ML20128Q275

Revised Nomad Code & Model

ML20128Q275
Person / Time
Site:	Surry, North Anna, 05000000
Issue date:	05/31/1985
From:	Berryman R, Bowman S, Dziadosz D VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
To:
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ML18142A429	List: ML20128Q275
References
VEP-NFE-1-A, NUDOCS 8506040140
Download: ML20128Q275 (100)

Text

. .

L NOkAD Code andModel NuclearEngineering EngineeringandConstruction Department VEP-NFE-1-A May,1985 I

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$8861868R83888380 p PDR ,

VEP-NFE-1-A THE VEPC0 NOMAD CODE AND MODEL BY S. M. BOWMAN NUCLEAR ENGINEERING GROUP ENGINEERING & CONSTRUCTION DEPARTMENT VIRGINIA ELECTRIC.AND POWER COMPANY RICHMOND, VIRGINIA MAY, 1985 Recommended for Approval:

. h ^=' " d M. Dziadofz Supervisor, Nuclear Engineering Approved:

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R. M. Berryman Director, Nuclear Engineering

____.____---_.____j

[ jo,, UNITED STATES i

,(, g NUCLEAR REGULATORY COMMISSION - ,, g g  ; WASHINGTON D.C.20655 6erl8I #

N  % ,,,,, March 4,1985 Rec'd. MAR 7 25 Mr. W. L. Stewart, Vice President Nuclear Operation Nuclear Operations Virginia Electric and Power Company Licensing Supervisor Richmond, Virginia 23261

Subject:

Acceptance for Referencing of Licensing Topical Report VEP-NFE-1, "The Vepco NOMAD Code and Model" We have completed our review of the subject topical report submitted by Virginia Electric and Power Company (VEPCO) letter Serial No. 545.

We find the report to be acceptable for referencing in license applications to the extent specified and under the limitations delineated in the report and the associated NRC evaluation, which is enclosed. The evaluation defines the basis for acceptance of the report.

We do not intend to repeat our review of the matters described in the repor't '

and found acceptable when the report appears as a reference in license applications, except to assure that the material presented is applicable to the. specific plant involved. Our acceptance applies only to the matters described in the report.

In accordance with procedures established in'NUREG-0390, it is requested that VEPCO publi: h accepted versions of this report, proprietary and non-proprietary, within three months of receipt of this letter. The accepted versions shall incorporate this letter and the enclosed evaluation between the title page and the abstract. The accepted versions shall include an -A (designating accepted) following the report identification symbol.

Should our criteria or regulations change such that our conclusions as to the acceptability of the report are invalidated, VEPCO will be expected to revise and resubmit the documentation, or submit justification for the continued effective applicability of the topical report without revision of the documentation.

Sincerely, M} A 0. . ^ ^ ^W Cecil 0. Thomas, Chief Standardization and Soecial Projects Branch Division of Licensing

Enclosure:

As stated l

ENCLOSURE .

SAFETY EVALUATION REPORT g

Report

Title:

The Vepco NOMAD Code and Model R: port Number: VEP-NFE-1 R; port Date: September,'1983 Originating Organization: Virginia Electric and Power Company RIviewed By: Core Performance Group, BNL and Core Performance Branch, NRC ,

INTRODUCTION i

Tha Virginia Electric and Power Company (Vepco) NONAD code and medel are described in references 1 and 2. The NOMAD code is a two-group diffusion theory program with themal-hydraulic feedback, and was developed to perfom -

one-dimensional axial core analyses in support of reactor startup and cycle

• operation of the b co Surry and North Anna reactors. The accuracy of the code and its ability (in conjunction with a number of other codes) to perform core analyses are demonstrated via comparisons with results from other codes, and with measurements taken at the Surry and North Anna Nuclear Powen Stations. The evaluation of the topical report follows.

SI N ARY OF TOPICAL REPORT NOMAD solves the finite difference form of the 2-group, one dimensional (axial) diffusion equation. The active core is partitioned into 32 intervals, while the top and bottom axial reflectors are each represented by three regions. The solution algorithm for the two-group fluxes employs, Gauss elimination for each group equation, with an accelerated power iteration for the coupled equations.

The flux at the center.of each mesh interval is then obtained by an inter-polation scheme based on the finite difference form of the diffusion equation.

l Since the boundary fluxes are known, the flux at the center of the interval is obtained directly. Simpson's rule of integration is then applied over the interval to obtain the average fast and thermal fluxes in the region. These fluxes are used in the calculation of the region power which is the coupling variable for the thermal-hydraulic feedback.

- The moderator temperature is calculated from the moderator enthalpy in the

'. region (which depends on the power, flow rate and inlet enthalpy) and the system pressure via the H0H (reference 3) subroutine. Single phase homo-geneous flow is assumed, with no bulk boiling or void formation.

The macroscopic cross sections for each region are then recalculated based on the moderator and fuel temperatures and a new flux calculation is. performed.

This process continues until the thermal-hydraulic convergence criterion is satisfied. . .

NOMAD accounts for the time dependent behavior of xenon and iodine by solving the analytical fom of the goverping equations. A solution for the equi-librium concentrations of xenon'and iodine is also available. The time-dependent solution of the equations is performed iteratively' for each time interval based on the fluxes from the present and the previous time steps. .

Iterations are performed until the flux, themal-hydraulic and xenon distri-butions converge.

Basic cross section' data for NOMAD are ob'tained frcIin a 1/4-core PDQU7 One Zone (reference 4) model depletion from BOC to EOC for the'particular cycle ~

andunitofintgrest. At various points 'in the dqpletion the relevant flux cnd concentration files are used to perform re-edit calculations (i.e., the fluxes and eigenvalue are not recomputed) to obtain the flux weighted macro-scopic cross sections that result from variations from nominal (reference) conditions in the fuel and moderator temperature, and boron and xenon con-centrations.

~

Reflector cross sections are obtained from the NULIF (reference 5) code, and control rods are represented by core averaged values of the absorption and removal cross sections obtained as the difference between PDQ07 rods-in and rods-out calculations.

The application of the NOMAD model to a desired reactor statepoint involves normalizations to Tesults from more detailed calculations. The Vepco PDQ07 .

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(Discrete (reference 6)andOneZone)andFLAME(reference 7)modelsforthe!

'particular reactor and cycle provide reference data for the NOMAD normalization.

.N Basically, three normalizations are performed: control rod worth, xenon concentration, and axial power distribution. Control rod worths for each bank inserted alone or for the banks inserted in sequence are normalized to -

the corresponding worths from PDQ07 Discrete model calculations via input control rod worth normalization factors. The fission yields for iodine and xenon are modified to force agreement of the NOMAD calculated equilibrium xenon concentration to that obtained from the PDQ07 One Zone model at 150 MWD /MTU.

i N:rmalization of the axial power distribution is achieved via the buckling coefficient search option in NOMAD. Axially dependent, radial buckling coefficients which force agreement between the NOMAD axial offset and core ,

c;idplane power, and corresponding values from the three-dimensional FLAME -

. . code, are obtained for a number of core conditions (80C HZP and HFP, and at cach depletion step from 150 MWD /MTU to EOC.) The resultant buckling coefficients are saved for use in subsequent calculations. The HFP ARO buckling coefficients resulting from the above searches are automatically ,

adjusted by NOMAD to account for the insertion of control rods, and for changes 'in power level.

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The NOMAD code and model are capable of performing a variety of reactor physics

, calculations:

1. The generation of core coverage axial power and burnup distributions.

2. Axial Offset control and load follow saneuver s'imulations.

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3. Peaking. factor analyses. *

4. Final Acceptance Criteria (FAC) analyses.

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. 5. Criticality searches on boron concentration, control rod bank position.

, core power level or hot full power inlet enthalpy.

6. Differential and integral control rod bank worths.

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7. Xenon worth and reactivity coefficients.

SUMMARY

OF REGULATORY EVALUATION The Vepco one-dimensional NOMAD code and model desciibed in references 1 and 2 are intended for use (along with the previously approved Vepco PDQ07 Discrete and One-Zone models, and the Vepco FLAME model) in performing veload core design and reload key' parameter generation. Vepco is currently developing an-axial power shape control methodology and the applications of NOMAD in this area will be the subject of a separate Topical Report which Vepco plans to ,

submit for staff review. -

The present,, review cons'idered the information presented in the topical report and in reference 2 (Attachment-1, Response to Questions and Cosuents on Vepco NOMAD Code and Model, and Attachment-2, Proposed Text Changes to the WOMAD ,

Topical Report). The review also considered the additional, NOMAD infomation-provided by Vepco at a meeting with the staff on April 16, 1984. .

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In general the information presented indicates that the NOMAD mode and model are similar in methodology to.other approaches currently in use for one- ,

dimensional reactor analyses. The NOMAD diffusion theory finite difference representation together with the prescription for determining the region-cIntered fluxes has been reviewed and found to be correct and consistent with standard industry practice. Thexenon/iodinecalcuiationshavealsobeen reviewed and found to provide an accurate technique for tracking the xenon and iodine isotopics, t

The NOMAD thermal-hydraulic feedback model employs an energy balance to determine the moderator axial enthalpy distribution. Axial moderator

.s

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cnthalpies and temperatures generated by the NOMAD thermal-hydraulic feedback

(~eodel are found to be in excell'ent agreement with the results from COBRA The fuel temperature fit (reference 8)foraNorthAnna120%overpowercase. -

is based on the Vepco PDQ07 thermal-hydraulic feedback model which has been previously reviewed and approved by the staff. It is concluded that the NOMAD thermal-hydraulic model is acceptable.'

NOMAD has been normalized to results from more accurate PDQC7 and FLAME calculations. The Yepco PDQ07 and FLAME calculational models have been From the results previously reviewed by the staff and found to be acceptable.

presented in references 1 and 2 it is ccncluded that the adjustments made to NOMAD in the course of the normalization ensurec acceptable agreement with the results from these more accurata calculations.

The ability of NOMAD to perform the required reactor physics calculations is ,

demonstrated by comparisons with measured and PDQ07 and FLAME calculated

- . results. Data are presented for differential boron worths, isothermal temperature coefficients, xenon worths (after .startup, orderly shutdown and

• trip), and differential and integral rod worths. Agreement'with measurement j

and/or higher order calculations is acceptable. ,

A number of axial power distribution comparisons with measured and FLAME -

l calculated data \are presented for both North Anna units and for Surry Unit-1.

Comparisons of flux difference and critical boron ~ data gener:ated by NOMAD in simulations of load reduction and power escalation tests at North Anna Unit-1 are also presented. While the measured data on critical boron for one of the tests is not extensive, the level of agreement between NOMAD and measurement and/or FLAME is reasonable. '

Mnal acceptance criteria analyses were performed for North Anna Units 1 and 2 and the results were compared to results from an accepted and verified vendor model used in the design and licensing of the Surry and North Anna reactors.

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There were minor differences between the Vepco results and the vendor results for both the 3 case and 18 case analyses.

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E At maximum values of the peaking factor (F g) NOMAD results are within 1% of 3 the vendor results and within +1% and -2.5% of the vendor results in the remainder of the core.

REGULATORY POSITION Based on the review of the NOMAD code and methodology, including comparisons to other calculations and to measurements described above, we find NOMAD represents an acceptable methodology for performing.the reactor 3,hysics

. analyses enumerated under the section entitled. " Summary df Topical Report",

above. These analyses are related to reload cores similar to.thos.e of the Surry and North Anna' reactors.

This report may be referenced in licensing submittals by Vepco for the Surry and North Anna reactors. .

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REFERENCES

' 1.

S. M. Bowman, "The VEPCO NOMAD Code and Model," V'EP-NFE-1, Virginia ElectricandPowerCo.(Sept.1983). .

2. Letter from W. L. Stewart (Vepco)~to H. R. Denton (USNRC), "Vepco NOMAD Code and Model Supplemental'Information," (July 6, 1984).

- 3. L. L. Lynn, "A Digital Computer Program for Nuclear Reactor Analysis Design Water Properties." WAPD-TM-680. Westingh6use Electric Corporation (July 1967).

4. J. R. Rodes, "The PDQ07 One Zone Model," VEP-FRD-20A, Virginia Electric andPowerCo.(July 1981).

5. P. D. Breneman, "The NULIFP01 Code " NFE Calculational Note PM-13, Virginia F

ElectricandPower.Co.(March 1979).

6. M. L. Smith, "The PDQ07 Discrete Model," VEP-FRD-19A Virginia Electric andPowerCo.(July 1981). .

7. W. C. Beck. "The Vepco FLAME Model," VEP-FRD-24A, Virginia Electric and PowerCo.(duly 1981).

8. F. W. Silz, "VEPCO Reactor Core Thermal-Hydraulics Analysis Using the COBRA IIIC/MIT Computer Code," VEP-FRD-33, Virginia Electric and Power Co.

(August 1979). .

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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.

i

ABSTRACT The Virginia Electric and Power Company (Vepco) has developed NOMAD, a one-dimensional (axial), two energy group, diffusion theory computer code with thermal-hydraulic feedback, and a calculational model designated as the Vepco NOMAD model.

The model utilizes the Vepco computer codes NOMAD, XSEDT, XSFIT, XSEXP, NULIF, FXYZ, FDEIR, and PCEDT. The model also uses data from the Vepco PDQ07 Discrete, PDQ07 One Zone, and FLAME models. The model is used to perform one-dimensional reactor physics analysis in support of reactor startup and cycle operation of the Vepco Surry and North Anna nuclear reactors. The accuracy of the NOMAD model is demonstrated through comparisons with other codes and with measurements taken at the Surry and North Anna Nuclear Power Stations.

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ACKNOWLEDGMENTS The author would like to thank Mr. T. W. Schleicher for his assistance in performing some of the computer calculations and data preparation required for this report and Mrs. Anna Pegram for typing of the manuscript. The author also wishes to express his appreciation to the people who reviewed and provided comments on this report.

