NucE 431W Core Design Presentation Bayshore Unit 1 Reload Core Design Group 13 Michael Bertino Michael Stachnik Submitted to: Dr. K Ivanov Dr. M. Avramova Mentor: Chris Wagener

Table of Contents Introduction Loading Pattern Development Safety Analysis Operational Data Thermal Hydraulics Analysis Conclusion

INTRODUCTION Student Objectives: To be able to use the codes and methods used by Westinghouse to generate a core loading pattern for a cycle 13 Bayshore Unit 1 reactor and perform reload design analysis. Perform an analysis for operational conditions and safety requirements for our core loading pattern. Perform a thermo-hydraulic analysis on our core loading pattern for both steady state and transient conditions.

What is ANC? ANC (Advanced Nodal Code) Multidimensional nodal code. Licensed by NRC for PWR analysis Calculates: Core reactivity Assembly power Rodwise Power Reactivity coefficients Core depletion Control rod and fission product worths

Reactor Core Design CE 2-PWR Loop Core Thermal Power=2700 MWt 4 Control Rods 217 assemblies 5 guide tubes

Plant Description Inlet core temperature is programmed to vary from 532 °𝐹 to 549 °𝐹 from 0 % to 100 % power. Control rods move from 0 to 137 steps withdrawn. Rod insertion limits are a function of power. Full power upper limit of the axial shape index (ASI) is -8 %.

Loading Pattern Development

Loading Pattern Development There are four criteria that must be evaluated to development an initial loading pattern (LP) Energy(cycle length) FΔ𝐻 peaking factor, ARO HZP, MTC (all power levels) Fuel Inventory

Loading Pattern Parameters

Gadolinia Burnable Absorber 68 feed assemblies 36 assemblies at 4.013 w/o U235 20 assemblies at 4.420 w/o U235 12 assemblies at 4.365 w/o U235 Mixed with UO2, displaces fuel from the core. Complex depletion chain. No placement restrictions. Optimized to reduced peaking within the assembly

Summary of ANC Runs to Final LP

Final Core Loading Pattern

Energy, Cycle Length Requirement EFPD is defined as the total amount of energy produced from BOC to EOC. Boron Concentration must be reduced to 10 ppm at HZP conditions The final burnup step is used to calculate the EFPD of the LP: 𝐸𝐹𝑃𝐷=𝐵𝑈∗ 𝑀𝑇𝑈 𝑃 0  𝐸𝐹𝑃𝐷=14700 𝑀𝑊𝐷 𝑀𝑇𝑈 ∗ 86.236 𝑀𝑇𝑈 2700 𝑀 𝑊 𝑡 = 𝐸𝐹𝑃𝐷=469.51

Energy, Cycle Length Requirement The final burnup step SL213_BE15 concentration target to around 10 ppm for an EFPD of 468.2 but the boron concentration of the input was 16 ppm with an EFPD of 469.51. This limit is confirmed at the final burnup step as it should be.

Energy, Cycle Length Requirement

FΔH Limit Confirmation FΔH is the normalized enthalpy rise in a given subchannel as the water flows from the bottom of the core to the top of the core. Represents a localized power with in the core (local power > average power) The peaking factor (FΔH) is defined in ANC by: FΔH= 𝑝𝑒𝑎𝑘 𝑖𝑛𝑒𝑔𝑟𝑎𝑡𝑒𝑑 𝑓𝑢𝑒𝑙 𝑟𝑜𝑑 𝑝𝑜𝑤𝑒𝑟 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑒𝑑 𝑓𝑢𝑒𝑙 𝑟𝑜𝑑 𝑝𝑜𝑤𝑒𝑟

FΔH Limit Confirmation

FΔH Limit Confirmation Below is the C-FDH for the 150 BU, the hottest step.

FΔH Limit Confirmation The figure below is the 12th step showing a peak in FΔH due to the boron burning up.

