ML19263C411

Generic Analysis of Control Rod Ejection Transient for Pwrs

ML19263C411
Person / Time
Site:	Prairie Island
Issue date:	01/31/1979
From:	Burnside R, Krysinki T, Pruitt D SIEMENS POWER CORP. (FORMERLY SIEMENS NUCLEAR POWER
To:
Shared Package
ML19263C410	List: ML19263C409 ML19263C411
References
XN-NF-78-044, XN-NF-78-44, NUDOCS 7902220079
Download: ML19263C411 (53)

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O XN-NF-78-44 ISSUE DATE: 02/06/79 A GENERIC ANALYSIS OF THE CONTROL R0D EJECTION TRANSIENT FOR PRESSURIZED WATER REACTORS PREPARED BY: R. J. BURNSIDE T. L. KRYSliiSKI D. W. PRUITT

XN-NF-78-44 ISSUE DATE: 02/06/79 A GENERIC ANALYSIS OF THE CONTROL R0D EJECTION TRANSIENT FOR PRESSURIZED WATER REACTORS PREPARED BY: RJ BURNSIDE TL KRYSINSKI DW PRulTT APPROVED BY: bk \\A A /OWN ~ ~ J.N.f10RGAN,MANkGER NEUTRONICS & FUEL MANAGEMENT $k E943 ,/ $3 V 7 C. E. LEACH, MANAGER THERMAL HYDRAULIC ENGINEERING 'I" fg @ t - r r-77 G. A. SOF D IANAG[R NUCLEAR FUELS ENGINEERING ACCEPTED BY: p,, /- 2 Ey1 gl. S. NECH0Dd, MANAGER LICENSING & COMPLIANCE / w, G.J. bus /ELMAN, MANAGER [ CONTRACT PERFORt1ANCE

U. S. CUSTOME R DISCL AIME R IMPORTANT NOTICE REGARDING CONTENTS AND USE OF THIS DOCUMENT PLE ASE READ CAREFULLY Exxon Nuclear Company's warranties and representations concersung the subject matter of this document are those set furth in the Aoreement betaecn Exxon Nuclear Company, Inc and the Customer pursuant to wtuch this document is issued. Accordingly, except as o:herwisa expressly provided..i such Agreement, neither Ex x on Nuclear Company, Inc. nor anv person acting on it. behalf makes any warranty or representation, en,iressed or implied, with respect to the accuracy, completeness, or usefulnes; of the information containext in this document, or that the use of any inf ormation, appa ra tu s, method or process disclnsM any liabdities with tespect to the use of, or for damages resulting from the use of any information, apparatus, melluxl or process disclosed in this dot ument, lhe mf or ma tion containn! hi r eiti is for the ude use of Customer. In order to avoul impairment of rights of E x xon Nui: car Company, loc. so patents or iriventions whu h may le ow ludisl m the mf.w main o s on tainel m this doc ument, the ret inient, by its n ceptant e of this doc ussiesit aspees not to pubbsh or mJbe pubhc use (in the patent sense of the term) of such inf or mation u ntil so authorizesi in writing by Exxon Nuclear Company, Inc. or until af ter six (6) months following termination or expiration of the aforesaid Agreement and any extension thereof, unMss otherwise expressly provnhtf in the Agreement. No rights or ht enses in or to any patents are emphed by the furnishing of this document XN NF F 00,765

i XN-NF-78-44 Table of Contents Section Page

1.0 INTRODUCTION

1

1.1 DESCRIPTION

OF ACCIDENT.......... 1 1.2 DESIGN AND LIMITING CRITERIA I 1.3 OBJECTIVE........................... 2 2.0

SUMMARY

3 2.1

SUMMARY

AND CONCLUSIONS.................... 3 3.0 METHODS OF ANALYSIS 5 3.1 EJECTED R0D TRANSIENT COMPUTER MODEL 6 3.2 REACTIVITY FEEDBACK TREATMENT........ 7 3.3 PEAKING FACTORS AND FUEL TEMPERATURE TREATMENT 8 4.0 SELECTION OF PARAMETERS AND SENSITIVITY ANALYSIS... 10 4.1 SELECTION OF PARAMETERS.................... 10 4.2 SENSITIVITY ANALYSIS 10 4.2.1 Doppler Reactivity Feedback.............. 11 4.2.2 Moderator Temperature Feedback 11 4.2.3 Reactivity Worth of Ejected Control Rod........ 11 4.2.4 Power Peaking Factors............. 12 4.2.5 Delayed Neutron Fraction 12 4.2.6 Mean Prompt Neutron L'ifetime, t* 13 4.2.7 Ejected Control Rod Velocity 13 4.2.8 Reactor Trip Delay Time................ 13

ii XN-NF-78-44 Table of Contents Continued Section Page 4.2.9 Heat Transfer Coefficients 13 4.2.10 Ini tial Fuel Enthalpy.......... 13 5.0 RESUL'S 20 5.1 POWER LEVEL AND FUEL TEMPERATURE TRANSIENT RESULTS 20 6.0 OVERPRESSURIZATION ASSOCIATED WITH R0D EJECTION ACCIDENT...... 33 6.' INTRODUCTION 33

6.2 DESCRIPTION

OF MODEL 33 6.3 EXAMPLE CALCULATION...................... 36 7.0 APPLICATION OF GENERIC ANALYSIS 40 7.1 NEUTRONIC DESIGN PARAMETERS............... 40 7.2 APPLICATION OF PARAMETRIC RESULTS............... 41

