ML20154S595
| ML20154S595 | |
| Person / Time | |
|---|---|
| Site: | Oyster Creek |
| Issue date: | 01/31/1986 |
| From: | Furia R GENERAL PUBLIC UTILITIES CORP. |
| To: | |
| Shared Package | |
| ML20154S594 | List: |
| References | |
| TR-021, TR-021-R00, TR-21, TR-21-R, NUDOCS 8604020097 | |
| Download: ML20154S595 (105) | |
Text
{{#Wiki_filter:_ _ _ _ _ _ _ _ _ _ _ ____ 1 TR-021 l I TITLE Methods for the Analysis of Boiling Water Reactors Steady State Physics TR 021 (Rev. 0) Project No: 5400-40716 R.V. Furia Author Date January 31, 1986 Approval S~/N~$8
' Nuclear Analysis & Fuels -
~
Date Director I l I I I GPU Nuclear I 100 Interpace Parkway Parsippany, New Jersey 07054
- B604020097 860325 I PDR p
ADOCK 05000219 PDR
I Abstract l l t This report describes the three-dimensional nodal methods used by-GPUN for steady state BWR core calculations. The methods employ an integrated neu-tronic (NODE-B) and thermal-hydraulic (THERM-B) models for detailed core analysis. The methods have been verified against operating data from Oyster Creek and Hatch I cycle 1. I I I i i I . I I I I I I 5 -2 tI
I Acknowledgment i I The author would like to express his appreciation to those who have contri-buted to this report, especially M.D. Beg, E.R. Bujtas, J.D. Dougher H. Fu and C.B. Mehta. I I I
- I t
i I I i i i 1 I .
I TABLE OF CONTENTS T Section Page l
- 1.
1.0 INTRODUCTION
7
~
2.0 CORE DESCRIPTION AND MODELING 8 3.0 TECHNICAL DESCRIPTION 11 3.1 Overview 11 3.2 Neutronic Model- 14 3.3 Thermal Hydraulic Model 20 3.4 Instrumentation Model 32 l 3.5 Haling Option 33 i 4.0 VERIFICATION 34 4.1 Comparison with Data Measured at Oyster Creek 34 1 4.1.1 Cold Criticals 34 4.1.2 Hot Reactivity Calculation 35 4.1.3 Power Distribution Comparison 35 4.2 Comparison with Data Measured at Hatch 1 68 4.2.1 Hot Reactivity Calculation 68 I 4.2.2 Power Distribution Comparison 69 4.2.3 Gamma Scan Comparison 69 5.0
SUMMARY
AND CONCLUSIONS 99
6.0 REFERENCES
101 I APPENDIX A 103 i Total 104 l 1e' I
I LIS". OF TABLES
.I Table Title . Page 1 4.1 Shutdown Margin Criticals for Oyster Creek Cycle 8 37 4.2 Shutdown Margin Criticals for Oyster Creek Cycle 9 38 4.3 Shutdown Margin Criticals for Oyster Creek Cycle 10 39 1 4.4 Key Information for Oyster Creek Cycle 8 Statepoints 40 4.5 Key Information for Oyster Creek Cycle 9 Statepoints 41 4.6 Core Reactivity and Power Distribution Comparison for Cycle 8 42 4.7 Core Reactivity and Power Distribution Comparison for Cycle 9 43 4.8 Key Information for Hatch 1 Cycle 1 Statepoints 71 4.9 Core Reactivity and Power Distribution Comparison for Hatch 1 Cycle 1 72 4.10 Summary of Hatch Gamma Scan Power Distribution Comparison 73 4.11 Hatch Gamma Scan Axial Average Residual and Standard Deviation 74
. I I I I 8 s ! I
I LIST OF FIGl;RES F_igurg i Title Page I s 2.1 Oyster Creek- Core Map 10 3.1 Flow Diagram of NODE-B 13 I 4.1-4.24 Comparison of Core Average Axial TIP Reading for the O.C. Cycle 8 and 9 Statepoints 44 4.25-4.41 Comparison of Core Average Axial TIP Reading for the Hatch 1 Cycle 1 Statepoints 75 4.42 106 Bundle Average Axial Ba-140 Distribution 92 4.43-4.47 Octant Normalized Axial Ba-140 Distribution for l l I 4.48 Fuel Assembiies Relative Bundle Integrated Ba-140 Distribution 93 98 8 i . I i 1 I I I I ' l 8
I I l.0 INTRODUCTION This report describes the three-dimensional co re simulation method in use at GPUN for its Oyster Creek Nuclear Generating St.ition. The method utilizes a one group neutronic model integrated with a thermal-hydraulic model. The integrated model was developed with the Electric Power Re-search Institute (EPRI) Power Shape Monitoring System (PSMS) at Oyster Creek. It is derived from the EPRI NODE-B and EPRI-THERM-B com-puter programs which are part of the EPRI Advanced Recycle Methodology Program'*' (ARMP) code package. A brief description of the Oyster Creek core is provided in Section 2.0 and the code methodology is given I in Section 3.0. The integrated code was extensively tested and verified under the PSMS project while undergoing significant improvements in the process. I The NODE-B/ THERM-B Code (hereafter referred to as NODE-B) was taken f rom the on-line PSMS computer and converted for use by GPUN on its IBM computer for of f-line core analysis. This enables the off-line analy-sis to correspond to the on-line PSMS analysis which is used to monitor
., core thermal limits. It also enables the performance of the off-line-code to be continually evaluated through the performance of the on-line code.
I The off-line NODE-B code is intended for use in fuel management studies and reload core analysis. The code calculates core exposure and core power distribution based on actual or projected core operating data. NODE-B is used in the development of refueling patterns, target end of cycle exposure and power distribution and target control rod patterns. I
The code calculates cold shutdown margin and hot excess reactivity. It is also used to analyze transients which can be simulated with steady I state nethods such as the fuel bundle mislocation and control rod with-drawal er ror. These applications are justified by the verification work I that has been perf ormed. l l The adequacy of NODE-B as a three-dimensional reactor simulator has al-ready been established by the performance of the PSMS. Additional verification work has been performed at GPUN to demonstrate the accuracy of the off-line NODE-B model and GPUN's capability to model reactor cores. The verification includes both cold and hot operating conditions a from Oyster Creek Cycles 8 and 9 and hot operating conditions from Hatch 1 Cycle 1. The verifications were performed against cold criticals, TIP measurerrents and gamma scan data. The results of GPUN's verification , I work is presented in Section 4.0 and establishes a basis of confidence I in using NODE-B for core analysis. 2.0 CORE DESCRIPTION AND MODELING Oyster Creek is a 560 bundle BWR-2 with a rated thermal power of 1930 MW. The core is controlled by 137 cruciform control rods and has incore instruments at 31 radial locations for monitoring power operation. At each radial location are four detectors at fixed axial locations and a traversing incore probe (TIP) (Figure 2-l). The core is divided into two hydraulic zones by orifices at the inlet of each assembly. The outer zone contains all those assemblies with one or more sides on the core e periphery while the inner zone consists of the remainder of the assem-l blies. The outer zone has a smaller orifice and a reduced core flow relative to the core average flow. V I_ I
I The reactor core is represented in the NODE-B model by a three di-mensional mesh of cuoic nodes, one node for each bundle in the hori- , zontal plane and 24 axially nodes. The model can handle multiple fuel designs as well as axial variations in the fuel lattice. The control rod pattern is input to the code explicitly, but the code modeling l homogenizes each node and treats the nodes as of'her controlled or uncontrolled. The instrument locations are identified and instrument reading can be predicted. 8 The Hatch I core, which was analyzed for verification purposes, is also a 560 bundle core with 137 control rods. It has a higher power density with a rated thermal power of 2436 MW. There are the same number of power range instruments, but the locations differ from the Oyster Creek layout. The model representation of the core was the same as for Oyster Creek. I I I I I l 1 I Figure 2-1 OYSTER CREEK CORE MAP I l=1 52 ll
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'3.0 TECHNICAL DESCRIPTION 3.1 Overview .
The three dimens'ional simulator code, NODE-B, is a coupled three dimensional neutronic and thermal hydraulic model which is able to predict reactivity, power and coolant-void distribution, and con-trol rod positions throughout the core lifetime. The program uses iterative solution techniques to solve for the interaction between power, coolant flow and voids, fuel temperature and xenon dis-tributions. The complete calculation consists of two levels of iterations, source and coolant voids. I The source iteration in NODE-B treats reflection at the surface of the core with an albedo and employs transport kernels (which track neutrons for a distance of only one node) to represent the coup-ling between nodes. The neutron source at each node is calculated ! as a function of the infinite multiplication factor, km, and the transport kernel. The latter is a simple f unction of the migra-tion area, M*, and the mesh spacing. The migration area is calculated at each node based on a fit to the moderator density. The infinite multiplication factor is calculated at each node including the effects of control rods, local moderator density, fuel exposure, fuel temperature and xenon concentration. The core
- effective multiplication factor is calculated on the basis of a neutron balance summed over the entire core in each iteration.
