NPP Simulators for Education Workshop - Passive PWR Models

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1 NPP Simulators for Education Workshop - Passive PWR Models Wilson Lam (wilson@cti-simulation.com) CTI Simulation International Corp. Sponsored by IAEA

2 Learning Objectives Understand the scope of the simulation of a passive PWR reactor. Describe approximations made in the math models for the simulation. Describe the difference between lumped parameter models and distributed parameter models. Explain reactivity as a global reactor concept and not a zone concept (i.e., it is not precisely correct to speak in terms of zone reactivity) Understand the origins of decay heat and how it is modeled in the CTI desktop simulations. Understand the origins of delayed neutrons and how they are modeled in the CTI simulation.

3 Other Reactivity Effects - Boron injection/removal PWR Modeling Diagram Boiler Drum Water Level Control Downcomer Flow & Inlet Enthalpy Feedwater Flow & Enthalpy Feedwater Heaters Reactor Power Control Control Rods Position In core Control Rods Reactivity Reactor Protection System Coolant Temperature Reactivity Doppler Reactivity Neutron Flux Xenon Reactivity Fuel Rod Thermal Output Flux shapes Changes Primary Coolant Heat Transfer to SG Coolant Enthalpy & Pressures at Hot Legs Core Primary Coolant Heat Transfer & Hydraulics SG Dome Pressure Steam Flow Rate Coolant Pumps Dynamics & Coolant Flow Boiler Pressure Control Turbine Generator & Unit Power Condenser Reactor Model Core Inlet Enthalpy & Pressures at Cold Legs

4 Point Kinetic Reactor Model dn dt = K β m Λ n + Σ λi C i=1 i dc i dt = β i n Λ λ i C i for I = 1.m Where ΔK = (Ke - 1) / Ke Λ = / Ke

5 Spatial Kinetic Model for Pressurized Water Reactor Nodal approach based on Avery s coupled region kinetics theory

6 12 point kinetics models to simulate the 12 reactor zones in core. Each zone reactor model based neutron balance DE, and 6 different neutron delay groups. Reactivity changes in each zone reactor - a function of (a) control rods position, (b) zonal concentration of Xenon (c) zonal fuel temp (d) zonal moderator temp. (e) boron conc. (f) zone reactivity coupling effects.

7 Reactivity due to zone couplings are calculated separately for each zone using ρ N j = Λ K α + N i ij i ij i ZONEj 1 m= 1 l i 6 λ N i m C m Sum up all the effects for any particular zone, and enter as one of the reactivity change for that zone. Total power from the 12 zone reactors are summed up and then divided by 12 to get normalized overall power.

9 Gray Rods Worth to Reactor Zones, as a function of Rods Position Normalized Rods Worth % Withdrawn from Core UPPER ZONES MIDDLE ZONES LOWER ZONES

10 Dark Rods Reactivity Worth to Reactor Zones, as a function of Rods Position 1.2 Normalized Rods Worth UPPER ZONES MIDDLE ZONES LOWER ZONES % Withdrawn from Core

11 The decay heat calculation within each zone assumes 3 separate decay product groups P = N flux - Σ (γ i. N flux - D i ) ddi/dt = λ i. (γ i. N flux - D i ) γ i = fission product fraction for Decay Group I λ i = decay time constant for Decay group i The decay heat from each zone used to calculate zone coolant temperature and fuel temp in each zone.

12 The average fuel energy equation is given by: Where f V f C f dt dt f = P UA ( T T ) c ρ (5.7-1) ρ f = volume average fuel density V f = fuel volume in one zone C f = average fuel specific heat capacity T f = average fuel temperature T c = average coolant temperature P = reactor power U = overall heat transfer coefficient A = overall heat transfer area for fuel channel f

13 The average core coolant energy equation is given by: Where dho ρ ( ) cvc = Wihi Woho + UA Tf Tc..(5.7-2) dt ρ c = volume average coolant density V c = coolant volume in one zone h i = average coolant specific enthalpy at inlet of the zone h o = average coolant specific enthalpy at outlet of the zone A = overall heat transfer area for fuel channel zone U = overall heat transfer coefficient T f = average fuel temperature T c = average coolant temperature W i = coolant mass flow rate at fuel channel zone inlet W o = coolant mass flow rate at fuel channel zone inlet

14 Reactor Pow er Controls Fig. 1 - Spatial Kinetic Reactor Model Reactivity Change due to Grey rods, Dark rods shutdow n rods, Xenon and fuel temperature Reactor Zone 1 Flux Reactor Zone 1 Zone Decay Heat Zone Fuel & Coolant T Reactor Zone 1 Flux Reactor Zone 2 Zone Decay Heat Zone Fuel & Coolant T Average Reactor Flux Calculation Zone 3 to 12 Flux Mapping To Display Reactor Zone 12 Zone Decay Heat Zone Fuel & Coolant T Reactor Zone 14 Flux reactivity changes due to temperature change, xenon poisoning and voiding are within each reactor zone coupling is modelled between each neighbouring zones according to prescribed formula

15 PWR Core Modeling Flow & Pressures in zone calculated by Hydraulic Flow Network CL1 Channel 1 SG1 CL2 Channel 2 HL1 Lower Plenum Channel 3 Upper Plenum CL3 Channel 4 HL2 SG2 CL4 Reactor Core Lower Zones Middle Zones Upper Zones