8.0 REFERENCES

43

iii XN-NF-78-44 LIST OF TABLES Table Page 6.1 EXAMPLE OVERPRESSURIZATION CALCULATION............... 38 LIST OF FIGURES Figure Pcge 4.1 CHANGE IN DEPOSITED ENTHALPY VS DOPPLER COEFFICIENT, HOT FULL POWER......................... 14 4.2 CHANGE IN DEPOSITED ENTHALPY VS DOPPLER C0 EFFICIENT, HOT ZERO POWER....... 15 4.3 DEPOSITED ENTHALPY VS CONTROL R0D WORTH, HOT FULL POWER,.......................... 16 4.4 DEPOSITED ENTHALPY VS CONTROL R0D WORTH, HOT ZERO POWER........................... 17 4.5 CHANGES IN DEPOSITED ENTHALPY VS s HOT FULL POWEP..........eff'............... 18 4.6 CHANGES Ih DEPOSITED ENTHALPY VS 8 HOT ZERO POWER..........eff'............... 19 5.1 RELATIAVE POWER VS TANSIENT TIME, R0D WORTH, HFP... 22 5.2 RELATIVE POWER VS TRANSIENT TIME. Beff, HFP 23 5.3 RELATIVE POWER VS TRANSIENT TIME, R00 WORTH, HZP. 24 5.4 RELATIVE POWER VS TRANSIENT TIME, Beff, HZP 25

iv XN-NF-78-44 List of Figures Continued Figure Page 5.a CENTERLINE AND AVERAGE FUEL TEMPERATURE VS TIME, Ap =.31%, S =.0061, HFP............ 26 g77 5.6 CENTERLINE AND AVERAGE FUEL TEMPERATURE VS TIME, Ap =.58%, S =.0061, HFP..................... 27 eff 5.7 CENTERLINE AND AVERAGE FUEL TEMPERATURE VS TIME, Ap =.58%, s =.0050, HFP..................... 28 eff 5.8 CENTERLINE AND AVERAGE FUEL TEMPERATURE VS TIME, Ap =.89%, s =.0061, HZP 29 eff 5.9 CENTERLINE AND AVERAGE FUEL TEMPERATURE VS TIME, Ap = 1.19%, S =.0061, HZP 30 eff 5.10 CENTERLINE AND AVERAGE FUEL TEMPERATURE VS TIME, Ap =.89%, B =.0050, HZP, P.F. = 12.8 31 eff 5.11 CENTERLINE AND AVERAGE FUEL TEMPERATURE VS TIME, Ap =.89%, s =.0061, HZP, P.F. = 12.8 32 eff 6.1 v

• AS A FUNCTION OF PRESSURE 39 2

1 XN-NF-78-44

1.0 INTRODUCTION

Exxon Nuclear Company (ENC) has performed a generic control rod ejection accident analysis for thermal pressurized water reactors (PWR's). The control rod ejection accident was simulated for a reload type reactor core. The ejected control rod accident can be parameterized by the following variables:

1) reactivity worth of ejected control rod, 2) power peaking factor, 3) reactivity coefficients dnd 4) delayed neutron fraction, S eff' With these variabics defined, the core size, bank worth, etc., are not si nifi ant. Therefore, the ejected rod analysis presented here will be app ble to all future ENC reloads for PWR type reactors.

1.1 DESCRIPTION

OF ACCIDENT f A control rod ejection accident is defined as the mechanical failure of a control rod mechanical pressure housing such that the coolant system pressure would eject & rodded control assembly (RCA) and drive shaft to a fully withdrawn position. The consequences of this mechanical failure is a rapid reactivity insertion together with an adverse core power distri-bution, possibly leading to localized fuel rad damage. The rod ejection accident is tne most rapid reactivity insertion that can be reasonably postulated. The resultant core thermal power excursion is limited primarily by the Doppler reactivity effect of the increased fuel temperatures and is terminated by reEctor trip of all remaining control rods, activated by neutron flux signals. 1.2 DESIGN AND LIMITING CRITERIA Although the rod ejection accident is not expected to occur, design and limiting criteria are applied to insure that the power reactor system i;

2 XN-NF-78-44 sufficiently protected against this accident. These design and limiting criteria are: 1. The average fuel pellet enthalpy at the hot spot will be equal to or less than 280 cal /gm. 2. The peak reactor pressure during any portion of the transient will be less than tr.e value that will cause stresses to exceed the emergency condition stress limits as defined in Section III of the ASME boiler and pres-sure vessel code. 3. Fuel melting will be limited to keep the off-site dose consequences well within the guidelines of 10 CFR Part 100, " Reactor Site Criteria". Tnese limiting c'.iteria are taken from the NRC Regulatory Guide 1.77 " Assumptions used for evaluating a control rod ejection accident for pressurized water reactors". 1.3 OBJECTIVE The objective of this study is to develop a parameteric set of curves, based on the criteria of Section 1.2, which quantify the consequences of the control rod ejection accident for combinations of significant parameters. As the detailed cycle desi;ns are completed for reactors reloaded by Exxon Nuclear Company, an analysis will be performed to demonstrate that the reactor system control rod ejection parameters limit tha accident within the specified safety criteria of this generic report.