The void calculation consists of the determination of the average steam quality at each node based on inlet velocity, inlet enthalpy I
l f 5 , and power integrated from the bottom of the channel to the node of interest. The flow of the calculation is to solve the source equation for an initial distribution of coolant voids, xenon, fuel exposure and t Doppler reactivity. The power distribution is then calculated and a new coolant void, Doppler and xenon distributions are deter-mined. This sequence is repeated until the power and coolant distributions converge to values within input criteria. In burnup Iy calculations, t.he fuel exposure distribution. is extended f rom the beginning to the end of the step using the converged power dis-tribution. Figure 3-1 shows a flow chart of the calculational sequence. The basic inputs to the code are the fuel element data (type, location and dimensions), core flow and power level, control rod position, fuel ele nent nuclear properties, and thermal-hydraulics characteristics. Nuclear properties for each fuel type are input as fits of M* vs. relative water density, k= vs. fuel expo-sure, fuel-temperature, relative water density and xenon, and fits of v2r and c{r vs. exposure weighted voids. Flow charac-Ii teristics are input as hydraulic constants for each fuel type in terms of dimensions and form loss coefficients. Feedwater flow and temperature are input for the determination of the core inlet subcooling. I Is 5
I i Figure 3-1. NODE-B FLOW CHART
~ r I
initialization l Y - Therm-B Calculate Moderator Density, Calculate Core b k co, M 2, Reactivity Components, I Flow Distribution 1 i.e., Doppler, Xenon, Exposure Y I I Power To Source Conversion l l > Compute S w y a. 8 g V " a I -8 -c No Source N b g x Converged N y Yes - Source to Power Conversion
, 2 No oderator
, Density 7
,8 ,Yes Compute incore ig Sensor Readings 3 i ! , Update Ex No hEk Yes E s , - s pose ,ure m, 9 e g -. Exit I A more detailed discussion of the PSMS NODE-B is provided in Re f e rence 1 including a description of therfits used for km. The following discussions are taken, in part, from Reference 1. 3.2 Neutronic Model The neutronic model of NODE-B uses a modified one group theory. The neutronic source, which is proportional to power, is calcu-lated at each node. The source S at node m is: S. = k./A E SnWn. 1 - k./A [1 -(6 - a.) W n] I where: n = index of neighboring nodes A = eigenvalue Wn. = probability of a neutron born in node n being absorbed in node m
- c. = leakage factor (albedo) for node m I k. = k-infinity for node m i
The leakage factor is zero for internal nodes and a linear func-tion of voids up the height of the bundles on the core edge. I . a = a. [1 + 0.95 (v-0.4)] m 5 where / is 1 or 2 (for the number of faces on the core edge) and v is the local void fraction. Leakage factors are also provided for T 8
' the top and bottuin of the core, a. and a. respectively.
I L
I The neutronic kernel, the probability of a neutron leaking f rom one node to another, is given by: . I E l 2 2 Wo = [(1-g) M, /2r.n) + g (M3/r .n)]//km I where M* is the migration area, and r.n is the distance be tween the center of nodes. The weighting coefficient or mixing factor, g, takes on the value of g, in the vertical direction and ga in the horizontal direction. I I 9 T The va lue s f o r a. , a. , a. , g , a nd g n are referred to as i normalization parameters and are determined empirically from plant operating data. The PSMS has an optimization routine to determine these values by minimizing the residuals between measured and predicted TIPS. A fixed set of parameters were obtained for Oyster Creek using cycle 8 data and have been used for cycle 9. A i new set of optimized parameters can be generated if model per-lh i M formance warrants it. lE j The eigenvalue,1, is re-evaluated af ter each iteration based on a neutron balance summed over the entire core by i A = [ S. - [ S. W.n (n. - a. )
- m m 1 Sm m k.
j where n. represents the number of external nodes adjacent to j "" Node m. The eigenvalue is used for convergence of the source only il W !h
I 4 the core k-ef fective in'N0DE-B is calculated by the more commonly used definition I S. k re = m I 1 S. + 2 S. W n (n.-a ) m k. m The value of k. is determined for each node ijk as follows: I O . . .
- k. = km (1 - ak/k. )ao r* (1 - ak/k.)x.* (1 - ak/k.)su A base value of k-infinity, k , is determined at average-power Doppler, no Xenon and zero exposure f or each f uel type. The base I value is determined as a function of relative moderator density, U, fcr rodded and unrodded conditions. U is defined as the moderator density relative to saturated water at the operating pressure. The base value of k. also includes the exposure dependence of control rod worth. The base value of k-infinity is then adjusted for Doppler, xenon and burnup.
I Doppler Reactivity The Doppler reactivity effect is calculated at each node ijk by , (akS) = ao fPijk*(Pth/ Prated)*(Tro.i - T..a) + T...-fTro.i I :jk _j yUn jw ~ l and ak=/k=
=
I a0 fTro.i -fT... I 5
l i I l l The ak=/km term is the relative change in k* due to - f uel hea ting j from the core average coolant tempe ra tu re ( Tm o.. ) to the core
,- t average f uel temperature (Tr o.1 ), and represents the core average
- Doppler defect. Tro,i must be consis tent with the core full power level (Pr. ..). The incremental fuel temperature (Trm.: - Tmoa) of each node is assumed to be proportional to the power in that node. The core incremental fuel temperature is then multiplied by Pijw, the relative power in the node ijk, to give the node average valae of the UOz temperature. The Pin /Pr. .a ratio accounts for the core power level relative to f ull power.
Xenon Reactivity Xenon effects in NODE-B are treated by computing the power in watts per cm', the ef fective thermal neutron flux, the iodine number density, the xenon number density, the xenon absorption cross section, and then computing (ak/k)x. for each node ijk. I The xenon concentration in each node is converted to changes in nodal k='s by: I (ak/k)ijk = 1 - 1/(1 + Nx, o$' k=no ..) ijk Q' i and Nx. is calculated internally using the thermal flux and power at each node. The xenon microscope cross section, oI*, is fitted as a function of U. I I _ 17 _ 8
I Exposure Reactivity The exposure reactivity ef fects are determined by computing the (ak/k)su for each node ijk. The (ak/k)su from zero ex-posure is obtained from fit of reactivity versus exposure and exposure weighted voids. I The nodal expo.sure is computed by I Ei3w (TS) = Pi3w
- aE(TS)
- WT + Eijn (TS-1) where Ei3w (TS) = nodal exposure at end of time step (TS) in GWD/MT E i3w (TS-1) = nodal exposure at the end of the previous
( time step ; Pi3w = nodal power at beginning of time step WT = a constant to account for differences in uranium weight between fuel designs AE (TS) = core average exposure length for the time step in CWD/MT The exposure weighted voids are computed by I Vi jw (TS) = Vijw (TS-1) + Pijw*aE(TS)*WT*[Uijw + CR (6 +1)] I I E g . 5
I where V ja (IS) i
= exposure weighted void at end of time step a for node ijk V 3= (TS-1) = exposure weighted voids at end of previous time step Uijw = relative moderator density at node ijk CR = a constant used to introduce control rod history effects 6 = 2f - 1 f = control rod fraction at node ijk Conversion of Source Distribution to Power Distribution The nodal burnup dependence of the macroscopic fission cross sec-tion, vEr, and the power source macroscopic cross section, cEr, is accounted for by fuel type. These macroscopic cross sections are input for each fuel type as one-group effective values (Westcott formulation). For two neutron groups:
, I I cEr = rEri &i + rE,2 4: ,and
$2 I
vEr = veri 4i + vErz $2 I
$2 where $. is the first energy group flux; and
$2 is the second energy group flux.
The group cross sections and fluxes are obtained as assembly averaged values f rom PDQ or CPM calculations. rIt is used to l E determine the thermal neutron flux for each node from the nodal l V l I l
I value of watts per em' for calculation of the iodine and xenon number densities. vEs and KEr are used for the internal conversion of nodal source to nodal pawer and for the utilization of the nodal power in the moderator density loop where kn is calculated. I The formulation used in N0DE-B for converting source to power (or vice-versa) uses the relationships i S ~ vEr, and P ~ <Ir, where: I vEr and KEr are obtained as defined above; and, thus P=S*5. I vEr_ i 3.3 Thermal Hydraulic Model i, The PSMS thermal hydraulic calculations are based on the THERM-B model, where the inlet flow distribution, void profile, and core inlet subcooling are computed. The core thermal power, feedwater flow, feedwater temperature, core pressure and core flow are the basic inputs to the computations. The core inlet subcooling is derived by a heat balance in the downcomer and the lower plenum region of the vessel. The channel flow distribution is obtained on an iterative basis by changing the coolant velocity to each fuel channel until it yields a pressure drop that corresponds to I 8
l the pumphead requirement within a specified tolerance. When a l
. flow distribution is obtained for all of the channels, the indi-vidual flow to each channel is summed and compared to the total required flow. If the flow is within a specified tolerance, the problem is converged. If it is not within the specified toler-ance, the pumphead is adjusted to reduce the error between the computed total flow and the flow specified by the input, and the entire iterative procedure is repeated.
A newly developed quality-to-void correlation with special treatment of the subcooled region has been implemented in the PS>fS . This mechanistic model has been reduced to an approximate formulation that in steady-state cases has been shown to be in good agreement with the original model. E - Flow Distribution and Pressure Drop For a specified total core flow rate, the flow rate distribution is determined by equalizing the pressure drop across each channel. The equation used to calculate the fuel assembly pressure drop in a BWR is I 2 aP = V in * [foL. + RfoLe + 2r + K ], 2ge De De where Vin = liquid coolant velocity in, ft/sec ge = gravitational constant
- f. = friction factor E I
I L. = non-boiling length, ft Le = bdiling length, ft , s De = equivalent diameter, ft I R =. ratio of the two phase friction loss to the single phase friction loss r = the acceleration multiplier K = form loss coefficient for fuel assembly entrance, exit, and intermediate spacers I Total flow through the individual channels is' calculated as a part of the NODE-B program. The input required for this calculation is the fuel assembly length, flow area, equivalent diameter, orifice loss coefficient, and intermediate spacer loss coefficient. A single velocity head loss is used for the fuel assembly loss co-efficient to the upper plenum. The form loss coefficients are , based on single-phase flow and are adjusted within the code for two-phase flow effects. The above equation treats friction loss for boiling and non-boiling regions. It also considers the losses resulting from the acceleration of the coolant due to two-phase j flow. I The velocity used in the above equation is the inlet velocity to the fuel assembly based upon the flow area within the fuel assembly. I I f I e . I
I i The f rictiori f actor for single-phase flow is determined f ro:n the 1 i following correlation, . 5
- f. = 0.19 (Nn.)- , where Nn. = Reynolds Number.
