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Multicomponent two-phase flow in porous media: Macro - kinetics of oscillatory regims

International Conference: Scaling Up and Modeling for Transport and Flow in Porous Media Dubrovnik, Croatia, 13-16 October 2008. Multicomponent two-phase flow in porous media: Macro - kinetics of oscillatory regims. Mojdeh Rassoulzadeh – LEMTA Irina Panfilova – LEMTA/Schlumberger

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Multicomponent two-phase flow in porous media: Macro - kinetics of oscillatory regims

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  1. International Conference: Scaling Up and Modeling for Transport and Flow in Porous Media Dubrovnik, Croatia, 13-16 October 2008 Multicomponent two-phase flow in porous media: Macro-kinetics of oscillatory regims Mojdeh Rassoulzadeh – LEMTA Irina Panfilova – LEMTA/Schlumberger Michel Panfilov – LEMTA Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée (LEMTA – CNRS UMR 7563)

  2. FLUIDE Subsurface waste storage Components : Gaz Water

  3. FLUIDE Oil and natural gas Components : Gaz Oil

  4. FLUIDE Oil and CO2 Components : Gaz Oil

  5. PT-Diagram Gas Liquid Gas + Liquid

  6. Classic systems Initial state Gas Liquid Gas + Liquid

  7. Initial state Gas Liquid Gas + Liquid Retrograde systems

  8. MAIN PROBLEM OF MULTICOMPONENT FLOW Non-equilibrium behaviour

  9. MAIN PROBLEM OF MULTICOMPONENT FLOW Non-equilibrium behaviour • Oscillatory regimes

  10. MAIN PROBLEM OF MULTICOMPONENT FLOW Non-equilibrium behaviour • Oscillatory regimes 2. Over-saturated zones

  11. PROBLEM 1 : Oscillatory regimes

  12. RETROGRADE GAS-OIL RESERVOIRS Liquid Gas Gas + Liquid

  13. RETROGRADE GAS-OIL RESERVOIRS Theory flow rate composition

  14. RETROGRADE GAS-OIL RESERVOIRS Field data flow rate composition

  15. TWO TIME SCALES IN OSCILLATIONS

  16. HYPOTHESES ON THE MECHANISM OF OSCILLATIONS Ganglion character of flow (V. E. Gorbunov, 1990) Each fluid becomes mobile only when it reaches its representative elementary volume (REV) Thermodynamic instability (V. Mitlin, 1990) Stability analysis of the compositional flow model shows that the system becomes instable when  is the total mixture density, P is the pressure

  17. OUR THEORY double phase transition: condensation coagulation of liquid  internal evaporation  internal gas evacuation

  18. OUR THEORY condensation  coagulation of liquid P leads to evaporation

  19. OUR THEORY Phase diagram for the initial fluid Phase diagram for the secondary liquid aggregates P  condensation  liquid coagulation  internal evaporation

  20. Double phase transition Initial state Liquid Gas Gas + Liquid

  21. Double phase transition Initial state Liquid Gas Gas + Liquid

  22. Double phase transition Initial state Liquid Gas Gas + Liquid

  23. Capillary condensation Double phase transition Initial state

  24. Capillary condensation Double phase transition Initial state

  25. Double phase transition Liquid coagulation

  26. Double phase transition Liquid coagulation Liquid aggregate

  27. Double phase transition Transition to the second phase diagram

  28. Double phase transition Internal evaporation (boiling) Transition to the second phase diagram

  29. Double phase transition Gas Evacuation

  30. TOTAL COMPOSITION OF THE SYSTEM: 4 PHASES Classic phases 1 2 3 4

  31. MODEL of DOUBLE PHASE TRANSITION Capillary condensation Minimisation of free Gibbs energy Coagulation Smoluchowski + effective media Evaporation Kinetics of Frenkel-Zeldovich Evacuation Gravity segregation + volume exceed mechanism

  32. CAPILLARY CONDENSAION Pore-scale modeling Correlated capillary network Liquid aggregates 1 and dispersed condensate 2, 3

  33. Results of modeling the liquid COAGULATION Dynamics of the averaged size of liquid aggregates

  34. COAGULATON: Effective medium approach Comparison of the effective medium theory and the network simulations Mean vale of particle for power law probability of coagulation kinetic of coagulation

  35. SECONDARY EVAPORATION (BOILING) Evaporation has 2 stages: A : formation and growth of germs of bubbles (Frenkel, Zeldovich) B : coagulation of bubbles • is the mass concentration of the aggregate  Is the mass concentration of the boiling gas

  36. EVACUATION: gravity segregation + volume exceed mechanism Internal exchange: formation of gas bubbles leads to the reduction of the liquid mass External exchange: geometrical “volume exceed” gravity-induced uplift of bubbles General kinetic for the external exchange

  37. aggregation evaporation evacuation by volume exceed evacuation by segregation evaporation Volterra generalized model = mass of liquid aggregates = mass of interior gas

  38. Phase portrait Rapid gas evacuation:

  39. Phase portrait Rapid gas evacuation: CENTER

  40. Stable Oscillations (case of rapid gas evacuation)

  41. Phase portrait Slow gas evacuation:

  42. Phase portrait Slow gas evacuation: FOCUS

  43. Attenuating Oscillations System oscillation: 1 sigma theta 0,8 sigma+theta 0,6 0,4 0,2 t 0 0 50 100 150 200 (case of slow gas evacuation)

  44. FLOW with DOUBLE PHASE TRANSITION

  45. FOUR-PHASE MODEL: Numerical tests Volterra kinetics production well Total liquid Saturation FLOW Radial coordinate

  46. PSEUDO THREE-PHASE MODEL - Mobile liquid is neglecting - Two-component system (light & heavy components)

  47. LIQUID SATURATION CLASSIC MODEL Flow direction

  48. LIQUID SATURATION CLASSIC MODEL

  49. LIQUID SATURATION MODEL with DOUBLE PHASE TRANSITION

  50. The macroscale oscillations – whether this is possible ?

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