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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,

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