3 XN-NF-78-44 2.0

SUMMARY

2.1

SUMMARY

AND CONCLUSIONS This control rod ejection accident is a result of the assumed failure of a control rod mechanism pressure housing which ejects the control rod from the core. It is considered that this accident wil! not occur due to th.! low probability of a control rod housing failure. The limiting criteria, given in Section 1.2, ensure that no long term reactor core cooling problems exist or that the radioactivity release limits according to 10 CFR 100, in the event the accident does occur, are not exceeded. The objective of this work is to demonstrate how the limiting criteria relate to ti;e important neutronic design parameters to ensure the safety of the neut onic design of the re.ctor core. A transient, two dimensional (R - Z geometry) computer model with fuel temperature feedback is utilized in this analysis. The model simulates the reactivity insertion caused by a control rod being ejected from the reactor core followed by the subsequent shutdown due to Doppler feedback and the scram bank entering the core. Prior to 1.he start of the accident, the core initial conditions are set at a near critical state. The transient mcdel computes the consequeaces for the accident in terms of the resultant peak energy (and temperature) deposition in the fuel. More details on the method are given in Section 3.0. The result of this generic rod ejection analysis is presented as a set of curves for both hot full power (HFP) and hot 'aro power (HZP) conditions which allow a determination of the peak deposited enthalpy for the specific

4 XN-NF-78-44 reload design parameters. This calculation.4111 determine if the plant will meet design and limiting criteria given in Section 1.2. No attemp: was made to determine the limiting value of each parameter. Rather the analysis as performed here, was to bound the parameters which impact on the rod ejection accident. Essentially the important parameters are:

1) reactivity worth of the ejected rod, 2) power peaking, 3) reactivity coefficients, and

4) delayed neutron fraction S Some other parameters and their effects eff.

are discussed in Section 4.0. Based on the current analysis the ejected rod accident is seen never to exceed the criteria set forth in Section 1.2 for expected values of the parameters affecting the rod ejection accident.

5 XN-NF-78-44 3.0 METHOD OF ANALYSIS The limiting consequence due to a control rod ejection accident is calculated in terms of peak energy deposition in the fuel. Gt!!aeline values of stored energy content are set out by the NRC in Reference 1. Thus the objective of the control rod ejection analysis is to determine if any fuel will exceed these ouideline values during the unlikely occurrence that a control rod is ejected. The analysis and its results are applicable to all ENC PWR reload reactor cores since all important fuel assembly and core neutronic paramete.rs used as input to the calculations were selected to envelope all current reload designs for which ENC has reload contracts. The sensitivity analysis dis-cussed in Section 4.0 is to ensure this.bjective is met. The general reactor core cond Pions assumed for this analysis are: A - Hot full power B - Hot zero power Only the two power levels were calculated in this analysis. By analyzing hot full power and hot zero power conditions, the core parameters affecting the control rod ejection accident are bounded. Hence, the operation at other power levels between HFP and HZP will meet the criteria since that power level lies between the values already analyzed. Beginning of cycle and end of cycle conditions are accounted for by the range of delayed neutron fractions utilized in the study. The accident transient was assumed to last for five seconds, whereas the ejected cortrol rod is completely out 2. the. ore in s0.1 seconds. All

"~ ~ s , h g- ._m._ ... '... _ _- km i ,,. T b. ..,c n w I = 6 XN-NF-78-44 j c of tne calculations herein reported have used a transient time of five seconds. The scram bank worth used in 'he model for hot full power is 2.62% Ap and l 3.487 An a t hot zero power. Both of these values are conservative when [g compared to the nominal scram bank worth avuilable in PWR reload cores. 3.1 EJECTED P.0D TRANSIENT COMPUTER MODEL The XTRAN computer code (Reference 2) is utilized for the ejected rod accident analysis. The XTRAN code, 5;ecifically F veloped to analyze 3 the ejected rod accident, is a two-dimensional tr - z cylindrical geometry) 1 computer program which solves the space and time dependent neutron diffusion [ equation with fuel temperature a1d moderator density reactiv'Ly feedbacks. XTRAN employs a nodal method based directly on a one energy group finite difference technique for the solution of the time dependarit neutron diffu= ion [ equation. The one-group macroscopic cross sections used in the iterative f flux solution are collapsed from macroscopic two-group values modified at 1 each time step by reactivity feedbacks. The space and time dependent neutionic model incorporated in XTRAN is capable of computing a rapid reactor transient initiated by the reactivity insertion due to a control rod being removed from the core. Since the model utilizes twc-dimensional (r-z) geometry, the code can calculate the rapidly changing flux distribution as a control rod travels out of the reactor core and the svain rod bank subsequently enters the reactor core. = 4 XTRAN initially aetermines the static flux and power distribution corresponding to the problem input. This steady-state calculation includes xe l M -.; _. n.-

• n r

7 XN-NF-78-44 heat transfer and determines the temperature distribution in the fuel rod and the peak center line temparature. The heat transfer coefficients are then set to zero for an adiabatic transient calculation and the initial time step for the transient analysis is 0.0001 seconds. The code then automati-cally determines the time step interval based on the number of iterations necessary to achieve convergence. This method permits small time steps during periods of slow change. Therefore, the code efficiently solves the transient problems without the user choosing time step sizes. Six groups of delayed neutron precursors are employed in this transient analysis. The decay constants and delayed neutron fractions utilized in the generic rod ejection analysis are typical of those calculated during normal PWR reload design efforts. XTRAN has been evaluated and ths_ results compared to other transient models, and has shown good agreement. Details of these comparisons are given in Reference 2. 3.2 REACTIVITY FEEDBACK TREATMENT The XTRAN code har the ability to model both moderator and Doppler feedback effects. In this study, the moderator feedbacks are conservatively set equal to zero and the transient performed adiabatically. Due to the rapid power excerions, typical of the control rod ejection transiant, tne scarm banks are tripped and enter the core before signficant perturbations occur in the moderator temperature. Therefore all the analysis completed in this report have r.o moderator feedbacks included.