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TABLE OF CONTENTS Page CLASSIFICATION / DISCLAIMER . ............ . ..... . i ABSTRACT . . . . . . . . . .... . .. . .. . . . .. ... . 11 ,

ACKNOWLEDGMENTS . . . . . . .... . ... . . . . ... .. . . iii TABLE OF CONTENTS . . . . . .... . .. . . . .. . . . .. . . iv LIST OF TABLES . . . . . . . ... . .. . .. . . .... .. . v LIST OF4 FIGURES . . . . . . .... . .. .. . .. . . . . .. . vi SECTION 1 - INTRODUCTION . .. .. . ... . . . .. . .. . . . 1-1 SECTION 2 - CODE DESCRIPTION . . . . . . . . . . . . . . . . . . 2-1 2.1 Introduction . ... .... . . . . . . . . .. . 2-1 2.2 Neutron Flux Calculation . . .. . . . . . ... . 2-3 2.3 Thermal-Hydraulic Feedback . . . . . . . . . . . . 2-7 2.4 Xenon Calculation . . ... .. . .. . . .. . . 2-8 2.5 Radial Buckling Coefficient Model . . . . ... . 2-10 1 2.6 Control Rod Model' . . .. . ... . . . . . . . . 2-12 2.7 Criticality Search . . . . . . . .. . .. . .. . 2-12 ,:

2.8 Delta-I Control .. . ... . . .. ... ... . 2-13 2.9 Boration and Dilution Calculations . . . ... . . 2-14 2.10 Final Acceptance Criteria (FAC) Analysis . ... . 2-15 2.11 Differential and Integral Rod Worth Calculations . 2-17 2.12 Xenon Worth Calculation .. . . .. . . . ... . 2-18 3 ,

SECTION 3 - MODEL DESCRIPTION . .. . ... . . ........ . 3-1.

3.1 Introduction . . .. .... . . ... . .. .. . 3-1 3.2 -Cross Section Generation . . ... . . .. .. . . 3-2 3.3 Model Normalization . .. . ... . .. . . . . . 3-4 3.4 1-D/2-D Synthesis . . ... .. . .... . . . . 3-6 3.5 FAC Analysis Model . . . . . . . . . . . . . . . . 3-7 SECTION 4 - USER IN70RMATION' . 4-1

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4~.1 Input Description . .... . . . . . .. ... . 4-1 4.2 . Error & Warning Messages . . . . .. . .... . . 4-9 4.3 Execution Time . . . . .. . . . . . . . . ... . 4-10 4.4 Output . . . .... . ... . .. . . . . . .. . 4-10 1

4.5 I/O Units . . . ... . . . . . . . . . . .. . . 4-13 SECTION 5 - RESUbTS . . . . . . .. . .. . . .. . . .. .. . . 5-1 5.1 Introduction . . .. . .. . . . . .. . . .. . . 5-1 5.2 Reactivity Parameters ... .. . . . .. . .. . 5-1 5.3 Thermal-Hydraulic Feedback . .. . ... . .. . . 5-2 5.4 Axial Power Distribution.. . .. . . . . . ... . 5-2 5.5 Differential and Integral Rod Worths . . .. . . . 5-2 5.6 Load Follow Maneuver Simulation . . .... . . . 5-3 5.7 FAC Analysis . ... . ... . . . . . .. . .. . 5-4 SECTION 6 -

SUMMARY

AND CONCLUSIONS . . . . . . . . . .. . .. . 6-1 SECTION 7 - REFERENCES . . .. . . ... . . .. . .. . . . . . 7-1 l iv i

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LIST OF TABLES Table '-

Title Page 3-1 Macroscopic Cross Section Variable Dependence . . . . . 3-8 s.

5-1 Reactivity Coefficients Comparison . . . . . . . . . . . 5-5 5-2 Comparison of NOMAD and COBRA Moderator Enthalpy

- ' and Temperature Distributions . . . . . . . . . . . . 5-6

'5-3 Rod Swap Comparison, Part 1

. . . . . . . . . . . . . . 5-7 5-4 Rod Swap Comparison, Part 2 . . . . . . . . . . . . . . 5-8 5-5 NIC2 70% Load Reduction Test Power and D-Bank History . . . . . . . . . . . . . . . 5-9 5-6 N1C3 Shutdown / Return to Power Case 1 Power and D-Bank History . . . . . . . . . . . . . . 5-10 5-7 NIC3 Shutdown / Return to Power Case 2 Power and D-Bank History . . . . . . . . . . . . . . . 5-12

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. LIST OF FIGURES

-Figure. .

Title Page 2-1 [ NOMAD Code Flow Diagram . . . . . . . . . . . . . . . . 2-19 2 Axial Mesh Points'and Regions . . . . . . . . . . . . . 2-21 g.. 2-3 Axial Region Center and Boundary Mesh Points . . . . . . 2-22 3-1 Vepco NOMAD Model Flow Diagram . . . . . . . . . . . . . 3-9 5-1 JXenon Worth After Startup, North Anna Unit 1 Cycle 3 . . 5-14 2 Xenon Worth'After Shutdown, North Anna Unit 1 Cycle 3 . 5-15

' 5 -3 Xenon Worth After Trip, North Anna Unit 1 Cycle 3 . . . . 5-16 5-4' Xenon Worth After Startup, Surry Unit 1 Cycle 6 . . . . 5-17 5-5 Xenon Worth After Shutdown, Surry Unit 1 Cycle 6 . . . . 18 Y' 5-6. Xenon Worth After' Trip, Surry Unit 1 Cycle 6 . . . . . . 5-19 7 Axial' Power Comparison, N1C2 HZP BOC . . . . . . . . . . 5-20 5-8 Axial Power Comparison, NIC2 HFP ARO Eq. Xe. BOC . . . . .5-21 5-9' Axial Power Comparison, N1C3 HZP BOC . . . . . . . . . . ' 5-22 5-14 Axial P'ower Comparison, N1C3 HFP ARO Eq. Xe. BOC . . . . 5-23

't 5-1! . Axial Power Comparison, NIC4 HZP BOC . . . . . . . . . . 5-24.

'5-12 Axial Power Comparison, N1C4 HFP ARO Eq. Xe. BOC . . . . 5-25 5 Axial Power Comparison, N2C2 HZP BOC . . . . . . . . . . 5-26 5-14 Axial Power Comparison, N2C2 HFP ARO Eq. Xe. BOC .

. . . 5-27 5-15 Axial Power Comparison, S1C6 HZP BOC . . . . . . . . . 5-28

5-16 Axial Power Comparison, SIC 6 HFP ARO Eq. Xe. BOC . . . . 5-29 15-17 Differential Rod Worth Comparison,

' North Anna Unit 1 Cycle 3 . . . . . . . . . . . . . . 5-30 5-18 -Integral Rod Worth Comparison, North Anna Unit 1 Cycle 3 . . . . . . . . . . . . . . ~ 5-31 E5-19 Differential Rod Worth Comparison,

-North Anna Unit 1 Cycle 4 . . . . . . . . . . . . . . 5-32 5 Integral Rod Worth Comparison, North Anna Unit 1 Cycle 4. . . . . . . . . . . . . . . 5-33

.5-21' Differential Rod Worth Comparison, North Anna Unit 2 Cycle 2 . . . . . . . . . . . . . . 5-34 vi

___-_L_-_- - _ _ - - _- - - - - - - . - - - -- - - - - - - -

5-22 Integral Rod Worth Comparison, North Anna Unit 2 Cycle 2 . . . . . . . . . . . . . . 5-35

'5-23 -Differential Rod Worth Comparison, Surry Unit 1 Cycle 6 . . . . . . . . . . . . . . . . . 5-36 5-24 Integral Rod Worth Comparison, Surry Unit 1 Cycle 6 . . . . . . . . . . . . . . . . . 5-37 5-25 Differential Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 1 Cycle 3 . . . . . . 5-38 5-26 Integral Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 1 Cycle 3 . . . . . . 5-39 5-27~ Differential Worth of Control Banks A thru D In Overlap Mode, North Anna Unit 1 Cycle 4 . . . . . . 5-40 5-28 Integral Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 1 Cycle 4 . . . . . . 5-41 5-29 Differential Worth of Control Banks A thru D In Overlap Mode, North Anna Unit 2 Cycle 2 . . . . . . 5-42

'5-30 . Integral Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 2 Cycle 2 .

. . . . . 5-43 5-31 Differential Worth of Control Banks A thru D in Overlap Mode, Surry Unit 1 Cycle 7 . . . . . . . . 5-44 5-32 Integral Worth of Control Banks A thru D in Overlap Mode, Surry Unit 1 Cycle 7 '

. . . . . . . . 5-45 5-33 N1C2 70% Load Reduction Test, Axial Flux Difference . . . . . . . . . . . . . . . . 5-46 5-34 NIC2 70% Load Reduction Test, Critical Baron Concentration . . . . . . . . . . . . . 5-47 5-35 N1C3 Shutdown / Return to Power Case 1, Axial Flux Difference . . . . . . . . . . . . . . . . 5-48 5-36 NIC3 Shutdown / Return to Power Case 1, Critical Boron Concentration . . . . . . . . . . . . . 5-49 5-37 N1C3 Shutdown / Return to Power Case 2, i Axial Offset . . . . . . . . . . . . . . . . . . . . . 5-50

.5-38 N1C3 Shutdown / Return to Power Case 2, Critical Boron Concentration . . . . . . . . . . . . . 5-51 5-39 -Fg(Z) Results, North Anna Unit 1 Cycle 4 . . . . . . . . 5-52 5-40 Fq(Z) Results, North Anna Unit 1 Cycle 4 . . . . . . . . 5 5-41 Fg(Z) Results, North Anna Unit 2 Cycle 2 . . . . . . . . 5-54 5-42 Fq(Z) Results, North Anna Unit 2 Cycle 2 . . . . . . . . 5-55 vil

d SECTION 1 - INTRODUCTION

-The purposes - of this report are to describe a reactor analysis computer code and model which were developed at Virginia Electric & Power Company '(Vepco) and to demonstrate the accuracy of this model by comparing analytical results generated by. the model to results from other codes and to; actual measurements from Surry= Units No. 1 and 2 and North Anna Units No. 1 and 2.

The' code to be-described .is a one-dimensional (axial), two energy group, diffusion theory (with thermal-hydraulic feedback) computer code

, and is named the NOMAD code. The model to be described is designated as i

the-Vepco NOMAD model. In addition to NOMAD, the model uses the Vepco

. -. - computer codes XSEDT 1

, XSFIT1 , XSEXP1 , FXYZ8 , FDELH8 , PCEDT8 , and NULIF".

i The model also utilizes data from tha Vepco PDQ07 Discrete C, PDQ07 One

' Zone' and FLAME 7 models. A detailed description of the input requirements, functioning, physical models, and output-capabilities'of

, , these codes can be obtained from the referenced code manuals or reports.

1 The types - of reactor physics calculations which can be performed

" within the general capabilities of the Vepco NOMAD model include:

p 1. Core average axial power and burnup distributions

[ 2. Axial offset

3. Peaking factors (Fq (Z), FXY(Z), F3 (Z))

I; 4 .' Final Acceptance Criteria (FAC) Analysis

5. Load follow-maneuver simulation

6. Criticality searches on boron concentration, control rod bank position, core power level, or hot full power (HFP) inlet enthalpy

7. Differential control rod bank worths

8. Integral. control rod bank worths as a function of rod bank position.

1-1

= .

_ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ = _ _ _ _ .

F '

The remainder of this report describes the Vepco NOMAD code, the purposes and interrelationships of the other ~ computer codes which comprise the Vepco NOMAD model, the specific modeling of a reactor core with these codes, and the comparisons of calculated results with appropriate results obtained with the- Vepco PDQ07 Discrete. and One Zone

'models, the Vepco FLAME model, and with core measurements obtained from the Surry and North Anna Nuclear Power Stations.

0 1-2

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SECTION 2 - CODE DESCRIPTION 2.1 Introduction The Vepco NOMAD (Nuclear Operations Model for Analysis in One Dimension) code provides a relatively simple and inexpensive method for calculating. axial power distributions and core reactivity. The calculation contains three levels of iteration: a source or flux calculation is performed during the inner iterations, thermal-hydraulic feedback in the second iteration level, and the xenon concentration in the outer iterations. The two outer levels of iteration are optional.

The neutron flux is calculated by solving the finite difference form of the two group diffusion equations using Gauss elimination. A Chebyshev polynomial scheme is used to accelerate convergence.

The thermal-hydraulic feedback model accounts for the effect of the nonuniform fuel and moderator temperature distributions on the flux distribution. Single phase flow with no bulk boiling is assumed.

Successive relaxation is used to accelerate convergence.

The NOMAD code provides two methods for calculating the axial xenon distribution. The equilibrium xenon calculation is based on the present flux distribution. The xenon depletion calculation is based on the flux distributions from the present and the previous timesteps using an iterative technique. The first method is applicable to fuel cycle design

- calculations, whereas the second is used for had follow maneuvers or xenon transients. Using the xenon distribution obtained, flux and thermal-hydraulic calculations are performed again. This process continues until the flux, thermal-hydraulic, and xenon convergence i

I criteria are satisfied.

The NOMAD code also contains the following capabilities:

1. Radial buckling calculation and normalization 2-1 b1- -- - --

- _ _ _____m_ -_.. _

2. ~ Criticality search on a selected variable

- 3. . Delta-I control

4. .Boration and dilution calculations

5. Final Acceptance Criteria (FAC) Analysis -

6. Differential and integral rod worth calculations -

7. Xenon worth calculation.

Figure 2-1 is a simplified flow diagram of the calculations performed by NOMAD.

The remainder of this section ' describes in greater detail the models used in the flux, thermal-hydraulic, and xenon calculations, and the methods employed in the seven calculations listed above.

2-2

- -,,e -, , - , - - , , - , - - - . . . - - , - v>= -,w,,0n-,-.,,-.,,---v--, .-,----m,g-,,-w_-- .~v.-- e,r-- - m.,n,~m e--. _ - - - - , -.----re

2.2. Neutron Flux Calculation NOMAD ' calculates the neutron flux by solving the following finite difference diffusion equations:

-d Dg (z)Idig(z) + I g(z)(f(z) = x gMz) + I,,g,7(z)(1-1(z), (2.2-1)-

dz .dz 1 i=1,2

-where i = the neutron energy group, Dg (z) = diffusion coefficient for group i at position z, d = neutron flux, 8

I g(z) = Dg (z)B (z) + I,,g(z) + Ip,g(z) = the total cross section, B* = tadial. buckling, I,= absorption cross section, e

I,= removal cross section, I = poison cross section, p

x1= fraction of fission neutrons born in group i (x =1,1 x =0),

2 2

G(z) = I VI f (z)(j(z) = the fission source, j=1 If = fission cross section, v = number of neutrons per fission, and 1 = eigenvalue = K,gg,

. Equation 2.2-1 is, of course, simply a set' of neutron balance equations, where neutron losses on the left-hand side must be balanced by neutron gains on the right-hand side. The first term on the left-hand side describes the leakage from a unit volume by neutron migration in the z-direction,- ' and . the second term represents all other losses. These include absorption (I, and Ip), leakage in the radial directions (DB8 ),

2-3

e 4

and . scattering out of the energy group (Ir,1). The sources on the

~

right-hand side are fission (x gG(z)/1), and scattering into the group from

'the~ next-higher energy group (I,,g.1).

