ML20078K336

VEPCO Nomad Code & Model

ML20078K336
Person / Time
Site:	Surry, North Anna, 05000000
Issue date:	09/30/1983
From:	Berryman R, Bowman S, Dziadosz D VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
To:
Shared Package
ML18141A163	List: ML18141A162 ML20078K336
References
VEP-NFE-1, NUDOCS 8310190057
Download: ML20078K336 (118)

Text

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _

l.

VEP-NFE-I SEPTEM BER,1983 Vepco i

THE VEPCO NOMAD CODE AND MODEL r

i a

BAAZ88Po8s8sio P

PDR POWER STATION ENGINEERING DEPARTMENT NUCLEAR FUEL ENGINEERING Virginia Electric and Power Company

1 THE VEPC0 NOMAD CODE AND MODEL

(

BY S. M. BOWMAN NUCLEAR FUEL ENGINEERING GROUP POWER STATION ENGINEERING DEPARTMENT SEPTEMBER, 1983 Reconsnended for Approval:

'Y D. Dziadosz, Supervisor Nuclear Fuel Engineering Approved:

MMw R. M. Berryman, Director Nuclear Fuel Engineering 1

i

CLASSIFICATION / DISCLAIMER l

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 e

written approval of the Virginia Electric and Power Company.

f I

1

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ABSTRACT The Virginia Electric and Power Company (Vepco) has developed NOMAD, a e

Cne-dimensional (axial), two energy group, diffusion theory computer code with thermal-hydraulic feedback, and a calculational model designated as the Vepco NOMAD model.

i The model utilizes the Vepco computer codes NOMAD, XSEDT, XSFIT, XSEXP, NULIF, FXYZ, FDELH, 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.

ii

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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, Ms. Bonnie Herndon for her typing of the draft, Ms. Pam Cooper and Ms. Diane Upchurch for their typing of the equations, and the Word Processing Staff for their typing of the final manuscripts. The author also wishes to express his appreciation to the people who reviewed and provided comments on this report.

t iii a

TABLE OF CONTENTS Page CL ASSIFIC ATI O N/ DI SC LAI MER........................................ i ABSTRACT........................................................

11 ACKNOWLEDGMENTS..................................................

iii 1

TABL E OF C 0 NTE NTS................................................ i v LIST OF TABLES................................................... Vi L I ST O F F I GU RE S.................................................. v i i SECTI ON 1 - I NTROD UCTI ON........................................

1 -1 SECTI ON 2 - C O DE DESCRIPTION.................................... 2-1 2.1 Introduction.....................................

2-1 2.2 Neutron Flux Calculation.........................

2-3 2.3 Thermal-Hydraulic Feedback.......................

2-8 2.4 Xenon Calculation................................

2-9 2.5 Radial Buckling Coefficient Model................ 2-11 2.6 Criticality Search...............................

2-13 2.7 Delta-I Control..................................

2-14 2.8 Boration and Dilution Calculations...............

2-15 2.9 Final Acceptance Criteria (FAC) Analysis.........

2-16 2.10 Differential and Integral Rod Worth Calculations. 2-18 2.11 Xenon Wor th Cal cu lation.......................... 2-19 SECTION 3 - MODEL DESCRIPTI ON................................... 3-1 3.1 Introduction.....................................

3-1 3.2 Cross Section Generation.........................

3-3 3.3 Mo de l Nor ma l i z a t i o n.............................. 3 -4 3.4 1-D/2-D Synthesis................................

3-6 3.5 FAC An a l ys i s Mo d e 1............................... 3 -7 3.6 Deep In sertion Control Rod Model................. 3-8 SECTION 4 - USER INFORMATION....................................

4-1 4.1 In p ut De s cr i ption................................ 4-1 4.2 Err or & Warn ing Mess ages......................... 4-9 4.3 Execution Time...................................

4-10 4.4 0utput...........................................

4-10 4.5 I/O Units........................................

4-12 iv

~

b,

S ECTI ON 5 - R ES U LTS.............................................

5-1 5.1 Introduction.....................................

5-1 5.2 React i vi ty Parame ters............................

5-1 5.3 Thermal-Hydrauli c Feedback....................... 5-2 5.4 Axial Power Distribution.........................

5-2 5.5 Differential and Integral Rod Worths.............

5-3 5.6 Load Follow Maneuver Simulation..................

5-3 5.7 FAC An a l ys i s..................................... 5 - 5 SECTION 6 -

SUMMARY

AND CONCLUSIONS.............................

6-1 SECTION 7 - REFERENCES..........................................

7-1 Y

v

LIST OF TABLES Table _

Ti tle h

3-1 Macroscopic Cross Section Variable Dependence.........

3-10 5-1 Reactivity Coefficients Comparison....................

5-6 5-2 Comparison of NOMAD and COBRA Moderator Enthalpy and Temperature Distributions.............................

5-7 5-3 Rod Swap Comparison, Part 1...........................

5-8 5-4 Rod Swap Comparison, Part 2...........................

5-9 5-5 NIC2 70% Load Reduction Test Power and D-Bank History..............................

5-10 5-6 N1C3 Shutdown / Return to Power Case 1 Power and D-Bank History..............................

5-11 5-7 NlC3 Shutdown / Return to Power Case 2 Power and D-Bank History..............................

5-14 5-8 Comparison of FLAME and uncorrected NOMAD Results For NIC3 Shutdown / Return to Power Case 2..............

5-16 l

t i

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LIST OF FIGURES Figure Title Page 2-1 NOMAD Code Flow Diagram...............................

2-20 2-2 Axial Mesh Points and Regions.........................

2-22 2-3 Axial Region Center and Boundary Mesh Points..........

2-23 3-1 Vepco NOMAD Model Flow Diagram........................

3-11 5-1 Xenon Worth After Startup, North Anna Unit 1 Cycle 3..

5-17 5-2 Xenon Worth After Shutdown, North Anna Unit 1 Cycle 3.

5-18 5-3 Xenon Worth After Trip, North Anna Unit 1 Cycle 3.....

5-19 5-4 Xenon Worth After Startup, Surry Unit 1 Cycle 6.......

5-20 5-5 Xenon Worth After Shutdown, Surry Unit 1 Cycle 6......

5-21 5-6 Xenon Worth After Trip, Surry Unit 1 Cycle 6..........

5-22 5-7 Axial Power Comparison, N1C2 HZP B0C..................

5-23 5-8 Axial Power Comparison, N1C2 HFP ARO Eq. Xe. 80C......

5-24 5-9 Axial Power Comparison, N1C3 HZP B0C..................

5-25 5-10 Axial Power Comparison, NIC3 HFP ARO Eq. Xe. BOC......

5-26 5-11 Axial Power Comparison, NIC4 HZP B0C.................. 5-27 5-12 Axial Power Comparison, NIC4 HFP ARO Eq. Xe. 80C......

5-28 5-13 Axial Power Comparison, N2C2 HZP B0C..................

5-29 5-14 Axial Power Comparison, N2C2 HFP AR0 Eq. Xe. BOC......

5-30 5-15 Axial Power Comparison, SlC6 HZP B0C..................

5-31 5-16 Axial Power Comparison, SIC 6 HFP ARO Eq. Xe. BOC......

5-32 5-17 Differential Rod Worth Comparison, North Anna Unit 1 Cycle 3.............................

5-33 5-18 Integral Rod Worth Comparison, No r th An n a Un i t 1 Cyc l e 3............................. 5-34 l

l vii

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a 5-19 Differential Rod Worth Comparison, North Anna Unit 1 Cycle 4.............................