This formula is a curve fit to the Fanning friction factor curve given in Reference 5. The Reynolcs number in the above correlation is a dimensionless parameter which is a measure of flow'and turbulence in a flow I channel. The definition of the Reynold's number is lI Nn. = D. V p , 'I where: De = equivalent diameter, ft; i V = liquid coolant velocity, ft/sec; p = liquii coolant density, lbs/ft'; and I p liquid viscosity, Ib/(sec-ft).
=
Subcooling Equations I i The subcooling is calculated in NODE-B by performing a heat balance in the downcomer and lower plenum regions of the BWR vessel. The subcooling is defined as H.c = (H.. , peor.)-(H i n),
.I I
I
I where: H,e = subcooling, ETU/lb; H,. , peor. = saturated linuid enthalpy at. core average . pressure, BTU /lb; and Hni = core inlet coolant enthalpy, BTU /lb. I The following heat balance is made to determine the core inlet coolant enthalpy. Han = [(WT - WST - WCU)HF + WCU*HG + WFW*HFW
+ HRD*WRD + QPUMP - QLOSS - QCL]
Han = Core inlet coolant enthalpy, BTU /lb; WT = Total core flow, lbs/hr; WST = Steam flow leaving reactor vessel, lbs/hr; WCU = Steam carryunder in recirculation flow entering, downcomer, lbs/hr; WFW = Feedwater flow, lbs/hr; QPUMP = Energy from recirculation pumps, BTU /hr; QLOSS = Heat loss f rom reactor vessel, BTU /hr; j HF = Enthalpy of saturated liquid entering downcomer I (evaluate at dome pressure), BTU /lb, l
)
HG = Saturated steam enthalpy of carryunder, BTU /lb; HFV = Feedwater flow enthalpy, BTU /lb; HRD = Control rod drive flow enthalpy, BTU /lb; WRD = Control rod drive flow, lbs/hr; and QCL = Energy loss to the cleanup system, BTU /hr. s I 1 I l l l
I The flows (WT,WFW, and WRD) and QLOSS are input to NODE-B. The steam flow is assumed to be eq,ual to (WFW + WRD). The saturated liquid and steam enthalpies are evaluated based'on the dome and core pressure which are input to the code. The enthalples for the i feedwater flow and control rod drive flow are evaluated based on l lg the inlet coolant temperatures. The energy from the recirculation l l 3 pumps is determined f rom the power drawn by each motor and the j efficiency of the pumps; these values are input to the code. The l steam carryunder flow is defined as a fraction of the total core i g W flow. l I Boiling Effect on Pressure Drop The equation solved to determine the non-boiling length in the l fuel channel is 1 I Lo l Ain
- 3600
- V n
- pin i (H... - Hin) = [ q(x)*p*dx, where:
H... = Saturated liquid enthalpy, BTU /lb; Hin = Inlet coolant enthalpy, BTU /lb; I pio = Inlet coolant density, Ib/ft'; Van = Inlet coalant velocity, ft/sec; q(x) = Heat flux as a function of axial location, x, within the fuel assembly BTU /hr-ft*; P = Perimeter of the heated surface, ft; Lo = Non-boiling length; and Ain = Fuel bundle flow area, ft'. I .. I
iI 1 , The boiling length Le is determined from the total length L and
~
the non-boiling length by I Le = L - L.. I l The ratio of the two-phase friction loss to singt, phase friction loss, R, is obtained from the Lottes-Flinn correlation I R = f two-phase = i*(1 + 1 )
- f. 1-a.
- a. = the void fraction at the end of the fuel channel.
lI The acceleration multiplier, r, used is the Martinelli-Nelson relationship derived for two-phase flow assuming complete sepa-ration of the phases. This relationship is given as l5 r = (1 - x.)*/(1 - a.) + x gi - 1,
- a. p.
where:
- x. = Channel exit quality;
- a. = Channel exit void friction; pt = Liquid phase density, Ibs/ft'; and
- p. = Steam phase density, lbs/ft'.
I !I E I
I The loss coefficient K is the summation of all of the form losses along the fuel assembly. The loss coefficient includes the fol-lowing: I
- Orifice loss to each fuel channel; Each intermediate spacer loss; and
- Exit loss from fuel channel to upper plenum (this loss is assumed to be one velocity head).
I The single-phase loss coefficients are input to NODE-B. In the bulk boiling region they are corrected for the local quality and
'.*oid condition within the fuel channel. The correction is I
- 7, K = K.in,t.-pn...
- 1-x .
1-a where: x = local equilibriui.. coolant quality evaluated in N0DE-B as Qijw; and a = local coolant void fraction. I This correction assumes that the pressure loss along the fuel channel can be based upon the liquid phase velocity. This correc-tion accounts for the decrease in the liquid phase mass flow due to steam formation and the increase in the liquid phase velocity due to the local steam void fraction. The value of the single phase loss coefficient is usually obtained experimentally. How-ever, if experimental data are not available, the coefficient can
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I \ be estimated by calculating the loss coefficient based upon standard coef ficients for entrance and exit ef f ects. I l In the boiling water reactor the water in the downcomer is either s,sturated or slightly subcooled, depending on where the feedwater is introduced. If the-feedwater is ad. d at the top of the down-comer and good mixing with recirculating water is achieved, the density in the downcomer is equal to .he density of the coolant at the fuel channel inlet. Due to the density difference between the downcomer and fuel channel, a driving pressure or buoyant head is I established. l If the feedwater enters the top of the downcomer, the downcomer density is an average based upon the two principal flow streams to the downcomer. The buoyant head associated with a particular I channel can be written as I
~
Buoyant Head = 1-pa pn L. + -hpt Ls. where: Buoyant head = feet of fluid at inlet density; pi = Average density of 1iquid phase in the channel over the non-boiling length L.; pi = Inlet liquid dersity, also downcomer liquid density; and
- p. = Average density of two-phase mixture over the boiling length, Ls.
s I
I As the coolaat flows through the various fuel channels, it en-counters resistances which are described in terms of pressure losses. The sum of these losses for a fuel channel less any buoyant head contribution then has to be recovered by the-pumps in the recirculation loop. I For the NODE-B code, the term pumphead is used to denote the dif-ference between the flow head losses and buoyant head. I Moderator Density Determination The nuclear characteristics of the fuel are represented, in part, I as a function of the relative moderator density, U sm. i The program determines Uijn by first calculating the nodal quality from the power and channel flow rates, then determining the steam volume fraction and finally converting this volume fraction to the relative mcderator density. Details of this calculation are I I described as follows. l I Node Quality Calculation The equilibrium quality at each node, Qija, is calculated from the expression I P Qi36 = Pr *W Wr 1 (F i j)*KMAX
- e E
.t= 1 Pijt - Pijk 2
* (Q..-Q.) + Q.
I t I I
i I where the summation is up channel ij and: 2 I We = ratio of rated to actual flow; . P_ = ratio of actual to rated power; Pr i ) IO1AX = the number of axial nodes in the problem; and i Fij = the ratio of flow in channel ij at power Pi3 to average channel flow. 1 The inlet and exit qualities, Q. and Q.., are obtained as i follows. !I i l j Q. = Hn - H... i , J Hr, j and I Q., = H,, - H .. = H., - Han + Q. , He, Hr, where Ha, is the heat of vaporization of water at the system pressure. Note that Hin - H..s is the inlet subcooling which is an input quantity and that H., - Han is just the total enthalpy rise in all channels: I H., - Han = (3.4129 x 10')
- P/W.
I I E - . . .
I Void-Quality Relationship The relationship betgeen local equilibrium quality and local void is provided by the Zolotar-Lellouche Profile Fit Model (Reference 3). The relationship is in the form a= x C. [x + Pa (1-x)] + P., V i I P G where: a = void fraction x = flow quality; C. = concentration parameter; V,i = drift velocity of the vapor, relative to the liquid; G = mass flux; P,, Pi = the mass densities of vapor snd liquid. The void model includes equations which specify the flow quality drift velocity and C. in terms of the thermal hydraulic I valuables. I Relative Moderator Density The relative moderator density, U, which is the ratio of the two phase density to the saturated water density, is then determined I from Uijn = 1.0 - an3a * (1 - p./pw) , where p. and pw are the saturated steam and water densities at system pressure and aiju is the void fraction for node ijk. I se' I
I I 3.4 Instrumentation Model The,in-core instrument readings are predicted by NODE-B. The prediction of an instrument reading at a given location is tmsed on the nodal power of the four fuel nodes adjacent to the instru-ment. The four nodal powers are multiplied by a conversion factor and summed to get the relative instrument reading, IR, as follows: IRijw = [ Piju
- RFijw ij where Pijn is the nodal pcwer and RFiju is the conversion factor. The conversion factor is a function of velds, exposure, fuel type and control rod presence. The conversion factor is obtained from CPM calculations. The values of RF are fitted to the equation:
RF = Cl + C2*E + C3*E* + C7*E' + (C5 + CS*E) * (1 - (U/UBASE) I where the C constants are input for each fuel type and E and U are the nodal exposure and relative moderator density, respecti"31y. A second set of C constants are used for controlled nodes. The relative instrument reading is multiplied by input factors XMONO and PTH to convert the reading to absolute readings in
- watts /cm*.
l l 1 l
7_____-_ r I 3.5 Haling Option The Haling option allows the user to determine the optimum s power shape for an operating cycle. The optimum power shape is the power shape that will maintain a minimum power peaking factor throughout the cycle. The Ealing principle states that for any given set of end-of-cycle conditions, the power peaking f actor is maintained at the minimum value when the power shape does not change during the operating cycle. The power, void and exposure distribution are iterated until these three distributions converge. Convergence is reached when the BOC
. power distribution is the same as the EOC power distribution (within a specified convergence criteria) after the core is burned with the BOC power distribution.
