NPP Simulators for Education Workshop - Passive PWR Models

Wilson Lam (wilson@cti-simulation.com) CTI Simulation International Corp. www.cti-simulation.com

Sponsored by IAEA

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.

Control Rods Reactivity

Reactor Protection System

Neutron Flux

Xenon Reactivity

Doppler Reactivity

Coolant Temperature Reactivity

Control Rods Position In core

Fuel Rod Thermal Output

Flux shapes Changes

Coolant Pumps Dynamics & Coolant Flow

Core Inlet Enthalpy & Pressures at Cold Legs

Core Primary Coolant Heat Transfer & Hydraulics

Downcomer Flow & Inlet Enthalpy

Steam Flow Rate

Coolant Enthalpy & Pressures at Hot Legs

SG Dome Pressure

Feedwater Flow & Enthalpy

Reactor Power Control

Boiler Pressure Control

Boiler Drum Water Level Control

Turbine Generator & Unit Power

Condenser

Feedwater Heaters

PWR Modeling Diagram

Other Reactivity Effects -Boron injection/removal

Reactor Model

Primary Coolant Heat Transfer to SG

Point Kinetic Reactor Model

dndt

=∆K − β

Λ⋅ n + Σ

i=1

m

λi ⋅Ci

dCi

dt= βi ⋅

nΛ− λi ⋅Ci for I = 1….m

Where ΔK = (Ke - 1) / Ke Λ = / Ke

Spatial Kinetic Model for Pressurized Water Reactor Nodal approach based on Avery’s coupled

region kinetics theory

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.

Reactivity due to zone couplings are calculated separately for each zone using

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.

∆ Λρ α

λ

ij i ij ij

i i

m mZONEjm

i

KNN l

C

N= +

=

∑1 1

6

1

2

3

4

5

6

87

Gray Rods Worth to Reactor Zones, as a function of Rods Position

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

% Withdrawn from Core

Nor

mal

ized

Rod

s W

orth

UPPER ZONES

MIDDLE ZONES

LOWER ZONES

Dark Rods Reactivity Worth to Reactor Zones, as a function of Rods Position

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

% Withdrawn from Core

Nor

mal

ized

Rod

s W

orth

UPPER ZONES

MIDDLE ZONES

LOWER ZONES

The decay heat calculation within each zone assumes 3 separate decay product groups

The decay heat from each zone used to calculate zone coolant temperature and fuel temp in each zone.

P = Nflux - Σ (γi. Nflux- Di) dDi/dt = λi. (γi. Nflux- Di) γi = fission product fraction for Decay Group I λi = decay time constant for Decay group i

The average fuel energy equation is given by:

)( cff

fff TTUAPdt

dTCV −−=ρ …………………(5.7-1)

Where

ρf = volume average fuel density Vf = fuel volume in one zone Cf = average fuel specific heat capacity Tf = average fuel temperature Tc = average coolant temperature P = reactor power U = overall heat transfer coefficient

A = overall heat transfer area for fuel channel

The average core coolant energy equation is given by:

)( cfooiio

cc TTUAhWhWdt

dhV −+−=ρ …………..(5.7-2)

Where

ρc = volume average coolant density Vc = coolant volume in one zone hi = average coolant specific enthalpy at inlet of the zone ho = average coolant specific enthalpy at outlet of the zone A = overall heat transfer area for fuel channel zone U = overall heat transfer coefficient Tf = average fuel temperature Tc = average coolant temperatureWi = coolant mass flow rate at fuel channel zone inletWo = coolant mass flow rate at fuel channel zone inlet

Reactor Zone 1

Reactor Zone 2

Average ReactorFlux Calculation

Flux Mapping

Reactor Zone 12

Zone 3 to 12

To Display

Reactor Zone 1 Flux

Reactor Zone 14 Flux

Reactivity Change due toGrey rods, Dark rodsshutdow n rods, Xenon and fueltemperature

Fig. 1 - Spatial Kinetic Reactor Model

reactivity changes due to temperature change, xenon poisoning and voiding arewithin each reactor zone

coupling is modelled between each neighbouring zones according to prescribed formula