5-35 5-20 Integral Rod Worth Comparison, Nor th An na Un i t 1 Cycle 4.............................

5-36 5-21 Differential Rod Worth Comparison, North Anna Unit 2 Cycle 2.............................

5-37 5-22 Integral Rod Worth Comparison, Nor th /W n a Un i t 2 Cyc l e 2.............................

5-38 5-23 Differential Rod Worth Comparison, Surry Unit 1 Cycle 6..................................

5-39 5-24 Integral Rod Worth Comparison, Surry Unit 1 Cycle 6...

5-40 5-25 Differential Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 1 Cycle 3............

5-41 i

5-26 Integral Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 1 Cycle 3............ 5-42 5-27 Differential Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 1 Cycle 4............

5-43 5-28 Integral Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 1 Cycle 4............

5-44 5-29 Differential Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 2 Cycle 2............

5-45 5-30 Integral Worth of Control Banks A thru D in Overlap Mode, North Anna Unit 2 Cycle 2............

5-46 5-31 Differential Worth of Control Banks A thru D in Overlap Mode, Surry Unit 1 Cycle 7.................

5-47 5-32 Integral Worth of Control Banks A thru D in Overlap Mode, Surry Unit 1 Cycle 7................. 5-48 5-33 N1C2 70% Load Reduction Test, Axial Flux Difference...

5-49 5-34 NlC2 70% Load Reduction Test, Critical Boron Concentration..........................

5-50 5-35 NlC3 Shutdown / Return to Power Case 1, 4

Axial Flux Difference.................................

5-51 5-36 NlC3 Shutdown / Return to Power Case 1 Critical Boron Concentration..........................

5-52 i

viii

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

~ _ -. _ _, _ _... -

. _, - _. _. - ~ _ - _ _. _ _, _ _ _ -. _, _ _, - -

5-37 NIC3 Shutdown / Return to Power Case 2, Axial 0ffset........................................

5-53 5-38 N1C3 Shutdown / Return to Power Case 2, Critical Boron Concentration........................

5-54 F (Z) Results, North Anna Unit 1 Cycle 4............

5-55 5-39 Z

F (Z) Results, North Anna Unit 1 Cycle 4............

5-56 5-40 Q

F (Z) Results, North Anna Unit 2 Cycle 2............ 5-57 5-41 Z

F (Z) Results, North Anna Un it 2 Cycle 2............ 5-58 5-42 Q

i l

l I

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IX

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 the Vepco NOMAD model.

In addition to NOMA 3, the model uses the Vepco computer codes XSEDT(I),XSFIT(I) XSEXP(I),FXYZ(2),FDELH(3),PCEDT(3) and I4)

The model also utilizes data from the Vepco PDQ07 Discrete (5)

NULIF PDQ07 One Zone (6), and FLAME (7) models. A detailed description of the 1

input requirements, functioning, physical models, and output capabilities of i

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

The types of reactor physics calculations which can be performed within the general capabilities of the Vepco NOMAD model include:

I 1.

Core average axial power and burnup distributions 2.

Axial offset 1

Peaking factois (F (Z), Fxy(Z), F (Z))

3.

Q Z

4.

Final Acceptance Criteria (FAC) Analysis 1-1 y,r.e.-,.s--w-

.,y-

,-u-e.+,y-y,

,p,c-,.

--+ - - - -

m

-r-e

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.

The remainder of this report describes the Vepco NOMAD code, the purposes and. interrelationships of the other computer codes which comprise the Vepco i

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.

I p

l 1-2 e-me----

,-,,,w-,,--w-m

,,--,.,,m p

,n+

e-,

SECTION 2 - CODE DESCRIPfl0N 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 1

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 polynominal 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, 1

l whereas the second is used for load follow maneuvers or xenon transients.

2-1

,---my-i- --

w-y

---

.wr-

-v-e r-

L i

Using the xenon distribution obtained, flux and thermal-hydraulic calculations are performed again. This process continues until the flux, thermal-hydraulic, and xenon convergence criteria are satisfied.

The NOMAD code also contains the following capabilities:

1.

Radial buckling calculation and normalization 2.

Criticality search on a selected variable 3.

Delta-I control l

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 snployed in the seven calculations listed above, i

i 2-2

--war--

- y w

y

, _ _ - ~ -

4--r

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

D (z 4(z)

-fg

+ E (z)4j(z) = Xj G(z)/A + I,1-1(z)4j_i(z),

(2.1-1) j j

j r

z i=1,2, where i = the neutron energy group, D (z)'= diffusion coefficient for group i at position z, j

4 = neutron flux, 2

E (z) = D (z)B (z) + E3,j(z) + r,j(z) = the total cross section, j

j p

2 B = radial buckling, r = absorption cross section, a

r = removal cross section, r

I = poison cross section, p

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

2 2

2 G(z) =

vr (z)4)(z) = the fission source, f

If = fission cross section, v = number of neutrons per fission, and A = eigenvalue = K eff.

Equation 2.1-1 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 2-3

second term represents all other losses. These include absorption (E and Ip ),

a 2

leakage in the radial directions (DB ), and scattering out of the energy group (tr,i ). The sources on the right-hand side are fission (xj G(z)/A),and scattering into the group from the next-higher energy group (Ep,j_g).

1z I, is subdivided into axial The z-axis in the region of solution, 0 Z

regions by mesh points at which the solution is to be determined. At some interior point z,. integrate from n

+ f h +'

-fhn-- to z +=z z

"Z n

n n

n-n where h and h + are the heights of the axial regions below and above point n-n z, respectively.

(See Figure 2-2.)

n The approximations d4(z) tj(z)-pzn-1) d4j(z)

_ 4j(z +1)-*i(z )

9 n

n n

~

dz.

z h

dz z+

h+

n-n-

n n

i

• n I+

i

[n+

n E (z)4 (z)dz = E (zn-)

• i(z)dz + Ij(z +)[

• i(z)dz j

j j

n z

z z

n-n_

n

_n n I (z )h

+ I.(zn+)h 4 (z )

I.4,

(2.1-3)

=

=

i n-n-

1 n+

i n

1 1 2

2 and D.(z"*)

= D "*

(2.1-4) j t

n l

l i

l l

2-4

~

l

o are used to obtain the difference equation n

_Ji-n-1 n+ n+1 a)&j (li + + D n

n-D &j

-Uj&

+

Ej

+

j j

2

{

n n

n n

x E

f.j *j r,i-1 1-1 j=1 From the form of the equations it can be se.en that the macroscopic cross-sections are required to be constant in each half-interval.

In 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 reflector regions and the flux at the outer boundaries of these regions is zero. The system of equations given by Equation 2.1-5 and the zero flux boundary conditions, may be expressed in matrix form as li&=1Q + h A

where M,, F,, and R, sre tridiagonal matrices.

NOMAD solves this system of equations by the method of power iterations using Gaussian elimination. The rate of convergence is accelerated by P

P replacing the pth iterate of i (i.e.1 )

with a linear combination ofi and the previous iterate, iP, SP E

P i

=1 (1 + e )

- iP-l P,

(2.1-7) e P

where e

is an acceleration parameter computed on the basis of Chebyshev polynomials.

2-5 i

i

r The eigenvalue for iteration n is calculated as N

2 n,

n-1[=1j-1"Ef J( *k) *] *k),

(2.1-8) x N

2 f,j(z)4)n-1(z)

E I

vr k

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

The converged solution to Equation 2.1-6 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 2m, label the top and bottom mesh points as t and b, respectively, and the region center as c.