8 Xft-fiF-78-44 Although the XTRAN model is two-dimensional, (r-z geometry) there is a radial and axial component tc its calculation. Due to this type of calculation no special weighting is performed for the Doppler feedbacks. The Doppler feedback is modelled by inputting the change in the macroscopic cross sections due to the change in fuel temperature. The effect of a change in fuel temperature upon the cross sections is modelled in terms of the square root of the two temperatees, where one is the reference fuel temperature of the cross sections. The modelling of the Dappler effect in this manner shows that for a change in temperature. the change in the cross section is constant. 3.3 PEAKING FACTORS AND FUEL TEMPERATURE TREATMENT The XTRAN model calculates the peaking factors at each node where a node is defined by the radial and axial mesh spacing of the geometry. This allows the simulation of the power peaking in the reactor core. The power peaking factors parameterized in thic analysis are calculated by XTRAN at the time when the ejected control rod has just moved out of the core. This transient peaking factor reflects some amount of Doppler feedback in its calculation. The neutronic calculation of the ejected rod parameters for a reload core is performed statically, that is, with no pointwise feedbacks. Hence, the neutronic design calculation will yield a conserative evaluation of the power peaking. The fuel temperature is calculated for each radial mesh interval as if there were a single fuel rod in that radial location. The fuel rod is divided into eight equal volume nodes plus one cladding node. The axial

9 XN-NF-78-44 direction is explicitly defined. Temperatures are calculated for each of the nine fuel rod nodes at each time interval based on the specific heat data for UO f R. A. Hein and P. N. Flogell (Reference 3). The modelling 2 details of this procedurc are also described in Reference 2.

10 XN-NF-78-44 4.0 SELECTION OF PARAMETERS AND SENSITIVITY ANALYSIS 4.1 SELECTION OF PARAMETERS _ Exxon Nuclear Company (ENC) has been contracted to reload a variety of pressurized water reactors. This generic rod ejection analysis report should cover all these eactor types. After reviewing the reactor types for which ENC has responsibility, D. C. Cook Unit 1 was chosen as the repre-sentative plant. This plant has a high power density (about 100 kw/ft). All parameters input in the analysis are typical D. C. Cook values. The parametric analysis then extends these D. C. Cook typical values to cover the range of values the parameters may have for cther specific plants. Uncertainties were not explicity applied to any of the values in tne ejected control rod analysis. The neutronic parameter conservatism is accounted for in uncertainties applied to the peaking factors and ejected rod worths as the design calculations are completed for each specific plant. Also for this ejected rod analysis, the thermal heat transfer parameter uncertainties are not vital since the c&lculations were completed with no heat transfer from the fuel. This procedure is conservative with respect to the calculation of the deposited enthalpy in the core. 4.2 SENSITIVITY ANALYSIS This section describes the results of varying the important parameters to show their sensitivity as well as er.able the future fuel management schemes for ENC plants to be covered by this analysis. This sensitivity study comprehensively parametarizes all the important parameters to the ejected rod analysis.

11 XN-NF-78-44 4.2.1 Dop p r R uctivity Feedback The Dont er fecaback effect on the control rod ejection accident is shown in Figures 4.1 and 4.2 for hot full power and hot zero power, respectively. The Doppler feedback has a larger effect at HZP than HFP. The Doppler reactivity coefficients used in the calculations are covered by the range of.8 to 1.35 pcm/0F which is conservative with respect to nomincl de :.ign s'alues of about 1.7 pcm/ F. The Doppler feedback is more effective at hot zero power temperatures since the f Jel will rise in temperature more for a given onthalpy increase than at hot full power temperatures. This can be observed from the heat capacity curve for UO which in the hot zero power range of temperatures 2 is relatively flat. For the full power temperature range (hot spot is >25000F) the heat capacity is initially larger than at HZP and rises rapidly with increasing temperature so the temperature change is smaller for a given enthalpy increase. 4.2.2 Moderator Temperature Feedback No parameteric analysis was performed, since all of the calculations excluded moderator feedback. 4.2.3 Reactivity Worth of Ejected Control Rod Figures 4.3 and 4.4 show the variation of the deposited enthalpy with the ejected rod worth for HFP and HZP coriitions, respectively. As expected the nagnitude of the accident increases with increasing rod worth. The reactivity worth of the ejected rod at HFP is smaller than at HZP due to the constraints imposed on the plant by the control rod insertion limits.

