436 0.440 0.917 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 MAX DIFFERENCE:

MAX DIFF CRPD>0.9) 3-23

.524 1.17

-0.62

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~2CB FOl (1000 MWD/HTU) HFP HAP I

I I

I 8

9 10 11 12 13 14 15 H

G 1.126 1.231 1.130 1.240 0.355 0.731 1.228 1.261 1.237 1.269 0.733 0.634 1.237 1.228 1.242 1.224 0.404

-0.326 1.292 1.227 1.287 1.230

-0.387 0.244 1.013 1.255

1. 015 1.249 0.197

-0.478 1.296 1.261 1.293 1.265

-0.231 0.317 0.993 1.067 0.997 1.067 0.403 0.000 0.367 0.280 0.369 0.282 0.545

o. 714 F

E D

1.238 1.292 1.013 1.243 1.287 1.014 0.404

-0.387 0.099 1.229 1.228 1.255 1.225 1.231 1.249

-0.325 0.244

-0.478 1.221 1.236 1.288 1.224 1.229 1.292 0.246

-0.566 0.311 1.235 1.231 1.245 1.228 1.232 1.238

-0.567 0.081

-0.562 1.288 1.247 0.870 1.292 1.241 0.870 0.311

-0.481 0.000 1.220 1.015 0.379 1.216 1.011 0.380

-0.328

-0.394 0.264 0.495 0.299 0.497 0.300 0.404 0.334 Figure 3-21 C

B A

1.295 0.992 0.367 1.291 0.996 0.368

-0.309 0.403 0.272 1.260 1.065 0.280 1.263 1.066 0.281 0.238 0.094 0.357 1.217 0.493 1.213 0.496

-0.329 0.609 1.009 0.296

l. 005 0.297

-0.396 0.338 0.362 0.363 0.276 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RHS DIFFERENCE:

0 HAX DIFFERENCE:

HAX DIFF CRPD>0.9) 3-24

)

.398 0.73 0.73

I I

I PDQ3D r2CB I

I I

8 9

10 11 13 14 15 I

VERSUS PDQ2D TWO ZONE F07 (7000 HWD/HTU) HFP H

G F

1.103 1.176 1.212 1.105 1.180 1.212 0.181 0.340 0.000 1.174 1.214 1.310 1.178 1.216 1.301 0.341 0.165

-0.687 1.211 1.309 1.232 1.211 1.300 1.229 0.000

-0.688 -o. 244 1.355 1.224 1.328 1.348 1.222 1.319

-0.517

-0.163

-0.678 1.016 1.293

1. 253 1.013 1.286 1.256

-0.295

-0.541 0.239 1.267 1.172 1.214 1.268 1.175 1.215 0.079 0.256 0.082 0.908 0.985 0.490 0.914 0.989 0.492 0.661 0.406 0.408 0.355 0.273 0.358 0.275 0.845 0.733 RPD COHPARISION HAP E

D 1.355 1.016 1.349 1.014

-0.443

-0.197 1.224 1.293 1.223 1.286

-0.082

-0.541 1.329

1. 254 1.320 1.256

-0.677 0.159 1.226 1.293

1. 227 1.293 0.082 0.000 1.294 0.882 1.294 0.886 0.000

0.454 1.030 0.398 1.031 0.399 0.097

o. 251 0.313 0.315 0.639 Figure 3-22 C

B A

1.267 0.908 0.355 1.268 0.914 0.358 0.079 0.661 0.845 1.172 0.984 0.273 1.175 0.989 0.275 0.256 0.508 0.733 1.213 0.489 1.214 0.491 0.082 0.409 1.027 0.311 1.028 0.313 0.097 0.643 0.385 0.387 0.519 RPD C TZ3D RPD C TZ2D

%DIFF C2D-3D/3D RMS DIFFERENCE:

0 HAX DIFFERENCE:

HAX DIFF (RPD>0.9) 3-25

)

