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

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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 - PowerPoint PPT Presentation

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  • Multicomponent two-phase flow in porous media: Macro-kinetics of oscillatory regimsLaboratoire d'nergtique et de Mcanique Thorique et Applique (LEMTA CNRS UMR 7563)International Conference: Scaling Up and Modeling for Transport and Flow in Porous Media Dubrovnik, Croatia, 13-16 October 2008 Mojdeh Rassoulzadeh LEMTAIrina Panfilova LEMTA/SchlumbergerMichel Panfilov LEMTA

  • GazWaterFLUIDESubsurface waste storageComponents :

  • GazComponents :FLUIDEOil and natural gasOil

  • GazComponents :FLUIDEOil and CO2Oil

  • LiquidGas + LiquidGasPT-Diagram

  • LiquidGas + LiquidGasInitial stateClassic systems

  • Retrograde systems

  • MAIN PROBLEM OF MULTICOMPONENT FLOWNon-equilibrium behaviour

  • Oscillatory regimesNon-equilibrium behaviourMAIN PROBLEM OF MULTICOMPONENT FLOW

  • Oscillatory regimesNon-equilibrium behaviour2. Over-saturated zonesMAIN PROBLEM OF MULTICOMPONENT FLOW

  • PROBLEM 1 :

    Oscillatory regimes

  • RETROGRADE GAS-OIL RESERVOIRSLiquidGas + LiquidGas

  • RETROGRADE GAS-OIL RESERVOIRSTheorycompositionflow rate

  • RETROGRADE GAS-OIL RESERVOIRSField datacompositionflow rate

  • TWO TIME SCALES IN OSCILLATIONS

  • Ganglion character of flow (V. E. Gorbunov, 1990) Each fluid becomes mobile only when it reachesits representative elementary volume (REV)

    Thermodynamic instability (V. Mitlin, 1990)Stability analysis of the compositional flow modelshows that the system becomes instable when is the total mixture density, P is the pressure HYPOTHESES ON THE MECHANISMOF OSCILLATIONS

  • double phase transition:

    condensation

    coagulation of liquid

    internal evaporation

    internal gas evacuation OUR THEORY

  • condensation coagulation of liquidP leads to evaporationOUR THEORY

  • P condensation liquid coagulation internal evaporationPhase diagram for the initial fluidPhase diagram for the secondary liquid aggregatesOUR THEORY

  • Double phase transitionLiquidGas + LiquidGasInitial state

  • LiquidGas + LiquidGasInitial stateDouble phase transition

  • LiquidGas + LiquidGasInitial stateDouble phase transition

  • Initial stateDouble phase transition

  • Initial stateDouble phase transition

  • Liquid coagulationDouble phase transition

  • Liquid coagulationLiquid aggregateDouble phase transition

  • Double phase transitionTransition to the second phase diagram

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

  • Double phase transition Gas Evacuation

  • TOTAL COMPOSITION OF THE SYSTEM: 4 PHASES 2341Classic phases

  • MODEL of DOUBLE PHASE TRANSITION Capillary condensation Minimisation of free Gibbs energyCoagulation Smoluchowski + effective mediaEvaporationKinetics of Frenkel-ZeldovichEvacuationGravity segregation + volume exceed mechanism

  • CAPILLARY CONDENSAIONPore-scale modelingCorrelated capillary network Liquid aggregates 1 anddispersed condensate 2, 3

  • Results of modeling the liquid COAGULATIONDynamics of the averaged size of liquid aggregates

  • COAGULATON: Effective medium approachMean vale of particle for power law probability of coagulation Comparison of the effective medium theory and the network simulations kinetic of coagulation

  • 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

  • EVACUATION: gravity segregation + volume exceed mechanismInternal 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

  • Volterra generalized model= mass of liquid aggregates

    = mass of interior gas

  • Rapid gas evacuation:Phase portrait

  • Rapid gas evacuation:Phase portraitCENTER

  • (case of rapid gas evacuation)Stable Oscillations

  • Slow gas evacuation:Phase portrait

  • Slow gas evacuation:Phase portraitFOCUS

  • (case of slow gas evacuation)Attenuating Oscillations

  • FLOW with DOUBLE PHASE TRANSITION

  • FOUR-PHASE MODEL: Numerical tests Volterra kinetics Total liquid SaturationRadial coordinateFLOW production well

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

  • LIQUID SATURATIONFlow directionCLASSIC MODEL

  • CLASSIC MODELLIQUID SATURATION

  • MODEL with DOUBLE PHASE TRANSITIONLIQUID SATURATION

  • The macroscale oscillations whether this is possible ?

  • TWO TIME SCALES IN OSCILLATIONS

  • Two scales of time= fast time,= slow time

  • Two-Scale FormulationAdditional condition : peridocity w.r.t.

  • Zero-order ModelVolterra modelin the fast timeNonlinear oscillations

  • First-order ModelLinear oscillator

  • Explanation to the macroscale oscillationsIncreae of Liquid (S) leads to the increase of Gas but The increase of Gas leads to rthe decrease of liquid

    Typical linear oscillator

  • Global Possible BehaviourMacroscale (slow) linear oscillations

    superposed with

    nonlinear (Volterra) microscale (fast) oscillations

  • CONCLUSIONS

    Alain,

    you are the best ...

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