12 XN-NF-78-44 4.2.4 Power Peaking Factors Also presented in Figures 4.3 and 4.4 are the effects of power peaking factors on deposited enthalpy for HFP and HZP, respectively. The magnitude of the accident increases with increasing peaking factors. As seen in the HZP case, there is an ejected rod worth below which the peaking factor has no effect ca the accident. This is due to the fact tnat the lower rod worth reactivity insertion does not initiate a high power transient. 4.2.5 Delayed Neutron Fraction The effective delayed neutron fraction, Seff, effect on deposited enthalpy (and hence fuel center line temperature) is shown in Figures 4.5 and 4.6 for HFP and HZP, respectively. The HFP transients are less sensitive to B since a smaller delayed neutron fraction results in a eff faster power reduction after the trip. Since a larger percentage of the energy deposition occurs after the trip for transients at HFP than at HZP a Igrger benefit is realized for the faster power reduction at HFP. This t nefit partially ccupensates for the larger reactivity insertion, expressed i i dollars, and results in a reduced sensitivity to S at HFP. eff Of all the parameters effecting the rod ejection accident only the moderator temperature coefficient (MTC), exposure distribution and the delayed neutron fraction significantly change from beginning of cycle to end of cycle. Since the analysis described herein has set the MTC eaual to zero, and no credit has been taken for the flattening effect of the E0C y exposure distribution on the core power distribution, only the B changes eff y v t t P

13 XN-NF-78-44 from BOC and EOC. Therefore, this subsection describing the effect of changing e n the rod ejection accident, also accounts for changes due eff to cycle burnup based upon the above assumption. 4.2.6 Mean Promp_ Neutron Lifetime t* The deposited enthalpy was found to be independent of t* in the 10 to 15 p/sec range. 4.2.7 Ejected Control Rod Velocity The deoosited enthalpy was found to be independent of the time for the ejected rod to leave the core. For a 20% increase to the ejected rod velocity (inc ease the reactivity insertion rats) there was no change in the deposited enthalpy. 4.2.8 Raactor Trip Delay Time _ The deposited enthalpy was found to be independent of the reactor trip delay time in the.5 to.6 second range. 4.2.9 Heat Transfer Coefficients No sensitivity studies were completed here since the transient analysis was performed with no heat transfer from the fuel. 4.2.10 Initial Fuel Enthalpy The transient incremental deposited enthalpy was found to be insensitive to the initial fuel enthalpy at HFP and HZP. Therefore, any changes in the initial fuel enthalpy due to power redistribution or heat conduction parameters during the steady state can be applied as a bias to the total depos-ited enthalpy. The initial peak fuel enthalpies in the rod ejection region for this study at HFP and HZP were 40.8 and 16.7 cal /gm, respectively.

14 XN-NF-78-44 7 i i i i i l.30 1.20 1.10 s fi 1.00 5 5 .9 5 .8 i I ,I i i .8 .9 -1.0 -1.1 -1.2 -1.3 -1.4 0 Doppler Coefficient, pr.m/ F Figure 4.1 Change in Deposited Enthalpy vs Doppler Coefficent Hot Full Power

15 XN-NF-78-44 I i i i i i i l.4 1.3 $ 1.2 2 \\ c LLJ C 1.1 E %5 1.0 - .9 .8 .7 1 I l i I I l .8 .9 -1.0 -1.1 -1.2 -1.3 -1.4 Doppler Coefficient, pcm/ F 0 Figure 4.2 Change in Deposited Enthalpy vs Doppler Coefficient Hot Zero Power

16 XN-NF-78-44 3 I I I I l 1 260 240 220 200 S bD 180 A S . e4 .e 2f 4 9 h / w 160 ,, b s / E

1. o*

/ co 'G o% I*ctof, A - E 9e3 $ 140 9e3gog 120 110 100 l I I I I I I .0 .1 .2 .3 .4 .5 .6 .7 Rod Worth, %t,o Figure 4.3 Deposited Enthalpy vs Control Rod Worth Hot Full Power

17 XN-NF-/8-44 I i l I i 220 200 180 160 140 S 0 / 2 u ( 2 120 g g-

• 5 q*

b o 100 +&@ + e' .2 4 s 5 80 qc++ / 60 40 / 20 i i i i i i i .5 .6 .7 .8 .9 1.0 1.1 1.2 Rod Worth, %Ao Figure 4.4 Deposited Enthalpy vs Control Rod Worth Hot Zero Power

18 XN-NF-78-44 I I I I I 1.50 1.40 1.30 1.20 s 15 1.10 B; e $ 1.00 5 s 5 r .90 .80 .70 1 I i 1 I .4 .5 .6 .7 .8 .9 8eff' I' Figure 4.5 Changes in Deposited Enthalpy vs s Hot Full Pcwer eff

19 XN-NF-78-44 I I I I i 1.50 1.40 1.30 1.20 D %5 6 1.10 E o '"n O %l.00 a C r-- 2 .30 u .80 .70 1 I I I I i .4 .5 .6 .7 .8 .9 8eff' % Figure 4.6 Changes in Deposited Enthalpy vs Seff Hot Zero Power

20 XN-NF-78-44 5.0 RESULTS 5.1 POWER LEVEL AND FUEL TEMPERATURE TRANSIENT RESULTS Although the results of the calculations to determine the deposited enthalpy for the rod ejection accident are described in Section 4.0, no dis-cussion has been mace of the power level and fuel temperature transients. The nuclear power transient calculation with no thermal heat transfer from the fuel was calculated with XTRAN. Figure 5.1 shows the nuclear power transient for rod worths of.58% as and.31% ap at hot full power for the first 4.0 seconds of the ejected rod accident. The Doppler coefficielt is -1.065 pcm/0F and s is.0061. Figure 5.2 shows the nuclear power transient eff fortheB0Ccase(seff =.0061) and the E0C case (Beff =.0050) for the.58% ap transient. Figure 5.3 shows the nuclear power transient for the hot zero power case at rod worths of 1.191% ap and.890% ap. The peaking factor here is 5.65, the Doppler coefficient is -1.027 pcm/ F, and 8 =.0061. Figure 5.4 shows the eff B0C (seff =.0061) and E0C (seff =.0050) nuclear transient for the op insertion of.89%. For these cases the peaking factor is 12.80. From the same calculations as discussed above, Figures 5.5., 5.6, and 5.7 show the peak fuel temperatures cad the average fuel temperatures for the hot full power cases. The hot zero power fuel temperature transients corres-ponding to Figures 5.3 and 5.4 are shown in Figures 5.8 through 5.11. These XTRAN results are from the same calculations which generated the nuclear power transient data. Notice that for the cases shown the fuel temperature is always beled 44000F. The peak fuel temperature in the cases shown, was 43330F