.The'z-axis in the region of solution, 0 1 z 1 Z, is subdivided into axial regions 'by mesh points. at which the solution is to be determined.

e At some interior point z ,, integrate from z ,, = z, - h ,,/2 to z,4 = z, +

h,,/2,- where h,,' and h,4 are the heights of the axial regions below and above point z,, respectively. - (See Figure 2-2.)

The. approximations deg (z) (f(z,)-(g(z,,1) deg (z) (f(z,,1)-(g(z,)

, (2.2-2) dz z,, h,, dz z,, hy ,.

• n+ *

• +

n

[ I (z)(g(z)dz g = Ig(z,,)[n-(f(z)dz+I(z,,)f(f(z)h f

n- *n- n

_n n

=[I g(z ,,) hn ./2=+ If (z,4) h,,/2] (f(z,) = I g(1, (2.2-3) and

_ ni Di (z,g) ' = D 1 (2.2-4)

-hg are used to obtain the difference equation

_n+. n+1 _n+ n- n n _n- n-1

-D g (g +' (D g +D g +I)(1 g Dg -(g 2 _._n n _n n

" xg /l' I VIf,j (j + I ,1-1 r 1'1.

1. - (2.2-5) j=1 From the form of the equations it can be seen that the macroscopic 2-4

~ . . . - - . . . . - + - - , - - -

' cross-sections are required to be constant in each half-interval. In

.1' fact, the code assumes these parameters are constant in each axial region.

~

The code also assumes that the three' top and bottom axial regions are r'eflector regions and the flux at the outer boundaries of these regions is zero. .The,' system of equations given by Equation 2.2-5 and the zero flux boundary conditions, may be expressed in matrix form as M ( = 1/1.F $ + R( (2.2-6) a where M is a tridiagonal matrix.

NOMAD solves this system of equations by the method of power

' iterations using Gaussian elimination. The rate of convergence is accelerated by replacing the pth iterate of ( (i.e. , ,P) . with a linear combination of 9P and the previous iterate, ,P-1 ,

~P P P P-1 P

.(-=(- (1 + 0') - $ 0, (2.2-7) where GP is an acceleration parameter computed on the basis of Chebyshev polynomials.

The eigenvalue for iteration n is calculated as N 2 n I I vIgg(zk) 'j *k) f n n-1 k=1 j=1 1=1 , (2.2-8)

N 2 n-1 I I vI f (zk ) 'j (*k). .

k=1 j=1 where N is the. total number of, mesh points.

-The converged solution to Equation 2.2-6 gives the fast and thermal fluxes at the mesh points between each axial region. Next, NOMAD calculates the fluxes at the center of each region.- For a region of height 2s, label the top and bottom mesh points as t and b, respectively, and the region center as c. (See Figure 2-3.)

l-2-5 i

h, Using.the approximations d(g(z) (f(c)-d (b) g . d(g(z) (f(t)-(f(c)

= ,

= , (2.2-9) dz b- .m dz t n

[- and t

I i(*)'i(z)dz = I (c)(g(c)*2m, g (2.2-10) and integrating Equation 2.2-1 yields 2(g(c)-(g(t)-(f(b)

Dg (c) + I (c)(g(c) g .

8 2m

!~ 2

" *10 I VIf,j(c)()(c) + Ir,1-1(c)(g,1(c). (2.2-11) 3"1 Since the fluxes at each region boundary, (g(b) and (f(t), are known, .,

NOMAD solves for the region center flux (f(c) directly. The code then integrates (f(b), (g(c), and (g(t) using Simpson's method to obtain the

average fast and themal fluxes in the region.

Finally, the relative power is calculated for each region Z KI gg(Z)i(Z).+ t KIf2(3)'2(3)

P(Z) = *R (2.2-12)

R _ _.

I KIgy(Z)(1(Z) + KIf2(Z)'2(Z)

Z=1 where P(Z) = relative power in axial region Z K = energy per fission (watt-sec) i(Z)=averagegroupifluxinregionZ f

R = total number of axial regions with fuel.

2-6

'2.3 ' Thermal-Hydraulic Feedback The thermal-hydraulic feedback model uses an energy balance to

, icalculate the moderator enthalpy as a function of axial position Enthalpy out = Enthalpy in + Power / Flow Rats,

. x where l Enthalpy out = moderator enthalpy exiting the region (BTU /lbe) l Enthalpy in = moderator enthalpy entering the region (BTU /lbm)

Power = power produced in the region (BTU /hr)

Flow Rata = core moderator flow rate (1bm/hr).

i Single phase, homogeneous flow is assumed with no bulk boiling or void formation. The moderator enthalpy and system pressure are input to the H0H subroutine', which calculates the corresponding moderator temperature.

The thermal-hydraulic feedback model calculates the fuel temperature rise above the moderator temperature as a function of relative power and burnup Fuel temp (Z) = Hod.' temp (Z) + (DGEFPD

• Burnup(Z) + FTFO)

• RPD(Z)

• PR, where Fuel temp (Z) = fuel temperature in axial region Z Mod, temp (Z) = moderator temperature in region Z DGEFPD = fuel temperature vs. burnup coefficient

(*R/EFPD

• Relative Power)

Burnup(Z) = burnup of region Z (EFPD)

FTF0 = fuel temperature vs. relative power coefficient

(*R/ Relative power) l 2-7

?

+

w.

m RPD(Z) u .= relative power. density in region Z PR = core relative power (fraction of full power).

s This fuel temperature fit is based on the one used in the Vepco PDQ07 thermal-hydraulic feedback mode 18 .

-NOMAD then recalculates the macroscopic cross sections based on the

[ u.w fuel and moderatur temperatures, perform = another flux calculation, f .and performs another thermal-hydraulic calculation. This process i

continues until the thermal-hydraulic convergence criteria is satisfied.

2.4 Xenon Calculation l NOMAD calculates the iodine and xenon concentrations for each axial l region using an analytic solution to the iodine and xenon rate equations.

This solution is simply an integration of the iodine and xenon rate equations which assumes that the flux and the cross-sections rsmain constant over the time interval for which the calculation is performed.

Prior to calculating the lodine and xenon concentrations, NOMAD normalizes the fant and thermal fluxes (in neutrons /cm8 -sec) to the core

!' power level l-i j N POWDEN

• PR

• RPD(Z) l 92(Z) = (2.4-1)

l. KI gg(Z)*dg (Z)/92 (3) + "If2(Z)

N N (g(Z) = (2(3) * '1(Z)/'2(Z) (2.4-2) where N

(g(Z) = normalized flux for group i in region Z (nou.trcns/cm8 -sec)

POWDEN n power density (watts /cc)

PR = core relative power (fraction of full power)

RPD(Z) = relative power density in region Z (g(Z) = region average relative flux for group i in region Z.

2-8

=

3 NOMAD then uses these normalized fluxes to calculate the lodine and 4

xenon concentrations I(Z)f,1 = [I(Z)g - TygI e/kg ) e-AI(ti+1-tg) + T I g(/1 (2.4-3) .

(Ty +TXe) fI ' IIIE)i-Tgg Ip Xe(Z)g,1 = Xe(Z)g - + e -LX(ti +1-tg)

LX ly -M z

l yI(Z)g-Tyg I4 (Ty +TXe)If ' 3

~

I(tg ,g-tg ) +

e (2.4-4)

A-M g M  ;

where I(Z)f,g = iodine concentration in region Z at step i+1 Tg = iodine fission yield -

ly = lodine decay constant .

t g4g = time (seconds) at step 1+1 e

N N '

I gd = KIf1(3)#1(Z) + "Z f2(Z)# 2(Z) / KAVG XAVG = average energy per fission Xe(Z)1+1 = xen n concentration in region Z at step i+1  :

TXe = xen a fissi n yield Xe Xe -

LX = lx , + cal #1 (E) + #a2 #2 (I)

]

XXe = xen n decay constant -

Xe o,) = xenon absorption cross section, group j.

To calculate the equilibrium iodine and xenon concentrations, the l

exponential terms in Equations 2.4-3 and 2,4-4 are set to zero.

2-9 _

.[.

Each xenon depletion is actually performed in two substeps. During the first substep, the xenon is depleted for 55% of the depletion time -

using the flux from the previous timestep. The second substep, which depletes the remaining 45% of the depletion time, is performed iteratively with the. flux calculation at the present timestep. Thus, the xenon is depleted with the flux from the previous timestep for 55% of the depletion and with the flux from the present timestep for 45% of the depletion.

After NOMAD calculates the iodine and xenon concentrations, the macroscopic cross-sections are adjusted and- the flux and thermal-hydraulic calculations are performed again. The lodine and xenon concentrations 'are calculated with the new fluxes. This process continues until the xenon distribution converges.

2.5 Radial Buckling Coefficient Model The radial buckling model accounts for radial leakage and compensates for the radial dimensions which are neglected in- a one-dimensional axial model. The buckling coefficients, which are used to calculate the radial buckling as a function of core height, are adjusted to obtain agreement with a three-dimensional code for axial offset and relative power at the core midplane. The equations for the radial buckling function expressed in terms of buckling coefficients are:

BUK1(Z) = B0 * (1 + BTILT * (Z - ZO) / HT)

• CZ(Z) (2.5-1)

BUK2(Z) = BTH

• BUK1(Z) (2.5-2)

CZ(Z) = cos(BMID

• PI * (Z - ZO) / HT) if BMID > 0.05

= 1./(cos(BMID

• PI * (Z - 20) / HT)) if BMID < -0.05

= 1.0 otherwise, (2.5-3) where BUK1(Z) = Fast group buckling 2-10

BUK2(Z) = Thermal group buckling B0 = Buckling amplitude coefficient BMID = Buckling curvature coefficient BTILT = Buckling tilt coefficient BTH = Thermal-to-fast group buckling ratio HT = Active core height Z = Axial position Z0 = HT / 2 PI = 3.1415927.

For a positive BMID, the function is a convex curve. For a negative _

BMID, the function is a concave curve. When BMID is near zero, the function is a straight line. BTILT adjusts the slope of the curve. If it

, is positive, the buckling is greater in the top half of the core. If it is negative, the buckling is greater in the bottom half of the core. B0 and BTH must always be positive so that the buckling-function is positive.

NOMAD has an _ automated buckling coefficient search option. The search iterates on BTILT, BMID and BO,.respectively, until the axial offset, midplane power, and eigenvalue converge on the target values (eigenvalue target is 1.0) or until a maximum number of iterations have been performed and a warning- is printed. When a buckling coefficient search is completed, the coefficients are written to a dataset with the core aversge burnup (in EFPH). This buckling coefficient dataset may be read and used in subsequent calculations by NOMAD. If the core average burnup lies between two burnups in the buckling coefficient table, linear interpolation is performed to determine the coefficients for that step.

NOMAD automatically adjusts the buckling coefficients at power levels below 100% power to compensate for changes in the radial buckling as a function of core power. Since the dependence of the cross sections 2-11

on moderator temperature are derived from a two-dimensional model, this adjustment is necessary to obtain consistent agreement between NOMAD and a three-dimensional ' model, where the moderator temperature varies in the axial direction.

2.6 Control Rod Model NOMAD accounts for the control rod cross sections in the top reflector and any rodded fuel regions. NOMAD adds the control rod macroscopic cross sections to the region macroscopic cross sections. If a particular control rod bank is located at step 225 (top of fuel) or less, then the top reflector is completely rodded with respect to that bank. If the bank is positioned at a higher step, the top reflector is partially rodded, and the rod cross sections are volume-weighted by the fraction of

. the reflector region which is rodded.

The code inserts each control rod bank by step (228 steps =

completely withdrawn, O steps = completely inserted). The distance per rod step is 0.625 inches in NOMAD. The fuel region which is partially rodded (where the tip of the control rod bank is located) is handled in the same manner as the partially rodded reflector region, by volume-weighting the rod cross sections.

The NOMAD control rod model includes the modeling of four control banks, two shutdown banks, and one part length bank, and the capability to-move all four control banks in overlap.

2.7 Criticality Search The criticality search option in NOMAD searches for the value of a selected variable (e.g., boron concentration, control rod bank position, core power level, HFP inlet enthalpy) which will give the desired target eigenvalue. The search takes the errors from the two previous guesses and 2 l

uses linear interpolation or extrapolation to guess what value of the selected variable - will give an error of zero. NOMAD performs another eigenvalue calculation with the new value of the selected variable. The search continues until the eigenvalue converges on the target value.

Since a control rod bank can only- be inserted in discrete steps, the -

criticality convergence criterion may not be satisfied when a control rod search is performed. In this case, the code optionally performs a critical boron search after the control rod bank position is adjusted as near to critical as possible.

2.8 Delta-I Control In order to simulate a load follow or other maneuver where the reactor is required to operate within a certain delta-I band, a delta-I control option is available that automatically adjusts the control rods to keep the delta-I within its operating b.md- Delta-I is defined as:

Power (top) - Power (bottom)

Delta-I(%) =

• PR

• 100, (2.8-1)

Power (top) + Power (bottom) where Power (top) = relative power in top half of core Power (bottom) = relative power in. bottom half of core PR = core relative power level.

When delta-I is outside the operating band, NOMAD moves D-bank from the bite position (216 steps) to the rod insertion limit by increments of 20 steps. Each of these points is used to determine the delta-I as a function of D-bank position by a cubic least squares fit. The cubic equation is then solved to find the D-bank position which will adjust delta-I to the designated value. If the desired delta-I cannot be 2-13

y

/

s l

achieved, then delta-I 'is adjusted to the nearest possible value. The user' may request l that the code _ adjust delta-I to (1) the target delta-I L(the center of - the operating band) or . (2) the nearest edge of the operating band. Adjusting delta-I to the edge of the band requires less

- boration or dilution to accomplish. The eigenvalue calculation is then performed at the adjusted D-Bank _ position. NOMAD automatically performs

.a critical boron search after the rods are moved to re-establish criticality.