(See Figure 2-3.)

Using the approximations d4(z)

= 4 (c)-4 (b) d4(z)

= 4 (t)-4 (c) 4 (2.1-9) dz l

m dz m

and tI (z)4 (z)dz = I (c)4 (c)2m, (2.1-10) and integrating Equation 2.1-1 yields D (c) 24 (c) - 4 (t) - 4 (b)

+ I (c)4 (c) 2m 2

x$

r,i-1(c)4 _ (c)

(2.1-11) vr (c)4 (c) + I

=

2-6

- \\

Since the fluxes at each region boundary, 4 (b) and 4 (t) are known, NOMAD 1

1 solves for the region center flux 4 (c) directly. The code then 1

integrates 4 (b), 4 (c), and 4 (t) using Simpson's method to obtain the average f

1 f

fast and thermal fluxes in the regi.on.

Finally, the relative power is calculated for each region Z IZII (Z) fy(Z)T (Z) + KEf2 2

KI y

P(Z) =

• a (2.1-12)

R fy(Z)iy(Z) + KEf2 2

IZI II E

KE Z=1 where P(Z) = relative power in axial region Z K = energy per fission (watt-sec) 4 (Z) = average group i flux in region Z f

R = total nunber of axial regims with fuel 2-7

2.

Thermal-Hydraulic Feedback The thermal-hydraulic feedback model uses an energy balance to calculate the moderator enthalpy as a function of axial position Enthalpy

= Enthalpyin + Power / Flow Rate, (2.3-1) out f

L where Enthalpy

= moderator enthalpy exiting the region (BTU /lbm) out Enthalpyin = moderator enthalpy entering the region (BTU /lbm)

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

Flow Rate = core moderator flow rate (lbm/hr).

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 (8), 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) = Mod. temp (Z) + (DGEFPD

• Burnup(Z) + FTF0)

• RPD(Z)

• PR, (2.3-2) l where L

Fuel temp (Z) = fuel temperature in axial region Z l

Mod. temp (Z) = moderator temperature in region Z l

DGEFPD = fuel temperature vs. burnup coefficient (OR/EFPD

• Relative power) 2-8

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

FTF0 = fuel temperature vs. relative power coefficient

( R/ Relative power)

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

This fuel temperature fit is based on the one used in the Vepco PDQ07 thermal-hydraulic feedoack model.(9)

NOMAD then recalculates the macroscopic cross sections based on the new fuel and moderator temperatures, performs another flux calculation, and performs another thermal-hydraulic calculation.

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

2.4 Xer.an Calculation NOMAD calculates the iodine and xenon concentrations for each axial 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 remain constant over the time interval for which the calculation is performed.

Prior to calculating the iodine and xenon concentrations, NOMAD normalizes the fast and thermal fluxes 2

(in neutrons /cm -sec) to the core power level 4 (Z) '= POWDEN

• PR

• RPD(Z)

(2.4-1)

IZ)

KIfy(Z)*$y(Z)/$ I I +

f2 2

& = 4 (Z)

• 4 IZ)/4 (Z)

(2.4-2) 1 2

2-9

2

&f(Z) = normalized flux for group i in region Z (neutrons /cm -sec) where i

POWDEN = power density (watts /cc)

PR = core relative power (fraction of full power)

RPD(Z) = relative power density in regicn Z

$g(Z) = region average relative flux for group'i in region Z.

NOMAD then uses these normalized fluxes to calculate the iodine and xenon concentrations

-A (t +1-t )

I i i

YE&

(2.4-3)

Y 4 e if I(Z) g,y =

I(Z)1 - 7f I

I_.

~

( i+1 t) g Xe(Z)1,1 = Xe(Z)1 - (y w } E

• A IIZI -Y E & e y Xe f I

i 7f

+

LX A -M 7

-A It +1~D )

I i i

(Yg)E 4 1 I(Z)g - y r4 e f

7 yf A-M u

7 where I(Z)i+1 = i dine concentration in region Z at step i+1 y = iodine fission yield y

A = iodine decay constant 7

t,y = h (seconds) at step hl i

E &' = KEfy(Z)& (Z) + Ef2IZ)

• Z) /kVG f

g g = average energy per fission Xe(Z)f,1 = xenon concentration in region Z at step i+1 Y

= xen n fission yield Xe 2-10

LX = g + o 4 (Z) + o

$ (Z) 1 2

A

= xen n decay constant h

= xenon absorption cross section, group j.

o To calculate the equilibrium icdine and xenon concentrations, the exponential terms in Equations 2.4-3 and 2.4-4 are set to zero.

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.

Af ter fl0 MAD calculates the iodine and xenon concentrations, the macroscopic cross sections are adjusted and the flux and thermal-hydraulic calculations are performed again. The iodine 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 2-11

l 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 the buckling coefficients are:

B0 * (1 + BTILT * (Z - 20) / HT)

• CZ(Z)

(2.5-1)

BUK1(Z)

=

BTH

• BUKl(Z)

(2.5-2)

BUK2(Z)

=

CZ(Z)

= cos (BMID

• PI * (Z - 20) / HT) if BMID 0.05

= 1.8 - cos (BMID

• PI * (Z - Z0) / HT) if BMID

-0.05

= 1.0 otherwise, (2.5-3) where BUKl(Z) = Fast group buckling BUK2(Z) = Thermal group buckling 80 = 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 2-12

~

.1

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 80, 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 performed, the coefficients are written to a data set with the core average burnup (in EFPH). This buckling coefficient data set 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.

2.6 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 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 search 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.

2-13

Y+&

9

> k/

IMAGE EVALUATION

(([/p%8( 4'4,%

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• % 4 TEST TARGET (MT-3) 9>

f 4

w

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[m EM l!!

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m

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IMAGE EVALUATION 4

f gq)7 e$+

TEST TARGET (MT-3)

%,h?

4

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'g m era "llEu i,l s5 lLie 1.8 1.25 1.4 1.6 4

150mm 4

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2.7 Delta-I Control i

'In order to simulate a load follow or other maneuver where the reactor is i

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 band.

Delta-I is defined as:

Delta-I(%) = Power (top)

Power (bottom)

• PR

• 100, (2.7-1)

Power (top) + Power (bottom) l 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 can not be achieved, then delta-I is adjusted to the i

nearest possible value. The user may request that the code adjust delta-I to l

(1) the target delta-I (the center of the operating band) or (2) the nearest i

l edge of the operating band. Adjusting delta-I to the edge of the band l

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 i

criticality.

i 2-14

_.__,.__.m

~ _ _ _. _,. _ - - - _. _ _,., - -

2.8 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 (10) l WATER (J) = -SYSMAS / H 00EN In 1+

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

(2.8-1) 2 (80R(J-1) - C n) i TIMEMN = WATER (J) / LDRATE, (2.8-2) where WATER (J) = Water processed (gallons) at step J SYSMAS = Total primary coolant system mass (1bm)

H 00EN = Water density in letdown line (8.2 lbm/ gal) 2 i

80"(J) = Boron concentration at step J BOR(J-1) = Baron concentration at step J-1 C n = Boron ',oncentration in letdown line i

TIMEMN = minimum time required to perform boration/ dilution LDRATE = Letdown rate.

u 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-l 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 l

l l

2-15 l

~

-r

-w

-g w-

,,w-9---sy,-

,,y-4-,,mw-n

,,,o,y__,wm y,,.,_,

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 baration (or dilution).