The Haling option is used to estimate cycle energy and to evaluate core loading patterns. It is used to generate the end of cycle exposure and void array and target power shape for the reload i analysis. I I me I
4.0 VERIFICATION l The verification work that has been performed was to establish con-fidence in the methods described here. Confidence is established by-the ability of the methods to reproduce criticality and power distri-bution data measured in operating plants over a period of time and l I conditions. The verification work, therefore, encompasses comparisions of N0DE-B calculations to measured data over several operating cycles. Since Oyster Creek is the primary focus for the applications of these methods, the majority of the verification is with Oyster Creek data. The addition of the Hatch 1, cycle 1 data was to also include gamma scan measurements that were made at end of cycle 1 in this verifi-cation. It also demonstrates the application of methods over a wider range of conditions and fuel designs. I 4.1 Comparison with Data Measured at Oyster Creek. 4.1.1 Cold Criticals The NODE-B cold model was evaluated against cold criticals performed at Oyster Creek during startup tests at the be-ginning of cycles 8, 9 and 10. The criticals were per-formed at the beginning of each cycle with the head of f the vessel and moderator temperature around 90*F. The criti-cals performed are local criticals with a series of posi-tive and negative periods to notch calibrate a control rod and measure shutdown margin. These criticals are rarticu-larly good to demonstrate the capability of the ucdel to c'alculate shutdown margin. I
1 I i i The criticals performed for each cycle are shown in Table 4.1 to 4.3 along with the calculated k-effectives I corrected f or temperature. The critical k-effective is corrected for period and temperature. The combined average k-effective for the 3 cycles is 1.00l93 with a standard deviation of 0.00293. Part of the variation in the k-effective from cycle to cycle is due to the different number of control rods used in and location of, the critical configurations. The critical k-effective with a minus one sigma uncertainty is used to predict shutdown margin. 4.1.2 Hot Reactivity Calculation NODE-B core follow calculations were performed for Oyster Creek cycles 8 and 9. Twelve statepoints were analyzed for each cycle. Key information for each statepoint is pro-vided in Tables 4.4 and 4.5. The core average k-effective is calculated for each statepoint and the mean k-effective for the cycle is provided in Tables 4.6 and 4.7. The mean k-effective for both cycles 8 and 9 is 0.986245 with a standard deviation of 0.00177. The consistency of the k-effective is very good both within cycle 8 and 9 and from cycle 8 to cycle 9. 4.1.3 Power Distribution Comparison The accuracy of the NODE-B power distribution was determined by comparing measured TIPS to TIPS predicted by NODE-B. I se'
I These comparisons were performed for the cycle 8 and 9 statepoints with the results shown in Tables 4.6 and 4.7. The TIP nodal uncertainty is given in percent RMS which is calculated as follows 1 Residual for node ijk Rijk = (M - C)/5
. Overall Nodal RMS errar E
I where: RMS = [ [
/,k R*(8, k)//
- k]
M = measured TIP for node ijk C = calculated TIP for node ijk M = average measurement
# = number of TIP strings k = nunber of axial nodes.
I The mean nodal RMS is 7.65% 1.41% for cycles 8 and 9. Figures 4.1 to 4.24 contain the comparison of the core average axial TIP between NODE-B and measurements. The nodal uncertainty of 7.65% is very good. Part of the un-certainty is in the TIP measurements themselves. The TIP asymmetry (unexplained differences between readings of symmetrically located TIPS) was 2.97% and 2.90% for cycles 8 and 9 respectively. ! i l 1
TABLE 4.1 SHUTDOWN MARGIN CRITICALS FOR CYCLE 8
- t t
Critical
- Calculated k Measured k Bias 4
1 Pos 1.00504 1.00122 0.00382 1 Neg 1.00469 0.99961 0.00508 2 Pos 1.00665 1.00121 0.00544 2 Neg 1.00591 0.99925 0.00666 3 Pos 1.00655 1.00122 0.00534 3'Neg 1.00507 0.99930 0.00577 4 Pos 1.00703 1.00089 0.00615 5 Pos 1.00586 1.00032 0.00554 Temperature = 97*F Critical k.,r = 1.00548 lo = 0.00083 Pos - positive period Neg - negative period I l l l I ! I I i
~~
8
I TABLE 4.2
~
SHUTD0'n'N MARGIN CRITICALS FOR CYCLE 9 I Critical Calculated k Measured k Bias 1 Pos 0.99688 1.00082 -0.00394 1 Neg 0.99646 0.99961 -0.00315 2 Pos 1.00043 1.00077 -0.00035 2 Neg 0.99979 0.99943 0.00036 1 3 Pos 1.00084 1.00076 0.00009 l 3 Neg 0.99931 0.99891 0.00040 4 Pos 1.00106 1.00083 0.00023 l 4 Neg 0.99863 0.99968 -0.00105 l Temperat.ure = 90*F Critical k.,, = 0.99907 lo = 0.00170 I l I i I 1 I i . I e I
I TABLE 4.~3 SHUTDOWN MARGIN CRITICALS FOR CYCLE 10 - I
~
Critical Calculated k Measured k Blas 1 Pos 1.00075 1.00075 0.00000 1 Neg 0.99999 0.99934 0.00065 2 Pos 1.00230 1.00094 0.00136 2 Neg 1.00144 0.99977 0.00167 I 3 Pos 1.00207 1.00068 0.00139 l I 3 Neg 1.00085 0.99966 0.00119 l 4 Pos 1.00242 1.00070 0.00172 4 Neg 1.00194 0.99994 0.00200 l Temperature = 93*F l Critical k.r, = 1.00125 lo = 0.00065 , I I I I I E t . j IB _ - - -
I TABLE 4.4 KEY INFORMATION FOR OYSTER CREEK CYCLE 8 STATEPOINTS I O Power Recire. Flow Core Avg. Exp. Rod % Rod I Date (MWth) (M1bs/hr) (GWD/MTU) Sequence Density i 01-26-79 1917.4 58.69 11.02 A 14.S9 02-22-79 1914.3 59.50 11.52 A 17.03 03-01-79 1916.8 58.08 11.64 A 17.03 03-20-79 1912.5 57.59 12.02 A 18.19 04-19-79 1912.3 59.95 12.30 B 18.49 06-08-79 1805.6 53.37 12.66 B 18.31 07-03-79 1910.3 59.41 13.15 B 16.85 , 07-26-79 1914.2 58.35 13.57 A 16.33 08-30-79 1892.3 56.79 14.25 A 12.68 09-06-79 1905.9 59.31 14.37 A 12.68 5 10-25-7, 1,07.3 57.4e 15.27 A 7.18 12-e,-79 1,,7.4 ,9.,e 1s.e, A 3.6, g I I I I , i i t i t
- I
{ TABLE 4.5 KEY INFORMATION FOR OYSTER CREEK CYCLE 9 STATEPOINTS i= Power Recir. Flow Core Avg. Exp. Rod 7. Rod l Date (MWth) (M1bs/hr) (CWD/MTU ) Sequence DensitL 07-30-80 1635.7 49.36 9.93 A 17.15 .i 4 08-29-80 1677.4 50.06 10.35 A 17.64 1 09-29-80 1928.7 60.23 10.81 A 18.30 11-11-80 1840.6 58.44 11.58 B 21.35 4 12-16-80 1833.1 57.24 12.07 B 20.38 02-27-81 1685.2 53.04 13.35 B 16.24 i l l 03-24-?1 1907.7 56.76 13.71 B 14.48 i 06-16-81 1923.1 60.50 14.32 A 11.53 07-09-81 1247.6 39.58 14.59 A 11.92 08-11-81 1274.8 49.69 15.02 A 10.71 11-25-81 1860.8 57.97 15.66 A 4.26 12-09-81 1840.4 60.89 15.92 A 4.01 I i I l I i I -- I
I TABLE 4.6 CORE REACTIVITY AND P0hER DISTRIBUTION COMPARISON FOR 0,YSTER CREEK CYCLE 8 TIP Nodal Uncertainty Statepoint Calculated k.r, in 7. RMS I 01 26-7'9 0.98666 10.16 02-22-79 0.98512 8.19 03-01-79 0.98394 7.77 ~ 03-20-79 0.98517 6.74 l 04-19-79 0.98476 6.92 l 1 06-08-79 0.98582 7.39 1 07-03-79 0.98810 7.28 07-26-79 0.98637 9.43 08-30-79 0.98624 8.24 09-06-79 0.98669 7.47 10-25-79 0.98906 7.17 12-05-79 0.98914 11.04 I Mean lo 0.98f 2 0.00 45 8.15 1.36 I i i a i I .