MTC Limit Confirmation The moderator temperature coefficient is defined as the reactivity change per one degree change in the fuel temperature. In a PWR, the moderator is water in the liquid form and the basic units of MTC are pcm/degree temperature. The MTC of water is negative at most conditions due to as temperature increases→water density decreases→moderation decreases→less reactivity The more boron that is dissolved in the moderator, the more positive the MTC will be. Water has a naturally negative temperature coefficient while boron has a naturally positive one.

MTC Limit Confirmation The MTC is checked at HZP conditions for the core, RELPOW=0 / The MTC should also have no xenon, DEPLETE= HDALL, NAXE /

MTC Limit Confirmation The calculation to solve for the MTC of the first case to see if the limit was below 0.50 pcm°F 𝑀𝑇𝐶 𝑝𝑐𝑚 °𝐹 = ln 1.000047 1.000009 ∗1𝐸5 537−527 °𝐹 =0.379 𝑝𝑐𝑚 °𝐹

Loading Pattern Limit Confirmation Margins Target Values Actual Values Energy 468.2 EFPD 469.51 EFPD ARO peaking factor(Fdh) 1.635 1.627 HZP, MTC (all power levels) .50 pcm/F .37 pcm/F Fuel inventory 68 Feeds Boron Concentration(ppm) 10 ppm 16 ppm

Safety Analysis

Westinghouse RSAC Process Reload Safety Analysis Checklist. Transient analyst does calculations to determine damage to the core and environment in case of accident. Core Designer must confirm that reload design does not violate assumed values. Always go to the extreme, worst case scenario Safety calculations done in conservative manner.(most limiting condition)

Safety Analysis Westinghouse RSAC Process: Rodded FΔH Rod Ejection Accident Shutdown Margin

Rodded FΔH Rodded FΔH must be met when the leading control rod bank is in to is insertion limit (RIL). The RIL is the deepest possible insertion for any rod bank. This is done to make sure there is enough rod worth left to shut down the core in case of accident or emergency.

Rodded FΔH Input file for rodded FΔH: Xenon must be reconstructed Xenon must be skewed to save time

Rodded FΔH

Rodded FΔH Below is the Rodded FΔH output from E-SUM:

Rod Ejection Accident A mechanical failure where a control rod is ejected from the core Causes large power increase, fuel and clad temperature increase and increase in DNB The limits found are the ejected rod worth Δρ(E), and the ejected rod hot channel factor FQ(E)

Rod Ejection Accident There are two limits evaluated at two conditions. BOC, HFP, ARO, equilibrium xenon EOC, HFP, ARO, no xenon BOC, HZP, ARO, equilibrium xenon EOC, HZP, ARO, non xenon

Rod Ejection Accident, HFP The most limiting rod ejection is at the EOC The most limiting FQ is at BOC Sample input deck from BOC RELPOW=1.00

Rod Ejection Accident, HFP The output E-SRW for HFP BOC

Rod Ejection Accident, HFP The output E-SRW for HFP EOC

Rod Ejection Accident, HFP 𝐻𝐹 𝑃 𝐵𝑂𝐶 = 16𝑝𝑐𝑚 1000 ±0.10∗ 16𝑝𝑐𝑚 1000 =0.016%+0.00192%=0.01792% →𝐿𝑖𝑚𝑖𝑡 𝑀𝑎𝑋 𝐸𝑗𝑒𝑐𝑡𝑒𝑑 𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ=0.25% 𝑀𝑎𝑥 𝐹 𝑄 =2.090+0.13∗2.090=2.3617→Max Allowable FQ=5.25 𝐻𝐹 𝑃 𝐸𝑂𝐶 = 18.9𝑝𝑐𝑚 1000 ±0.10∗ 18.9𝑝𝑐𝑚 1000 =0.0189%+0.00189%=0.02079% 𝑀𝑎𝑥 𝐹 𝑄 =1.990+0.13∗1.990=2.2487→Max Allowable FQ=5.25

Rod Ejection Accident, HZP The rod ejection for HZP is the same thing except RELPOW=0 /