2.9 Final Acceptance Criteria (FAC) Analysis NOMAD is capable of performing Final Acceptance Cri.eria (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:

TE I (Z) = j=1 b i

i=1,2, (2.9-1)

Th3 3=1 where f3(Z) = group i flux in region Z for timestep j (neutrons /cm2 - sec) tj = length of timestep j (hours)

T = total number of timesteps specified.

This flux distribution is substituted into Equation 2.1-12 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.

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 (Z), FXY( ) calc.,

XYf ) allowable, Z

and F (Z) calc. NOMAD performs the following sequence at each step in the q

FAC analysis case.

First, it determines the rodded configuration 2-16 L

(i.e., ARO. D in, D+C in) for each axial region. Then the code selects the Fyy(Z) that corresponds to the axial level and the rodded configuration of each region. NOMAD checks each FXY(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:

I FXYREL = FXY(Z) * (1 + ADJUST * (1 - PR)),

(2.9-2) where FXYREL = FXY(Z) adjusted for the core relative power level FXY(Z) = FXY at axial region Z for 100% power ADJUST = FXY p wer adjustment factor (e.g., 0.3 for North Anna, 0.2 for Surry)

PR = Core relative power levei.

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

q FQTEST = FXYREL

• RPD(Z)

• PR

• FQGRID, (2.9-3) where FQTEST = F (Z)

• PR for this step q

RPD(Z) = Relative axial power in region Z FQGRID = Correction factor for grids

• uncertainty factor

= 1.025

• UF l

UF = 1.03 (3 case FAC analysis)

UF = 1.00 (18 case FAC analysis).

2-17 l

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

saved:

F (Z) calc. = FQTEST (2.9-4) 4 Fyy(Z) calc. = FXYREL (2.9-5) yy(Z) allowable = F (Z) limit / (F (Z)

• PR

• FQGR.ID)

(2.9-6)

F q

Z F (Z) = RPD(Z).

(2.9-7)

Z Once the entire load follow simulation has been completed and the final values IIIallowable, and F (I) calc. have for F (Z), FXY(Z) calc.,FXY q

7 been obtained, NOMAD checks for any limit violations for FXY(2) calc.,

yy(Z) allowable, and F (Z) calc. and flags them in the FAC ANALYSIS F

q RESULTS output.

2.10 Differential and Integral Rod Worth Calculations Differential and integral rod worth calculations are available in NOMAD.

The control rod banks may be inserted or withdrawn in any order chosen by the user (e.g., single bank, multiple banks in overlap, multiple banks together, etc.) The differential worth is calculated as follows:

j 1/RKEF1)

• lE+5 / ISTEPS, (2.10-1)

(1/RKEF3 DIFF(I)

=

where DIFF(I) = Differential rod worth for case I (pcm/ step)

RKEF3 = K,ff for case I+1 RKEF1 = K for case I-l gff ISTEPS = Nuniber of steps rods moved from case I-l to I+1.

i 2-18 l

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

NOMAD calculates the integral worth as follows:

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

• IE+5, (2.10-2) where RINT(I) = integral rod worth for case I (pcm)

RKEF2 = K for case I eff RKEF = K for 1st case of rod worth sequence.

eff The integral worth is calculated for every step of the rod worth sequence.

2.11 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:

i l

Xenon worth =

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

• lE+5.

(2.11-1) l Keff (no xenon)

• Keff (w/ xenon)

The program then restores the saved xenon distribution. Thus, the xenon worth at any ticestep of a problem can be determined without interrupting the flow of the other calculations being perforr.ed.

2-19 1

START

>l 1 t l Initial Xenon Calculation v

Instaal TIF Calculation lHF Calculation u

n Xenon Calculation b

Nuclear Calculation 4

9 n

o W

93 r

i Calcul Yes FF o

THF?

Converged?

g EL No Yes 9.

E, Calculate Yes No Xeno e

No Yes c

]

if r

i CoefT e t Searctu Yes No m gxg Criticality Search, or Converged?

Guess Delta-I Control Yes b

i

r Calcuir,te yg3 Boratten/

0 *""

No Cratterlaty Yes Pwforo Boration/

Dalution

- System Copacit9 Search on 2nd Soorch slut Calculation Suffectent variable?

No YM No f

y' q Yes Porform Nuolear tio Calculation with No Xenon Yes FAC Op

Calculot. F,y (Z), F (Z), F (2) q 2

m

=,

=

c k

O.,plett

> Perform Fuel and Xenon Depletion N

N/

4m4

,=

?

Yes Another s'

se?

g S

No 3r Print Summaru Output Yes Worth

Different al/ Integral Rod Worth Calculation No FAC Yes FAC Analysis Sumraarg Opti No STOP j

FIGURE 2-2 Axial Mesh Points and Regions O

n+1 i

l 4

G h

h+

2n+

n h+

n 2

i I f I f 2"

a L

j g n

hn-2 Y

h e

n-Zn-l l

l

^

• n-1

(

2-22

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

i a

t m

i t O

I s s C

i M

II

=

b i

l

)

k i

E 2-23 i

l 1 ----.,... _ _, _... _. _. _ _ _, _ _ _ _ _ _

_____,I F"

w-**eq mwvg

---

e._.,,,

SECTION 3 - MODEL DESCRIPTION 3.1 Introduction The Vepco NOMAD model is used 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 thre, aattom 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 l

quarter core PDQ07 One Zone (6) 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 E0C. The core average macroscopic cross sections from these calculations are then processed for input into the NOMAD computer code. These cross-sections, as well as the cycle normalization data (i.e., B0C core average axial burnup distribution, equilibrium iodine and xenon concentrations, 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, thermal-hydraulic feedback, and xenon concentration. The neutron flux calculation is performed first based on initial guesses of fuel and moderator temperatures and xenon 3-1 r-

,n-,

, +., -

+

J concentrations. Then a new set of fuel and moderator temperatures are calculated. Using these new temperatures, another flux calculation is perform %. Once the flux and temperatures have both converged, a new set 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 ccdes provide either ' input data or data manipulation. The PDQ07 One Zone model and the XSEDT(I) code are used to generate core average macroscopic cross sections at different core conditions. The XSFIT(I) and XSEXP(I) codes process these data for use by NOMAD. NULIF(4) 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 (5), and FLAME (7) models supply cycle normalization data.

The FXYZ(2) code provides Fyy(Z) input to NOMAD for FAC analysis.

FDELH(3) and PCEDT(3) perform 1-D/2-D syntisesis 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

3.2 Cross Section Generation The Vepco NOMAD code requires the following two group macroscopic cross sections for the solution of the axial flux and power distributions:

• E D, I,1, Irl' " fl'

• fl, 2'

a2' "Ef2' f2*

y 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 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 E0C.

(The B0C step is not included because there is no xenon present). Using the input flux and concentration files, PDQ only performs the flux-weight'ed macroscopic cross section calculations (i.e., no flux or eigenvalue calculation). The cases contain variations in the fuel and moderator temperatures and the boron and xenon concentrations which should include all core conditions encountered during reactor operation. The range covered for each variable is:

(

l l

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

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.

3-3

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

The variables upon which each macroscopic cross section have been found to be dependent are listed in Table 3-1.

The XSFIT code analyzes the PDQ07 macroscopic cross sections and generates base macroscopic cross sections and polynomial coefficients which express these cross sections in terms cf these variables.

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 which smooths several of the fast group polynomial coefficients 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 B0C and greater than the core average at E0C. The XSEXP codes writes this final set of base cross sections and polynomial coefficients to a data set which is read by NOMAD.

l 3.3 Model Normalization 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 l

unit and cycle.