I TABLE-4.7 ,I , CORE REACTIVITY AND POWER DISTRIBUTION COMPARISON
,, . FOR OYSTER CREEK CYCLE 9 I TIP Nodal Uncertainty Statepoint Calculated k.,r in 7. RMS I 07-30-80 0.98517 7.60 08-29-80 0.98523 7.56 09-29-80 0.98527 6.63 11-11-80 0.98385 6.14 12-16-80 0.98534 6.26 02-27-81 0.98747 6.15 03-24-81 0.98578 6.30 06-16-81 0.98707 6.30 07-09-81 0.98562 7.89 08-11 "
0.98317 10.83 11-25-81 0.98953 7.31 12-09-81 0.98931 6.85 I Mean lo 0.98607 0.00195 7.15 1.32 1 i i 1 1 8
I Figure 4.1 1 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE
, OC CYCLE 8 STATEPOINT 01-26-79 .
- I 1
100 Measured Calculated 80 - 70 -
's',
E E $ l yu - i ik I ~ e a 50 - g
$- \ *g gE 40 -
s
\
$ \
30-- % t
\
l 20 - g i 10 - 1 I ! ! ! I I I I I I I I 0 l l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial P! odes I i l5 l 1 E . I l
I I
- Figure 4.2 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE s OC CYCLE 8 STATEPOINT 02-22-79 i
, a 100 Measured Calculated 80 - g , ,--- ... h 60 /
*s'~~------
g / g~ 50 - e f 40 -
. a.
30 - 20 3 10 - 1 0 ! I I I I I I l l l l l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I~~
- 4e -
g
I I Figure 4.3 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE s OC CYCLE 8 STATEPOINT 03-01-79 . I I I 100 Measured 90 - Calculated 8 80 - I 70 - h / U 60 - / *s i g ___ l 50 - i
& 40 -
l a
. 30 -
I 4 R 10 - i l I I I I I o I I I I I I l 0 2 4 6 8 10 12 14 16 18 20 22 24 l Axial Nodes !I i 1 I I Figure 4.4 COMPARISON OF CORE AVERAGE AXIAL TIS READING FOR THE
, OC CYCLE 8 STATEPOINT 03-20-79 I
I 100 90 - Measured Calculated 80 - 70 - s *~ 60 - 3: , ( 50 - 40 - n. 30 - 20 - 10 - I I I I I I I I I I I l 0 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I g .- 8 -4,-
- 3 Figure 4.5 i COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE ,
j OC CYCLE 8 STATEPOINT 04-19-79 I I 100 I Measured 90 - Calculated t y _ = "'~ r I
~
~
60 - s a 50 - 4 40 - e 30 - 20 - 10 - I I I I I I I I I I I I 0 o 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I
'I I !
- An
i Figure 4.6 )l
- g COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE OC CYCLE 8 STATEPOINT 06-08-79
- 1g i
i I !E L i 100 it ! 90 - Measured Calculated i 80 -
- I 4m 70 _
b 60 - -
^ * ~ ~ ~% * ~ ~ ~m-s /
4 5 s0 -
/
}l I 1 i
/
~
ll 1 i g 40 s s
- r !l I
I 20 - 10 - 0 I I I I I I l i I I i l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I l 5 -
.g g - 4e -
I Figure 4.7 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE
. OC CYCLE 8 STATEPOINT 07-03-79 j
- I I
iI i 100 4 90 - Measured Calculated 80 - !g E 70 - I E g _____ _ g 60 -
/
I 3
~
S0 -
,/
l g 40 -
- 3 30 -
20 - 10 - I O l I l l l [ [ [ [ ; ; 2 4 6 8 I O 10 12 14 16 18 20 22 E9 Axial Nodes
- I l5 .
- ee .
's
I i
'l Figure 4.8 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE OC CYCLE 8 STATEPOINT 07-26-p J !I
- I
, 100 'I Measured 90 -
Calculated 80 - l
!3 15 m _
j,,
~
g , ___< ____________ i s' l 8
, 50 -
/
i2e - g l : s
& \
30 - g 20 - g 10 - 0 I I I I I I I I I I l l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I 3 - e1 -
l Figure 4.9 i COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE l O.C CYCLE 8 STATEPOINT 08-30-79 1 ) 1' !I t l 100 iI ! 90 - l Calculated 80 - J 70 - E E 5 60 - e"" 3 5
,/p -%'..-- ,.
l
/
I 50 - [
' l 5 i
\
I 40 - 1 5 n. p I 30 -
\
\
\
20 -
\
10 - I I I I I I I l l l I l 0' 0 2 4 6 8 10 12 14 16 18 20 22 24 Axlal Nodes I I g ..
- s2 -
g
- 5
. Figure 4.10 l COMPARISON OF CORE AVERAGE-AXIAL TIP READING FOR THE OC CYCLE 8 STATEPOINT 09-06-79 I,
I I 100 Measured Calculated 80 - 70 - E I $
- = _.. s ~
~
g s0 - it: / , E c /
} s0 l
l 1 i
& 40 -
I 30 - 20 10 - I I ! ! I I I I I I l l 0 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes B
~
I g . I I l Figure 4.11 COMPARISON OF CORE AVERAGE AXlAL TIP READING FOR THE OC CYCLE 8 STATEPOINT 10-25-79 . I l I I 100 90 - Measured Calculated 80 - 70 !g . EQ ~~.. -- - I -; / g 50 -
/
m 40 - g E 30 -
\
l 20 - i 10 -
! I I I l l l l l 0 l l l
! 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I
- I -
- g
8 I Figure 4.12 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE . OC CYCLE 8 STATEPOINT 12-05-79 . I I I 100 90 - Measured Calculated 80 - 70 60 - # t l I s
.E en 50 I
I
, '~~,,~~,
s%s\ s I i E 3 40 - gl I s%g Ng
- a. N 30 -
- 20 -
10 - I a l i I I I I I I I I I I l I O 2 4 6 8 10 12 14 Axial Nodes 16 18 20 22 24 i . l E ,
I Figurs 4.13 l COMPARISON OF CORE AVEDAGE AXIAL TIP READING FOR THE OC CYCLE 9 STATEPOINT.07-30-80 5 I I I 100 Measured 5 90 - Calculated 80 -
,, 70 -
E E y, -~ ~ i 60 -
/,
I 3 s a 50 - p l
/
,*s'~
~~~~._'%s 4 / '~s h 40 -
p'
- a. I i: 1 30 -
20 I 10 - i 1 1 I l i I I I I I I 0 .I 0 2 4 6 8 10 12 14 Axial Nodes 16 18 20 22 24 I I E .
I Figure 4.14 COMPARISON OF CC.*3 AVERAGE AXIAL TIP READING FOR THs ' ' OC CYCLE 9 STATEPOINT 08-29-80 . I I I 100 Measured calculated 70 -
/ s = 60 -
f l i l s\s 5 5a
,~~~~
r l l 1 j 40 -
~\s's c.
30 - 20 - l 10 - l I I I I I I I I I l l o 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I lI - e> -
I Figure 4.15 l COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE OC CYCLE 9 STATE, POINT 09-29-80 iI i I iI, 4 iI 100 Measured 90 - 80 -
, - ~~~~
i E
- 60 - *%'
I 5 50 -
?
I 1 g 40 - I > 30 - 20 - 10 - g 0 I I i l l l l l , , , ; O 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I l 3
- ee -
3
I I Figure 4.16 CO(APARISON OF CORE AVERAGE AXIAL TIP READING FOR THE OC CYCLE 9 STATEPOINT 11-11-8 0 l I I I 100 90 - Measured Calculated 70 - I IE
~~~~~.
.y g 60 - ,, ,
,,'s i iB:
A \ 50 - g i i j 40 - I $ 30 - 20 - 10 - 0 I I I I I I l l l l l l O 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I g .. j -
.I i Figure 4.17 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE
! OC CYCLE 9 STATEPOINT 12-16-80
!I I i { 100 i g _ Measured i j -- Calculated i !l 70 -
- W IE jg g 60 -
---- + ___ - -,
jg ik '%g
- E \
50 - E i 5 h 40 - i n. I P 30 - ll i 20 10 - ! o I l l l I l l l l l l l 0 2 4 6 8 10 12 14 16 18 20 22 24 3 i Axial Nodes l
'l I
I Figure 4.18 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE
,0C CYCLE 9 STATEPOINT 02-27-81 i I
I I I 100 90 - Measured Calculated I 80 - 70 - I E g 60 - I 3: E 50 -
'=h -- -_
F I i j 40 - n. 30 - 20 10 - 0 I I I I l l l l l l l l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I
~
~
I I
- Al -
5 Figure 4.19 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE OC CYCLE 9 STATEPOINT 03-24-81 I I I 100 Measured 90 - Calculated 70 - I S _
$,60 -
,/ -
I
~....- - -
3 f
/ ,'%s
~ 50 -
,5 I i j 40 -
a. I 30 - 20 - 10 - 0 I I I I I I I I l l l l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I l I I i
.2-
- I i
l ' Figure 4.20 COMPARISON OF CORE AVERAGE AXlAL TIP READING,FOR THE OC CYCLE 9 STATEPOINT 06-16-81 - ) !I i I 100 Measured l 90 - i Calculated i 80 - l j E
- $ s*s*s jE g 60 -
, 3, ; g 3 %- . -
7 i E 50 - I i g <0 - a. b I 30 - 1 20 - 4 l 10 - 0 I I I I I I I I l l l l
} 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I
I I ' I - s, .