2.9 Boration and Dilution Calculations Boration and dilution calculations are important when studying a possible load follow maneuver to insure that the water processing system

,can handle the rapid changes in boron concentration. NOMAD performs boration and dilution calculations for every step following the first criticality search if the boration/ dilution parameters are input. NOMAD solves the following equations":

1 + (BOR(J) - BOR(J-1)

WATER (J)-= -SYSMAS / H20 DEN

• In (2.9-1)

(BOR(J-1) - Cin)

TIMEMN = WATER (J)./ LDRATE, (2.9-2) where WATER (J) = water processed (gallons) at step J SYSMAS = total primary coolant system mass (1bs)

H20 DEN = water density in letdown line (8.2 lbe/ gal)

.BOR(J) = boron concentration at step J

-BOR(J-1) = boron concentration at step J-1 Cin = boron concentration in letdown line TIMEMN = minimum time required to perform boration/ dilution LDRATE = letdown rate.

2-14

I WATER (J) is multiplied by -1 in a dilution case in order to distinguish between boration and dilution cases.

If TIMEMN is greater than the time between steps J-1 and J, NOMAD calculates the maximum achievable change in the boron concentration and prints a warning message to indicate that the minimum time required for

' the boration or dilution is greater than the time allowed. If instructed, the code then performs another criticality search on control rod bank position, core power level, or inlet enthalpy at the maximum (or minimum) boron concentration achievable in the boration (or dilution).

2.10 Final Acceptance Criteria (FAC) Analysis NOMAD is capable of performing Final Acceptance Criteria (FAC) analysis. One part of this capability is the average power distribution calculation for a load follow depletion. The code integrates the axial flux distributions over the timesteps specified to obtain the average flux distribution:

T I (gj(Z) t)

_ . - j=1

( (Z) = , i=1,2 (2.10-1) i T I

j=1 t) where (g)(Z) = group i flux in region Z for timestep j (neutrons /cm8-sec) t) = length of timestep j T = total number of timesteps specified.

This flux distribution is substituted into Equation 2.2-12 to obtain the average power distribution and Equations 2.4-3 and 2.4-4 to obtain the average iodine and xenon distributions. The load follow depletion is then performed using these power and xenon distributions.

2-15

F To perform a FAC analysis, NOMAD combines the axial power distributions that it _ calculates in the load follow calculations with the FXY(Z) data input to the code to determine F g(Z), F C2)cale., XY FXYCI)allwable, and F (Z) q calc. NOMAD performs the following sequence at each step in the FAC analysis case. First, it determines the rodded configuration (i.e., ARO, D in, D+C in) for each axial region. Then the code selects the FXY(Z) that corresponds to the axial level and the rodded .

. configuration of each region. NOMAD checks each Fg(Z) to insure that it is not less than the minimum FXY(Z) allowed for that rod configuration as specified in the user input. If the reactor is not at full power, NOMAD adjusts the FXY(Z) as follows:

FXYREL = FXY(Z) * (1 + ADJUST * (1 - PR)), (2.10-2) where FXYREL = FXY(Z) adjusted for the core relative power level FXY(Z) = FXY at axial region Z for 100% power ADJUST = FXY power adjustment factor (e.g. , 0.3 for North Anna and Surry) i PR = core relative power level.

(

Next, NOMAD calculates the F (Z) for this case:

q FQTEST = FXYREL

• RPD(Z)

• PR

• FQGRID, (2.10-3) where FQTEST =q F (Z)

• PR for this step RPD(Z) = relative axial power in region Z FQGRID = correction factor for grids a uncertainty factor

= 1.025

• UF UF = 1.03 (3 case FAC analysis)

UF = 1.00 (18 case FAC analysis).

2-16

T; I-

'If FQTEST is greater than the-previous F q (Z), then the following values are saved:

Fq(Z) calc. = FQTEST .(2.10-4)

FXYkZ) calc. " b (2.10-5)

FXYII)allwable = F (Z)q limit / (F (Z)* g PR

• FQGRID) (2.10-6)

Fg(Z) = RPD(Z) (2.10-7)

Once the entire load follow simulation has been completed and the

j. final values for F (Z),

g FXY( ) calc. , FXY(3)allwable, and F (Z) q calc. have

-been obtained, NOMAD checks for any limit violations for XY F II) calc.'

(

FXY C3) allowable, and F (Z) q calc. and flags them in the FAC ANALYSIS RESULTS output.

2.11 Differential and Integral Rod Worth Calculations l

j Differential and integral rod worth calculations are available in l NOMAD. ~The control rod banks may be inserted or withdrawn in any order l

l chosen by the user (e.g., single bank, multiple banks in overlap, multiple banks together, etc.). The differential worth is calculated as follows:

DIFF(I) = (1/RKEF3 - 1/RKEF1)

• 1E+5 / ISTEPS, (2.11-1) where DIFF(I) = differential rod worth for case I (pcm/ step)

RKEF3 = Keff for case I+1 RKEF1 = Xeff for case I-1 i-l ISTEPS = number of steps rods moved from case I-1 to I+1.

The differential worth is not calculated for the first or last case of the rod worth sequence.

NOMAD calculates the integral worth as follows:

2-17

s RINT(I) = (1/RKEF2.- 1/RKEF)

• 1E+5, (2.11-2) where RINT(I) = integral rod worth for case I (pcm)

RKEF2 = Keff for case I RKEF = Keff for 1st case of rod worth.segaence. ,

The integral worth is calculated for every step of the rod worth '

sequence.

2.12 Xenon Worth Calculation NOMAD can automatically calculate the xenon worth at any selected timestep(s). When the xenon worth option is on, NOMAD saves the calculated xenon distribution in a separate array, resets the xenon distribution to zero and performs another eigenvalue calculation. It calculates the xenon worth from the two eigenvalues:

Keff (no xenon) - Keff (w/ xenon)

Xenon worth =

• 1E+5. (2.12-1)

Keff (no xenon)** Keff (w/ xenon)

The program then restores the saved xenon distribution. Thus, the xenon worth at any timestep of a problem can ba determined without interrupting the flow of the other calculations being performed.

s s

2-18 L..

" Eir f 2go9k , V 1

$2 t

x E

n .o a kc u a l

a M u

l c -

a C

n o

n e

X l o N

l

?

d s e e g Y n e r

o v n

a

o. o i o C c N i.C -

n i

N o

Y s

e ye s n: W T

i' s

l n

o l l s

s

_3Y Y e

n y

. e t o n Y .r l

a ca o '

hc o D lt i

u t ,

c l u

a arhl c o e

yN l l a c u r t

C l c a o o S .re.t n u a l N b

= 1 p n n o

} C Lf C a l c

u l_ l c-u N t S a yI Co --

G4 I

n W r l

a l t -

X e T a C C ax li a e f at l

a l

a l

e feicI u

n t

u b ot i Cr J

a I

r C l

l Y D 1,. !.l  :  ;

r Calrulste 0 *#"

yy Borction/ No Criticality y,, p ,7 Boration/  : Dalution  ; 69 5t" Copacitu  ; Search on 2nd  ;

gg slut Calculatson Surfactont variable?

No YM No f

Yes Perform Nuolear-(800 tio / Calculation with No Xenon No .

n' FAC Option?f N v.s r Calculot. F,y (Z), FqiZ), F1(Z) w '

=

, cn b

rn Depletion? Y'*

PdmFMMxm %km m

?

g No -

RO r'

5 Yes Another $

c Case? g v

1f Print Seamary Output b Yes

• Worth  : Differential / Integral Rod Worth Calculation Opt No -

7

,-N ..

FAC Analgs s Summerg Opt No ,

STOP J

\

\

\

. FIGURE 2-2 Axial Mesh Points and Regions h

zn+1 e

• + n h+ n h+ n 2

' t n r n J L i

h

.n-2 e v h,_

Z n-lf O

z n-1 N .-

2-21

FIGURE 2-3 Axial Region Center and Boundary Mesh Points t

m I P g

C M

If O

b l

2-22 I

SECTION 3 - MODEL DESCRIPTION 3.1 Introduction The Vepco NOMAD model is use-1 to calculate axial power distributions and core reactivity for one-dimensional geometries in which the core is represented by 32 axial fuel regions and three top and three bottom reflector regions. The method used by the Vepco NOMAD model to perform these calculations is'a finite difference solution of the two energy group diffusion theory equations. Moderator and fuel temperature effects are accounted for by thermal-hydraulic feedback.

The Vepco NOMAD model incorporates several calculational steps.

First, a quarter core PDQ07 One Zone' depletion is performed and the flux and concentration files at each burnup step are saved for the particular unit and cycle being studied. Then PDQ performs flux-weighted macroscopic cross section calculations for a series of change cases at each burnup step from 150 MWD /MTU to EOC. The core average macrocopic cross sections from these calculations are then processed for inp2t into the NOMAD computer code. These cross-sections, as well as the cycle normalization data (i.e., BOC - core average axial burnup distribution, equilibrium iodine and xenon concentratior.s, integral control rod bank worths, and axial offset and core midplane power at each depletion step),

are then used by NOMAD to perform an iterative, two-group finite difference diffusion theory calculation for the neutron flux as a function of core height. The method of solution comprises three levels of iteration: neutron flux, thernal-hydraulic feedback, and xenon concentration. The neutron flux calculation is performed first based on initial guesses of fuel and moderator temperatures and xenon concentrations. Then a new set of fuel and moderator temperatures are calculated. Using these new temperatures, 'another flux calculation is performed. Once the flux and temperatures have both converged, a new set 3-1

3 of xenon.- concentrations is calculated. Using the 'new xenon concentrations, the flux and thermal-hydraulic feedback calculations are performed again.

This process continues until the convergence criteria for all three levels are satisfied.

, Several interrelated computer codes are used to perform the

calculations outlined above. The computer codes comprising the Vepco NOMAD model and their interrelationships are presented in the flow diagram in Figure 3-1. The NOMAD computer code is the principal analytical tool in'the Vepco NOMAD model. The other codes provide either input data or data manipulation. The PDQ07 One Zone model and the XSEDT1 code are used to ~ generate , core average macroscopic cross sections at different core conditions. The XSFIT1 and XSEXP 1 codes process these data for use by i

NOMAD. NULIF" 'is used to calculate the top and bottom reflector macroscopic cross sections. These generally remain the same from cycle to cycle. The Vepco PDQ07 One Zone, PDQ07 Discrete', . and FLAME' models supply cycle normalization data. The FXYZ" code provides Fg(Z) input to NOMAD _ for FAC analysis. FDELH8 and PCEDT 8perform 1-D/2-D synthesis of' NOMAD and PDQ07 Discrete or One Zone results.

The remainder of this section describes in greater detail the input to and functioning of the computer codes used in the Vepco NOMAD model.

.3.2 Cross Section Generation L

, ' The Vepco NOMAD code requires the following two group macroscopic cross sections for the solution of the axial flux and power distributions:

Dy ,- 1,1, I,y , vIgy, KIgy, D2 ' Ia2' " f2, and KIf2*

These cross sections actually consist of base macroscopic cross sections and polynomial coefficients that adjust the base cross. sections

for changes in the fuel and moderator temperatures and the boron and xenon concentrations. The cross sections are generated from the.PDQ07 One Zone 3-2 s , - - . . . -,,.---w.,----. ,..,,,-,-,.,,-%w. ,-~u..-,%,,.,#-,fn 3, _ - _fr_. ,, ..-m, .,,----,,% ,,,,-,--,-.p.y e-

model for that unit and cycle.

The PDQ07 One Zone model is depleted to EOC and the flux and

. concentration files are saved at each burnup step. A series of restart calculations are performed at each burnup step from 150 MWD /MTU to EOC.

(The BOC step is not included because there is no xenon present.) Using the input flux and concentration files, PDQ only performs the flux-weighted macroscopic cross section calculations (i.e., no flux or eigenvalue- calculation). The cases contain variations in the fuel and moderator temperatures and the bo'ron and xenon concentrations which should include all core conditions encountered during reactor operation.

The range covered for each variable is:

Fuel Temperature 331 to 2052 degrees Fahrenheit (N. Anna) 487 to 2326 degrees Fahrenheit (Surry)

Moderator Temperature- 543 to 613 degrees Fahrenheit (N. Anna) 526 to 596 degrees Fahrenheit (Surry)

Boron Concentration 0 to 1800 ppm Xenon Concentration 0 to 2.00 E-08 atoms /bn-cm.

The XSEDT code copies the core average macroscopic' cross sections obtained from each of these calculations to a dataset which is read by the XSFIT code.

The ycriables upon which each macroscopic cross section have been found to be dependent are listed in Table 3-1. The XSFIT code analyzes the PD007 macroscopic cross sections and generates base macroscopic cross sections and palynomial coefficients which express these cross sections in terms of these variables:

l

SIGt = SIGtbase + (IV1'* COEFt1 + ... + IVx

• COEFtx) 3-3 4

F ,

where SIGt = macroscopic cross section type t for a certain set of independent variables SIGtbase = base macroscopic cross section type t IVx = value of independent variable x COEFtx = coefficient for SIGt versus independent variable x

= delta SIGt/ delta IVx.

It then compares the PDQ07 cross sections to those calculated with the polynomial coefficients to verify the accuracy of the coefficients.

These base cross sections and polynomial coefficients are passed to the XSEXP code khich smooths several of the fast group polynomial coef#icients and calculates base cross sections and polynomial coefficients beyond the lower and' upper burnup extremes using a linear least squares extrapolation. These extrapolated cross sections are needed to account for axial regions with burnups less than the core average at BOC and greater than the core average at EOC. The XSEXP codes writes this final set of base cross sections and polynomial coefficients to a dataset which is read by NOMAD. .

3.3 Model Normalization l

The Vepco NOMAD model for a particular. unit and cycle must be normalized to the Vepco PDQ07 Discrete, PDQ07 One Zone, and FLAME models for the'same unit and cycle.

