1 S. OLADYSHKIN, M. PANFILOV Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée Ecole Nationale Supérieure de Géologie Institut National Polytechnique de Lorraine STREAMLINE SPLITTING THE THERMO- AND HYDRODYNAMICS IN COMPOSITIONAL FLOW THROUGH POROUS MEDIA APPLICATION TO H 2 -WATER IN RADIOACTIVE WASTE DEPOSITS

2 Sommaire P r e s e n t a t I o n Flow Model Limit compositional model Streamline HT-splitting Introduction Validation to the limit thermodynamic model

3 Introduction Physical description

4 Hydrogen generation in a radioactive waste deposit Gas generation: Waste storage Storage pressure growth : - Initial : 100 bar - Increased by H 2 : 300 bar Monitoring problem : H 2 transport through porous media accompanied with radionuclides H 2 + CO 2 + N 2 + O 2 + … Corrosion in storage tank underground: m Water

5 Fluid structure Phases : Components : GasLiquid H 2 CO 2 N 2 O 2 H 2 0 … Gas Liquid 2 phases

6 Similar phenomena in an underground H 2 storage Well GAS and LIQUID H H 2 + CO 2 + CH 4 + … Hydrogen storage

7 Initial state L L + G G Phase behaviour Critical point

8 Flow Model

9 2 phases (gas & liquid) N chemical components Compositional model Mass balance for each chemical component k : Momentum balance for each phase (the Darcy law) Phase equilibrium : Phase state : ( = the chemical potential) or Closure relationships: or

10 Limit contrast compositional model

11 Canonical dimensionless form of the compositional model gas flow liquid flow transport of basic chemical components

12 Mathematical type of the system Parabolic equation Hyperbolic equation

13 gas flow liquid flow transport of basic chemical components Characteristic parameters of a gas-liquid system

14 Perturbation parameter: Parameter of relative phase mobility: Perturbation propagation time Reservoir depletion time Characteristic parameters of the system

15 Limit behaviour Semi-stationarity : p and C (k) are steady-state, while s is non stationary gas flow liquid flow transport of basic chemical components

16 Streamline HT-splitting

17 Integration of the transport subsystem gas flow liquid flow transport of basic chemical components This subsystem can be integrated along streamlines : Asymptotic contrast compositional model : A differential thermodynamic system

18 Hydrodynamic subsystem (limit hydrodynamic model): Thermodynamic subsystem (limit thermodynamic model): HT-splitting

19 variation of the total composition in an open system The thermodynamic independent system is monovariant: all the thermodynamic variables depend on pressure only The new thermodynamic model is valid along streamlines Split Thermodynamic Model Properties

20 Due to the monovariance, the thermodynalmic differential equations may be simplified to a “Delta-law”: Thermodynamic “Delta-law” “Delta-law”

21 Individual gas volume Individual condensate volume Interpretation of the delta-law

22 gas flow liquid flow Split Hydrodynamic Model

23 Validation to the limit thermodynamic model

24 These functions have been calculated using Eclipse simulation data for a dynamic system F1F1 F2F2 Validation of the Delta-law

25 Phase plot Fluid composition CH 4 H 2 C 10 H 22 Initial conditions: P 0 = 315 bar T = 363 K T P Flow simulation: Fluid properties

26 Well Flow simulation: Flow problem

27 Validation of the Delta-law F1F1 F2F2 These functions have been calculated using the Eclipse simulation data “Delta-law”

28 Liquid mole fractions Gas mole fractions Validation of the total limit thermodynamic model Composition variation in an open thermodynamic system Compositional Model (Eclipse) - points; Limit thermodynamic model - solid curves

29 Finita