I Figure 4.21 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE - OC . CYCLE 9 STATEPOINT 07-09-81 I I I 100 g _ Measured Calculated 80 - I 70 - EE g 60 - I I 50 #
/
s's\s f -g E I 3 i j 40 - l 's\s
*%g I 30 - C- -
20 - 10 - 0 I ! I I I I I I I I I I O 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I I - e4 -
E Figure 4.22
, COMPARISON OF CORE AVERAGE AXIAL TIP READING ~
FOR THE OC CYCLE 9 STATEPOINT 08-11-a1 i lI I s i I 100 g _ Measured l Calculated 80 - 1 ) , ~ 70 - j
.E -
' {
~
60 - / s\ e f 3; / 'l E ~ i So _1 % 4 . , s i e % fl i cg 40 - l N % i ! >= %*% %' 1 30 - j ,** ==.., 20 - 10 I o I l l I l l l l l 1 l l 0 2 4 6 8 10 12 14 16 18 20 22 24 i Axial Nodes !I. lI J
I I Figure 4.23 COMPARISON OE CORE AVERAGE AXIAL TIP READING FOR THE 0,C CYCLE 9 STATEPOINT 11-25-81 I I I 100 g _ Measured i Calculated
, 80 -
i 70 -
.E
- 60 -
E
%~_
50 - ]l
- 1 j 40 c.
30 - 20 - 10 - 0 I I I I I I I I I I I I O 2 4 6 8 10 12 14 16 18 20 22 24 l Axial Nodes lI !I . I I - ee -
fl Figure 4.24 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE OC CYCLE 9 STATEPOINT 12-09-81 ,
- I i
100 g _ Measured Calculated 80 - 70 - 5 - 60 - 5 !
-, 50 -
s E l j 40 - n. 30 - 20 - 10 - 0 I I I I I I l l l l l l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I' I
I 4.2 Co:nparison with Data Measured at Hatch 1 4.2.1 Hot Reactivity I . NODE-B
- core follow calculations were perf ormed for Hatch 1, cycle 1 operating history' * '. Seventeen statepoints (Table 4.8) were analyzed for the cycle with the core average k-effective shown in Table 4.9. The mean k-effective is 0.98498 with a standard deviation of I 0.00537. The mean k-effective is similar to what was seen in Oyster Creek but with a larger standard deviation. This is due to the period following the 10-24-75 statepoint when the core k-effective decreased to less than 0.9800 and re-mained low through the 09-16-76 statepoint. After this statepoint, the core k-effective increased to 0.99 and I
remained there for the last six statepoints. During an outage just prior to the 10-24-75 statepoint, holes in the lower grid plate (unused locations for instru-l l 3 ment tubes) were plugged. The hole plugging decreased the l bypass flow and created voiding in the bypass region of the core. NODE-B does not have a bypass void model. However, the lack of a bypass void model does not appear to be the cause of the decrease in core k-ef fective. The same be-havior in k-effective was seen in similar studies for the period following plugging where a bypass void model was used. In order to account for the change in core condi-tions during this period, the normalization parameters were re-evaluated at the beginning and end of the period. A I
I steam leak repaired during an outage in April 1976 indicates problems with the data as opposed to modeling deficiencies.
- I.
4.2.2 Power Distribution Comparison The accuracy of the N0DE-B model during the cycle was determined by comparing predicted and measured TIPS. The results for the 17 statepoints are summarized in Table 4.9. The overall nodal RMS is 9.14%. The cycle performance is generally in the 8 to 9% range except for the pericd following the bypass hole plugging where per-formance was in the 9 to 12% RMS range. The nodal asymmetry for- Hatch cycle 1 is 4.02%. A comparison of the measured and predicted core average TIPS are shown in Fig-ures 4.25 to 4.41. I 4.2.3 Gamma Scan Comparisons The end of cycle gamma scan measurements provide data to directly evaluate core power distribution predictions. The EOC 1, Hatch 1 gamma scan measurements' were made on 106 fuel assemblies; 75 comprising a complete octant of the core and 31 assemblies in octant symmetric locations. All 106 fuel assemblies were measured at a minimum of 12 axial positions. I The results of the gamma scan are summarized in Table 4.10. The core axial RMS is presented in I
Table 4.11. The comparison of predicted and measured core average axial is shown in Figure 4.4.2. Individual bundle power distribution comparison are shown in Figures 4.43 to
- 4.47. Figure 4.48 shows the radial comparison (Bundle integrated RMS) for all 106 fuel assemblies. The defi-nition of the residuals and statistics are provided in Appendix A.
I The results were generally good. The overall nodal RMS of 7.95% is acceptable and falls below the 8.54% mean RMS of the TIP comparison for the last five statepoints. These were the power distributions used to generate the predicted end of cycle Ba-140 distribution used in the comparison. It demonstrates that the ability of the model to predict the TIPS is indicative of the models ability to predict power distribution. I I I I I I I
TABLE 4.8 KEY INFORMATION FfR HATCH 1 CYCLE 1 STATEPOINTS Power Recire. Flow Core Avg. Exp. Rod 7. Rod Date (MWth) (M1bs/hr) (GWD/MTU) Sequence Density 03-28-75 1218 34.5 0.70 A 9.8 05-24-75 2189 68.0 1.28 A 7.5 08-26-75 2331 78.7 2.58 B 9.4 09-25-75 2098 66.7 3.12 B 10.8 10-24-75 2091 60.'9 3.65 B 11.3 01-13-76 1947 64.3 4.16 B 14.2 01-25-76 1853 78.5 4.32 A 17.2 05-25-76 2104 73.5 5.79 B 17.5 07-22-76 2021 62.4 6.59 ?, A 18.2 08-13-76 2269 75.3 6.98 A 18.2 09-16-76 2230 78.4 7.62 B 19.9 11-29-76 2037 78.5 8.94 B 19.9 12-29-76 2231 78.2 9.40 A 16.2 01-21-77 2131 78.7 9.83 A 16.2 01-25-77 2153 71.3 9.88 A 15.7 02-23-77 2208 73.6 10.12 A 15.7 03-07-77 2114 77.2 10.31 A 15.7 I I I I 1
I TABLE 4.9 CORE REACTIVITY AND POWER DISTRIBUTION COMPARISON FOR HATCH 1 CYCLE 1 i E l
- TIP Nodal Uncertainty I
Statepoint Calculated k re 1 03-28-75 0.98333 6.21 05-24-75 0.98425 6.26 08-26-75 0.98531 7.80 j 09-25-75 0.98435 8.90 10-24-75 0.98452 8.82 ) 01-13-76 0.97938 10.70 01-25-76 0.97709 11.98 05-25-76 0.98093 9.75 i 07-22-76 0.97861 9.16 08-13-76 0.97937 9.23 09-16-76 0.97973 - 8.29 11-29-76 0.99319 9.23 12-29-76 0.99229 8.70 01-21-77 0.99124 8.09 01-25-77 0.99093 8.17 f I 02-23-77 0.99005 8.92 03-07-77 0.99017 8.80 l l Mean 0.98498 9.14
- lo 0.00537
- I 1
I l TABLE 4.10 SbDIARY OF HATCH GA>D1A SCAN POWER DISTRIBUTION COMPARISON Comparison % RMS l Nodal 7.95 Integral 2.82 l Peak Node 6.07 i I Axial 5.81 I l
- I I
1 I I I I .
I ' TABLE 4.11 HATCH GA.T1A SCAN AXIAL AVERACE RESIDUAL AND STANDARD DEVIATION , Standard NODE Residual Deviation 23 -1.46 3.99 I 21 19 17
-13.40
-1.77 1.28 6.10 6.36 7.79 15 7.60 9.47 I 13 11 7.36 3.10 5.71 3.83 9 -1.94 4.54 7 -7.10 4.34 5 -2.19 3.92 3 3.18 2.70 1 5.34 1.61 RMS = 5.81 1
I I 'I
- I lI ll
'E I I I
I Figum 4.25
' . COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE HATCH.1 CYCLE 1 STATEPOINT ON 03-28-75 I
i 1.8 Measured Calculated 1.4 / \ I x
\
I 1.2 - g 4* ! g i" - lI, __ _ _ _ _ s 0.8 - f e i E f \ I 0.6 -
\
g s 0.4 - j \
.\
0.2 - 0.0 I I I I I I I ! I ! 0 2 4 6 8 10 12 14 16 18 20 22 p, Axial Nodes i I I -- I -"- 4
E Figure 4.26 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE HATCH 1 CYCLE 1 STATEPOINT ON 05-24-75 1* , I l l t 1.8 Measured I _ Calculated 1.4 I
/ '%
/ \
. I 1.2 - 1 F '
i N
% *g I E 1.0 -
% _ , Y,
- a. \
P \ g 0.8 - E i
$ 0.6 g E I I 0.4 -
g i, 0.2 - s 0.0 I l l l l l l l l l l l 0 2 4 6 8 10 12 14 16 18 20 22 24
..lai m e.
1 I ~ l
.I l Figure 4.27 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE HATCH 1 CYCLE 1 STATEPOINT ON 08-26-75 -
i I !l -
- g 1.8 4 ,
1.6 - Measured { f
/** Calculated I 1.4 -
[ g , \s - I I h a 1.2 - \ g E
- 1.0 -
I f
's\
B & I s% , ",, ~~'s%g H I %*=== \ y I s I y 0.8 -l E Ei I 3
\
g
\
z 0.6 - 0.4 I
\
0.2 -
- l l l ! ! ! ! ! ! ! I I 0.0 O 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I
g I g
I Figure 4.28 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR
, THE HATCH 1 CYCLE f STATEPOINT ON 03-25-75 l l t
i 1.8 I 1.6 - I
/'
g Measured f Calculated
\
i 1.4 -
\
\
\
l g 1.2 -
\
j \ 30 1 m 0.8
-f. N g
b %, 2 0.6 - \
\
0.4 - 1 0.2 - F I I i i i I I I I I I I O 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes !1 1 , g g - >e .