The BOC axial burnup distribution from the Vepco FLAME model is input to the NOMAD model in the cycle / geometry deck.' There is a one-to-one correspondence between the fueled axial regions in the NOMAD model and the axial nodes in the FLAME niodel. The NOMAD BOC axial power distributions at NZP and HFP are normalized to the FLAME BOC axial power distributions using the buckling coefficient search option in the NOMAD code. This search finds a combination of buckling coefficient values which give a -

3-4 4

L

- . . ~_ -- -.

i l

buckling distribution that forces the axial offset and the power at the  ;

core midplane to match those from FLAME for the same conditions.

The NOMAD model xenon parameters are normalized to the PDQP One Zone model. The NOMAD model is depleted fros' BOC to 150 MWU/MTU using the xenon ~ paramet'ers from the previous cycle. The fast and thermal xenon microscopic absorption cross sections are assumed to remain constant. The Iodine 135 and Xenon 135 fission yields are modified to force the NOMAD '

equilibrium iodine and xenon concentrations to agree with those from the PDQ07 One Zone model at 150 MWD /!frU:

Ty (new) = Ty(old)

• I18'(PDQ)./ I18'(NOMAD) (3.3-1)

.. Xe18'(PDQ)

TXe("*") * { Xe( Id) + Ty (old) ] * - T I(new) (3.3-2)

Xe185(NOMAD)

The NOMAD .model is depleted again from BOC to 150 MWD /MTU with the new fission yields. to verify that the concentrations now agree with the PDQ07-One Zone model.

The axial- power distributions obtained from the NOMAD model are

. normalized to the FLAME model results for the remainder of the cycle by performing buckling coefficient searches at each depletion step from 150 MWD /! flu to EOC. These buckling coefficients are saved in a table which is' input to the NOMAD code for all subsequent calculations.

[ The NOMAD model control rod cross sections are normalized by forcing agreement between the NOMAD and PDQ07 Discrete rod bank integral worths.

.In the cass'of rod swap worth calculations, the NOMAD bank worths are normalized to the PDQ07 Discrete bank worths for each bank inserted alone.

Otherwise, rhey are normalli.ad to the' PDQ07 worths for the banks inserted in sequence (e.g. , D in, D+C in, D+C+B in. , etc. ) .

The core average cross sections Ial' Ia2, and Ir1 fr a the PDQ07 " Rod bank out" case are subtracted from the same cross sections for the " Rod -

3-5 9

l bank in" case. These values are input to the NOMAD code for that bank, the control rod normalization is set tc 1.0, and the integral bank worth

~

.is calculated with NOMAD. The PDQ07 bank worth is divided by the NOMAD bank worth, and the control rod normalization is multiplied by that ratio.

The bank worth is calculated again with NOMAD to verify that the worth now agrees with the PDQ07 Discrete model. This process is repeated for each re,d bank.

3.4 1-D/2-D Synthesis Prior to the execution of the 1-D/2-D synthesis option in NOMAD, a 2-D PDQ07 case is run for each of the rodded configurations present in the synthesis case (e.g. , ARO, D in, D+C in, etc.). The IFM average power

files from these PDQ07 cases are saved for input to the FDELH code. An input dataset is created for FDELH, omitting the axial power sharing l values. The job and case ID's for the IFM files are listed in the order that the rodded configuations occur from bottom - to top of core. NOMAD reads this input dataset and re-writes it with the axial power sharings

=which it calculates. FDELH subsequently reads this data and performs the L 1-D/2-D synthesis:

F (x,y) = P p 1

• F py (x,y) + P 2 *F p2(x,y) + P3 *Fp3(x,y), (3.4-1)

.where F (x,y) = relative power for fuel in location (x, y) p P, = axial power sharing from NOMAD for rod configuration n Fp ,(x, y) = F p(x, y) for rod cenfiguration'n.

The PCEDT code then performs a power census edit which provide.; ' the percentage of pins in the core whose relative power is greater than the specified value for percentage values of 1%,- 2%, . . . , 9%, 10%, 20%,...,

80%, and 90%.

3-6~

L

r 3.5 FAC Analysis Model The Vepco FXYZ code provides NOMAD with FXY(Z) values at each burnup step for each different rodded configuration which appears in the load follow calculations. It calculates these based on the three-dimensional power distributions obtained from FLAME and the F AH data from the PDQ07 Discrete model F (X,Y,Z) FAH(X,Y) q FXY(Z) =

• *F CON *F XEN (3.5-1)

P(Z) RPD(X,Y)

Maximum.

where Fq(X,Y,Z) = relative power in node (X,Y,Z) from FLAME

-P(Z) = core average axial power in plane Z from FLAME FAH(X,Y) = peak pin power in assembly (X,Y) from PDQ07 Discrete RPD(X,Y) = relative power in assembly (X,Y) from FLAME F

CON

=F E

• F U FE = engineering heat flux hot channel factor = 1.03 F = measurement uncertainty factor = 1.05 U

F = radial xenon re-distribution correction factor = 1.03.

XEN l

If FAH(X,Y) is less than RPD(X,Y), a value of 1.0 is substituted for that ratio.

I NOMAD reads the FXY(Z) data from a file where FXYZ stores them.

Usually only data for ARO and D in rod configurations are necessary for FAC analysis. NOMAD then performs the FAC analysis calculation as previously described in Section 2.10.

3-7

TABLE 3-1 MACROSCOPIC CROSS SECTION VARIABLE DEPENDENCE Cross- Fuel Mod. Boron (Boron * (Boron

• Section Temp. Temp. Conc. Mod. Temp.) Xenon Xenon 2 Xenon)

D 1

X -X' X I X X X X rl.

I,y X X X X v! X X X fl KE gg X X X D

2 X' X X X X I X X X X X X X a2- ,

v! X X X X X f2 KZ f2, X X X X X 3-8

PD087 Cross Section R*fl*Ci*F {

II'** j l One Zone ) I Discrete i  ! (fDarrcte I Lsbrary Desce Ptton od* de de Mode

)

u

XSEDT l

Core Average NU 1F Cg le I Cross Socitons_ Norme13:etion Footors

ir u l XSFIT Reflector FxyI Z)vs.Burnup 1 Cross Sections i

XSEXP o

5 Base Cross Sections & ' E Polynomtal Coefficsonts co rn D007 NOMAD screte "I' .

One Zone y o

Model o ua C

! Axsol Power Axial Burnup Axtel Xenors Rod Worth Axial Power Radial Power g Distribution Distributaon Shape Sherin9* Distribution Distribution l l u

FDELH l Synthessmed Fa(X.D u

! E@

n Power Census Edit

l l

l

.i SECTION 4 - USER INFORMATION 4.1 Input Description

' NOMAD input is read as a series of numbered and categorized cards.

The 010 through 060 cards are required at the beginning of every job.

However, the 040 card can be omitted if a buckling coefficient table is input. The 070 through 090 cards are optional and should only be input when needed. Each card is free format. The data for a single card number may be continued onto subsequent cards, but the card number only appears on the first card. A 500 card is always the last card for each case (or step), and the user may run up to 749 dependent cases following the independent (i.e., first) case. Any of the numbered input cards may appear in a dependent case, but, each case must end with a 500 card.

During the delta-I control and the criticality search options, the i power, control rod positions, or boron concentration may be changed by the code. To use the values calculated by the code in the previous step, the user-inputs a negative value for the appropriate variable (s) on the 500 card.

A detailed description of each input card begins on the following page.

4-1 l

k..

F i

010 CARD -- Title (1 line, 80 characters maximum) 0'20 CARD -- General Parameters VARIABLE NAME TYPE DESCRIPTION 1 NRCNS INTEGER Number of axial regions.

2 EPS REAL Eigenvalue convergence limit 3 IWRITE(1) INTEGER Temp. , power, arid burnup edit:

0 => Do not write edit 1 => Print & fiche edit 2 => Fiche edit 4~ IWRITE(2) INTEGER Macroscopic cross-section edit 5 , .IWRITE(3) INTEGER Iodine, xenon and flux edit 6 IWRITE(4) INTEGER Axial xenon and RPD plot file 7 IWRITE(5) INTEGER Axial power sharing edit and flux squared edit (must =1 for 1-D/2-D synthesis)

O 4-2

030 CARD -- Thermal-Hydraulic Data VARIABLE NAME TYPE DESCRIPTION 1 ITMAX. INTEGER Maximum number of thermal iterations 2 TAU REAL Thermal relaxation parameter 3 'THCON REAL Thermal convergence criterion 4 TMO . REAL Moderator reference temperature-(*Farenheit) 5 TF0 REAL Fuel reference temperature

(* Rankine) 6 DGEFPD' REAL Fuel temperature vs. burnup coefficient

(*R / (SFPD

• relative power))

7 FTF0 REAL Fuel temp. vs. relative power coefficient

(*R / relative power) 8 ENTHIN(1) REAL HZP inlet enthalpy (BTU /lbm) 9 ENTHIN(2) REAL HFP inlet enthalpy (BTU /lbm) 10 HEIGHT REAL Core height (centimeters) 11 POWER REAL HFP core power level (watts) 12 FLORAT REAL Core flow rate (Ibm / hour) 13 SYSPR REAL System pressure (psia) 14 fPOWDEN REAL Power density (watts /cc) 4-3 w: .

040 CARD.-- Buckling Coefficient Input (Not required if buckling coefficient table is used)

VARIABLE NAME TYPE DESCRIPTION 1 B0 REAL Buckling amplitude 2 BMID REAL Buckling curvature coefficient 3 BTILT REAL Buckling tilt coefficient 4 BTH REAL Thermal buckling fraction 5 ~RPDMID REAL Target power at midplane 6 AXOFFT REAL Target axial offset 7 ILOCK INTEGER Buckling coefficient table flag.

Use this card instead of table:

0 => For this step only 1 => For subsequent steps 050 CARD - . Control Rod Cross Sections (Seven cards: control D-A, shutdown B&A, PL rods)

(Number 050 appears on the first card only)

VARIABLE NAME TYPE DESCRIPTION 1 RODWTH(1,I) REAL Fast macroscopic absorption cross section 2 RODWTH(2,I) REAL Thermal macroscopic absorption cross section 3 RODWTH(3,I) REAL Fast macroscopic removal cross section 4 RODWTH(4,I) REAL Control rod normalization 5 IOVRLP(I) INTEGER Bank overlap (1st 3 cards only) 6 RDBANK(I) REAL Bank name (8 characters in ' ')

4-4

060 CARD -- Delta-I Control and Criticality Search Parameters VARIABLE NAME TYPE DESCRIPTION

1. IDCNTL INTEGER Delta-I control option. .

If delta-I out of allowed 9 nd:

-1 => adjust to edge of band 0 => do not adjust

+1 => adjust to target value 2 TARGET REAL Target delta-I (%)

3 DELTIL REAL Lower delta-I band (%)

4 DELTIH REAL Upper delta-I band (%)

'S RILHFP REAL D-bank HFP insertion limit (steps) 6 RILHAF. REAL D-bank insertion limit at 50% power (steps)

'7 EIGEN REAL Criticality search target eigenvalue 8 EPS2 REAL Criticality search convergence limit 9 ICRIT INTEGER Criticality search variable:

1 => Boron concentration (ppm) 2 => D-bank position (steps)

-2 => D-bank followed by boron conc.

3 => Power (%)

4 => HFP inlet enthalpy (BTU /lbe) 10 CRTHAX REAL Maximum value of ICRIT

11. CR1 MIN REAL Minimum value of ICRIT 4-5

070 CARD -- Core Average Fixed Parameters (Optional Card)

VARIABLE NAME TYPE- DESCRIPTION 1 IFX1 INTEGER Fixed fuel a.I moderator temperature flag:

0 => Do not fix 1 => Fix

, 2 IFX2 INTEGER Fixed burnup flag 3 IFX3 INTEGER Fixed xenon flag 4 IFX4 INTEGER Time flag:

-1 => continuous clock

+1 => 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> clock 5 TMFX REAL Moderator temp. (*F) 6 TFFX REAL Fuel temperature (*R) 7 EFPDFX REAL Burnup (EFPD) 8 ~XENFX REAL Xenon concentration (Atoms /bn-cm) 9 TIMEFX REAL Initial clock time (hours) 080 CARD -- Boration / Dilution Input (Optional Card)

VARIABLE NAME TYPE DESCRIPTION 1 SYSMAS REAL Primary system mass (1bm) 2 CBBOR REAL Boration line boron conc. (ppm) 3 _CBDIL REAL Dilution line boron conc. (ppm) 4 FLOBOR. REAL Boration line flow rate (gpm) 5 FLODIL REAL- Dilution line flow rate (gpm) 6 NXCRIT REAL If boron system incapable of maintaining criticality:

0 => Print warning only

.1 => Adjust D-bank position 2 => Adjust power level 3 => Adjust inlet enthalpy 4-6

090 CARD -- FAC Analysis'In'put (Optional Card)

VARIABLE NAME- TYPE DESCRIPTION 1 FQGRID REAL Grid correction factor:

1.056 => 3 case 1.025 => 18 case 2 ADJUST REAL F XY Power adjustment factor 3 .NMAPS INIEGER Number of FXY(Z) maps input 4 FXYMIN(I) REAL Minimum FXY(Z) values (

• FU *F) E (I=1,NMAPS) for each FXY(Z) map 5 MPBURN(I) INTEGER Burnup (tMD/MTU) at which each

.(I=1,NMAPS) FXY(Z) map is printed 6 FQLIMX(J) REAL X-coordinate for Fq limit curve (core height in feet) 7 FQLIMY(J) REAL Y-coordinate for Fq limit curve (Fq (Z) limit)

[ Repeat variables 6 & 7 in pairs for J=1,4]

8 FXYLMX(J) REAL X-coordinate for F II"I* II"*

XY (core height in feet) 9 FXYLMY(J) REAL Y-coordinate for' F XY limit line

.(FXY II) II"IU)

[ Repeat variables 8 & 9 in pairs for J=1,4]

100 CARD -- Recovery File Options (Optional Card)

VARIABLE NAME TYPE DESCRIPTION 1 DFILE REAL Recovery file flag SAVE => Save new recovery file RESTORE => Restore old file 2 FNAME REAL 8 character file name l [ Note: 1 space must be placed between variables 1 and 2] -

l 4-7

r 500 CARD -- Case Card VARIABLE NAME TYPE DESCRIPTION 1 TIME REAL Depletion time interval (hours) 2 PCTPOW REAL' Core average power (%)1 3 IRDPOS(1) INTEGER D-Bank position (steps)1

-4 IRDPOS(2)- INTEGER C-Bank position (steps)"

5 -IRDPOS(3) INTEGER B-Bank position (steps)1 6 IRDPOS(4) INTEGER A-Bank position (steps)1

7. IRDPOS(5) INTEGER SB-Bank position (steps)1 8 IRDPOS(6) INTEGER SA-Bank position (steps)1 L 9 , IRDPOS(7) INTEGER PL-Rods position (steps)1 10 BORON REAL Boron Concentration (ppm)1 L 11 IXEN INTEGER Xenon Option:

l l -1 => Xenon from previous step 0 => Xenon depletion t-1 => No xenon i

2 => Equilibrium xenon-l 12 IOPT INTEGER Case Option:

L 0 => Static case 1 => Depletion 2 => 1st step of rod worth sequence 3 => Criticality search 4 => 1st step of FAC analysis 5 => Xenon worth calculation 6 => Buckling coefficient search 7 => Frozen THF 8 => 1st step of average power distribution calculation

-8 => Final step of average power distribution calculation; perform load follow depletion i-1 If a negative value is input for any of these variables, the value from the end of.the previous case is used.