.440 0.85

-0.69

I I

I PDQ3D VERSUS PDQ2D TWO ZONE RPD COHPARISION

~2CB FOGS (16500 HWD/HTU) HFP HAP I

I I

I H

G F

l.070 1.131 1.174 8

1.062 1.126 l.170

-0.748

-0.442

-0.341 l.130 l.174 1.343 9

1.125 l.170 l.342

-0.442

-0.341

-0.074 1.173 1.342 1.216 10 1.169 1.342

l. 214

-0.341 0.000

-0.164 1.329 1.199 1.358 11 1.327 1.197 l.360

-0.150

-0.167 0.147 l.026 1.322 l.202 12 l.021 1.323 1.202

-0.487 0.076 0.000 1.236 1.134 l.184 13 1.235 1.132 1.185

-0,. 081

-0.176 0.084 0.921 0.995 0.531 14 0.922 0.996 0.532 0.109 0.101 0.188 0.418 0.320 15 0.419 0.321 0.239 0.312 E

D 1.329 1.026 1.327 l.021

-0.150

-0.487 1.200 1.322 1.197 1.323

-0.250 0.076 1.358 1.203 1.360 1.202 0.147

-0.083 1.181 1.251 1.180 1.254

-0.085 0.240 1.252 0.887 1.254 0.889 0.160 0.225 1.023 0.435 1.026 0.436 0.293 0.230 0.355 0.356 0.282 Figure 3-23 C

B A

1.236 0.922 0.418 1.235 0.922 0.419

-0.081 0.000 0.239 1.134 0.995 0.320 1.132 0.996 0.321

-0.176 0.101 0.312 1.184 0.531 1.185 0.531 0.084 0.000 1.022 0.353 1.025 0.355 0.294 0.567 0.424 0.425 0.236 RPD

( TZ3D RPD C TZ2D 7.DIFF C2D-3D/3D RMS DIFFERENCE: a MAX DIFFERENCE: -

MAX DIFF CRPD>0.9) 3-26

)

.238 0.75

-0.75

I I

I 1*

3.3 CONTROL BANK WORTHS Integral control rod bank worths were calculated for each bank individually at BOC, HZP for 4 North Anna and 4 Surry cycles.

Table 3-2 presents the 2-D versus 3-D integral control bank worth comparison for D, C, B, A, SB, and SA banks for each cycle analyzed.

The 2-D versus 3-D bank worth comparison statistics (Table 3-4) show a mean difference of 0.3% (2-D worth greater than 3-D worth) with a standard deviation of 0.77..

Cold-Zero-Power (CZP) ARI 2-D versus 3-D bank worth comparisons were also made and the differences calculated.

Table 3-3 presents these comparison results.

The CZP calculations were run using a HZP ARO critical boron input.

Statistics for these comparisons (Table 3-5) show the 2-D model underpredicted the average worth by -20 pcm with a standard deviation of 44 pcm.

3-27

I I

UNIT/

CYCLE N1C8 N1C8 N1C8 N1C8 N1C8 N1C8 N1C9 NlC9 N1C9 N1C9 N1C9 N1C9 N2C7 N2C7 N2C7 N2C7 N2C7 N2C7 N2C8 N2C8 N2C8 N2C8 N2C8 N2C8 TABLE 3-2 HZP INTEGRAL CONTROL ROD BANK WORTH COMPARISON PDQ TWO ZONE 2-D VERSUS 3-D DATA PDQ 2-D PDQ 3-D PCM PERCENT WORTH WORTH DIFFERENCE DIFFERENCE BANK (pcm)

(pcm)

(2D-3D)

(2D-3D/3D*100)

B 1312 1313

-1

-0.08 D

946 938 8

0.85 C

838 833 5

0.60 A

317 317 0

0.00 SB 1036 1028 8

0.78 SA 962 967

-5

-0.52 B

1182 1184

-2

-o. 17 D

1035 1028 7

0.68 C

810 803 7

0.87 A

296 297

-1

-0.34 SB 1064 1055 9

0.85 SA 914 918

-4

-0.44 B

1346 1347

-1

-0.07 D

979 971 8

0.82 C

744 737 7

0.95 A

310 310 0

0.00 SB 991 982 9

0.92 SA 1032 1037

-5

-0.48 B

1267 1266 1

0.08 D

1010 1007 3

0.30 C

727 719 8

1.11 A

339 339 0

0.00 SB 1009 1002 7

0.70 SA 1053 1055

-2

-o.19 3-28

I

-I TABLE 3-2 (Continued)

I HZP INTEGRAL CONTROL ROD BANK WORTH COMPARISON PDQ TWO ZONE 2-D VERSUS 3-D DATA I

PDQ 2-D PDQ 3-D PCM PERCENT UNIT/

WORTH WORTH DIFFERENCE DIFFERENCE I

CYCLE BANK (pcm)

(pcm)

(2D-3D)

(2D-3D/3D*lOO)

