compositional simulation

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  • L o g o

    Compositional

    Simulation

  • Applications

    Black oil models

    Immiscible flow

    Hydrocarbon phase has fixed composition of two component oil and gas

    Fluid properties are a function of pressure

    Fluid properties are a function of pressure and solution gas

  • Applications

    Compositional gas models

    Significant mass transfer between oil and gas phases

    Fluid properties are dependent on pressure and composition

    Examples processes Volatile oil reservoir depletion

    Gas condensate reservoir depletion

    Gas cycling

    Miscible flooding by CO2 or enriched gas

    injection

  • Compositional Models

    Fussell and Fussell (1978)

    Coats (1980) : Fully implicit

    Nghiem et al. (1981) : IMPES-type

    Young and Stephens (1983)

    Acs et al. (1985) : IMPEStype

    Watts (1986) : Sequential implicit

    Collins et al. (1986) : Adaptive implicit

  • Formulations

    IMPES Type

    Solve pressure and saturation separately

    Adaptive implicit

    In each time step solve few gridblocks implicitly and the rest explicitly

    Fully implicit

    Solve for pressure, saturation, and composition simultaneously

  • Applications

    Compositional chemical models

    Injection of of liquid chemicals to displace oil

    Phase behavior

    Reduction in interfacial tension between oil

    and liquid

    Example processes are

    Surfactant/polymer

    Surfactant/alkaline/polymer

    Surfactant/foam

  • Displacements

    Immiscible flow under reservoir conditions

    fluids with different properties mix

    Displacement of oil by miscible or partially

    miscible fluids

    Displacement using chemicals that can

    affect fluid properties

    Non isothermal flow or combustion reaction

  • Displacements

    Miscible

    Two or more components flow within a

    single phase

    Flow of oil by solvent

    Transport of salts

    Polymer

    Tracers

    Contaminant in water

  • Commercial Compositional Gas Reservoir Simulator

    VIP (Landmark Graphics)

    Eclipse 300 (Geoquest)

    CMG-GEM (Computer Modeling Group)

    Simbest (Formerly SSI and now Bakers)

  • Oil Reservoir Simulator

    Black oil model for immiscible

    processes

    Miscible black oil model for first

    contact miscible process where

    injected fluid is directly miscible with

    oil at reservoir pressure and

    temperature

  • Reservoir Simulators

    Compositional gas models for multiple contact miscible displacements

    Inject CO2 to mobilize and displace residual oil saturation through multiple contacts

    between oil and CO2 phases

    Intermediate and higher molecular weight hydrocarbons are contacted into the CO2rich phase

    Under proper conditions CO2 becomes miscible with the original reservoir oil

  • Reservoir Simulators

    Compositional chemical models for

    chemical flooding processes

    Thermal models for steam flooding and

    in situ combustion

  • Mathematical Models Isothermal conditions

    No flow boundary

    Permeability tensor is orthogonal and aligned with the coordinate system

    No precipitation or chemical reaction

    Negligible adsorption

    Physical dispersion follows Ficks law Water is treated as a separate component present

    only is water

    No mass transfer between water and oil or gas phases

    Hydrocarbon phase compose of nc hydrocarbon components which may include nonhydrocarbons such as CO2, N2, or H2S

    Assume instantaneous thermodynamic equilibrium between hydrocarbon phases

  • Mass Conservation Equation

    termSourceR

    FluxF

    onAccumulatiW

    RFt

    W

    i

    i

    i

    iii

    0

  • Mass Conservation Equation

    jphaseinicomponentoffractionmolex

    jphaseforsaturationS

    jphasefordensitymolar

    porosity

    xSW

    ij

    j

    j

    ijj

    n

    jji

    p

    1

    Accumulation term

  • Mass Conservation Equation

    111

    2

    ,........1

    SW

    and

    nhydrocarbonixSW

    c

    p

    n

    c

    n

    jijjji

    Since there is no hydrocarbon component in the water phase

    Accumulation term

  • Mass Conservation Equation

    Phase Index

    J = 1 water

    J = 2 Oil

    J = 3 Gas

  • Mass Conservation Equation

    Flux Term

    ijijjjjij

    n

    jji xKSuxF

    p

    1

    Convective Flux Dispersive Flux

  • Mass Conservation Equation

    DepthD

    jphaseofweightspecific

    jphaseofitycosvis

    typermeabilirelativek

    mobilityrelative

    tyPermeabiliK

    DPku

    j

    j

    rj

    k

    rj

    jjrjj

    j

    rj

    Darcy's law

  • Mass Conservation Equation

    1ccb

    ii n,n,.....1i

    V

    qR

    Source term:

    Vb= Bulk volume

    qi = Molar flow rate of component i

    producer : negative value

    Injector : Positive value

  • Physical Dispersion

    Diagonal terms

    zzij

    yyij

    j

    2zj

    j

    Tj

    j

    2yj

    j

    Tj

    j

    2xj

    j

    Ljijxxij

    KandKfortermsSimilar

    u

    u

    Su

    u

    Su

    u

    S

    DK

    zzzyzx

    yzyyyx

    xzxyxx

    ij

    KKK

    KKK

    KKK

    K

    tydispersiviTransverse

    tydispersiviallongitudin

    tortuosity

    dispersionmolecularD

    T

    L

    ij

  • Physical Dispersion

    Off Diagonal terms

    2zj

    2yj

    2xjj

    zyij

    yzij

    zxij

    xzij

    yxij

    xyij

    j

    yjxj

    j

    TjLjxyij

    uuuu

    where

    KK

    KK

    KK

    u

    uu

    SK

  • L o g o

    Compositional

    Simulation

  • Mass Conservation Equation

    Set of coupled, nonlinear, partial differential

    equations with ncnp+6np+2 variables

    1,,.........1

    011

    cc

    b

    in

    jijijjjjijj

    n

    jijjj

    nni

    V

    qxKSuxxS

    t

    pp

  • Pressure Equation

    Acs et al. formulation where total fluid volume is equal to the pore volume

    )(),( PVNPV pt

    t

    P

    P

    V

    t

    N

    N

    V

    t

    P

    P

    V pn

    i

    i

    ikNPi

    t

    N

    tc

    ki

    1

    1)(,

    reffref PPc 1 frefpp cVPV

  • Pressure EquationFrom mass conservation equation, we have

    ij

    n

    1jjjbi

    cc

    i

    n

    1jijijjjjijjb

    i

    xSVNwhere

    1n,n,.........1i

    0qxKSuxVt

    N

    p

    p

    Define partial molar volume as

    )(, ikNPi

    tti

    k

    N

    VV

  • Pressure Equation

    Neglect physical dispersion and cjj PPP

    1

    1

    1

    1 1

    c

    c p

    n

    iiti

    n

    i

    n

    jjcjijjrjtib

    tf

    ref

    p

    qV

    DPxkVVt

    P

    P

    VcV

    Initial conditions: known pressure and known no. of moles

    for each component

    Boundary conditions : No flow boundary

  • Variables No. of variables

    1

    Sj np

    ij np

    xij (np-1)nc

    Krj np

    j np

    Pj np

    j np

    qi nc+1

    Total nc np+6 np+2

    List of Variables

  • Equations Name No. Of Eq.

    Mass conservation nc+1

    fij = fil Phase equilibrium nc(np-2)

    Saturation constraint 1

    Phase composition

    constraint

    np-1

    Formation porosity 1

    Equation of State np

    Equation of State np

    Viscosity np

    11

    pn

    jjS

    11

    cn

    iijx

    P

    ),(

    )(11

    jjj xP

    P

    ),(

    )(11

    jjj xP

    P

    ),(

    )(11

    jjj xP

    P

    Number of Equations

  • Equations Name No. Of Eq.

    Phase

    Relative permeability np

    Phase pressure np-1

    Well model nc+1

    Totalnc np+6 np+2

    ),,( xSPkk rjrj

    ),( xSPP jj

    ),,( xSPqq ii

    Number of Equations

  • IMPES Computational Procedure

    Establish initial conditions

    Phase saturation

    Component moles

    Viscosity

    Density

    Relative permeability

    Capillary pressure

    Original in place

    Fluid volume

  • IMPES Computational Procedure

    1. Solve pressure equation implicitly using

    explicit saturation and phase composition

    dependent properties

    2. Compute flow rate and bottomhole pressure

    for wells

    3. Solve mass balance equation explicitly for

    component mole number and overall

    hydrocarbon composition

    4. Solve for phase equilibrium and hydrocarbon

    phase saturation

  • IMPES Computational Procedure

    5. Compute phase densities

    6. Calculate phase viscosities

    7. Calculate phase relative

    permeabilities

    8. Compute capillary pressures

  • Special Case

    2 hydrocarbon oil and gas phases

    No physical dispersion

    Use Darcys law

    jrjj ku

  • Special Case

    Water equation is the same as

    black oil model

    w

    www

    w

    w

    B

    S

    tq

    B

  • Mass balance for component i

    ggiooiigggioooi SySxt

    qyx

    cowcogg

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