I i Figure 4.29 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR s l THE HATCH 1 CYCLE 1 STATEPOINT ON 10-2'4-75 . i I I 1.8
/ Measured 1.6 -
l Calculated I 1.4 -
\
\
p 1.2 -
\
! g
- Ng 1.0
~~~_ _______--.,Ng
;0.8 '
y -l \ i !
\
0.6 - g 0.4 - 0.2 - l I I I I l l l l l l 0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I .. 5 (
I E 1 l l Figure 4.30 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE HATCH 1 CYCLE 1 STATEPOINT ON 01-13-76 - 8 8 I 1.8 I [ Measured 1.6 - f
\
l
\ Calculated f
I g 1.4 - I g I i i g i g 1.2 -f \
} 's g 1.0 -
~%*s p s*%
I- 2 5 0.8 -) * '~~~..,'%g
$ 's 0.6 -
g 0.4 - i - I s g l 0.2 - \ I ! ! I I I l I 0.0 l l I l l 0 2 4 6 8 10 12 14 16 30 j 18 22 24 '- Axial Nodes iI I Ig - so -
I Figure 4.31 COMPARISON OF CORE AVERAGE AXlAL TIP READING FOR THE HATCH 1 CYCLE 1 STATEPOINT ON 01-25-76 , I l I I 2.0
~
/ \ Measured 1.8 -
g f [ I 1.6 - i I g g
\
Calculated l
; -l \
I
. 1.2 j
\
9: 1 %
- 1.0 I \
g
*s 0.8 - '-
]
~ T ' ' %s*sN I
l!i z 0.6 - 0.4 -
\
0.2 -
\
0.0 I I ! ! I I I I I l 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I E B
I Figure 4.32 COMPARISON OF SORE AVERAGE AXIAL TIP READING FOR g THE HATCH t CYCLE 1 STATEPOINT ON 05-25-76 l 1 I i 1.8 1.6 - Measured Calculated
/,,~,['~~,
E a 1.2 - '% % S I f
's s 1.0 -
[ s / %s'ss I V
.E 0.8 I
,1 A
g
\
g 5 0.6 -
's l
g 0.4 -
\
0.2 - g I I I I I I I I I I I I o.o O 2 4 6 8 10 12 14 16 18 20 22 24 I 3 g -
I i Figure 4.33 COMPARISON OF CORE AVERAGE AXIAL IIP READING FOR I THE HATCH 1 CYCLE 1 STATEPOINT ON 07-22-76 I i 1.8 Measured Calculated 1.4 - i
-%g%g%
I
; p 1.2 -
%*%s
} *s j 1.0 -
'%s~%
!l p
3 j 0.8 - N s\ E \
! i \t 0.6 -
I i 4
; 0.4 -
' \
, 0.2 - I.
! ! ! I I I ! l l l
!' 0.0 l l O 2 4 6 8 10 12 14 16 18 20 22 24 i Axial Nodes
!I !I 4
1
- 3 - es .
.I
\
Figure 4.34 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR g THE HATCH 1 CYCLE 1 STATEPOINT ON 08-13-76 I I i 1.8 1.6 - Measured Calculated 1.4 -
's g en 1.2 -
h ~~%
%s s 30 1
ss l 2 y 0.8 E
~%
N g s 0.6 -
\
0.4 - 0.2 - l l I I I ! ! ! ! I I 0.0 O 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I 1
- e4 g
I Figure 4.35 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE HATCH 1 CYCLE 1 STATEPOINT ON 09-16-76 g I I i 1.8 1.6 - Measured Calculated I 1.4 -
,s**~~s, a 1.2 -
- l / *%g a / s N
1.0 - g f'
, / \\ $ 0.8 - / g f '
i O.6 - 0.4 -
\
A 0.2 - i I
! ! ! I l l l l l l l 0.0 0 2 4 ,6 8 10 12 14 16 18 20 22 24 u.,
I I - es -
, l ,a W Figure 4.36 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR e g THE HATCH 1 CYQLE 1 STATEPOINT ON 11-29-76 '
- I
- I 1.8 Measured
'gy 1.6 -
% Calculated 1.4 -
I *% Ng g 1.2 - I $ 'A CE g 1.0 - g i \
\
I y 0.8 -
/ g E \
f 0.6 - [ \
/ \
' \
i 0.4 -
/
I / \ i O.2 I ! ! ! I I I l l l 0.0 l l 5 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I
't I -
- ee -
g
!,I g Figure 4.37 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR l THE HATCH 1 CYCLE 1 STATEPOINT ON 12-29-76 lE i l lE, I i
- I l
Measured 1.6 - Calculated 1.4 -
~~~ .,,** ~~s a 1.2 -
/, %,
2 %
\
3 1 i
, 1.o - ,e/' \s
- y \
3
\
~
\l + h'* g ,
,1 s o.s
,i
- g !
1 i l o.4 g \
\
E i i 1 o.2 -
- l 1
g 0.0 a a I I 4 I e i l
,o l
,2 l
,4 i ; ; ; ;
~al m..
- g I
I .. E , - -
1
- E . Figure 4.38 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR -
THE HATCH 1 CYCLE 1 STATEPOINT ON 01-21-77 l , l I i 4
- Measured 1.6 -
Calculated l 1.4 -
- 3 i g -~~
i "" % "" f M Ag [ 1'2 \ l 1 / \ 1.0 -
/
f'I 1 m i /
/ \
s I j 0.8 - 15 0.6 - 4 i 3 0.4 -
' I \
l l I I \ 0.2 - 1 0.0 I I I l l l l 5 0 2 4 6 8 10 12 14 16 18 20 22 24
. . , ~ . .
g I E
i Figure 4.39 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR il ! THE HATCH 1 CYCLE 1 STATEPOINT ON 01-25-77 l I
- I 1.8 '
Measured 1.6 - Calculated l 1.4 - Y
,/
--- "" \
1.2 - g l i l
.s
/
/, \\ !
/ \
E. g E n. 1.0 -
/
/ \
g i: / 2
.tt 0.8 -
/
/ :
l . , f E o 1 z 0.6 -
- \
0.4 -
\ ' ),
0.2 - i
! ! I l l l l l l l l l 0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 1
I ! Axial Nodes l l
\
I l B
,8 ~
Figure 4.40 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR g THE HATCH 1 CYCLE 1 STATEPOINT ON 02-23-77 ,
- I i
- I i
1.8 Measured Calculated 1.4 - l "~'s
,/,
m \ I s
/s'
\
1 \ i 1.0 / I
\
a, / \ p / E / I 0.s y
,/
b / o / z 0.6 / I I g i i
\
0.4 - \
\
I 0.2 - o,o I -l l I I I I I I I I i I 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I ' I l
l Figure 4.41 COMPARISON OF CORE AVERAGE AXIAL TIP READING FOR THE HATCH 1 CYCEE 1 STATEPOINT,ON 03 07-77 ,5l lI i i !I l 1.8 1.6 - Measured Calculated I 1.4 -
,,/'%
~~~
\
g 1.2 -
/ \
I "a. 1.0 5
/
/
# g 2 0.8 - /
E /
/
0.6 - #
\
g 0.4 - 1 0.2 - l l l I I I I I I I l I 0.0 O 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I .. I
i
!I Figure 4.42 106 BUNDLE AVERAGE AXIAL Ba-140 DISTRIBUTION -
i !I !I J !I i i 2.0 i Gamma Scan {W 1.8 - Node-B j 1.6 -
\
1.4 -
/
#,f 'g 1.2 ,' I g
fl a ' } . ?. m 1,o _ p l / 8 # 5 / i f ;e 0.8 -
,s' s'
0.6 - l 0.4 - 0.2 - I I I l l l l l l l l g O.0 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I - . 5 1 I l Figure 4.43 OCTANT NORMALIZED AXIAL Ba-140 DISTRIBUTION FOR FUEL ASSEMBLY HX-169 (LOCATION 14,08) I I I 2.0 Gamma Scan 1.8 - Node-E 1.6 -
/ 's I /
\
/ \
,/
I 1.4 -
\
____ g 4 o 1.2 - f \ E l 1.0 - [
= t I i E 0.8 -
/
0.6 -
/
i
/
0.4 -
/
i ' i 0.2 - O.0 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I g 4
- g B Figure 4.44 OCTANT NORMALIZED AXIAL Ba-140 DISTRIBUTIQN 4
g .FOR FUEL ASSEMBLY HX-373 (LOCATION 15,08) I I I 2.0 q I 1.8 - Gamma Scan Node-B
^
\
g
\
1.6 -
\
g
\
\
I 1.4 \ g
\
/ \
o 1.2 - I
/
l 3 1.0 -
/
g I a
$ 0.8 -
,s' I 0.6 -
/l 0.4 -
I 0.2 , CONTROL BLADE AT NOTCH 14 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I l ' l
I l Figure 4.45 OCTANT NORMALIZED AXIAL Ba-140 DISTRIBUTION , . I FOR FUEL ASSEMBLY HX-393 (LOCATION 14,09)
- I i
I 2.0
, 1.8 -
Gamma Scan Node-B 1.6 - je
'e \
l \
/
I o 1.2
}
I [ 1.0 - l $ E 0.8 - / l f l 0.6 -
/
/
/
0.4 - 0.2 E CONTROL BLADE AT NOTCH 34 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I g -e -
l I Figure 4.46 OCTANT NORMALIZED AXIAL Ba-140 DISTRIBUTION FOR FUEL ASSEMBLY HX-141 (LOCATION.15,09) ] lI i J i s !l l 8 2.0 1.8 - Gamma Scan ) l NM&B 1.6 -
/
/
j/ \ j \ g 1.4 -
/,/ \
/ g l / g
, S 1.2 -
/ s v s
- A '
/
/
g 1.0 ig = / 5 i E 0.8 - /
/
0.6 - f 0.4 - 0.2 - I ! ! ! l l l l l l l l 0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I I .