SlClO B

1207 1209

-2

-0.17 I

SlClO D

1197 1192 5

0.42 SlClO C

883 878 5

0.57 SlClO A

336 334 2

0.60 S lClO SB 1075 1073 2

0.19 I

SlClO SA 953 952 1

0.11 SlCll D

1250 1255

-5

-0.40 SlCll C

754 755

-1

-0.13 I

SlCll B

1091 1078 13

1. 21 SlCll A

493 488 5

1. 02 SlCll SB 826 823 3

0.36 SlCll SA 1211 1207 4

0.33 S2Cl0 B

1346 1357

-11

-0.81 S2Cl0 D

1172 1163 9

0. 77 S2Cl0 C

835 814 21 2.58 I

S2Cl0 A

331 335

-4

-1.19 S2Cl0 SB 1164 1139 25 2.19 S2Cl0 SA 967 981

-14

-1.43 I

S2Cll B

1364 1374

-10

-0.73 S2Cll D

1086 1083 3

0.28 S2Cll C

905 897 8

0.89 S2Cll A

271 271 0

0.00 I

S2Cll SB 1164 1156 8

0.69 S2Cll SA 1010 1020

-10

-0.98 I

I I

I 3-29 I

I I

UNIT/

CYCLE NlC8 N1C8 NlC8 NlC9 NlC9 NlC9 N2C7 N2C7 N2C7 N2C8 N2C8 N2C8 SlClO SlClO SlClO SlCll SlCll SlCll S2C10 S2C10 S2C10 S2Cll S2Cll S2Cll TABLE 3-3 CZP ARI INTEGRAL CONTROL ROD BANK WORTH COMPARISON PDQ TWO ZONE 2-D VERSUS 3-D DATA PDQ 3-D PDQ 2-D PCM PERCENT BURNUP WORTH WORTH DIFFERENCE DIFFERENCE (Mwd/Htu)

(pcm)

(2D-3D)

(2D-3D/3D*100) 0 5532 5552 20 0.36 7000 5676 5638

-38

-0.67 15000 5917 5888

-30

-0.50 0

5269 5303 33 0.63 7000 5245 5215

-30

-0.58 10100 5286 5248

-38

-o. 72 0

5376 5406 30 0.56 7000 5559 5549

-10

-0.18 15000 5830 5828

-2

-0.03 0

5468 5494 26 0.47 7000 5505 5469

-36

-0.65 15000 5693 5653

-40

-0.71 0

5850 5885 35 0.59 7000 5979 5981 2

0.03 13000 6117 6075

-42

-0.68 0

6108 6118 9

0.15 7000 6080 6004

-76

-1.25 13000 6181 6076

-105

-1. 70 0

6349 6409 59 0.94 5000 6358 6310

-48

-0.76 11164 6395 6297

-98

-1.53 0

6454 6477 23 0.35 7000 6195 615'3

-42

-0.68 16500 6338 6261

-78

-1.22 3-30

I I

TABLE 3-4 PDQ TWO ZONE CONTROL ROD BANK WORTHS INTEGRAL BANK WORTHS FORD, C, B, A, SB, SA

% DIFFERENCE (2D-3D/3D*l00)

NUMBER OF STANDARD DESCRIPTION POINTS MEAN DEVIATION MAX.

INTEGRAL BANK 48 0.3%

0. 8 7.

2.6 %

TABLE 3-5 PDQ TWO ZONE CONTROL ROD BANK WORTHS CZP ARI INTEGRAL BANK WORTHS PCM DIFFERENCE (2D-3D) AND% DIFFERENCE (2D-3D/3D*100)

NUMBER OF STANDARD DESCRIPTION POINTS MEAN DEVIATION MAX.

CZP ARI BANK 24 20 pcm 44 pcm 59 CZP ARI BANK 24

-0.32 7.

0.73 7.

0.9 %

3-31 HIN.

-1.4 7.

HIN.

-105

-1. 7 7.

I I

3.4 CRITICAL BORON CALCULATIONS The accuracy of the 2-D PDQ Two Zone model to predict core criticality has been evaluated in four ways:

1) Comparison of HFP and HZP critical boron predictions to the 3-D PDQ model predictions at BOC, MOC, and EOC for 8 cycles.

2) Estimated Critical Position (ECP) differences (for 32 core restarts)

3) Comparison of HFP boron letdown to measured and 3-D PDQ data.

4) Comparison to measured critical conditions at HZP based on 32 core restarts and 8 BOC startups.

Table 3-6 presents the 2-D versus 3-D critical boron comparison statistics for 4 North Anna and 4 Surry cycles at BOC, MOC, and EOC, HFP and HZP conditions.

The HZP 2-D versus 3-D critical boron statistical comparison showed a mean difference of -12 ppm (underprediction) with a standard deviation of 9 ppm.