The B0C 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 l

correspondence between the fueled axial regions in the NOMAD model and the l

axial nodes in the FLAME model. The NOMAD BOC axial power distributions at l

3-4

f HZP and HFP are normalized to the FLAME B0C 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 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 PDQ07 One Zone i

model. The NOMAD model is depleted from B0C to 150 MWD /MTU using the xenon parameters 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 mocel at 150 MWD /MTU:

y (new) =.7(old)

• Il35(PDQ)/ID (NOl@D)

(3.3-1) y

• Xe (PDQ).

)

Xe( Id) + yj(old)

YXe(new) =

y Xe (IO9D)

The NOMAD model is depleted again from B0C to 150 MWD /MTU with the new fission l

yields to verify that the concentrations now agree with the PDQ07 One Zone l

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 I

buckling coefficient searches at each depletion step from 150 MWD /MTV to E0C.

These buckling coefficients are saved in a table which is input to the NOMAD code for all subsequent calculations.

l 3-5 L

The NOMAD model contr01 rod cross sections are normalized by forcing agreement between the NOMAD and PDQ07 Discrete rod bank integral worths.

In the case of rod swap worth calculations, the NOMAD bank worths are normalized to the PDQ07 Discrete bank worths for each bank inserted alone. Otherwise, they are normalized to the PDQ07 worths for the banks inserted in sequence (e.g., D in, 0+C in, D+C+B in., etc.)

E from the PDQ07 " Rod The core average cross secticns Ial' a2, and Ir1 i

bank out" case are subtracted from the same cross sections for the " Rod bank in" case. These values are input to the NOMAD code for that bank, the control rod normalization is set.o 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 nonnalization 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 rod bank.

3.41-D/2-D Synthesis Prior to the executinn of the 1-D/2-D synthesis option in NOMAD, a 2-0 PDQ07 case is run for each of the rodded configurations present in the synthesis case (e.g., ARD, 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 data set is created for FDELH, omitting the axial power sharing values. The job and case ID's for the IFM files are listed in the order that the rodded configurations occur from bottom to top of core. NOMAD reads this input data set and re-writes it with the axial power sharings which it calculates. FDELH subsequently reads this data and performs the 1-D/2-D synthesis:

F (x, y) = P1*Fp1(x, y) + P2*Fp2(x, y) + P3*Fp3(x,y),

(3.4-1) p 3-6 L

where F (x, y) = relative power for fuel in location (x, y) '

p P = axial power sharing from NOMAD for rod configuration n n

pn(x, y) = F (x, y) for rod configuration n.

F p

The PCEDT code then performs a power census edit which provides 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%.

3.5 FAC Analysis Model The Vepco FXYZ code provides NOMAD with the 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 data from the PDQ07 Discrete AH model F (X,Y,2)

FAH(X,Y)

• FCON

• FXEN (3.5-1)

FXY(Z) =

Q P(Z)

RPD(X,Y)

Maximum.

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

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 i

3-7

F

=F

• F CON E

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

= radial xenon re-distribution correction factor = 1.03.

,FXEN If FaH(X,Y) is less than RPD (X,Y), a value of 1.0 is substituted for that ratio. NOM /D reads the Fyy(Z) data from a file where FXYZ stores them.

Usually only data for AR0 and D in rod configurations are necessary for FAC analysis. NOMAD then performs the FAC analysis calculation as previously described in Section 2.9.

3.6 Deep Insertion Control Rod Model The radial buckling distribution must be adjusted to effectively predict the results of an unusual load follow or slow transient case where the control rods are deeply inserted (i.e., D-bank below 170 steps). This adjustment is not necessary for the load follow calculations performed in FAC analysis, since the rods usually arc not very deep. Adjustment of the buckling distribution accounts for the radial flux re-distribution that occurs during l

deep control rod insertion.

Four steps are necessary for determining the buckling coefficients to i

compensate for the rod insertion:

(

1.

Examine the anticipated (if predicting axial power behavior for a possible operational strategy) or actual (if analyzing measured data) control rod and core power history for the case in question and 3-8 i

select several control rod positions, roughly 20 steps apart, that cover the range of rod movement.

(An ARI case is not necessary, because the ARO buckling coefficients are sufficient for this case.)

Then' select core power levels that generally correspond to those rod positions.

l 2.

Use NOMAD to perform a critical boron search at the appropriate cycle burnup with the HFP, AR0 equilibrium xenon distribution for each of l

the rod positions r d corresponding power levels selected above.

3.

Perform a FLAME calculation at the same burnup for each of the above cases with the same rod positions, power levels, and critical boron concentrations.

i 4.

Perform a buckling coefficient search with NOMAD for each of these cases to normalize to FLAME results. Because FLAME is a three dimensional code, it accounts for the radial flux re-distribution.

Therefore, the new radial buckling coefficients obtained by this method also account for that effect. The xenon distribution is frozen at HFP, AR0 equilibrium conditions in both the NOMAD and FLAME calculations. This insures consistent results with both codes.

t f

1 3-9 l

l l

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

Boron (Boron

• Xenon Xenon 2 (Boron

• Section Temp.

Temp.

Conc.

Mod. Temp.)

Xenon)

D X

X X

y I

X X

X X

l r1 I

X X

X X

d vI X

X X

fy er X

X X

fy D

X X

X X

X 2

I X

X X

X X

X X

a2 vI X

X X

X f2 KI X

X X

X X

f2 l

l l

i 3-10

Flame Crew Section R-J1ector Fltma J

Dise i

(

l q

Descriptann g3 Library u

XSEDT Core Average NU IF Cg le Cross Sectsons Normalization Factors Y

if u

Reflector Fxy (Z) vs. Burnup XSFIT Cross Sections f

XSEXP Eo 19 o

Base Cros Sections &

f Polynorstal Coefficients aE Y

R!5 3m u69 ag *-

n

One Zone, y

Model a

o v

e

' Axial Power Axsol Burnup Axtel Xenon Rod Worth Axial Power Rodaal Power 2"

Distr 2bution Distribution Distribution Shepe Shorin9*

Distribution l

I FDELH Synthesized Fan (X,Y) u E@

u Power Census Edit

SECTION 4 - USER INFORMATION 4.1 Input Description NOMAD input is read as a series of numbered and categorized car.;s. 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 tha delta-I control and the criticality search options, the 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.

I l

l 4-1 i

m

010 CARD --- Title (1 line, 80 characters maximum) 020 CARD --- General Parameters VARIABLE VARIABLE NAME TYPE DESCRIPTION 1

NRCNS INTEGER Number of axial regions 2

EPS REAL Eigenvalue convergence limit 3

IWRITE(1)

INTEGER Temp., power, and burnup edit:

i 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 Flux squared / power sharing edit (must =l for 1-D/2-D synthesis) i i

4-2

~

- - +,

-.4.--.-

,_w.

mwr

030 CARD --- Thermal-Hydraulic Data VARIABLE VARI ABLE NAME TYPE DESCRIPTION 1

ITMAX INTEGER Max. no. of thermal iterations 2

TAU REAL Thermal relaxation parameter 3

THCON REAL Thermal convergence criterion 4

TM0 REAL Moderator ref. temperature (O Farenheit) f 5

TF0 REAL Fuel reference temperature (O Rankine) 6 DGEFPD REAL Fuel temperature vs. burnup coefficient (OR/(EFPD*Rel. power))

7 FTF0 REAL Fuel temp. vs relative power coeff. (OR / 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 Total core power level (watts) 12 FLORAT REAL Core flow rate (Ibm / hour) 13 SYSPR REAL System pressure (psia) 14 POWDEN REAL Power density (watts /cc) l l

l l

l 4-3

.,__a,-

.,..--e_.

gn------,_--a

,n--

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

VARIABLE VARIABLE NAME TYPE DESCRIPTION 1

B0 REAL Buckling amplitude-4 2

BMID REAL Buckling curvature coefficient 3

STILT REAL Buckling tilt coefficient 4

BTH REAL Thermal buckling fraction 5

RPDMID REAL Target power at midplane 6

AX0FFT REAL Target axial offset 7

ILOCK INTEGER Buckling coeff. 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 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) i 6

RDBANK(I)

REAL Bank name (8 characters in )

4-4

060 CARD -- Delta-I Control and Criticality Search Parameters VARIABLE VARIABLE NAME TYPE DESCRIPTION 1

IDCNTL INTEGER Delta-I control option.