4-8

NOMAD also reads a cycle / geometry deck. The data in this deck remains constant for a particular unit and cycle. The cycle deck contains reflector. macroscopic cross sections, xenon parameters, axial region dimensions, and the BOC axial burnup distribution.

The cycle / geometry deck is read in free format in the following order:

D 1 I,g. I rl (Bottom reflector fast cross sections)

D 2

Z a2 (B ttom relector thermal cross sections)

D Z I (Top reflector fast cross sections) 3 al r1 D I (Top relector thermal cross sections) 2 a2 Xe Xe o o T T (Iodine and xenon parameters) al a2 I Xe

-Height (cm) BOC burnup(=0.0) (Region 1 -- bottom reflector)

Height (cm) .BOC burnup(=0.0) (Region 2 -- bottom reflector)

Height (cm) BOC burnup(=0.0) (Region 3 -- bottom reflector)

Height (cm) BOC burnup(EFPD) (Region 4 -- bottom fuel region)

Height (cm)' BOC burnup(EFPD) (Region NRCNS-3 -- top fuel region)

Height (cm) BOC Burnup(=0.0) (Region NRCNS-2 -- top reflector)

Height (cm) BOC Burnup(=0.0) (Region NRCNS-1 -- top reflector)

Height (cm) .BOC Burnup(=0.0) (Region NRCNS -- top reflector) 4.2 Error & Warning Messages NOMAD prints error messages whenever it detects an error in input or execution. If it is an input error, it will terminate after checking the remainder of.the input for that case for errors. If the error occurs during execution, the job is terminated.

The code also. prints warning messages for less severe problems, such as a criticality search not converging. Execution continues after a warning message is printed.

NOMAD returns a condition code of zero for a successful job 4-9

p .s

. comp 1'etion in most cases. Other programmed return codes are:

11.- Power sharing calculated for 1-D/2-D synthesis

~

-333 - Job terminat'ed . recovery file could not be found

.444'-' Job terminated, thermal-hydraulic feedback did not converge 1

555 - Job terminated, maximum number of cases' exceeded 666 --Job terminated, buckling search did not converge 777-- Job terminated, cross section file error 888 -: Job-terminated, FAC analysis input error 999 - Job terminated, input error.

'4 3- Execution'. Time-

' Approximate ; execution (CPU) times for NOMAD for several types of cases are given below:

~HZP, no xenon. 0.1 seconds HFP, eq. xenon- 1.1' seconds I HFP, xenon depletion, 0.7 seconds  !

criticality search

.HFP, eq. xenon, 3.4 seconds criticality. search ,

Buckling coefficient search . 4 - 6 minutes (10. depletion steps)

FAC analysis 5 - 8 minutes.

-(72 hour8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br /> load follow)

Output.

-4.4 I NOMAD. offers .the user flexibility in its output control. - The cutput H

' options are IWRITE(1) - IWRITE(5) on the 020 card. All five of these p

' options are turned off and on by.. values of .0 and 1, respectively. All

^ edits are written to tite printer 'except IWRITE(4), which writes to a plot

. file.

4-10 r w e- eir- *-t"<--- --,wm-es - vm* - > -m+ -- we -

-e -

~

b -

V ,

I l The1 temperature, power, and burnup edit is'a one page edit.which l' .

L ' includes the k-effective, delta-I, axial offset, number of iterations to l

reach convergence, and: cycle' average burnup. It also prints for each axial region and .the core average the values ~ of each of. the following L

~

parameters:. .k-infinity,. moderator- enthalpy (BTU /lba), moderator h' ftemperature (*F), fuel temperature (*R), relative power density (RPD),

t and fuel burnup . (EFPH) . This edit is generally the most useful one in L '. design calculations. The' macroscopic cross section edit is a two page edit which provides the fast and thermal cross sections for each axial

. region and the core average. This edit is recommended only for debugging purposes or special applications.

'The; iodine,. xenon, and flux edit lists the-xenon and iodine concentrations and the^ fast and thermal fluxes by axial region and core L

e average. This edit is required for normalization of the xenon model. The Jaxial - power sharing edit gives the fraction of.-the axial power which ,

t

-exists in each axial segment with a different rodded configuration.- This' i

edit is necessary to perform 1-D/2-D synthesis. The flux squared sharing edit gives the . fraction 'of the. fast group flux squared which exists in each axial segment with a different rodded configuration. This edit is an

.importance weighting function which may be used in performing rod swap worth calculations.

These edits are normally printed once per case,-but they may appear

,more than once when a criticality. search or a delta-I control adjustment is performed. The first occurrence of each edit contains the results of

'. 'the nuclear calculation prior to any variable adjustments. The final occurrence contains the results of the final nuclear calculation after all s

searches have been completed.

In addition to the output options selected, NOMAD always prints the following output:

4-11

l (1) Input card image listing

~

(2) Cycle / geometry deck card image listing (3) Buckling coefficients & distribution and reflector cross sections (4) . Input summary (5) 1-D analysis case summary.

. NOMAD offers two options for writing output to a dataset for creating plots. The first is~ IWRITE(4), which writes the axial xenon and relative power distributions to a file. Each distribution is labeled with the cycle burnup for that step, so that several distributions may be saved in the same file. The user is advised to not use this option in any job where IOPT := 2, 4, or 5 (rod worth, FAC analysis, or xenou worth). These options also write data to the same plot file. The plot output for these three options is similar to the printed output for them.

The second plot option writes most of the data which appears in the 1-D Analysis Case Summary to a file. The data includes the case number, time, power, boron, D-bank position, delta-I, peak power, k-effective, and xenon. If the boration/ dilution calculations are performed, the water processed per step is written instead of the xenon concentration.

This option is exercised by assigning a dataset to the appropriate unit (see Section 4.5).

4-12

4.5 I/O Units The I/O units used by NOMAD are:

Unit NoI. Description 2 Buckling coefficient table (input)

'3 Cycle / geometry input deck 4' Cross section input S Card input 6- Printer and microfiche 8 FXY(Z) Input 9 Case summary plot file 10 Plot file for:

RPD, xenon dist., rod worth, FAC analysis, xenon worth 11 Buckling coefficient table (output)1 12 Microfiche 13 Recovery file 14 Scratch disk space 21 FDELH code input for 1-D/2-D synthesis.

" Data is written to unit 11 only when a buckling coefficient search is performed.

1 -.

4-13

T' SECTION 5 - RESULTS 5.1 Introduction The purpose of this section it, to demonstrate the predictive capability of the NOMAD model for ca.le;1ations of axial power distributions, delta-I and axial offsets, critical boron concentrations, differential and integral control rod worths, load follow maneuvers, and core peaking limits for FAC analysis. This section presents: 1) .

reactivity parameter comparisons to measured data from the Surry and North Anna Nuclear Power Stations and to other Vepco codes; 2) a thermal-hydraulic feedback calculation comparison to COBRA 11; 3) axial power distribution comparisons to measured data from Surry and North Anna; 4) differential and integral control rod worth comparisons to measured data and the Vepco FLAME model; 5) comparisons of load follow maneuver .' simulations of delta-I, axial offset, and critical boron concentration to measured data from North Anna; and 6) FAC analysis

^

results obtained with NOMAD.

5.2 Reactivity Parameters Differential boron worths were calculated with NOMAD at BOC, HZP and EOC, HFP. The BOC, HZP values are compared to measured data and the EOC, HFP values are compared to the Vepco PDQ07 Discrete model in Table 5-1.

Isothermal temperature coefficients obtained with NOMAD at BOC, HZP also are compared to measured data in Table 5-1.

Figures 5-1 'through 5-6 compare NOMAD xenon worths after startup, orderly shutdown, and trip to results obtained with XETRN18, Vepco's zero-dimensional xenon transient code. Note that XETRN-assumes the xenon worth is a linear function of the xenon concentration, whereas NOMAD calculates the xenon worth directly from the eigenvalues.

5-1

E5.3 Thermal-Hydraulic Feedback' The accuracy of the thermal-hydraulic feedback model has been

. verified by direct comparison with the COBRA code. Both NOMAD and COBRA were. run 'for a North Anna 1207, overpower case. The COBRA model used four 17 x 17' fuel assemblies to represent the core. COBRA also used as input the axial power' distribution calculated by NOMAD. The system pressure, core - flow rate, and inlet enthalpy were identical for both COBRA and NOMAD. Table 5-2 shows a comparison of . the moderator enthalpy: and moderator temperature distributions calculated by NOMAD and COBRA.

5.4 Axial Power Distribution Axial power distribution comparisons between the Vepco NOMAD model and measurements are presented in Figures 5-7 through 5-16 for BOC, HZP, no xenon and BOC, HFP, equilibrium xenon conditions. Representative axial power distributions comparisons are shown for North Anna 1 Cycle 2, North Anna 1 Cycle 3, North Anna 1 Cycle 4, North Anna 2 Cycle 2, and Surry 1 Cycle 6.

The NOMAD predictions attempt to simulate the actual core t conditions. However, NOMAD does not represent the spacer- grids in order to increase calculation efficiency. The accuracy which is compromised is insignificant.

5.5 Differential and Integral Rod Worths The Vepco NOMAD model predictions and startup' physics measurements for differential and integral control rod bank worths for B-bank are compared in Figures 5-17 through 5-24. B-bank was the rod swap reference '

bank for each of these cycles and its worth was measured by boron dilution.

In addition, NOMAD results for Banks A through D moving in overlap 5-2

are compared to the Vepco FLAME model in Figures 5-25 through 5-32. No measurements were performed at these conditions.

Integral control rod bank worths were calculated for banks measured by rod swap using an importance weighting technique. NOMAD performed a critical boron search with the refere~nce bank fully inserted. Another bank was then fully inserted, and NOMAD performed a criticality search on

-the reference bank position and calculated the flux-squared sharings.

These flux-squared sharings were then used to determine a weighted average of the PDQ07 Discrete bank worths for the bank inserted alone and the bank inserted with the reference bank. These synthesized bank worths and the measured worths are compared in Table 5-3. The critical position

~

of tite reference bank predicted by NOMAD for each bank fully inserted is compared to measurement in Table 5-4.

5.6 Load Follow Manuever Simulation NOMAD's load follow simulation capability has been verified by comparison ~ to three sets of measured data for load follow type cases.

The first set of data consists of hc.urly delta-I readings and two critical boron measurements from a 70*. load reduction test performed near the end of North Anna Unit 1 Cyc1'e 2. The power and D-bank history for this case is listed in Table 5-5. Figures 5-33 and 5-34 compare NOMAD results to the measured delta-I and critical boron concentrations.

Two additional sets of measured data were recorded near the end of North Anna Unit 1 Cycle 3 during power escalations following reactor trips. The first incident occurred on April 16-20, 1982, and the second on April 30 - May 2, 1982. The power and D-bank histories for these two cases are given in Tables 5-6 and 5-7. The negative times listed in Table 5-6 are simply the number of hours before the comparisons in Figures 5-35 and 5-36 begin. The data prior to 0.0 hours0 days <br />0 hours <br />0 weeks <br />0 months <br /> was not plotted because it was at HFP, equilibrium conditions (delta-I is virtually 5-3

I- constant) or low power levels . -(no . delta-I data available). Hourly

~

readings of delta-I and eight critical boron measurements were taken

(_

during the first case. Results from the NOMAD simulation are plotted

- versus these data in Figures 5-35 and 5-36, respectively. During the second case, both ex-core delta-I readings and INCORE axial offset measurements-were performed, since delta-I cannot be measured accurately at ~ low l power levels. (The INCOREs were performed on only a limited number of assemblies each time.) The delta-I readings have been converted to axial offsets in order to compare NOMAD results to both types of data in Figure 5-37. Figure 5-38 plots the NOMAD critical boron concentrations versus thirteen measured values for this case.

5.7 FAC Analysis Standard three and eighteen case FAC (CAOC) analyses were performed with the Vepco NOMAD model for North Anna- 1 Cycle 4 and North Anna 2 Cycle

2. The Vepco NOMAD model results were found to be consistent with the reload analysis results from an accepted and verified vendor model which has been used in the design and licensing of the Surry and North Anna reactors. Both models indicated minor technical specification violations near the core bottom in the three case analyses and no violations in the eighteen case analyses.