The HFP statistical comparison had a mean difference of 2 ppm (overprediction) with a standard deviation of 7 ppm.

Although the 2-D Two Zone model tends to underpredict critical boron versus 3-D at HZP, criticality predictions for the 32 ECP cases shows almost no bias when compared to measured data (see Table 3-7).

Figures 3-24 through 3-31 show the predicted 2-D versus 3-D and measured boron letdown curves based on HFP all rods out (ARO) operation.

Differences are typically limited to about 30 ppm which is consistent with the HZP startup data. As stated in VEP-NAF-1 1, the letdown curve slope, shape, and overall agreement indicate that the 50 ppm reliability factor 3-32

I I

I I*

is appropriate for 3-D HFP predictions.

Based on the 2-D model calculational results versus the 3-D model and the HFP letdown curves, this reliability factor is appropriate for the 2-D model as well. Some.

data points shown on the letdown curves deserve mention. The N2C7 letdown curve shows a slope change at mid-cycle, due to the implementation of a 6 degree core average temperature reduction at about 7000 Mwd/Ktu burnup.

This reduction continued through the remainder of the cycle. The N1C9 predicted and measured data cross at about 10,000 Hwd/Htu burnup which is approximately the time the unit was shutdown for steam generator tube inspection and plugging and reduced ( lOOi. to 95i.) power operation.

In addition, soluble boron 810 depletion _is a possible cause for more boron letdown curvature (higher than expected mid-cycle measured boron concentration) than predicted..

Comparisons for eight cycles of BOC HZP startups versus Two Zone 2-D and 3-D predictions is given in Table 3-7. The 2-D versus measured comparisons show a mean difference of 5 ppm (overprediction) with a standard deviation of 35 ppm.

The 3-D versus measured comparisons show a mean difference of 16 ppm (overprediction) with a standard deviation of 30 ppm.

Note that one 2-D Two Zone HZP BOC startup point exceeds 50 ppm difference (+55 ppm). This point appears to be an outlier because the next largest positive difference is +39 ppm for BOC startups and the largest positive value for all ECP cases is +41 ppm.

Note that this point is consistent with 3-D results which show a difference of +55 ppm for the same cycle (SlClO).

Considering these factors, the 50 ppm NRF remains appropriate for HZP 2-D model calculations.

3-33

I I

I, I

DESCRIPTION HZP HFP Note:

TABLE 3-6 PDQ TWO ZONE CRITICAL BORON CONCENTRATIONS (PPM) DIFFERENCE 2-D VERSUS 3-D NUMBER OF STANDARD POINTS MEAN DEVIATION MAX.

24

-12 9 ppm 3

23 2

7 ppm 14 MIN.

-31

-13 Data includes HZP (BOC, MOC, EOC) and HFP (BOC, MOC, EOC) for NlC8, N1C9, NZC7, N2C8, SlClO, SlCll, S2C10 and S2Cll.

TABLE 3-7 PDQ TWO ZONE CRITICAL BORON CONCENTRATIONS FOR HZP STARTUPS (PPM) DIFFERENCE 2-D and 3-D VERSUS MEASURED DATA NUMBER OF STANDARD DESCRIPTION POINTS MEAN DEVIATION MAX.

MIN.

ECP DATA 32

-0.6 23 ppm 41

-46 2-D HZP STARTUP 8

5 35 ppm 55

-35 3-D HZP STARTUP 8

16 30 ppm 55

-19 3-34

E

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- -i 1,600 1,500 1,400 1,300 1,200 1,100 1,000 900 800 700 600 500 400 300 200 100 0

NlC8 IJC)RON LETDC)WN C'.llf{VI~:

~h 14i..r----t---t----1----+----+---

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1-----r--J 1----1----+----+~---""li-*..,-+---t---,----f----t-;

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?.., ooo A,ooo 6,ooo

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700 ~--1---+---'--+---t-__:~~~~;:--. --r--

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-s Cl) w I

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-...J 1111;.. -!.. --,--.-- - -

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900 800 700 U

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~

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-~

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PDQ TWO ZONE 3D MEASURED PDQ TWO ZONE ~D lO C -s Cl) w I

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~ -z 0 -

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0 P:l 1,500 1,-100 l,JOO 1,200 l, I 00 1,000 900 ------

N2C8 f30RON IJETDOWN Cl.JRVf~

800 ~---+---t----t 700 l-----t-----t---

600 1----+----t---- --

500 400

. ------*+---~-------...... -*-*---------* *---* ---. ---*-**

300 1-----t----t--~

200 I-----+-----'---;--------- - -- -- ------ -------- -

100 --

0 l---1----L.-->---L-~- __,__...__..___~---* -----**-'-

____ ___,__~-~

o i,ooo A,ooo o,ooo

'o,ooo \\ o,ooo \\ i.ooo \\ A.ooo \\ o,ooo BURNUP(MWD/MTU)

PDQ TWO ZONE.\\I)

ME,\\Sl J l~E I>

f:

Pl><} TWO ZONE -~1>

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'"1 f'D w

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µ=l u z 0 u z

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1,000 900 800 -

700 600 -

500 400..

