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Non-Condensable Gas Solubility Modelling

J. Downing and S. Lockley

November 2007

Rolls-Royce currently use: Modified version of RELAP5/mod2

Non-condensable gas solubility added to this code Presentation contents:

Model description Equilibrium relations Volumes initially water-filled Two-phase gas redistribution

Absorption and desorption of gas Bubble collapse Convection of dissolved gas

Verification and validation LOCA transient

Effect on depressurisation Heat exchanger gas locking

Presentation Overview

Phase Change Heat Transfer, G. Hetsroni

Zurich Multiphase Flow Course

IntroductionCritical temperature of a gas < any temperature in the system

Non-condensable gas (e.g nitrogen, hydrogen, air)Standard RELAP allows non-condensable gas in vapour

phase only No dissolved gas in the liquid phase Gives a degree of uncertainty in analysis results

Evidence of significant effect on other PWR plants (Sarrette et. al.)

Phase Change Heat Transfer G. Hetsroni

Zurich Multiphase Flow Course

Model Description

Fortran source code modified to include gas solubility Explicit non-condensable model

State modified at end of time step Implicit model would give improved stability

Too time consuming / expensive First quantify the magnitude of the effect

Dissolved non-condensable gas in the liquid phase Non-condensable transfer between phases

Reduction in condensation heat transfer Bell and Ghaly method

Previously implemented

Equilibrium Relationships

Equilibrium mole fraction (Mn) in the liquid phase related to the gas partial pressure (pn)

pn=HMn

Henry’s constant (H): Tabulated for given solute/solvent

combinations Varies with temperature Small variation with pressure

neglected Helium, hydrogen, nitrogen,

oxygen, air in water Himmelblau ‘Solubilities of

Inert Gases in Water’ Perry’s chemical handbook

Argon as oxygen (data scarce)

Volume Initially Water-Filled Volume initially filled with

subcooled water Expanded No non-condensable gas

Steam bubble drawn at psat

With non-condensable gas Steam / gas bubble drawn

at psat +pn

Consider change of liquid density w w

Utilising thermodynamic partial differential available in RELAP5:

w

bnsat

u

w pppp

pb

Vw = V

w=mw/VVol, V

psat +pn

w=mw/V(1-

wmw (1+ /VVapour

Gas Redistribution Under Two-Phase Conditions Driving force for gas transfer

Pressure difference Effective pressure of gas in liquid (w) Partial pressure of gas in vapour (s)

Henry’s constant converted to a mass fraction basis

F is a user supplied rate coefficient Estimated from comparisons with

experimental data A is the interfacial area

Available in RELAP5 Calculate the mass transfer from vapour to

liquid New time masses in vapour and liquid For each dt the mass transfer may not

overshoot equilibrium

w

wnmwn m

mHp ,,

VRTm

p ngsnsn

,,

)( ,, wnsnn ppFAm

At equilibrium:

wnsn pp ,,

HV

mTRm

mwgn

neqsn

1

,,

Criteria For Two-Phase Gas Redistribution For two-phase gas redistribution

Sufficient levels of steam, water and non-condensable must be present

Areas where gas redistribution is not allowed is summarised below:

Absorption of Gas into the Liquid Phase Dissolved gas changes from Ts to Tw

Calculate new internal energies Pressure and voidage is calculated in two

steps Change of pressure at constant voidage

Gives different pressures for vapour and liquid

Pressure in vapour phase Sum of steam and gas partial

pressures Pressure in liquid phase

Utilising the thermodynamic partial differentials available

Change of voidage to equalise vapour and liquid pressures Gives final pressure and voidage

))()(( wnsnw

nw TuTu

m

mu

)(

)(

ns

snns mm

Tumu

u

w

pw

ww

w

P

uu

p

VRTm

pp snsteams

Pressure Equalisation

Vary void fraction until vapour and liquid pressures are equal Hold mass and energy in each phase constant

ws

sw

pppp

12

)( 12

wweq

ppp

w

w

ww

p

p

)1(

Desorption of Gas into the Vapour Phase Assumed to be no intermediate change in the state of the liquid

Gas transferred at internal energy corresponding with liquid temperature

No intermediate change of liquid pressure Pressure and voidage is calculated in two steps

Change of pressure at constant voidage Vapour phase only Three independent properties specify the state for a two component

mixture To utilise available RELAP5 variables choose p, u, Xn

Change of voidage to equalise vapour and liquid pressures As for Absorption

)( wnns Tumu

n

n

Xu

s

pun

sn

Xps

sss

s

p

XX

uu

p

,

,,

Collapse of the Steam / Gas Bubble

If steam / gas bubble shrinks to negligible size

Bubble is collapsed Voidage 1.0E-6 Mass of gas must not be

sufficiently large to enable the bubble to immediately reform

Effective non-condensable pressure in water > psat +pn

When bubble collapsed Volume water filled Pressure adjusted

Thermodynamic derivative Small change as bubble is tiny

Non-condensable gas taken into liquid phase

p

ppw

wtotoldnew

Convection of Dissolved Gas Convection of vapour non-condensable

handled in standard version If receiving volume water filled

Previously non-condensable gas was lost

mass conservation issue Now added to dissolved gas mass

Convection of dissolved gas added Assuming mn << ml

Both masses are variables Rogers and Mayhew general formula

d(mn) and d(ml) Amounts of dissolved gas and water

convected through a junction in dt Related by dissolved gas concentration

in donor volume

lnn mmC /

dyy

zdx

x

zdz

xy

l

lnnn m

mdCmddC

)()(

)()()( lnn mddonorCmd

Verification

Isolated volume Gas distribution

Several variations on initial conditions

Junction added Allow applied pressure to be

varied Expansion of a water-filled

volume Compression of a two-phase

volume Input processing and gas handling

of a range of components pipe, pump, branch, time

dependent volume

Validation

LOCA investigation rig A number of gas trials

Experimental apparatus modelled Run with standard and modified

codes Plant cool-down trial

Six non-condensable gas injections Gas bottles

Standard version Elevated pressure as gas

could not dissolve Modified version

Improved correlation

LOCA Transient Analysis

A PWR input deck was defined Representative but fictional Maximum dosage of dissolved gas

A LOCA transient was run with the new code 0.2% of full bore break by area With and without dissolved non-condensable gas

Demonstrates the effects of gas on the LOCA transient As plant depressurises dissolved gas comes out of solution

Rises to the top of the system Can gas lock heat exchangers

Reducing cooling effect to approximately zero Modifies pressure and inventory profiles

Effect of Gas on Pressure Profile

Heat Exchanger Gas Locking

High elevation cooler Non-condensable can collect in header

Gas locking Heat removal reduces to approximately zero

Excess heat in the system Potentially damage plant

Effect of Gas on RPV Inventory

Conclusions

A gas solubility version of RELAP has been created This model is explicit

State modified at end of time step An implicit model would theoretically give greater stability

The basic functionality of the model has been verified Isolated volume tests Input processing and gas handling checks for other

components The accuracy of the model has been validated against test data A LOCA analysis of a representative PWR has been carried out

Dissolved gas can evolve out of solution and significantly effect a LOCA transient

Pressure and inventory profiles can be modified Heat exchanger gas locking