Figures 5-39 through 5-42 show the NOMAD results for the eighteen case analyses. The F q(Z) plots in Figures 5-40 and 5-42 contain the radial xenon re-distribution factor and an uncertainty factor of 10.9%,

which ' includes the engineering hot channel factor, the measurement uncertainty factor, and the grid correction factor.

l 5-4

. TABLE 5-1 REACTIVITY COEFFICIENTS COMPARISON'

, Differential Boron Worth, BOC HZP (pcm/ ppm)

' Unit / Cycle. NOMAD PDQ Discrete Measured % Difference 1

~NIC2 -9.15 -9.10 -8.88 3.04 N1C3 -8.15 -8.08 -8.54 -4.57 NIC4 -7.70 -8.04 -8.25 -6.67 N2C2' -8.97 -8.91 -8.46 6.03 S1C6 -8.27 -8.31 -8.78 -5.81 SIC 7 -8.43 -8.44 -8.44 -0.12

~

Differential Boron Worth, EOC HFP~(pcm/ ppm) ~

Unit / Cycle NOMAD PDQ Discrete  % Difference 2 NIC2 -9.06 -9.43 -3.92 N1C3 -8.17 -8.47 -3.54 NIC4 -7.90 -8.62 -8.35 N2C2 -8.91 -9.40 -5.21 S1C6 -8.81 -9.31 -5.37 S1C7 -8.93 -9.16 -2.51 Isothermal Temperature Coefficient, BOC HZP (pcm/*F)

Unit / Cycle NOMAD PDQ One Zone Measured Difference 8 NIC2 -5.07 -3.87 -2.36 -2.71 NIC3 -3.99 -3.40 -4.36 0.37 NIC4 -4.90 -3.52 -4.92 0.02 N2C2 -5.29 -3.27 -2.27 -3.02 S1C6 -4.28 -3.79 -2.32 -1.96 SIC 7 -6.49 -5.68 -5.85 -0.64 1'% Difference = (NOMAD - Measured) / Measured x 100

• % Difference = (NOMAD - PDQ07)/PDQ07 x 100 8

Difference = NOMAD - Measured 5-5

C' s _ m. , .- ,

TABLE 5-2

' COMPARISON OF NOMAD AND COBRA MODERATOR ENTHALPY AND TEMPERATURE. DISTRIBUTIONS-F Position Enthalpy (BTU /lba)

~

Moderator Temperature (*F)

(inches) NOMAD COBRA NOMAD COBRA-4 544.9 545.1 548.4 548.0 8 -546.8 546.9 549.9 549.5 12 549.1 549.3 551.8 551.4 16 551.8 552.0- 554.0 553.5 20' 554.7 554.8 556.3 555.8 24 557.7 557.8 558.7 558.2

. 28 560.8 560.9 561.1 560.6.

32- . 563.9 564.0 563.6 563.0 36 567.0 567.1 566.0 565.5 40 570.2 570.2 568.4 567.8 44 573.3 573.4 570.9 570.3 48 576.5 576.6 573.3' 572.6 52 579.6 579.7 575.7 575.0 56 582.8. 1582.9 578.1 577.3

60. 586.0 586.1 580.4 579.7 64 589.2 589.3 582.8 582.1 l 68 592.4- 592.5 585.2 584.5 I

72 595.7 595.8 587.5 586.9 76 598.9 599.0 589.9- 589.3 80 602.2 602.3 592.2 591.7 84 605.5 605.6 594.6 594.1

.. 88 608.8 608.9 596.9 596.5

• 92 612.2 612.3 599.2 598.9 96 615.5 615.6 601.5 601.3 100 618.9 619.0 603.8 603.7 104 622.3 622.3 606.1 606.4 108- 625.6 625.7 608.4 608.3 112 629.1 629.1 610.7 610.6 116 632.5 632.5 612.9 612.9 120 635.5 635.9 615.2 615.1 124 639.1 639.2 617.3 617.4 128 642.4 642.4 619.4 619.5 132 645.3 645.4 621.3 621.4

'136 648.0 648.0 623.0 623.0 140 650.1 650.1 624.4 624.3 144 651.6 651'.5 625.3 625.2 i

5-6

TABLE 5-3 ROD SWAP COMPARISON, PART 1 Integral Bank Worths (pcm)

North Anna Unit 1 Cycle 3 Bank- ' NOMAD /PDQ Measured  % Difference D 1048 1089 -3.76-C 839 777 7.98 A 620 722 -14.13 SB 1006 919 9.47 SA 1096 1238 -11.47 North Anna Unit 1 Cycle 4 D1 N/A N/A - N/A C 808 843 -4.15 A 479 562 -14.77 SB 980 1023 -4.20 SA 997 1094 -8.87

' North Anna Unit 2 Cycle 2 D 1010 1015 -0.49 C- 780 757 3.04 A 757 812 -6.77 SB 713 664 7.38 SA 912 948 -3.80 Surry Unit 1 Cycle 6 D 1228 1234 -0.49 C 819 815 0.49 A 538 551 -2.36 SB 1018 1013 0.49 SA 1093 1137 -3.87 2

D-bank worth was measured by a combination of rod swap & dilution.

5-7

9 TABLE 5-4  ;

ROD SWAP COMPARISON, PART 2

' Reference Bank Critical Position (Steps)

North Anna Unit 1 Cycle 3.

' Bank NONAD Measured  % Difference

'D .143 143 0 C 117 103 14

-A .

97' 97 0 SB 143 119 24 SA '158 170 -12 North Anna Unit 1 Cycle 4 D1 N/A. N/A N/A C 154 163 -9 A 114 122 -8

SB 182 190 -8

SA. 186 201 -15 North Anna Unit 2 Cycle 2 D 186 195 -9 C 171 168 3 A 167 175 -8

'SB 166 155 11 SA 181 189 -8 Surry Unit 1 Cycle 6 D 179 175 4 C 123 110 13 A 93 83 10 SB 154 138 16 SA 166 157 9

• D-bank worth was measured by a combination of rod swap & dilution.

5-8 c

.c .

q TABLE 5-5

~

NIC2 70% LOAD REDUCTION TEST POWER AND D-BANK HISTORY Time ~Pcwer D-bank

.(Hours) -(%)- (steps) 00.00 98.8 228 01.00 82.9 190 02.00 56.2 186 03.00 32.8 150 l 04.00 29.5 152 05.00 29.2 166

~'

06.00 29.2 162 07.00 29.6 157 08.00 30.0 156 09.00 30.6 145 10.00 30.5 143

, 11.00 30.3 145 12.00 30.2 141 3 13.00 30.2 140 14.00 29.9 138 15.00 29.5 137-16.00 29.5 137 17.00 28.9 136 18.00 29.3- 136 19.00 29.0 136 20.00 27.9 136 21.00 28.4 137 22.00 28.4 137 23.00 27.5 145 24.00 27.3 151 25.00 27.2 155 26.00 27.2 157 27.00 26.7 160 28.00 26.7 160 29.00 26.7 160 30.00 26.7 160 l

l r 5-9 l

m -- - _ .

TABLE 5-6

-N1C3 SHUTDOWN / RETURN TO POWER CASE 1 POWER AND D-BANK HISTORY Time Power D-bank

-(Hours) (%) . (steps)

-23.00 100.9 215

-22.00 100.4 215

-21.00 100.6 215

-20.00- 100.5 215

-19.00 100.6 215

-18.00 100.8 215

-17.00 100.7- 215

-16.00 100.6 215

-15.00 100.5 215

-14.00 100.0 215

-13.00 99.9 214

-12.00 -100.6 - 215

-11.00 100.5 215

-10.00 100.6 215

-9.00 0.0 0 1 -8.00 0.0 0

--7.00 0.0- 0

-6.00 0.2 47

-5.00 1.2- 156

-4.00 1.9 179

-3.00- 0.0 0

-2.00 0.2 185

-1.00 4.9 193

.0.0 17.7 197 1.00 23.* 186 2.00 27.t 160 3.00 29.7 160 4.00 30.1 160 5.00 .30.2 . 160 6.00 29.8 160 7.00 30.7 160 8.00 29.3 -158 9.00 29.2 151 10.00 29.4 143 L 11.00 29.4 143 l 12.00 29.4 142 13.00 30.9 141 14.00 45.7 141 15.00 48.9 144

- 16.00 49.0 159 L 17.00 48.7 170' L 18.00 48.4 178 L 19.00 48.0 181 20.00 47.5 182

[

i 21.00 47.3 183 22.00 47.6 184

~ 23.00 47.7 184 24.00 47.3 182 25.00 47.7 180

, 5-10 I

l

((

7~

TABLE 5-6 (Continued)

^

26.00 47.7 178 27.00 48.8 177 -

28.00 49.0 175 29.00 49.0 172 30.00 48.4 170 31.00 48.9 169 32.00 48.4 168 33.00' 48.4 168 34.00 47.7. 168 35.00 48.3 ~ 168 36.00 48.4 167 37.00 48.8 165 38.00 55.6 172 39.00 69.9 181 40.00 73.4 183

,. 41.00 73.2 183 l 42.00 76.9 190

, 43.00 87.7 205 l-44.00 92.0 209 45.00 99.6 211 i- 46.00 -99.7 '

211 47.00 100.2 211 48.00 99.6 211 49.00 99.8 211 ~

50.00 100.0 211 p 51.00 100.1 211 L

52.00 99.8 211 53.00 100.0 211 54.00 100.3 211 55.00 100.2 211

, 56.00 100.2 211 I 57.00 100.2 211 58.00 0.0 0 59.00 0.0 0 60.00 0.0 0 61.00 1.4 88 62.00 5.1 128 63.00 26.9 200 64,00 28.3 182 65.00. 28.1 172

66.00 30.1 160 67.00 30.0 160 68.00 30.0 160 69.00 29. 8 ~ ' 160

-70.00 44.3 170 71.00 50.4 161 72.00 49.5 161

! 73.00 47.2- 161' l

74.00 47.6 161 75.00 47.2 161 76.00 47.1 158 77.00 47.3 158 5-11

U i-

[,

TABLE 5-7

.N1C3 SHUTDOWN / RETURN 'IT) POWER CASE 2 POWER AND D-BANK HISTORY

'Date Time Power D-bank (Hours). (%) (stops)

I' . 4 30 82 16.20 ' 100.3 218 4 30 82 '18.60- 99.7 218 4 30 82 _18.85 99.8 218 4 30.82 20.72 100.2 218 l

4 30 82 21.50 95.2 .209 4 30 82 21.78 92.1 206 4.30 82 22.06 , 88.3 200 .

4 30 82 -22.35 83.6. 190

_ 4 30 82 22.63 75.8 180 4 30 82 23.15 66.0- 171 1

4 30 82 23.70 58.2 158

5. 1 82 0.50 44.0 ~127

.5 182- 1.30 30.1 110 5 1~ 82 2.08 18.2 110 5 1 82 2.85 3.2 90 5-'1-82 3.87 2.3 145 5 1 82' 4.70 2.0 162 5 .1 82 5.77 2.1 173 6.78 5 1 82 2.3 177 l 5 1 82 7.81 2.5 174 5 1 82 8.84 2.2 169 5 1 82 -9.88 0.0 0 5 1 82 10.88 0.0 0 5 1 82 11.90 0.0 0

. 5 1 82. 12.95 0.0 0 5 1 82 13.20 0.0 91 5' 1 82 13.53 0.0 91 5 1 82 13.95 1.3 91 5 1 82 14.27 1.3 91 5 1 82 14.95 1.7 81 5 1 82 15.73 1.7 81 5 .1 82 15.95 1.3 69 5 1 82 16.85 1.8 61 5 1 82 17.58 1.8 61 l

5 1 82 17.85 1.8 59 i 5 1 82 18.95 1.6 59

l. 5 -1 82 19.95 2.1 59 L 5 1.82 21.00- 1.8 45 5 1 82 22.07 1.8 45 l 5 1 82 23.07 1.7 45

! 5 1 82 23.97 2.1 45 5 2 82 1.00 2.2 45 5 282 2.02 2.3 45 i 5 2 82 3.07 2.2 45 l 5 2 82 3.95 2.4 45 5 2 82 4.37 2.4 45 5 2 82- 4.98 2.2 45 5 2 82 6.01 2.3 45 5 2 82 6.35 2.3 45 2

j. 5-12 l~

i

TABLE 5-7 (Continued)

~

5 2 82 6.95 2.3 45 5 2 82 8.00 2.8 46 5 2 82 8.17 7.3 50 5- 2 82 8.53 7.3 50 5 2 82 9.05 7.3 64 5 2 82 9.17 17.6 63 5 2 82 9.44- 22.6 63

'5 2 82 10.14 29.8 68 5 2 82 10.55 29.8 68 5 2 82 11.00 31.8 69 5 2 82 12.25 31.8 71 5 2 82 13.05 31.8 71 5 2 82 13.25 29.1 71 5 2 82 14.22 39.9 108 5 2 82 15.19 51.6 155 5 2 82 16.21 64.8 174 5 2 82 17.31 67.1 181 5 2 82 18.21 68.7 185 5 .2 82 19.21 69.2 185 5 2 82 20.21 73.9 193 5 2 82 21.24 83.0 201 5 2 82 22.24 91.1 208 5 2 82 23.24 96.1 214 5 2 82 23.87 19 <8. 7 214 s

5-13

XENON WORTH AFTER STARTUP

~

NORTH RNNA UNIT 1. CYCLE 3 3000] 100%

x x  :: x  :: 75%' 2(

~

/ u :c  :: c n 2500- c n

/ ,,

50%

/ n/^,

X i x :c  :: x x l'

t E

N 2000-0 ['

m N i

X  :: 7 25%

}jij N m L

= 0 1500--

) , y :c :c H H X x m

x x

- 1000-~

i T

x

/ -

P X C  : -

M  :

500-; - /"

x '

0~'J. .. . . . ... . . . . . . . . ..

0 10 20 30 40 50 60 '70 80 90 100 tit 1E (HOURS 1

= N 0 t190 X XETRAN ,

5i n "m

0 0 ,

1 0

9 N C 0 W 8 O

D T - 0 7

U H3 SEL C

h^* 0 6

1 RCY S R

E1 TT Wb 0 5

U O

H

(

0 A 9

1 N

R FIN N E t

0 E T

AU M N X A

HNRN NN 0

4 I

T a X T H N RTR

• OON W \ N b 0 3

x N l O N 0 N

E  %

0 0

5 x

a 1

N s s

2 X 1 7 T 2 0

1 rc- - - -

J 0

0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 5 0 5 0 5 0 5 0 5 4 4 3 3 2 2 1 1 X 10 aT M

3 m 0

, 0 1

0 9

0 8

P I

R T

w,0 7 R3 r EEL

_ 0 6

TCY )

S FC R N%,0 A1T U

O O N H R A 5 N TR

(

HINU E O E N N X T I R.RN w T =X N 0

- OR 4 WH T N

R O 's N NN 'c 0

3 O x x N x E k (- -

m 0 X x x x 2 x

k^g \x h"x x

x 0

1

% %. t  % . X ,

0 0 m " 54X

[xx 2  ;

1 .

x *

1. X -

0

- - f- f - i :-

0 0 0 0 0 0 0 U 0 U 0 0 0 0 0 0 0 0 U 0 U 0 5 0 5 0 5 0 5 0 S 5 4 4 3 3 2 2 1 1 EN0N W0 H N

[c n

7 3nE c T*

t

' L. , 0

. 0 1

0 5 0 5 . -

0 7 5 2 - .