Rod Ejection Accident, HZP The output E-SRW for HZP BOC

Rod Ejection Accident, HZP The output E-SRW for HZP EOC

Rod Ejection Accident, HZP 𝐻𝑍 𝑃 𝐵𝑂𝐶 = 12.4𝑝𝑐𝑚 1000 ±0.12∗ 12.4𝑝𝑐𝑚 1000 =0.0124%+0.001488%=0.01448% →𝐿𝑖𝑚𝑖𝑡 𝑀𝑎𝑋 𝐸𝑗𝑒𝑐𝑡𝑒𝑑 𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ=0.60% 𝑀𝑎𝑥 𝐹 𝑄 =2.142+0.49266=2.6347→Max Allowable FQ=15.0 𝐻𝑍 𝑃 𝐸𝑂𝐶 = 13.1𝑝𝑐𝑚 1000 ±0.12∗ 13.1𝑝𝑐𝑚 1000 =0.0131%+0.001572%=0.01467% 𝑀𝑎𝑥 𝐹 𝑄 =2.187+0.503=2.69→Max Allowable FQ=26.25

Rod Ejection Accident

Shutdown Margin The amount of reactivity in the core at subcritical following a trip. Shows that the operators will be able to safely shut down the core. There are components that affect the SM in ANC: Doppler Defect-fuel pellet temperature increases with power and so does resonance absorption due to Doppler. Doppler decrease reactivity Voids-Local boiling in the moderator can also cause small voids to form. Voids decrease reactivity but collapsing gives a small increase. Axial Flux redistribution-enthalpy in the core rises causing a flux tilt towards the bottom of the core. When its goes from HFP to HZP(power defect) there is no rise in enthalpy causing the flux to shift to the top of the core which increases reactivity.

Shutdown Margin 4. Power Defect- amount of total reactivity associated with a change in power. It is larger at EOC because the MTC is more negative due to less boron. So reactivity increases. 5. Rod insertion allowance- cannot assume a full worth of control rod banks. The core may have only partially inserted rods at trip. The reactivity depends on how much rod worth there is. 6. Variable Moderator Temperature- The moderator temperature is greater at HFP so when it trips to HZP causes the temperature to decrease causing a spike in reactivity.

Shutdown Margin Use six cases for ANC input: K1- Base Case at Burnup of Interest (BOC or EOC) EOC, boron should be set to 0 ppm BOC, boron should be constant K2-Rods at Insertion Limits Lead bank is inserted which means less rod worth out of the core Less negative reactivity upon trip K3-Over-power/Over Temperature, Skew Power to Top of Core Increase core power from 100%to 105% Higher power means that the initial temperature will be higher and it will increase power defect Xenon is skewed so that the AO shifts to most positive side(xenon to the bottom of the core, shifts power to the top Increases the worth of partially inserted rods and the power defect

Shutdown Margin K4-Trip to Zero Power K5-Full Core-All Rods In Holds the Xenon, boron and D bank and it goes from HFP to HZP K5-Full Core-All Rods In All rods inserted in full core K6-Worst Stuck Rod Out Removes the worst stuck rod

Shutdown Margin To calculate the shutdown margin we took the worst stuck rod case at BOC and EOC 𝑆𝐷 𝑀 𝐵𝑂𝐶𝑐𝑎𝑙𝑐 = 0.9∗ln 𝑘 4 𝑘 6 ∗100000= ln 1.012737 .936952 ∗100000=7000.18𝑝𝑐𝑚 𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦= ln 𝑘 4 𝑘 3 ∗100000 = ln 1.01237 0.997822 ∗1𝐸5=1483.69𝑝𝑐𝑚 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆𝐷𝑀=𝑆𝐷 𝑀 𝑐𝑎𝑙𝑐 −𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦−𝑣𝑜𝑖𝑑 𝑒𝑓𝑓𝑒𝑐𝑡= 7000.18−1483.69−50= 5466.49𝑝𝑐𝑚 1000 =5.466% →𝐿𝑖𝑚𝑖𝑡 𝑆𝐷𝑀=3.6% This meets the limit for the shutdown margin by 1.866%Δ𝑝.