16 The fuel heat transfer calculations (equation 5.7-1, 5.7-2) start with the lower zones, with zones inlet temperatures derived from the core lower plenum temperatures; with coolant flows derived from hydraulic flow network computation at the lower plenum. After obtaining the lower zone coolant outlet temperatures and average fuel temperatures, the calculations proceed to the middle zones, and then to the upper zones accordingly. At the core upper plenum, the coolant temperatures from the 4 lumped channels are mixed by flow turbulence, and the temperatures at the hot legs will be the coolant mixing temperatures at the upper plenum

17 Steam Generator Model Lumped Parameter Model

18 More Detailed Distributed Parameter Model Add more dynamic details - drum, downcomer, U-tubes heat transfer, riser etc. Depends on training needs or boiler design evaluation requirements etc. Multi-Nodal Thermal-hydraulic Model

19 Multi-Nodal Thermalhydraulic Model Ws, Hs Weq X2 Wr.X, Hg Pd Wrh, Hrh Wf, Hf NHB Wr.(1-X), Hl Wr1 Wr.(1-X), Hl Wr, Hl Wr2 NHA A8 8 9 B8 A B7 A B6 A B5 A B4 X 01 A3 A B3 B2 X 01 A B1 HNC_X01 Wp1, Tp1 NHC_X02 Wp2, Tp2

21 Thermalhydraulic of Feedwater System

24 BOP Processes Main Steam Utilization: main steam piping; mass and energy distributions. Turbine Generator Condenser & Condensate Extraction Feedwater & Feedwater Heating Electrical Systems

25 Reactor Power Cycle - Rankine Cycle T T 1 T saturation line P 1 W net P : Turbine Expansion 2-3: Steam condensed in condenser 3-4: FW pump condensate to boiler 4-5: FW heated up by reactor thermal power 5-1:Sat. water vaporizes to sat. steam. Q R S 2 S 1 S

26 Reactor Power Cycle Turbine shaft work W T = H 1 - H 2 Pumping work W P = H 4 - H 3 Heat input Q in = H 1 - H 4 NPP Efficiency = Net Work Output/Energy In η = W T W P Q in = W NET Q in

27 Turbine Generator 1st stage throttle valve HP Stage blading Moisture Separator/ Reheater LP Stages Number of turbine stages for turbine expansion Steam expansion is a isentropic expansion: Condenser P.V γ = C where γ = C p C v Stage efficiency does not change

28 Turbine Model Assuming choked flow to HP Cylinder, the turbine steam flow through the throttle valve is : W s = k ttv A ttv ( P ttv T ttv ) 1 ( φ φ cr 1 φ cr ) 2 where φcr P ttv T ttv k ttv φ = P 1st P ttv is the throttle valve pressure ratio = critical pressure ratio (superheat steam = 0.547) = Upstream pressure at turbine throttle valve = Upstream temperature at turbine throttle valve = turbine throttle valve flow coefficient P 1st = turbine 1st stage pressure A ttv = cross-section float area of turbine throttle valve

29 Turbine Model (cont d) The relationship between the 1st stage temperature and throttle valve temperature is given by: k 1 k T 1st = T ttv.φ k = constant, 1.3 for superheated steam The turbine expansion equation is used to determine the pressure stage relationship: P 2 = (1 ( W s ) 2 ) P 1 k 1st k 1+ k k 1st = stage expansion coefficient

30 Turbine Model (cont d) H inlet enthalpy H 1 P 1 H 1 turbine expansion line outlet enthalpy H 2 isentropic outlet enthalpy H s H s η. H s P 2 H 2 saturation line S 1 S Mollier Diagram for turbine expansion H 2 = H 1 η. H s H 2 = H 1 η.(h 1 H(P 2,S 1 ))

31 Turbine Model (cont d) Turbine mechanical power: P TB = W s (H 1 H 2 ) Electrical Power: P e = P TB when TG connected to large grid P e = P eb (1+ α PF δ f ) For grid island situation: where P eb = island load; δ f = turbine frequency deviation α PF = power/frequency coefficient Frequency swing equation: d(δ f ) = D e dt 2I (δ f ) + D e = generator damping constant I = turbine inertia constant f s = turbine synchronous frequency f s 2I (P TB P e )

32 Approach to Main Steam & Turbine Modeling Use Compressible Hydraulic Flow Network and Turbine Stages Algorithms

33 1 2 N7 X1 N1 N2 N3 N4 N5 N6 Boiler Drum Pressure Prim SH Sec SH Main Steam Hdr Gov Valve 3 4 N8 X6 X2 X3 X4 X5 5 Condenser #1 HP FW Heater #2 HP FW Heater Deaerator LP Heater

34 Thermalhydraulic network models used for Passive Cooling System single phase & two phase

35 Explain the Passive Cooling Systems Go to the Passive PWR Simulator Manual P.59, Section 4.20

The exergy of asystemis the maximum useful work possible during a process that brings the system into equilibrium with aheat reservoir. (4.

Energy Equation Entropy equation in Chapter 4: control mass approach The second law of thermodynamics Availability (exergy) The exergy of asystemis the maximum useful work possible during a process that