If delta-I out of allowed band:

-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 (%)

5 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 position followed by boron concentration 3=

Power (%)

4=

HFP inlet enthalpy (Btu /lbm) 10 CRTMAX REAL Maximum value of ICRIT 11 CRTMIN REAL Minimum value of ICRIT i

l 8

4-5

(

1 070 CARD --- Core Average Fixed Parameters (Optional Card)

VARIABLE VARIABLE NAME TYPE DESCRIPTION 1

IFX1 INTEGER Fixed fuel and 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 temperature (OF) 6 TFFX REAL Fuel temperature (OR) 7 EFPDFX REAL Burnup (EFPD) 8 XENFX REAL Xenon conc. (Atoms /bn-cm) 9 TIMEFX REAL Initial clock time (hours) 080 CARD --- Boration/ Dilution Input (Optional Card) l VARIABLE VARIABLE NAME TYPE DESCRIPTION i

l 1

SYSMAS REAL Primary system mass (1bm) 1 2

CBBOR REAL Boration line boron conc.

l (ppm) 3 CBDIL REAL Dilution line boron conc.

(ppm) 4 FLOB0R 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 i

4-6

.=

.I 090 CARD --- FAC Analysis Input (Optional Card) i VARIABLE VARIABLE NAME TYPE DESCRIPTION i

i 1

FQGRID REAL Grid correction factor:

1.056 =

3 case l.025 =

18 case i

I 2

ADJUST REAL FXY power adjustment factor:

North Anna i

~0.3

=

Surry 0.2

=

4 i

3 NMAPS INTEGER Number of FXY(Z) maps input.

t 4

FXYMIN(I)

REAL Minimum FXY(Z) values XY(Z)U

• F ) for each (I = 1, NMAPS)

(

• F E

F map l

5 MPBURN(I)

INTEGER Burnup (MWD /MTU) at which (I=1,NMAPS) each FXY(Z) map is printed 1

i 6

FQLIMX(J)

REAL X-coordinate for Fg limit curve (core height in feet)

I 7

FQLIMY(J)

REAL Y-coordinate for F0 limit (Input variables 6 & 7 in pairs for J=1, 4)g(Z) limit]

curve (F 8

FXYLMX(J)

REAL X-coordinate for FXY limit

(

line (core height in feet) 9 FXYLMY(J)

REAL Y-coordinate for FXY limit (Input variables 8 & 9 in pairs for J=1, 4)Y(Z) limit) line (FX 100 CARD --- Recovery File Options (Optional Card)

VARIABLE VARIABLE NAME TYPE DESCRIPTION 1

DFILE REAL Recovery file flag:

SAVE = Save new recovery file RESTORE = Restore old file L

2 FNAME REAL 8 character file name (Note:

1 space between variable 1 and variable 2) 4-7

500 CARD -- Case Card VARIABLE VARIABLE NAME TYPE DESCRIPTION 1

TIME REAL Depletion time interval (EFPH) 2 PCTPOW REAL Core average power (%) **

3 IRDPOS(l)

INTEGER D-bank position (steps) **

4 IRDPOS(2)

INTEGER C-bank position (steps) **

5 IRDPOS(3)

INTEGER B-bank position (steps) **

6 IRDPOS(4)

INTEGER A-bank position (steps) **

7 IRDPOS(5)

INTEGER SB-bank position (steps) **

8 IRDPOS(6)

INTEGER SA-bank position (steps) **

9 IRDPOS(7)

INTEGER PL-Rods position (steps) **

10 BORON REAL Baron concentration (ppm) **

11 IXEN INTEGER Xenon Option:

-1 = Xenon from previous step 0=

Xenon depletion 1=

No xenon 2=

Equilibrium xenon 12 IOPT INTEGER Case Option:

0=

Static case 1=

Depletion 2=

1st step of rod worth sequence 3=

Criticality search i

4=

lst step of FAC analysis l

5=

Xenon worth calculation l

6=

Buckling coefficient search 7=

Frozen THF 8=

lst step of average l

power distribution l

calculation

-8 = Final step of average power distribution calculation; perform load follow depletion 1

O*If a negative value is input for any of these variables, the value from the Gnd of the previous time step is used.

4-8 l

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 E

E (Bottom reflector fast cross sections) y al rl D

z (Bottom reflector thermal cross 2

a2 sections)

D I

(Top reflector fast cross sections) y al rl.

D I

(Top reflector thermal cross sections) 2 a2 0

O Y

Y (Iodine and xenon parameters) 7 Xe Region height (cm)

B0C Burnup (=0.0)

(Region 1 - bottom reflector)

Region height (cm)

B0C Burnup (=0.0)

(Region 2 - bottom reflector)

P.egion height (cm)

B0C Burnup (=0.0)

(Region 3 - bottom reflector)

Region height (cm)

B0C Burnup (EFPD)

(Region 4 - bottom fuel region)

Region height (cm)

B0C Burnup (EFPD)

(Region (NRCNS-3) - top fuel region)

Region height (cm)

BOC Burnup (=0.0)

(Region (NRCNS-2) - top reflector)

Region height (cm)

BOC Burnup (=0.0)

(Region (NRCNS-1) - top reflector)

Region height (cm)

B0C Burnup (=0.0)

(Region (NRCNS) - top reflector) i 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 mecsages for less severe problems, such as a criticality search not converging. Execution continues after a warning message is printed.

E 4-9

NOMAD returns a condition code of zero for a successful job completion in most cases. Other programmed return codes are:

11 - Power sharing calculated for 1-D/2-D synthesis 333 - Job terminated, recovery file could not be found 444 - Job terminated, thermal-hydraulic feedback did not converge 555 - Job terminated, maximun number of cases exceeded 666 - Job terminated, buckling search did not converge l

777 - Job terminated, cross section file error 838

. 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 :econds i

HFP, xenon depletion, 0.7 seconds criticality search j

HFP, eg. xenon, 3.4 seconds l

criticality search l

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) l 4.4 Output NOMAD offers the user flexibility in its output control. The output options are IWRITE(1) - IWRITE(5) on the 020 card. All five of these options l

4-10

are turned off and on by values of 0 and 1, respectively. All edits are written to the printer except IWRITE(4), which writes to a plot file.

The temperature, power, and burnup edit is a one page edit which includes the k-effective, delta-I, axial offset, number of iterations to reach convergence, and cycle average burnup.