Shutdown Margin

Shutdown Margin BOC WORTHS (pcm) EOC WORTHS (pcm) POWER DEFECTS 1483.7   BOC WORTHS (pcm) EOC WORTHS (pcm) POWER DEFECTS 1483.7 2548.22 Void Effects 50 Total Control Bank Requirement(1) 1533.7 2598.22 SDMCALC 7777.97 8489.18 Less 10% (2) 7000.18 7640.26 Available SDM (2)-(1) 5466.49 5042.03 Required SDM 3600

Operational Data

Operational Data Calculations that must be performed to make sure the core is running at normal conditions Rod Worth Xenon Worth Differential Boron Worth Isothermal Temperature Coefficient Critical Boron Concentration

Rod Worth Measured at BOC, HZP The rodworth is found using the boron dilution method: Core at BOC, HZP, ARI, subcritical (high CB) Withdraw rods (ARO) Dilute CB to ARO critical boron, CBARO Insert lead control bank (Bank D) Insert Remaining Control Banks, One at a Time, in Normal Sequence

Rod Worth As more rod worth is inserted, the fraction of rated thermal power decreases. The lead bank in our case is bank5

Rod Worth

Rod Worth Configuration CB (ppm) Inserted Worth (ppm) ARO 1605 ----- D 1479 126 D+C 1436 43 D+C+B 1336 100 D+C+B+A 1247 89 D+C+B+A+BANK1 1197 50 D+C+B+A+BANK1+BANK6 884 313 D+C+B+A+BANK1+BANK6+BANK7 503 381

Xenon Worth Reactivity due to the absorption on neutrons Xe-135 in the core. A fission product with a high absorber worth produced from the decay of I-135 𝑑𝐼 𝑑𝑡 = 𝛾 𝐼 Σ 𝑓 Φ 2 − 𝜆 𝐼 𝐼 𝑑𝑋𝑒 𝑑𝑡 = 𝜆 𝐼 𝐼+ 𝛾 𝑥𝑒 Σ 𝑓 Φ 2 − 𝜆 𝑥𝑒 𝑋𝑒− 𝜎 𝑎 𝑥𝑒 Φ 2 𝑋𝑒 Xe-135 is removed by two effects: Absorption by thermal neutron flux Radioactive decay

Xenon Worth Xenon reactivity after startup and trip is what is calculated using ANC Startup BOC,MOC,EOC at 50 % and 100 % Power 2. Trip

Xenon Worth Speed up calculations core is collapsed from 3-D to 2-D Deplete the Xenon for over 100 hours

Xenon Worth Use the Eigenvalues to calculate the reactivity 𝑆𝑎𝑚𝑝𝑙𝑒 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑅𝑒𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 =100000∗𝐿𝑁 1.031188 1.031512 =−31.41𝑝𝑐𝑚

Xenon Worth, Startup

Xenon Worth, Startup

Xenon Worth, After Trip ~9Hours

Xenon Worth, After Trip

Differential Boron Worth Change in reactivity due to a unit change in boron concentration. Calculated at both HZP and HFP varying by ±25 ppm. Input sample from HZP job file At HZP, differential boron worths were calculated at a wide range of boron concentrations

Differential Boron Worth DBW = 𝐿𝑁 0.998117 1.001894 ∗100000 50 =-7.554 𝑝𝑐𝑚

Differential Boron Worth Shows the amount of soluble boron throughout the cycle at HFP

Differential Boron Worth HZP DBW for 5 different boron concentrations over the length of the cycle

Isothermal Temperature Coefficient ITC is defined as the change in reactivity of a core with a change in core temperature. DTC is defined as the reactivity change per one degree change in the fuel temperature. In a PWR, the fuel is UO2 in ceramic form and the basic units of DTC are in pcm/F or pcm/C. 𝐼𝑇𝐶=𝑀𝑇𝐶+𝐷𝑇𝐶 It will follow the behaviors of both the MTC and DTC. DTC remains constant, ITC will follow the MTC, boron decreases so does ITC. In ANC the most limiting case is at BOC HZP where the boron is at the highest.