- ee -
3
]l - Figure 4.47 OCTANT NpRMAllZED AXIAL Ba-140 DISTRIBUTION I FOR FUtl ASSEMBLY HX-413 (LOCATION 4,11) lI
- I 4
iI j 2.0 i g _ Gamma Scan Node-B \ g N t 1.6 -
\
g
\
\
/
!I ) o 1.2 - l
/
?,
\\
g f i j / t I g 1.0
/ \
h '
/
sE 0.8 -
/
/
I 0.6 - 0.4 -
/
I 0.2 -
- ' s/
CONTROL BLADE AT NOTCH 20 0 2 4 6 8 10 12 14 16 18 20 22 24 Axial Nodes I I g .. I - e> -
I l Figure 4.48 RELATIVE BUNDLE INTEGRATED Ba-140 DISTRIBUTION , I 0.699 0.682 0.663 0.616 0.5 72 GAMMA I=1 0.773 0.746 0.718 0 667 0.524 NODE-B
-7.238 -6.284 -5.428 -5 047 4 746 % RMS 0.904 0.881 0.843 0.846 0.790 0.685 2 0.953 0.929 0.902 0.884 0.802 0.617
-4.789 -4 694 -5.783 -1 715 -1 194 6 677 I 3 4
1.059 0.970 1.038 0 914 0.893 1.043 OS33 OS25 0.997 1.072 0.957 0963 0.971
-0.448 -1.893 -3.136 -2.539 1063 0.966 0.984 0.899 0.904 1852 -0.452 1.039 1.010 0.795 0823
-2.767 OS59 0691 0 722
-3.062 0.904 0.590 0.546 4369 0.776 0594 1.064 0.976 1.087 OS92 0.976 1.064 1.065 1.054 1003 0933 I
0.809 0.584
-0 569 0.581 -1.483 '-2.489 1 232 -0.136 -2541 -4 412 -4 333 2.888 -3 241 0969 1.C75 1.118 1.110 1.124 1.122 1 054 1.040 1D93 1.070 1.019 OS39 0.770 5 1.064 1.105 1.117 1.110 1.105 1.064 1.070 1.101 1.094 1.049 0.972 0.807 0.999 1.249 -0.739 1312 1.663 -0 983 -2.879 -0 788 -2399 -2 980 -3 294 -3632 I 6 1.128 1.112 1.580 1.130 1.125 1.11 2 1.250 0332 1.148 1D99 4 885 0.972 1.100 1.084 1.578 1.184 1.075 1.077
-0.156 1.167 1.118 1.107 1 079 0.999 1.096 1.097
-0 057 0.984 1.082 1.099
-1642 1.102 7
I 1.106 0.929 0.939 1.125 1.139 0.980 0.969 1.068 2371 0354 3 230 5871 2 698 1 915 1.478 1 377 1.134 0.941 0.970 1.221 1.187 1.048 1.006 1.091 1.008 8 1.111 0.946 0.956 1.173 1.174 1.006 0.973 1D85 1.043 2300 0.472 1394 4.741 1.286 4 094 3.263 -0.438 -3.427 I 9 1.113 1.133
-1.880 1.183 1.150 1259 1.202 1.180 2.154 1.238 1.228 1.229 1.234 0S99 -0.487 1.191 1.167 2.343 1.036 1D46
-0 973 1.025 1D51 2.516 1.139 1.193 1.232 1.255 I 10 11 1.142
-0.269 1.206 1.178 1.167 2.628 OS75 OS68 1.179 5.184 1.009 0 974 1.237 1.770 1.215 1.173 I
2 679 0 674 3.451 4 097 1.198 0.993 OS94 1.165 0.955 1.107 0.951 12 1.200 0.982 0.964 1.140 OS37 1.084 0S55
-0.233 1.097 3.008 2.407 1.767 2.234 0350 1.247 1.200 I
1.115 1.145 1094 1D91 13 1.263 1.193 1.127 1.119 1.094 1.067
-1559 0.662 -1 111 2.638 0.018 2 290 14 I 15 1.086 0.938 16 1.077 OS39 0 896 -0.091 1.042 1.043 17 I
1.034 1.044 0 777 -0.049 1.169 1.135 18 1.150 1.133 1880 0.230 I J= 19 0322 0.946
-2.422 1.143 1.111 3.158 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 g - ee -
I 5.0
SUMMARY
AND CONCLUSIONS This report describes the code used at GPUN for steady state analysis s of the Oyster Creek core. The
- code is an improved version of NODE-B which developed under the PSMS program sponsored by EPRI. It is a one group neutronic model integrated with a thermal hydraulic model (THERM-B).
The Oyster Creek core is modeled in nodes, one node radially and 24 axially for each fuel assembly. The neutron source, S, at each node is calculated in terms of km and W.n. W.n is the probability of a neutron born in node m and is absorbed in node n and is a function of the migration area, M*. The nodal ka is a function of fuel, exposure, coolant density, fuel temperature, control fraction and xenon concentration. The core k-effective is based upon a neutron balance
- summed over the entire core. The core flow distribution is calculated by equalizing the pressure drop across each channel. An EPRI developed mechanistic model is used to determine void fraction.
The nodal model was verified against measurements from Oyster Creek l l W cycles 8 and 9 and Hatch I cycle 1. The verification data includes 1 gamma scan measurements, TIP data and cold criticals. A variety of core conditions were covered and both 7x7 and 8x8 fuel designs were covered. The verification work from Oyster Creek data showed: a hot reactivity of 0.986245 with a standard deviation of 0.00177; a cold Keffective of 1.00193 with a standard deviation of 0.00293; 99 - I
4 a nodal uncertainty of 7.65% based on comparison to TIP measure-4 ments. l The verification from Hatch I cycle 1 data showed: j I - a hot reactivity of 0.98498 with a standard deviation of 0.00537; a nodal uncertainty of 9.14% based on comparison to TIP measure- ! ments;
- a nodal uncertainty of 7.95% based on comparison to gamma scan measurements.
- iI The results of GPUN's off-line verification agree with the on-line benchmarking sponsered EPRI. It demonstrates the adequacy of the off-line code.
I I I I I I - 100 - I
6.0 REFERENCES
- 1. " Power Shape Monitoring System (PSMS). Technical Description," e EPRI Report NP-1660,'Vol. 2. Prepared by Quadrex Corp.,
February 1981.
- 2. "ARMP: Advanced Recycle Methodology Program," EPRI CCM-3, October 1976.
I "BWR Hybrid Power Shape Monitoring System, Volume 1: Technical 3. Description and Evaluation." EPRI Report NP-3195-CCM, prepared by Systems Control, Inc., Nuclear Associates International and Hitachi, Ltd., September 1983.
- 4. "BWR Hybrid Power Shape Monitoring System, Volume 5: Benchmark Report," EPRI Report NP-3195-CCM, prepared by Systems Control, Inc. and Utility Associates International, September 1983.
- 5. " Mechanistic Model for Predicting Two-Phase Void Fraction for Water in Vertical Tubes, Channels, and Rod Bundles," EPRI-NP-2246-SR, Prepared by G.S. Lelbouche and B.A. Zolotar, Special Report, February 1982.
- 6. McAdams, W.H., " Heat Transmission," 3rd ed., McGraw-Hill Book Company, Inc., New York (1954).
se'
- 101 -
I
1 i i
- 7. Lottes, P.A. and W.S. Flinn, "A Method of Analysis of Natural Circulation Boiling Systems," Nuclear Science and Engineering, 1.
461-476 (1956). I 8. Martinelli, R.C., " Prediction of Pressure Drop During Forced Circulation Boiling of Water," Transactions of the ASME (August 1948). I
- 9. Haling, R.K., " Operating Strategy for Maintaining an Optimum Power Distribution Throughout Life," ANS Topical Meeting on Nuclear Per-formance of Power-Reactor Cores, 1963 (TID-7672).
- 10. Larsen, N.H. and Goudey, J.L., " Core Design and Operating Data for Cycle 1 of Hatch 1," EPRI NP-562, 1979,
- 11. Shiraishi, L.M. and Parkos, G.R., " Gamma Scan Measurements at Edwin I. Hatch Nuclear Plant Unit 1 Following Cycle 1,"
I EPRI-NP-511, 1978.
- 102 -
Appendix A
\
STATISTICAL DEFINITIONS - The following definitions are used for residuals and their statistics. Residual I R = [M(#,k) - P(t,k)]/5 I where M(#,k) - measured value for bundle / at node k P(#,k) - predicted value for bundle / at node k 5 - average value of measured readings L - number of bundles , K - number of nodes Overall Nodal RMS error RMSn =[ { R*(t,k) //*k]2 t,k I I Individual bundle l Es(l) = { R(t,k)/K k RMSs(l) = [ { R*(t,k)/K]* k ,
- 103 -
k Integral l 1 i j RMS =[ } E*(#)/L ] ( B i }. f Axial Average 4 1 } i fg Ea(k) = { R(#,k)/L 4
- E
)
ig SDa(k) = [ [ (R(#,k) - Ea(k))*/L-1] tem ig # f tez RMSa =[ [ E*(k)/K] e Peak Node RMSp..a = [ 2 R*(/,kp..w)/L ] 2
/
I I .. I - 104 -}}