300 -

200 S1C10-10A BORON LE1-,l)C)WN ClJRVI~

---l---------t

- ----- ~--

PDQ TWO ZONE JD MEASURED

- t' PDQ TWO ZONE 2D 100 1---------4----+-----L----*--

0 0

2,000 4,000 6,000 8,000 10,000 12,000 14,000 BURNUP(MWD/MTU)

-n lO C:

""'S C1) w I

N (X)

g

~

---z 0

~

<C

~

w

~

I z

~

0 u z 0 u z

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0 P'.:l 1,000 900 800 700 600 500 400 300 200 100 0

S1C11 BORON I_jETDOWN ClJRVE r------.----i---~--~---i---*- -------.---. PDQ TWO ZONE 3D L_~__l

__.l___...L __ L__J__-L__..__~~----'----.L---'-",.,'f..--~

MEASURED PDQ TWO ZONE 2D 0

2,000 4,000 6,000 8,000 10,000 12,000 14,000 BURNUP(MWD/MTU)

<.O C:

'"1 ro w

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1,100

~ 1,000

~

900 z

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~

700

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0 400 u

z 300 0

~

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~

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S2C 10 BORON I_JETDOWN CURVE PDQ TWO ZONE JD MEASURED PDQ TWO ZONE 2D 2,000 4,000 6,000 8,000 10,000 12,000 BURNUP(MWD/MTU)

""Tl

\\0 C:

-s Cl) w I w 0

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~ 1,300

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I I

3.5 ISOTHERMAL TEMPERATURE COEFFICIENTS The calculation of the isothermal temperature coefficient ( ITC) values at the hot zero power (HZP) condition is important because they can be compared to plant measurements taken during startup physics testing and therefore, can provide a basis for evaluating the accuracy of isothermal temperature coefficient, moderator temperature coefficient (MTC), and Doppler coefficient (OTC) design prediction.

The isothermal temperature coefficient is derived by dividing the change in core reactivity caused by a uniform temperature change by the change in temperature.

Table 3-8 presents a comparison of 2-D versus 3-D, ITC's and 2-D versus measured ITC' s for unrodded configurations at BOC, HZP conditions.

Relative to measured data, all 8 points are well within the current startup criteria of+/- 3 pcm/°F.

The cycles compared show good agreement between models with a mean of +0.9 more positive than the 3D model and a standard deviation of 0.16.

TABLE 3-8 PDQ TWO ZONE ISOTHERMAL TEMPERATURE COEFFICIENTS (PCM/°F) DIFFERENCE 2-D VERSUS 3-D AND MEASURED DATA NUMBER OF STANDARD DESCRIPTION POINTS MEAN DEVIATION MAX.

MIN.

2-D VS. 3-D 8

0.9 0.16 1.1 0.7 2-D VS. MEAS.

8 0.3 0.56 0.9

-0.6 3-43

I I

3.6 BORON WORTH CALCULATIONS Table 3-9 shows the 2-D versus 3-D and measured differential boron worth comparison at BOC, HZP conditions.

The cycles compared show good agreement between the 2-D and 3-D models with a mean bias of O.Bi. and a standard deviation of O.57.. The 2-D versus measured also shows good agreement with a mean bias of -0.2% and a standard deviation of 2.3%.

Based on the close agreement at 3-D and 2-D predictions, the +/-5% NUF reported in VEP-NAF-1 remains appropriate for the 2-D model.

TABLE 3-9 PDQ TWO ZONE BORON WORTHS

i. DIFFERENCE ((2D-3D)/3D*l00)

NUMBER OF STANDARD DESCRIPTION POINTS MEAN DEVIATION HAX.

HIN.

2-D vs. 3-D 8

0.8 %

0.5 i.

1.5 0.0 2-D vs. MEAS.

7

-0.2 i.

2.3 i.

2.0

-3.5 3-44

I I

I I*

I 1*

3.7 ESTIMATED CRITICAL POSITION Estimated critical rod positions are calculated prior to restarting the reactor after a period of time at zero power (such as after a trip or maintenance outage).