ReactorPow erControls

Reactor Zone 1 Flux

Zone Decay Heat

Zone Decay Heat

Zone Decay Heat

Zone Fuel & Coolant T

Zone Fuel & Coolant T

Zone Fuel & Coolant T

PWR Core Modeling Flow & Pressures in zone calculated by Hydraulic Flow Network

SG1

SG2

Lower Plenum

Upper Plenum

HL1

HL2

CL1

CL2

CL3

CL4

Channel 1

Channel 2

Channel 3

Channel 4

Lower Zones

Middle Zones

Upper Zones

Reactor Core

The fuel heat transfer calculations (equation 5.7-1, 5.7-2) start with the lower zones, withzones inlet temperatures derived from the core lower plenum temperatures; with coolantflows derived from hydraulic flow network computation at the lower plenum. Afterobtaining the lower zone coolant outlet temperatures and average fuel temperatures, thecalculations 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 flowturbulence, and the temperatures at the hot legs will be the coolant mixing temperatures at the upper plenum

Steam Generator Model

Lumped Parameter Model

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

A2

X01

A3

A4

A5

A6

A7

A8

A1

B8

B7

B6

B5

B4

B3

B2

B11

2

3

4

5

6

7

8 9

10

11

12

13

14

15

16

HNC_X01 NHC_X02

X01

NHB NHA

Wp1, Tp1 Wp2, Tp2

Wf, Hf

Weq

Wr1 Wr2Wr, Hl

Wrh, Hrh Wr.(1-X), Hl Wr.(1-X), Hl

Wr.X, Hg

X2

Ws, Hs

Pd

Multi-Nodal Thermalhydraulic Model

Thermalhydraulic of Feedwater System

BOP Processes

Main Steam Utilization: main steam piping; mass and energy distributions.

Turbine Generator Condenser & Condensate Extraction Feedwater & Feedwater Heating Electrical Systems

Reactor Power Cycle - Rankine Cycle

saturation line T

S

T1

T2

P1

P2

QR

1

2 3

4

5

1-2: 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.

Wnet

S1 S2

Reactor Power Cycle

Turbine shaft work WT= H1 - H2

Pumping work WP= H4 - H3

Heat input Qin= H1- H4

NPP Efficiency = Net Work Output/Energy In η =

WT −WP

Qin

=WNET

Qin

Turbine Generator

throttle valve HP Stage blading

Moisture Separator/ Reheater

LP Stages

• Number of turbine stages for turbine expansion • Steam expansion is a isentropic expansion: • Stage efficiency does not change

P.V γ = C where γ =

Cp

Cv

Condenser

1st stage

Turbine Model

Ws = kttv Attv (

Pttv

Tttv

) 1− (φ − φcr

1−φcr

)2

Assuming choked flow to HP Cylinder, the turbine steam flow through the throttle valve is :

where is the throttle valve pressure ratio φ =

P1st

Pttv

φcr

Pttv

Tttv

kttv

= Upstream pressure at turbine throttle valve

= Upstream temperature at turbine throttle valve

= turbine throttle valve flow coefficient

= critical pressure ratio (superheat steam = 0.547)

P1st = turbine 1st stage pressure

Attv = cross-section float area of turbine throttle valve

Turbine Model (cont’d)

The relationship between the 1st stage temperature and throttle valve temperature is given by:

T1st = Tttv .φk−1

k

The turbine expansion equation is used to determine the pressure stage relationship:

P2

P1

= (1− (Ws

k1st

)2 )k

1+ k

k = constant, 1.3 for superheated steam

k1st= stage expansion coefficient

Turbine Model (cont’d) H

S

H1

H2

P1

P2

inlet enthalpy H1

outlet enthalpy H2

isentropic outlet enthalpy Hs

saturation line

turbine expansion line

Mollier Diagram for turbine expansion

∆Hs η.∆Hs

S1

H2 = H1 −η.∆Hs

H2 = H1 −η.(H1 − H (P2 ,S1))

Turbine Model (cont’d)

PTB =Ws(H1 − H2 )Turbine mechanical power:

Pe = PTB when TG connected to large grid For grid island situation:

Electrical Power:

Pe = Peb(1+α PFδ f )where Peb = island load;

δ f = turbine frequency deviation

α PF = power/frequency coefficient Frequency swing equation:

d(δ f )dt

= −De

2I(δ f ) +

fs

2I(PTB − Pe )

De = generator damping constant I = turbine inertia constant fs = turbine synchronous frequency

Approach to Main Steam & Turbine Modeling Use Compressible Hydraulic Flow Network

and Turbine Stages Algorithms

X1 N1 N2 N3 N4 N5 N61 2 N73 N84 X65

Gov Valve

Prim SH Sec SH

Main SteamHdr

X2 X3 X4 X5

#1 HP FWHeater

#2 HP FWHeater

Deaerator LP Heater

Condenser

Boiler DrumPressure

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

Explain the Passive Cooling Systems

Go to the Passive PWR Simulator Manual P.59, Section 4.20