21 XN-NF-78-44 corresponding to the case with c a =.58%, seH.0050 and a peaking factor U of 5.65. This is only 69 F higher than the identical case with s equal eff to.0061.

g 22 XN-NF-78-44 I i .58% Rad Worth (s =.0061) 10 eff .31% Rod Worth (B =.0061) eff C E S Pi 11 .5 1 g 10 5 g 3g g z 3 ~ E x / s N \\ U \\ 10 0 1 2 3 Transient Time in Seconds Figure 5.1 Relative Power vs Transient Time Hot Full Power

23 XN-f1F-78-44 1 2 .58% Rod Worth B0C (B =.0061 ) 10 eff 58% Rod Llorth E0C (B =.0050) eff l 1 l ll 2 e I l o 1 I 10 1 g g l S \\ c { ie 1 s i 5 \\ e \\ \\ \\ \\. N ) \\ 100 's i I i 0 1 2 3 Transient Time in Seconds Figure 5.2 Relative Power vs Transient Time Hot Full Power

24 XN-NF-78-44 -r I i i -l ~_l 2 1 - l l .89% Rod Worth (s =.0061) eff 10 _ll 1.191 Rod Worth (s .0051) 5 eff 51 = C 4 10 E l o R ~ m 11 \\ i \\ s \\ u N I \\ O 10 \\ s' \\ Z 3 \\ z N m x N \\ ~ N N I N N ] w'7 2 10 1 ~ Figure 5.3 'lelative Power vs Transient Time ~ Hot Zero Power l Transient Time in Seconds I 10 I 0 1 2 3'-

.m 25 XN-NF-78-44 1 I l l i 5 10 .89% Rcd Worth (Beff =.0061) ,__ __.89% Rod Worth (Feff =.0050) 10 y r \\ og N \\ 3 N 10 h \\ s \\ e. x b N g N \\ e a 2 2 10 1 10 t I 0 1 3 Transient Time in Seconds Figure 5.4 Relative Power vs Transient Time Hot Zero Power

XN-NF-78-44 26 I l l l 1 4600 4500 Ao = .31% 4400 4300 E'o % 4200 t g 4100 T, 4000 E g 3900 e 3 3800 N b f b 1900 1500 c, 5 b 2' T2 8, E as 4 1000 0 1 2 3 4 5 6 Transient Time in Secoiids Figure 5.5 Centerline and Average Fuel Temperature vs Transient Time, Hot Full Power

27 XN-f4F-78-44 I I l 1 I g 4400 O no =.58% 2e s =.0061 eff 0 4200 N 2 2 8 { 4000 b B: u 3800 / / 1900 1800 1700 1600 E 3 1500 Eo g1400 r T 1300 E e 1200 E s. s' 1100 1000 i t i i 0 1 2 3 4 5 6 Transient Time in Seconds Figure 5.6 Centerline and Average Fuel Temperature vs Transient Time, Hot Full Power

28 XN-NF-78-44 i i i 1 4400 Ap =.58% 4300 g ff =.0050 e ~ 4200 m 5 4100 I $ 4000 0 k 3900 ~ 3800 1 7 2000

• /

8 B $ 1500 Et' I "o E E 2 r 100t. i i i 0 1 2 3 4 5 6 Transient Time in Seconds Figure 5.7 Centerline and Average Fuel Temperature vs Transient Time, Hot Full Power

29 XN-NF-78-44 I I I l l 2600 2500 tip =. 89 f, 6 =.0061 eff 2400 2300 2200 2100 2000 Fuel 1900 Centerline E 1800 B {1700 a Bs 1600 T 2 1500 1400 1300 800 Average 700 7 600 500 I 1 1 i i 0 1 2 3 4 5 6 Transient Time in Seconds Figure 5.8 Centerline and Average Fuel Temperature vs Transient Time, Hot Zero Power

30 XN-NF-78-44 3400 i i i i i i 1.19% op t .0061 s = 3200 eff 3000 Fue'. Centerline 2800 2600 g 2400 B 2 E y2200 22 2000 / / 1100 1000 Average 900 800 700 600 500 t e i i U 1 2 3 4 5 6 Transient Time in Seconds Figure 5.9 Centerline and Average Fuel Temperature vs iransient Time, Hot Zero Power

31 XN-NF-la-44 i I i i i j 3500 Fuel Centerline - Ao = .89% .0050 fl = eff e 3000 2500 B 2 E S s G11 1 2000 900 800 9 700 600 1 ~ 500 i O I 2 3 4 5 6 Transient Time in Seconds Figure 5.10 Centerline and Average Fuel Temperature vs Transient Time, Hot Zero Power