Isothermal Temperature Coefficient Input deck and E-Sum for ITC

Isothermal Temperature Coefficient ITC must be calculated by doing it the old fashion way, by hand. MTC and DTC are found by ANC and ITC is found using the equation below: 𝐼𝑇𝐶= ln 𝑘 ­ +5 𝑘 −5 ∗ 10 5 Δ 𝑇 𝑎𝑣𝑔 𝐼𝑇𝐶= ln 0.999959 1.000026 ∗ 10 5 537.0−527.0°F 𝐼𝑇𝐶=−.670 𝑝𝑐𝑚/°𝐹

Critical Boron Concentration Critical boron concentration is found at BOC, HZP, ARO, no xenon It is done to predict cycle length and reactor control. It has a heavy effect on MTC and Xenon Worth. Good agreement between the measured value and the value predicted by the design code. Gives accuracy of the design model of the reactor. NRC says that the difference should not exceed 1 %.

Critical Boron Concentration

Thermal-Hydraulic Analysis

Why Thermal-Hydraulic Analysis is Needed A thermal-hydraulic analysis is necessary for any core design before the design is implemented. The goal is to determine the range of operation and the conditions that the reactor can safely operate without resulting in fuel failure over the reactor life considering both steady-state and anticipated transient operation. With thermal hydraulic analysis, the temperature distribution throughout the core can be determined with a given fission power distribution and coolant inlet condition.

Core Design Subchannel Code (CDSC) CDSC is a three-dimensional thermal hydraulic code that solves for mass flow, quality, void fraction, fluid temperature, and pressure for each subchannel. CDSC also models assembly-to-assembly mixing as well as subchannel-to-subchannel mixing. CDSC assumes homogeneous equilibrium two-phase flow (no slip and same temperatures for each phase). The output provides a 3D enthalpy and flow distribution and data for the evaluation of thermal safety limits.

Boundary Conditions Nominal Power Inlet Mass Flux: 3033.889kg/ 𝑚 2 /s System Exit Pressure: 15MPa Inlet Temperature: 278 𝑜 𝐶 Power Input: 485676.91 w/ 𝑚 2 Spacer Grid Loss Coefficient: 0.8 3D power Distribution

Geometry of the Subchannel Analysis Flow Channel Dimensions Rod Dimensions Flow Channel Gap and Distance Heated and Wetted Parameters

Overpower Uncertainties 5% decrease in Inlet Mass Flux: 2882.21kg/ 𝑚 2 /s 50psia Increase in Exit Pressure: 15.34MPa 7 𝑜 𝐶 Increase in Inlet Temperature: 285 𝑜 𝐶 Power Input Increased until DNBR of 1.3: 734000.91w/ 𝑚 2 10% Increase in Spacer Grid Loss Coefficient: 0.88 Decrease of Pitch by 0.006 inches in Hottest Subchannel: 0.5in

Nominal and Overpower Cases Type Power Hottest Rod Hottest Channel Axial Location (m) Min DNB Ratio Nominal 100% 16 22 2.8935-3.0382 3.3969 Overpower+unc 151% 28 3.1828-3.3275 1.3007

Bayshore Reactor Vessel at Nominal Power and Overpower Water In at 285 C Water In at 278 C Water Out at 327.13 C Water Out at 344.79 C

Coolant Temperature

Fuel Temperature in Nominal and Overpower

Cladding Temperature

Departure From Nucleate Boiling Ratio

Void Fraction

Mass Flux

Conclusion Learned how to develop a loading pattern under restrictions. Made sure our core was safe using the RSAC process. Calculated operational data to confirm that our core performed properly at all phases of the cycle. Performed thermal-hydraulics calculations to evaluate the subchannels and rods to nominal and overpower conditions.

References 1.Dr. K. Ivanov, Dr. M. Avramova. Nuclear Engineering 431W: Nuclear Reactor Core Design. Department of Mechanical and Nuclear Engineering, The Pennsylvania State University: Spring 2014. 2. C. Wagener. Core Design Training Course. Westinghouse Electric Company, presented to Penn State University: Spring 2014

QUESTIONS?