It also prints for each axial region and the core average the values of each of the following parameters:

k-infinity, moderator enthalpy (BTU /lbm), moderator temperature (degrees F),

fuel temperature (degrees R), relative power density (RPD), and fuel burnup (EFPH). This edit is generally the most useful one in 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 denugging 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 average. This edit is required for normalization of the xenon model. The flux squared / power sharing edit gives the fraction of the flux squared and the power which occurs in each axial segment with a different rodded configuration. This edit must i

be on to perform 1-D/2-D synthesis or rod swap worth calculations, and it may l

be useful for other 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 occcurrence contains the results of the final nuclear calculation after all searches have been completed.

t l

4-11

(

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

(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 output to a data set 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 xenon worth). These options also write data to the same plot filr..

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 ta a file. The data includes the case number, time, power, boron, D-bank position, delta-I, peak power, k-effective, and xenon.

If the beration/ dilution calculations are performed, the water processed per step is written instead of the xenon concentration. This option is exercised by assigning a data set to the appropriate unit (see Section 4.5).

J 4-12

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

Unit No.

Function 2

Buckling coefficient table (input) l 3

Cycle / geometry input deck 4

Cross section input 5

Card input 6

Printer and microfiche

~

8 FXY(Z) input i

9 Case summary plot file 10 Plot file for RPD, xenon, rod worth, FAC analysis, xenon worth 11 Buckling coefficient table (output) 12 Microfiche 13 Recovery file 14 Scratch disk space 21 FDELH code input for 1-D/2-D synthesis.

Data is written to unit no. 11 only when a buckling coefficient search is performed.

4-13

SECTION 5 - RESULTS 5.1 Introduction The purpose of this section is to demonstrate the predictive capability of the Vepco NOMAD model for calculations 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 COBRAUII; 3) axial power distribution comparisons to measured data from Surry and North Anna; 4) differential and integral control rod worth comparisons to measured date 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.

f Figures 5-1 through 5-6 compare NOMAD xenon worths after startup, orderly O2) shutdown, and trip to results obtained with XETRN

, Vepco's zero-dimensional xenon transient code. Note that XETRN assumes the xenon 5-1 j

l

~

worth is a linear function of the xenon concentration, whereas NOMAD calculates the xenon worth directly from the eigenvalues.

5.3 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 120% 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 moderatur 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 B0C, 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 conditions.

However, NOMAD does not represent the spacer grids in order to increase calculation efficiency. The accuracy which is compromised is insignificant.

l l

l l

l 5-2 wY

.+

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 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 a 1-D/2-D synthesis technique.

NOMAD performed a critical boron search with the reference 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 the reference bank predicted by NOMAD for each bank fully insertea is compared to measurement in Table 5-4.

l l

5.6 Load Follow Maneuver 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 l

data consists of hourly delta-I readings and two critical boron measurements from a 70% load reduction test performed near the end of North Anna Unit 1 l

Cycle 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.

(

1 i

5-3

Two additional s9.ts 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 PFP, equilibrium conditions (delta-I is virtually 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 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.

l l

All three of these cases were simulated with NOMAD using the deep control rod insertion model described in Section 3.6.

Buckling coefficient searches to normalize to FLAME were performed at several different conditions for each The final column of Tables 5-5 through 5-7 lists the normalization case.

conditions for the buckling coefficients which were used at each step of the i

calculation. For example, in Table 5-5, the buckling coefficients normalized at 100% power and D-bank at 228 steps are used for the first three steps.

The remainder of the calculation is performed with the buckling coefficients normalized at 30% power and D-bank at 139 steps.

l l

l 5-4

~

The necessity of this model can be seen in Table 5-8, which compares FLAME to NOMAD results obtained without any compensation for deeo rod insertion.

Notice the difference between the axial offset results when the rods are deep in the core. These parallel calculations are a simplified simulation of the history listed in Table 5-7.

The time 0.0 hours0 days <br />0 hours <br />0 weeks <br />0 months <br /> in Table 5-8 corresponds approximately to 22.63 hours7.291667e-4 days <br />0.0175 hours <br />1.041667e-4 weeks <br />2.39715e-5 months <br /> on 4/30/82 in Table 5-7.

5.7 FAC Analysis Three case and eighteen case FAC analyses were performed with the Vepco NOMAD model for North Anna 1 Cycle 4 and North Anna 2 Cycle 2.

The cases were performed for the following conditions:

BOL Base Load Depletion 100%-70%-100%

(150 MWD /MTU) 100%-50%-100%

100%-30%-100%

85% E0L Base Load Depletion 100%-70%-100%

100%-50%-100%

100%-30%-100%

85% E0L Losd Follow Depletion 100%-70%-100%

100%-50%-100%

100%-30%-100%

These nine cases were performed twice, with IDCNTL set to +1 and -1.

The three case analyses consisted of the 1000-50%-100% cases with IDCNTL= -1.

[

The Vepco NOMAD model results were found to be consistent with the 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 (Z) plots in Figures 5-40 and 5-42 contain an uncertainty q

factor of 10.9%.

5-5 j

TABLE 5-1 REACTIVITY COEFFICIENTS COMPARISON Differential Boron Worth, BOC HZP (pcm/ ppm)

Unit / Cycle NOMAD PDQ07 Discrete Measured

% Differencel 9.10

-8.88 3.04 NlC2

-9.15 4.57 8.08

-8.54 NlC3

-8.15 6.67 8.04

-8.25 NIC4

-7.70 8.91

-8.46 6.03 N2C2

-8.97 5.81 8.31

-8.78 SIC 6

-8.27 0.12 8.44

-8.44 SlC7

-8.43 Differential Boron Worth, E0C HFP (pcm/ ppm)

Unit / Cycle NOMAD PDQ07 Discrete

% Difference 2 3.92 9.43 NIC2

-9.06 8.47

-3.54 NIC3

-8.17 8.35 8.62 N1C4

-7.90 9.40 5.21 N2C2

-8.91 9.31 5.37 SlC6

-8.81 9.16 2.51 SlC7

-8.93 Isothermal Temperature Coefficient BOC, HZP (pcm/0F)

Unit / Cycle NOMAD PDQ07 One Zone Measured Difference 3 2.71 3.87

-2.36 NIC2

-5.07 3.40

-4.36 0.37 NlC3

-3.99 3.52

-4.92 0.02 NIC4

-4.90 3.02 3.27

-2.27 N2C2

-5.29 1.96 SlC6

-4.28 3.79

-2.32 0.64 5.68

-5.85 SlC7

-6.49 L

l % Difference = (NOMAD - Measured) / Measured x 100 2 % Difference = (NOMAD - PDQ07)/PDQ07 x 100 3 Difference = NOMAD - Measured 5-6 yw-

-+

g--m,

-,--5

- ~-,

-%y

--y, p

vr

,..,,w.--w-

-,,,y-

--eww-,-s-.-

-n

.--y or

TABLE 5-2 COMPARISON OF NOMAD AND COBRA MODERATOR ENTHALPY AND TEMPERATURE DISTRIBUTIONS Position Enthalpy (BTU /lbm)

Moderator Temperature (OF)

(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 44 573.3 573.4 570.9 570.3 576.5 576.6 573.3 572.6 52 579.6 579.7 575.7 575.0 56 582.8 582.9 578.1 577.3 60 586.0 586.1 580.4 579.7 64 589.2 589.3 582.8 582.1 68 592.4 592.5 585.2 584.5 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 96 615.5 615.6 601.5 601.3 100 618.9 619.0 603.8 603.7 104 622.3 622.3 606.1 606.4 108 625.6 625.7 608.4 608.3 112 629.1 629.1 610.7 610.6 116 632.5 632.5 612.9 612.9 120 635.8 635.9 615.2 615.1 124 639.1 639.2 617.3 617.4 128 642.4 642.4 61 9.4 619.5 132 645.3 645.4 621.3 621.4 136 648.0 648.0 623.0 623.0 140 650.1 650.1 624.4 624.3 144 651.6 651.5 625.3 625.2 5-7