All reactivity elements of the model are tested in this prediction because boron worth, power defect, partially inserted control rod worth, axial flux redistribution effects, transient fuel isotope and fission product worth (such as Xel35, Pml49, Np239 decay to Pu239, and others) are all involved.

The xenon concentration may be higher or lower than the HFP equilibrium value depending on the power history and decay time. Because the partially inserted control rod worth cannot be calculated with a 2-D model, the FLAM3 code 3 was used to provide rod worth versus insertion curves which were normalized to the 2-D PDQ Two Zone D and C bank insertion worth.

Table 3-10 is the ECP summary table with calculated ECP results compared directly to measured results reported as ECP difference (measured vs predicted critical conditions):

Note that these differences are all relative to a previous measured critical condition (PCC) at which the calculation is initiated (the model is effectively normalized to a previous measured critical condition).

The maximum calculated errors for all 32 ECP' s are +219 pcm (core more re_active than expected) and -251 pcm (core less reactive than expected).

Table 3-11 provides statistics for the cal cu lated ECP differences.

These differences include uncertainty associated with FLAM3 rod worth shapes as well as with the measurement of the PCC and the ECP (primarily boron concentration). The results 3-45

I I

indicate good agreement of the model to the measurements and indicate the accuracy of the model predictions for Xenon worth, boron worth, power defect, and isotopic decay over a wide range of burnups. These are the same 32 cases used for direct criticality comparisons (PDQ 2-D Two Zone versus Measured) which are presented on Table 3-7 of section 3.4.

3-46

I I

1.

I I

I TABLE 3-10 ECP COMPARISON

SUMMARY

TABLE PREVIOUS CONDITIONS STARTUP CONDITIONS ECP DIFFERENCE*

UNIT/

CYCLE BURNUP BORON POWER D-BANK TRIP/ HOURS D-BANK BORON (pcm)

RAMP DOWN N1C7 1324 1230 100. i.

228 Trip 23.80 152 1404

-178 N1C7 2576 1146 100. 7.

228 Trip 42.90 144 1584 17 N1C7 3937 1032 100. 7.

228 Ramp 70.60 92 1579

+201 N1C7 9372 573 100.%

228 Trip 39.30 36 936

+ 42 N1C8 5464 1088 98.%

228 Ramp 365.00 172 1652

+ 33 N1C9 2269 1332 100.%

228 Trip 223.50 173 1936

+ 44 N1C9 3941 1219 99.9%

228 Trip 314.40 169 1803

- 85 N1C9 4693 1151 99.9%

228 Trip 23.00 79 1269

-119 N1C9 10096 664 100.%

228 Ramp 1752.00 172 1251

-251 N2C6 3682 1090 100.%

228 Ramp 49.00 74 1535

+163 N2C8 12621 404 100.%

228 Trip 29.10 69 665

- 59 N2C8 14026 261 100.%

228 Ramp 43.20 96 753

+219 N2C8 17360 1

89.3%

228 Trip 12.60 90 0

-233 N2C9 1014 1361.

100.%

228 Ramp 33.40 128 1722

+ 19 N2C9 3887 1180 100.%

228 Trip 22.60 108 1315

-106 SlClOA 7253 529 100.%

224 Trip 24.90 176 730

- 60 SlClOA 12400 135 100.%

216 Trip 258.60 94 593

+138 SlClOA 13222 58 100.%

217 Trip

31. 75 82 329

+192 SlCll 12425 51 100.%

224 Trip 150. 00 171 544

+ 78 S1C12 78 1340 7 2. i.

166 Trip 7.80 171 1347

-213 S2C9 533 1022 100.%

193. Ramp 8.80 176 1024

-110 S2C10 415 1000 99.8%

205 Ramp 1033.90 191 1545

+206 S2Cl0 6340 595 100.%

223 Trip 96.25 185 1101

+ 32 S2C10 6340 594 100. i.

219 Trip 49.90 166 1026

+ 24 S2C10 9319 368 100.%

221 Trip 29.93 179 662

+ 26 S2C10 11165 219 100. i.

216 Ramp 615. 50 212 735

-150 S2Cll 905 1320 100. 7.

213 Trip 96.80 156 1861

+188 S2Cll 1710 1408 60.%

178 Trip 217.10 186 1834

+ 22 S2Cll 2952 1238 100. i.

223 Trip 111. 00 187 1757

-135 S2Cll 4333 1150 100.%

221 Ramp 156. 50 195 1686

- 45 S2Cll 4333 1686

0. i.