32 XN-NF-78-44 I i i l I l 3600 .89% Ap = .0061 a = 3400 \\ Fuel 3200 Centerline 3000 i 2800 E B 2 E 2600 ,S. f 2 2200 2000 / / 900 Average l I l 1 0 1 2 3 4 5 6 Transient Time in Seconds Figure 5.11 Centerline and Average Fuel Temperature vs Transient Time, Hot Zero Power

f .f- %i - C mi. g '. ? ?. -i< 5 ;.. O ^. w y y. ._......,if.___......_.m_. m.. .h.gr W t. n. t. s 33 Xfi-flF-78-44 J 6.0 OVERPRESSURIZATI0ft ASSOCIATED WITH R0D EJECTI0fl ACCIDEf4T f*. 6.1 lilTRODUCT10fl 1 g-d Following the unlikely occurrence of the ejection of a control l, <n ) rod, an increase in reactor system pressure results due to the deposition l c of the energy produced during the transient into the coolant. In order to insure that the reactor system is sufficiently protected against excessive l.4 i .y overpressurization, a limiting criterion has been established and defined Ii, in Section 1. A model to compute this pressure rise has been developed and is explained in detail in the following sections. The model was apolied to t -j the example rod ejection transient which reasonably envelopes the antici-

• f pated overpressurization.

For this example, the model indicates that the s "i maximum pressure anticipated is well below the allowable maximum transient ". *i % pressure limit. Thus, adherence to the overpressurization criterion is met. .. xe J v ., a 6.2 DESCRIPTI0f10F MODEL

Qj ) T

4

/ The objective of the model is to calculate the pressure increase e v,y due to the abrupt increase in reactor power following a rod ejection. The 3..NT ' m '; 3 9 model is based on six major assumptions as discussed below: ~' (1) Energy is immediately transferred to the coolant. The energy s oroduced by the rod ejection is produced in the fuel rods. Thus, there is L' ( ** g a i a delay time due to the thermal resistance of the fuel and gap and the heat capacity of the fuel before the heTt is released to the coolant.

However, A

) this delay time is conservatively i'nored, producing a larger energy release 1k, %' to the coolant than exists during the accident. s. i) M s Vy 4 M w i .f [ .,-4 7 x, '~ 9 --=,4 h ? t, 'p ) gl'

34 XN-NF-78-44 (2) Single phase water is ir..ompressible. The water in the loops and reactor vessel is treated as incompress.31e. This assumotion is conservative since accounting for the compressibility of the water the pressure surge would be reduced by about five percent. (3) No mixing between water in the pressurizer at the start of the tra:isient and sater entering the pressurizer from the loops. Since the water in the loop is cooler than the pressurizer water, if mixing were allowed, additional steam condensation would occur thus reducing and/or eliminating the pressure surge altogether. (4) No heat removal from the steam generators. Since heat removal from the steam generators would lower the average temperature during the transient, the thermal expansion of the coolant would be lower, reducing the pressure surge. This assumption thus maximizes the magnitude of the calculated pressure surge. (5) Thermodynamic equilibrium in the pressurizer. This assump-tion allows for inmediate ;ondensation of the steam in the prr ssurizer. (6) Complete mixing in the reactor primary system. This assumes at; equal tempeiature rise in all parts of the reactor primary system. With those assumptions the calculation proceeds as follows for the pressure increase associated with the rod ejection. The total energy increase is computed as: T AE = p(r)dt (1) o

m _. t 35 XN-NF-78-44

where, p(r) is the calculated time dependent reactor power level over the calculated time transient time T - t.

g p(T) is calculated using the neutronics model described in this document. The reactor primary system internal energy associated with Eq. (1) is then defined as: U = V) +5 (2) M

where, U) is the initial primary system internal energy M is the primary coolant total mass.

From the steam tables the specific volume of the primary coolant at the end of the transient is determined and the increase in primary coolant volume is determined as: AV = (v) - vj) M (3)

where, v) and vj are the primary coolant specific volume before and after the transient.

Knowing the change in volume (AV) an isentropic compression of the fluid in the pressurizer is calculated, that is V =V - AV. (4) 2 2 and s =s (5) 2 2-

36 XN-NF-78-44 M =M (6) 2 2 Combining Equations 3 and 5 results in 2 " "2 ' I"2 () v Equations 5 and 7 uniqJely determine the thermodynamic state of the water in the pressurizer and, thus, tae pressurizer pressure at the end of the transient. The above method results in a conservative estimate of the pres-sure surge associated with the rod ejection transient. An alternative approach, which would result in a more reasonable pressure surge estimate, is to model the entire reactor system using the calculated P(T) es a driv-ing function. The alternate approach would use a plant transient simulation model consistent witn that used in determining the effects of anticipated reactor transients on thermal margins. It is recommended that the model described herein be used to conservatively estimate the pressure surge associated with the rod ejection transient. However, the use of the alternate approach is allowed if the estimate, as defined above, is overly conservative. The alternate approach will be used only on a case-by-case basis. 6.3 EXAMPLE CALCULATION An example calculation of the pressure surge associated with the rod ejection transient was selected from the results used in determining the parametric curves as shown in Section 4. The neutronics parameters

37 XN-NF-78-44 for the example calculations are shown in Table 6.1, along with the total energy released during the transient. This transient was selected as being representative of the rod ejection transients for the ENC reload fuel. The values of P(1) throughout the transient were determined from the appropriu.e XTRAN computer output and numerically integrated to obtain t1E. Using the total energy deposition as appears in Table 6.1, one obtains the new pressurizer specific volume (v2) as equal to 0.04626 ft /lb. On the basis of an isentropic process, one obtains the new pres-surizer pressure (P2 ) in the example case as a function of v2 This appears in Figure 6.1. Using Figure 6.1, one can estimate the peak pres-surizer pressure as no greater than 2400 psia. This value is well below the allowable peak transient pressure of 2720 psie. for the reactor vessel and pressurizer, presenting no impact upon existing plant technical speci-fications.