1 .

: i e ", . 0 9

P  ;

l i "

, . 0

. 8 U .

T .

R c c

e s

',' . 0 A . 7 T .

S c r (

6 s y L

> 2 0 REL 6 1

S EC R TC Y c (

0 H U

O D N A A F1 , u L, '

. 5 t MR A

O T T E E M N X I

HUN I

. m

, [

T X

. 40 TYR RRU

,[ I

,/

OS W .' fC .

0 3

N O s d  :

0 N ./: i . 2 E [ x/

• x X 'o *: u 0

4" .

1 x

~

. 0

f - _::' '::  ::

0 0 0 0 0 0 O 0 0 0 0 0 0 0 5 0 5 0 5 3 2 2 1 1 XEN0N W0RTH - PCM uyu

XENON WORTH AFTER SHUTDOWN SURRY UNIT 1 CYCLE 6 5000_

1001. .

4000-~

• f 7 51 ,

m N 3000_ . -

0  % m X

f ^-

• H 2000- $

253 ,\

P s  %

x x

x N 1000- - \

'\ wNk o;

A x::

st A w h 7-0 10 20 30 40 50 60 70 80 90 100 TINE IHOURS1

= N0nAD

, X XETRAN .

aEA

' 0 0

. 1 '

. 0

. 9

- ,0 8

P I

R -

~

. 0

. 7 T

R E6

~ .

0 6

TEL .

)

S FCY R AC 1

N% .

0 5

U O D N H A A

(

MR HT T

O E EN M X TIN RU OYR

~

N% 0 4

I T=X WR N

U S

h [' "

'C N 0 3

O N K E ,

h*

' c

' 0 2

X

• x 4 k 0 0

0 5

7 0 sh 1

1 f 2A F

E 0

.!  : _: - .  : l - - : : '

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 3 2 1 X N W0 H - PCH mL,e

AXIAL POWER COMPARISON

~

N)C2.HZP B0C.

2,n-

~

1.8f R 1. 5-E  :

L -

R . ,

I l 2- 3 V' y 8

8 N

E

<;n 0.9- "

P 0 -

W  :

R ,

0.3-0.0- . ,- .,. -

O' 20 40 60 80 100 120- 140 CORE HEIGHT tlNCHES)

• NOMRD X HERSURED

~

AXIAL POWER COMPARISON NIC2 HFP RRO E0. VE. 80C 1 2-L

-k

1. 0-'

R 0.9- -

E L  :

0.8- n A

m T  : y

• I m

U V 0 . 7-'

E Y'

w j

P 0.6- J 0  :

W .:

E 0.5-0.4 _x

1 1

0 . 3-' L 0 20 40 60 80 100 120 140 CORE HEIGHT tINCHES1

= NOr190 X MERSURED

AXIAL POWER CO~MPARISON N1C3 HZP BOC.

l.75-1 50 R 1.25- -

E ~

L R -

I l-.00- -

~

I m y -

E E

k E 0.75-m P

- - e 0  :

W _

E 0.50-R  :

0.25-

~

0.00-b 2b 4b- 6b 8b lb0 120- 140 CORE HEIGHT llNCHES) a NONRO X HERSURED

AXIAL POWER COMPARISON NIC3 HFP RRO E0. XE. BOC 1.4-12k R  :

E 1.02' /

L /

R B w i g T  : - :o 4

w I -

• V 0.82 '

E E P  :

0  :

H 0.62 '

E  :

R j 0.4f 0.22 .. ... ... ... .... . ... . .,.. ,,.

0 20 40 60 80 100 120 140 CORE HEIGHT (INCHES)

= N0t1R0 X MERSUREO

3

~

i AX1AL POWER COMPARISON NIC4 HZP BOC  ;

1.75- ,

W 1.50- .

R E 1.25-

~

L n R 5 T

!ii I I rn 2 y 1.00_

Y' E  : -

P 0.75-0 -

W _

E _

R 0.50-

~

0.25-O.00 ,,, , ,,, , ,,, , ,, ,

0- 20' 40 60 80 100 120- 140 -

CORE HEIGHT tlNCHES)

= NOM 90 X MEASURED

AXIAL POWER COMPARISON NIC4 HFP ARO E0. XE. 80C 1 4-3 1- -

R E 1.02 '

L n R

T y

T I A

= v 0.8-~

Y' E

P  :

0  :

W 0 . 6-~ .

E -

R j 0.4j 5

0.22 ... ... ... ... .

0 20 40 60 80 100 120 140 CORE HEIGHT tlNCHES)

= N0t1R0 X HERSURED

A-XIAL POWER COMPARISON

~

N2C2.HZP BOC.

2.t :

I 8-R ~

E 1.5-L ~

R - n I h Y' I 2k g M h E .

Y

~

C P 0.9- l 0

Y '

R 0.g_

0.3-0.0-' --

e-- 's-O' 20 49 60 80- 100 120- 140

• " lGHI'tINCHEst

, ygng9 X HERSURED

AXIAL POWER COMPARISON N2C2 HFP ARO EO. (E. 80C l.3-1.2f 1.): d' 10 fL  :

R o.g; @

m  :-

i

$ I M V O.a: m E  ;

L.

y O.7f -

u -

E o .g - -

, ^

R _

.k 0.5 f.

G.4 ): l 0.3 b L f a- . ,,, s- ,,, ' s- '<-

O gg 40 60 80 100 EU 140

' "i iINCHES3 e nong X t1ERSuggg

AXIAL POWER COMPARISON

~

SIC 6 HZP BOC 1.75-1.50f R 1 25-E L

R '

T I.00- n I E T v !ii m

y E 0.75- T P G 0  :

H E 0.50-R _

0.25- ,

0.00 , . .

0- 20- 40 60 80 100 120 140 CORE HEIGHT-IINCHES) m NOMAD X MER5URED

I l ,1 I!ll ll ,l m ETm 0

s 4 1

- 0 s

2 N 1 O

S I 0 RC s 0 1 I AOB S

E H

P. - C N

MEX s I

( O O.0 - 80 T 0 R E

CE G 0 9

H1U t

S O I R E EN RRR -

H=1 t E P a 0

6 E X WFH .

R O

O 6 C

PC I s

0 S 4 L

I A

X -

A s 0

2 s

0 2: 2- :2:' - -

4 2 0 8 6 4 2 1 1 1 0 0 0 0

~

RELR vE P0WER 7U

DIFFERENTIAL ROD WORTH COMPARISON NORTH ANNR UNIT 1 CYCLE 3 13.5-

*Ww 0 *

• j "j 9.0,

,/

[ g r

• /;

P "1

l//

((

h #AM i

C M 4.5

s

,e , J $, \

S T 3.0-

***d (

D' / "

1 ..T...

0 20 40 60 80 100 120 140 160 180 200 220 240 B BANK POSITION (STEPS)

NOMRO X FLAME = MERSURED

INTEGRAL ROD WORTH COMPARISON ~

h NORTH ANNA UNIT 1 CYCLE 3 i I

1500-1250-T A

T 1000_

n m -

m L, R 750- *

~

T H

.k. ~

~

500- T P

C .

M _

250- ,

~

0- . . ..

=

0 20 40 60 80 100 120 140 160 180 200 220 240 B BANK POSITION (STEPS)

NOMAD X FLAME = MERSUREO

. , . - . ., ? - ., . . . . v .w . .

.~s+-

. - ., . . m ; + ; , mc ev_ w .e e .vv r =:.:-- . . .

w r ~ t. ..:. . m m : ~ v t l.:^ - L' 9

DIFFERENTIAL ROD WORTH COMPARISON NORTH ANNA UNIT 1 CYCLE 4 90, D 7 5- b' k " -"

p **.1h*

6 . 0 -- ,

W -

2 '

0 .

m R  : 8 T 4.5-A

~ H a, \

e l w i P -

C 3.0-M I

i t

S T 1.5-l l E

- I

~

P 0 0- s , ,, ,, ,

1 0 20 40 60 80 100 120 140 160 180 200 220 240 B BANK POSITION (STEPS) 1 NOMAD X FLAME = MERSURED  :

l 1

l

~'

i. ' .i 'e-w.: ...-

• f %'. ' ;6 * . : ; '. . " V. } 9' '/.

-_.y- ;,* c yg ; ; ' ~ m ' -. ,"' '" k  ;.-;, . .; - % t . ,' ,-  ;'- -

[N I

'  : ^l

. . .; .. ,.

6 7 ' i ._

i .', [#0 ? .- ',c. [ ' * ' ,} , , ' * . - . , . l'r-' ' , , , . -h* ,, ' , ,.

., ~ _ '

fg# N .* ') 9-[. [.' . - ' , ' '

I " -  ! %C ,'f[, . .,~

.i g c

,~. .-

.:  ; je ,~-!.

~

', l- ", , . - . , ,

l

• i %,

, ' . , .#  ;. ', S

+

,j ,

.; , ,3- -

• -[k, . -

k:f,[:' 5[ t * ~7[ .' . r:- }', , ,' ', t l '

A - .;; " , : , . , .' '" h l. - Ek f,' & ' ] ' . . ~.L . . , "; [ ,

~

. '+ . ' ,~ ' , , ,;. . . '

'd.'- ,N .

- _ _ _ _ _ _ _ _ _ _ __ _ _ m _ _ .. _ _ . , . . . .. _

INTEGRAL ROD WORTH COMPARISON NORTH RNNA UNIT 1 CYCLE 4 1250.

xxx  :'4 :' q 1000_

b I  :

N  :

~

750-

• W 3

m  : sii 0 m g R m

I  : A H 5002 A-P -

C -

H 250' ,

0 ...

0 20 40 60 80 100 120 140 160 180 200 220 240 8 BANK POSITION (STEPS 1 NOMAD X FLAME = MERSUREO

DIFFERENTIAL ROD WORTH COMPARISON NORTH ANNR UNIT 2 CYCLE 2 13.5-0 ' (

I 10.5-

"i i H:?? \\

W

R T

7 . 5-'

// .,**

\t i, r

m

1. 4 H  :

f g g, t h

6.0_ +

g, ,, g,- r r.,, .

C M 4.5-

[ +/ [

S  !

• T 3.0-1 5- 7,

)

0.0 ' ,, # :L 0 20 40 60 80 100 120 140 160 180 200 220 240 B BANK POSITION (STEPS)

NOMRO X FLAME = MERSUREO

INTEGRAL ROD WORTH COMPARISON NORTH ANNR UNIT 2 CYCLE 2 1350-e ee p 1200- 4 1050--

h -

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FIGURE 5-25 l

DIFFERENTIAL WORTH OF CONTROL BANKS A THROUGH 0 IN OVERLAP MODE NORTH ANNA UNIT 1. CYCLE 3 X NOMAD

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FIGURE S-26 INTEGRAL WORTH OF CONTROL BANKS A THROUGH 0 IN OVERLAP MODE NORTH ANNA UNIT 1, CYCLE 3 X NOMAD C - FLAME O

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FIGURE 5-27 DIFFERENTIAL WORTH OF CONTROL BANKS A THROUGH 0 IN OVERLAP MODE

[ NORTH ANNA UNIT 1. CYCLE 4 .

b w

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5-43

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• 5

SECTION 6 -

SUMMARY

AND CONCLUSIONS The Vepco NOMAD code and model are operational at Vepco for the purpose of performing one-dimensional reactor physics analyses and supporting the evaluation of core performance. The model consists of NOMAD with the NULIF, XSEDT, XSFIT, XSEXP, FXYZ, FDELH, and PCEDT codes providing either input or data manipulation. The accuracy of the Vepco NOMAD model has been established through extensive comparison of calculations to measurements from the units at the Surry and North Anna Nuclear Power Stations and to calculations from other Vepco codes. The results of these comparisons indicate that the Vepco NOMAD model (which _

includes normalization to the Vepco PDQ07 Discrete, PDQ07 One Zone, and FLAME models) provides the capability to predict core peaking factors, axial power distributions, differential and integral tod worths, and load follow maneuvers as well as perform Final Acceptance Criteria (FAC)

Analysis.

Verification of and improvements to the Vepco NOMAD code and model will continue to be made as more experience is obtained through the application of the model to the units at the Surry and North Anna Nuclear l

Power Stations.

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}

SECTION 7 - REFERENCES

1. S. M. Bowman, "VEPCO 1-D Code Development: Final Report", NFE Technical Report No. 250, March, 1983 (Virginia Electric and Power -l Co.).

2. D. A. Daniels, "Fxy(Z) Synthesis Methodology and Computer Code", NFE [

Technical Report No. 180, January, 1981 (Virginia Electric and Power L Co.).

3. J. G. Miller, "The FDELHP01 and PCEDTP01 Codes", NFE Technical Report No. 201, July,1981 (Virginia Electric and Power Co.).

4. P. D. Breneman, "The NULIFP01 Code", NFE Calculational Note PM-13, March,1979 (Virginia Electric and Power Co.).

5. M. L. Smith, "The PDQ07 Discrete Model", VEP-FRD-19A, July, 1981 (Virginia Electric and Power Co.).

6. J. R. Rodes, "The PDQ07 One Zone Model", VEP-FRD-20A, July, 1981 (Virginia Electric and Power Co.). ..

7. W. C. Beck, "The Vepco FLAME Model", VEP-FRD-24A, July,1981 (Virginia Electric and Power Co. ) .

8. L. L. Lynn, "A Digital Computer Program for Nuclear Reactor Analysis Design Water Properties", WAPD-TM-680, July, 1967 (Westinghouse Electric Corporation).

9. J. G. Miller, " Thermal-Hydraulic Feedback Input to the Two-Dimensional PDQV2 Code", NFE Calculational Note PM-19, June,1979 (Virginia Electric and Power Co.).

10. Course Notes " Basic PWR Physics Course", September, 1980 (Westinghouse Electric Corporation) .

11. F. W. Sliz and K. L. Basehore, "VEPCO Reactor Core Thermal-Hydraulics Analysis Using the COBRA IIIc/MIT Computer Code", VEP-FRD-33-A, October, 1983.

12. D. A. Daniels, "XETRN and SMTRN", NFE Technical Report No. 112, February,1980 (Virginia Electric and Power Co.).

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