~

TABLE 5-3 R0D 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 D*

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 0

1228 1234

-0.49 C

819 815 0.49 A

538 551

-2.36 SB 1018 1013 0.49 SA 1093 1137

-3.87

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

5-8

1-f TABLE 5-4 R0D SWAP COMPARISON, PART 2 Reference Bank Critical Position (Steps)

North Anna Unit 1 Cycle 3 Bank NOMAD Measured Difference D

143 143 0

C 117 103 14 A

97 97 0

SB 143 119 24 SA 158 170 12 i

North Anna Unit 1 Cycle 4 D*

N/A N/A N/A C

154 163

-9 A

114 122

-8 i

SB 182 190

-8 SA 186 201

-15 i

North Anna Unit 2 Cycle 2 D

186 195

-9 C

171 168 3

A 167 175

-8 SB 166 155 11 SA 1 81 189

-8 l

Surry Unit 1 Cycle 6 i

D 179 175 4

C 123 110 13 L

A 93 83 10 SB 154 138 16 SA 166 157 9

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

i 3

5-9

~

,m.m.

-._.,y.

,,,,,-...,__.,.,,.____.-,,____._,,,___m

.._,,_.,___.._c.

.--mm....

TABLE 5-5 NlC2 70% LOAD REDUCTION TEST POWER AND D-BANK HISTORY Time Power D-bank Buckling Normalization (Hours)

(%)

(steps)

Power / D-bank 00.00 98.8 228 100% / 228 01.00 82.9 190 02.00 56.2 186 03.00 32.8 150 30% / 139 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 13.00 30.2 140 14.00 29.9 136 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

~

5-10

TABLE 5-6 N1C3 SHUTDOWN / RETURN TO POWER CASE 1 POWER AND D-BANK HISTORY Time Power D-bank Buckling Normalization (Hours)

(%)

(steps)

Power / D-bank

-23.00 100.9 215 100% / 228

-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

-8.00 0.0 0

-7.00 0.0 0

1

-6.00 0.2 47 2% /

95

-5.00 1.2 156 5% / 182

-4.00 1.9 179

-3.00 0.0 0

i

-2.00 0.2 185 l

-1.00 4.9 193 0.0 17.7 197 1.00 23.5 186 l

2.00 27.8 160 30% / 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 l

9.00 29.2 151 l

10.00 29.4 143 30% / 139 l

11.00 29.4 143 l

12.00 29.4 142 l

5-11 4m

,,,yy

__,.,m,_.%.

_,y,.,,..

y.,__,,,--,,,.,,._.-__-r-.-~y,.,

f g_

TABLE 5-6 (Continued) 13.00 30.9 141 14.00 45.7 141 15.00 48.9 144 16.00 49.0 159 48% / 175 17.00 48.7 170 18.00 48.4 178 19.00 48.0 181 20.00 47.5 182 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 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 69.9 181 100% / 228 40.00 73.4 183 41.00 73.2 183 42.00 76.9 190 43.00 87.7 205 44.00 97.0 209 45.00 99.6 211 46.00 99.7 211 47.06 100.2 211 48.00 99.6 211 49.00 99.8 211 50.00 100.0 211 51.00 100.1 211 52.00 99.8 211 53.00 100.0 211 54.00 100.3 211 5-12

i TABLE 5-6 (Continued) 55.00 100.2 211 56.00 100.2 211 57.00 100.2 211 58.00 0.0 0

59.00 0.0 0

60.00 0.0 0

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l l

l i

5-13 j

l l

i:

e TABLE 5-7 NIC3 SHUTDOWN / RETURN TO POWER CASE 2 POWER AND D-BANK HISTORY Date Time Power D-bank Buckling Normalization (Hours)

J%)

(steps )

Power / D-bank 43082 16.20 100.3 218 100% / 228 4 30 82 18.60 99.7 218 4 30 82 18.85 99.8 218 43082 20.72 100.2 218 43082 21.50 95.2 209 i

43082 21.78 92.1 206 43082 22.06 88.3 200 43082 22.35 83.6 190

- 43082-22.63 75.8 180 75% / 182 43082 23.15 66.0 171 43082 23.70 58.2 158 60% / 160 5 1 82 0.50 44.0 127 30% / 117 5 1 82 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 60% / 160 5 1 82 4.70 2.0 162 5 1 82 5.77 2.1 173 5 1 82 6.78 2.3 177 5 1 82 7.81 2.5 174 5 1 82 8.84 2.2 169 5 1 82 9.88 0.0 0

100% / 228 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% /

81 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 i

5 1 82 17.58 1.8 61 5 1 82 17.85 1.8 59 5-14 i

i r-

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TABLE 5-7 (Continuea) 5 1 82 18.95 1.6 59 5 1 82 19.95 2.1 59 5 1 82 21.00 1.8 45 2% /

45 5 1 82 22.07 1.8 45 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 2 82 2.02 2.3 45 5 2 82 3.07 2.2 45 5 2 82 3.95 2.4 45 l

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 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 30% / 117 5 2 82 15.19 51 6 155 60% / 160 5 2 82 16.21 64.8 174 75% / 182 l

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 2 0.21 73.9 193 100% / 228 5 2 82 21.24 83.0 201 5 2 82 22.24 91.1 208 l

5 2 82 23.24 96.1 214 l

5 2 82 23.87 98.7 214 l

I 1

1 5-15

. l

TABLE 5-8

(

i COMPARIS0N OF FLAME AND UNCORRECTED NOMAD RESULTS FOR NlC3 SHUTDOWN / RETURN TO POWER CASE 2 Time Power D-bank Boron Conc.

Axial Offset (%)

(Hours)

(%)

(steps )

(ppm)

FLAME NOMAD 0.00 75.0 182 100

-5.60

-5.64 i

3.00 30.0 110 120 2.09

-14.89 5.35 2.5 167 125 53.18 32.68 12.39 0.0 0

63 78.21 73.77 15.71 1.5 81 100 70.68 49.42 20.36 2.2 45 200 57.35 27.63 1

34.67 25.0 67 300 20.91

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40.72 65.0 175 320

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SUMMARY

AND CONCLUSIONS The Vepco NOMAD code and model are operational at Vepco for the purpose of j

performing one-dimensional reactor physics analyses and supporting the evaluation of core performance.

The model consists of ROMAD 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 rod worths, and load follow maneuvers as well as perform Final Acceptance Criteria (FAC)

Analysis.

l Verification of and improvements to the Vepco NOMAD code and model will i

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 Power Stations.

i l

l l

l l

6-1

i SECTION 7 - REFERENCES 1.

S. M. Bowman, "VEPC0 1-D Code Development: Final Report", NFE Technical Report No. 250, March, 1983 (Virginia Electric and Power Co.).

2.

D. A. Daniels, "Fxy(Z) Synthesis Methodology and Computer Code", NFE Technical Report No. 180, January, 1981 (Virginia Electric and Power 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 P!bl9, June, 1979 (Virginia and Electric Power Co.).

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

11. F. W. Sliz, "VEPC0 Reactor Core Thermal-Hydraulics Analysis Using the COBRA IIIc/MIT Computer Code", VEP-FRD-33, August, 1979.

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

7-1

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