195 Trip 17.40 134 1610

- 37 S2Cll 11000 632 100.%

224 Trip 288.00 100 1134

-182

Difference between actual critical core condition and 2-D predicted core critical conditions.

3-47

I I

I TABLE 3-11 ECP COMPARISON STATISTICS ECP DIFFERENCES EXACT CALC.

North Anna Surry COMBINED Number of data points 15 17 32 Sample Mean X

- 22

- 2

- 11 Sample Std. Deviation s

146 132 137 Average Absolute Mean 118 108 113 3-48

I I

3.8 HOT TO COLD TEMPERATURE DEFECT CALCULATIONS PDQ Two Zone 2-D and 3-D model CZP and HZP calculations were run to determine hot to cold temperature defect consistency between models.

The hot to cold defect is an important component of shutdown margin calculations.

These cases were calculated at beginning, middle and end of cycle for each of the eight cycles. A HZP, ARO 2-D critical boron search was made at each burnup step and this boron was used as the input boron to both the 3-D and 2-D cases.

K-effective comparisons at CZP ARO conditions show that the 2-D model underpredicts reactivity relative to the 3-D model by an average of 200 pcm with a standard deviation of 102 pcm. The CZP ARI 2-D versus 3-D comparison yields a 180 pcm average underprediction by the 2-D model with a standard deviation of 109 pcm.

The 2-D model reactivity bias at HZP is smaller at 97 pcm (underprediction) with a standard deviation of 79 pcm. Table 3-12 presents the 2-D versus 3-D reactivity comparison results.

HZP to CZP temperature defect comparison at ARO conditions show that the 2-D model underpredicts the temperature defect by an average of 103 pcm with a standard deviation of 65 pcm versus the 3-D predictions.

Therefore CZP reactivity is under-estimated using the 2-D Two Zone model (when compared to 3-D Two Zone model) which is nonconservative for shutdown margin calculations. Because of this, the addition of 300 pcm to the calculated HZP to CZP defect is recommended to bound the total nonconservatism in the HZP to CZP defect and CZP ARI rod worth observed 3-49

I I

for the 8 cycles of data analyzed.

Table 3-13 presents these 2-D versus 3-D temperature defect comparison results.

3-50

I I

I 1*

TABLE 3-12 PDQ TWO ZONE K-EFFECTIVE COMPARISON (PCM Difference 2-D Versus 3-D Model Data)

NUMBER OF STANDARD DESCRIPTION POINTS MEAN DEVIATION MAX.

MIN.

HZP ARO CZP ARO CZP ARI Note:

24

-97 79 23

-282 24

-200 102 49

-335 24

-180 109 91

-323 Data includes HZP (BOC, MOC, EOC) and CZP (BOC, MOC, EOG) for N1C8, N1C9, N2C7, N2C8, SlClO, SlCll, S2C10 and S2Cll. All cases run using 2-D HZP ARO critical boron as the input for each case.

TABLE 3-13 PDQ TWO ZONE TEMPERATURE DEFECT COMPARISON (PCM Difference 2-D Versus 3-D Model Data)

NUMBER OF STANDARD DESCRIPTION POINTS MEAN DEVIATION MAX.

MIN.

HZP to CZP 24

-103 65 27

-222 Note:

Data includes HZP (BOC, HOC, EOC) and CZP (BOC, MOC, EOC) for N1C8, N1C9, N2C7, N2C8, SlClO, SlGll, S2C10 and S2Cll. All cases run using 2-D HZP ARO critical boron as the input for each case.

3-51

I I

SECTION 4 -

SUMMARY

AND CONCLUSIONS The Virginia Power PDQ 2-D Two Zone model has been developed for the purpose of performing two dimensional reactor physics calculations.

The 2-D Two Zone model is intended to serve as a design tool for core reload designs, for core follow calculations, and to support reactor operations and safety analysis.

Capabilities demonstrated in this report include critical boron concentrations, integral control rod bank

worths, assemblywise radial power distributions, estimated critical position data (Xenon

worth, boron

worth, total power

defects, isotope decay reactivity), HZP reactivity coefficients, and shutdown margin calculation components (temperature defects and CZP bank worths).

The accuracy of the 2-D Two Zone model has been demonstrated for each of the above production calculations through comparisons with Two Zone 3-D calculations and with measurements taken at Surry Units No. 1 and 2 and North Anna units No. 1 and 2. Comparison to the 3-D model serves to verify consistency between the models and allows for conclusions to be drawn for the 2-D model based on the nuclear uncertainty factors (NUF) determined for the 3-D model. For these comparisons, 2-D NUF estimates have been made and compared to the current Nuclear Reliability Factors (NRF's) given in VEP-NAF-1.

