©2007 rolls-royce plc the information in this document is the property of rolls-royce plc and may...
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©2007 Rolls-Royce plcThe information in this document is the property of Rolls-Royce plc and may not be copied or communicated to a third party, or used for any purpose other than that for which it is supplied without the express written consent of Rolls-Royce plc.This information is given in good faith based upon the latest information available to Rolls-Royce plc, no warranty or representation is given concerning such information, which must not be taken as establishing any contractual or other commitment binding upon Rolls-Royce plc or any of its subsidiary or associated companies.
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