1. ©2007 Rolls-Royce plc The 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

2. 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

3. Introduction Critical 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

4. 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

5. Equilibrium Relationships Equilibrium mole fraction (M n ) in the liquid phase related to the gas partial pressure (p n ) p n =HM n 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)

6. Volume Initially Water-Filled Volume initially filled with subcooled water Expanded No non-condensable gas  Steam bubble drawn at p sat With non-condensable gas  Steam / gas bubble drawn at p sat +p n Consider change of liquid density   w  w Utilising thermodynamic partial differential available in RELAP5: p b V w = V  w =m w /V Vol, V p sat +p n  w =m w /V(1-   w  m w (1+  /V Vapour

7. 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 At equilibrium:

8. 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:

9. Absorption of Gas into the Liquid Phase Dissolved gas changes from T s to T w 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

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

11. 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, X n Change of voidage to equalise vapour and liquid pressures  As for Absorption

12. 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 > p sat +p n When bubble collapsed Volume water filled Pressure adjusted  Thermodynamic derivative  Small change as bubble is tiny Non-condensable gas taken into liquid phase

13. 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 m n << m l Both masses are variables  Rogers and Mayhew general formula d(m n ) and d(m l )  Amounts of dissolved gas and water convected through a junction in dt  Related by dissolved gas concentration in donor volume

14. 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

15. 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

16. 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

17. Effect of Gas on Pressure Profile

18. 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

19. Effect of Gas on RPV Inventory

20. 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