The uncertainty of the 2-D calculations has either been a) shown to be bounded by existing Nuclear Reliability Factors orb) determined such that a model bias can be applied to existing NRF's to ensure conservative use of the model predictions. Table 4-1 summarizes the results of comparisons to 3-D PDQ Two Zone model predictions. Table 4-2 summarizes the results of comparisons to measured data. With only one 4-1

I I

exception, existing NRF's are appropriate for the 2-D model. For shutdown margin calculations, 300 pcm should be added to the existing 50 ppm uncertainty to bound possible non-conservative HZP-CZP temperature defects and control rod worths.

Verification and improvements will continue to be made for this model.

In particular, Virginia Power intends to add pin power reconstruction to the 2-D model using the same techniques described in VEP-NAF-1.

Future enhancements to the buckling model may result in improved CZP reactivity agreement with the 3-D model and HZP-CZP temperature defect capability.

4-2

I I

.r.

TABLE 4-1

SUMMARY

COMPARISONS OF TWO ZONE 2-D PDQ CALCULATIONS TO 3-D TWO ZONE PDQ CALCULATIONS DESCRIPTION MEAN/ STANDARD 3-D CALCULATION OF DATA DEVIATION NUF HFP RPD'S 8 cycles @ BOC

-0.09% / o.37%

1.028

> 0.9 MOC, and EOG ROD WORTH 8 cycles @ HZP 0.3% I 0.8% HZP 1.06 (HZP & CZP)

BOC, and CZP@

-0.3% I 0.7% CZP BOC, MOC, & EOG REACTIVITY 8 cycles @ BOC

-12 I 9 ppm HZP 50 ppm (HZP & HFP)

MOC, and EOG 2 I 7 ppm HFP REACTIVITY 8 cycles @ BOC

-200 /102 pcm ARO 50 ppm (CZP)

MOC, and EOG

-180 /109 pcm ARI w/ARO and ARI TEMPERATURE 8 cycles @ BOC

-103 / 65 pcm N/A DEFECT MOC, and EOG (CZP to HZP)

ITC (HZP) 8 cycles @ BOC 0.9 / 0.16 pcm/°F 3 pcm/°F HZP CONDITIONS BORON WORTH 8 cycles@ BOC o.8% / o.5%

1. 05 (HZP)

HZP CONDITIONS NOTE 2-D NUF ESTIMATE

< 1.04

< 1.10 50 ppm see note 1 see note 1

< 3 pcm/°F

< 1.05

1) 50 ppm for HFP/and HZP calculations. Add 300 pcm bias at CZP conditions.

4-3

I I

CALCULATION REACTIVITY (ECP STARTUPS)

REACTIVITY (BOC STARTUPS)

REACTIVITY (ECP METHOD)

ITC (HZP)

BORON WORTH (HZP)

NOTE TABLE 4-2

SUMMARY

COMPARISONS OF TWO ZONE 2-D PDQ CALCULATIONS TO MEASURED DATA DESCRIPTION MEAN/ STANDARD OF DATA DEVIATION NRF Latest 32 returns -o.6 / 23 pp11 50 ppm to power for 12 cycles. HFP crit-ical boron 8 HZP BOC 5 I 35 ppm 50 ppm startup critical borons Latest 32 returns

-11 / 137 pcm 50 ppm to power for 12 cycles 8 cycles@ BOC 0.3 / 0.6 pcm/°F 3 pcm/°F HZP CONDITIONS 7 cycles @ BOC

-0.27. I 2.37.

1. 05 HZP CONDITIONS 2-D NUF ESTIMATE 50 ppm 50 ppm see note 1 50 ppm

< 3 pcm/°F

< 1.05

1) One value exceeds 50 ppm. This value seems to be an anomaly based on the other 39 HZP points.

4-4

I I

SECTION 5 - REFERENCES

1) R. A. Hall, "PDQ Two Zone Hodel", NAF Topical Report VEP-NAF-1 7 /1990.

2) J. R. Rhodes, "The PDQ07 One Zone Hodel", Topical Report VEP-FRD-20A, Revison O, 7/1981.

3) W. C._ Beck, "The Vepco FLAHE Hodel", Topical Report VEP-FRD-24A, Revision O, 7/1981.

4) R. A. Hall, "The Virginia Power RECON Code Manual", Technical Report NE-788, Revision O, 6/1990.

5) C. B. LaRoe, "Fuel Management Scheme 33A", Technical Report NE-907, Revision O, 9/1992.

5-1

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