38 XN-NF-78-44 Table 6.1 Example Overprassurization Calculation Parameter Value Delayed neutron fraction, B 0.00606 eff Control rod worth, % i.191 Peaking factor 5.79 Doppler coefficient, pcm/0F -1.027 Initial power level, MW l.0 3 Total energy released, MW-sec 8.342 x 10 MW-sec Peak reactor pressure, psia 2400 Maximum allowable pressure, psia 2720

a 39 XN-NF-78-44 O O 4 0 L 3 v1 O O L O bo C O r-O 4 4 in r O M M C N CL '3 to 10 N e O L 3 L71 e e N O to O et M O N O H r > l l l l 1 I cn co s e m ey et et V V O O O O O b O O (9t/cU) 2e 4

40 XN-flF-78-44 7.0 APPLICATION OF GENERIC ANALYSIS 7.1 NEUTRONIC DESIGN PARAMETERS The key neutronics parameters used for the actual control rod ejection accident evaluation are to be calculated for each cycle using PWR Neutronics methods consistent with ENC's methodology, which has been reviewed and accepted by the NRC. The most severe control rod to be ejected is normally the maximum worth rod at hot full power and hot zero power conditions at any point in the cycle. The ejected rod worths and hot pellet peaking factors, before and after the ejection of the rod, are calculated with no pointwise feedbacks. Thus, no credit is taken for the power flattening effects of Doppler or mod-erator feedback in the calculation. The maximum rod worth and peaking factor, after ejection, are then applied to the parametric curves presented in Section 4.0 to determine the base deposited enthalpy for the accident. This base energy deposition is then corrected to account for differences in the Doppler coefficient, delayed neutron fraction, s, and initial conditions between the plant specific value s and the generic rod ejection accident. The Doppler reactivity coefficients as presented in Figures 4.1 and 4.2 are the differenctial coefficients evaluated for unccntrolled assemblies. In the reference transient analysis, the XTRAN model spatially treats the controlled and uncontrolled nodes with appropriate Doppler coefficient. How-ever, to facii t tate application of the parr..netric results for plants, only the uncontrolled Doppler coefficient needs to be calculated in order to be consis-tent with the reference control rof ejectioc. analysis.

41 XN-NF-78-44 The delayed neutron fraction, s, is to be evaluated at the appro-priate core exposure for each plant and cycle. As defined ric e, is deter-mined by an importance weighted homogeneous core calculation of he effective delayed neutron fraction. For fuel designs with similar enrichments, s, is primarily exposure dependent. If the rod ejection accident is to be evaluated at a different set of initial conditions than the generic report, a steady-state XTRAN calcula-tion:must be made. This calculation will provide a bias in the initial fuel enthalpies between the specific operation conditions and the generic report. Since the transient is performed adiabatically this bias can be applied directly to the parametric calculation as illustrated in the next subsection. 7.2 APPLICATION OF THE PARAMETRIC RESULTS As a sample illustration, the peak deposited enthalpy resulting from a set of hypothetical conditions is deterr.ed using the parametric results presented in Section 4.0. The HZP conditions prescribed for this sample case are as follows: Initial fuel enthalpy (cal /gm) 21.7 Maximum control rod worth (%Ap) 1.00 Doppler coefficient (pcm/ F) - 1.00 Power peaking factor 6.00 Delayed neutron fraction, 8 .0058 Using Figure 4.3, the peak deposited enthalpy is determined to be 92.0 cal /gm for the 1.00% ap rod worth with a 6.00 power peaking factor. The difference in initial fuel enthalpy is determined as 5 cal /gm from Sec-tions 4.2.10. This bias is summed to the 92.0 cal /gm to yield 97.0 cal /gm.

42 XN-fiF-78-44 U For a -1.00 pcm/ F Doppler coefficient, the relative peak deposited enthalpy is to be increased by 1.03 as obtain2d from Figure 4.2. The deposited enthalpy is thus 1.03

• 97.0 cal /gm or 99.9 cal /gm.

The multiplicative adjustment due to a B f.0058 is 1.04 as determined from Figure 4.6 and the peak deposited eff enthalpy is 1.04

• 99.9 cal /gm or 103.9 cal /gm.

Thus, the total enthalpy for this hypothetical case is 103.9 cal /gm. This resultant enthalpy is then com-pared to the 280 cal /gm limit to determine if the cycle design is acceptable with respect to a postu bted control rod ejection accident. The same procedure, as applied here for a sample case, can be employed to compute ti e peak deposited enthalpy result:ng from a control rod ejection accident for any PWR plant.

i 43 XN-NF-78-44

8.0 REFERENCES

1. " Assumptions Used for Evaluating a Controlled Ejection Accident for Pressurized Water Reactors", NRC Regulatory Guide 1.77. 2. J. N. Morgan, XTRAN-PWR: A computer code for the calculation of rapid transients in pressurizea water reactors with moderator and fuel temperature feedback", XN-CC-32, September, 1975. 3. R. A. Hein, P. N. Flagett, "Enthalpy Measurements of UO nd 2 0 Tungsten to 3260 K, February, 1968 (GEMP-578). _ _. _...}}