Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 32 views

    High Pressure VLE

    Uploaded by

    ayush
    This document discusses different types of vapour-liquid equilibrium (VLE) formulations and corrections needed for gas and liquid phases at different system pressures. It specifically addresses high pressure VLE where the system pressure is greater than 10 bar and non-ideality is described using cubic equations of state for both phases. It provides the general equations for high pressure VLE calculations using fugacity coefficients from cubic equations of state and describes how to calculate bubble and dew pressures using De Priester nomographs.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    High Pressure VLE

    Uploaded by

    ayush
    32 views12 pages
    This document discusses different types of vapour-liquid equilibrium (VLE) formulations and corrections needed for gas and liquid phases at different system pressures. It specifically addresses high pressure VLE where the system pressure is greater than 10 bar and non-ideality is described using cubic equations of state for both phases. It provides the general equations for high pressure VLE calculations using fugacity coefficients from cubic equations of state and describes how to calculate bubble and dew pressures using De Priester nomographs.

    Original Description:

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    This document discusses different types of vapour-liquid equilibrium (VLE) formulations and corrections needed for gas and liquid phases at different system pressures. It specifically addresses high pressure VLE where the system pressure is greater than 10 bar and non-ideality is described using cubic equations of state for both phases. It provides the general equations for high pressure VLE calculations using fugacity coefficients from cubic equations of state and describes how to calculate bubble and dew pressures using De Priester nomographs.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    32 views12 pages

    High Pressure VLE

    Uploaded by

    ayush
    This document discusses different types of vapour-liquid equilibrium (VLE) formulations and corrections needed for gas and liquid phases at different system pressures. It specifically addresses high pressure VLE where the system pressure is greater than 10 bar and non-ideality is described using cubic equations of state for both phases. It provides the general equations for high pressure VLE calculations using fugacity coefficients from cubic equations of state and describes how to calculate bubble and dew pressures using De Priester nomographs.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 12

    High Pressure System VLE

    Types of Vapour-Liquid Equilibria Formulations


    Type of VLE Corrections Needed for Gas / Liquid Phases

    Raoult’s Law VLE System pressure atmospheric or less

    Liquid-phase forms ideal solution

    Low to Moderate System pressure between 1-10bar (approx); non-


    Pressure VLE ideality described fugacity coefficients based on
    Virial EOS
    Liquid-phase non-ideality described by activity
    coefficients using suitable activity model

    High Pressure VLE System pressure > 10 bar, non-ideality described


    fugacity coefficients based on Cubic EOS
    Liquid-phase non-ideality described by fugacity
    coefficients based on Cubic EOS
    P-V plots at constant temperatures, both vapour
    and liquid phases can be described by cubic EOS
    High Pressure Vapour-Liquid Equilibria
    Pure Component: f iV = f i L
    iV P = iL P
    iV = iL

    Mixture: fˆiV = fˆi L

    yiˆiV P = xiˆiL P
    y ˆV = x ˆ L
    i i i i

    yi / xi = ˆiL / ˆiV = Ki (T , P, yi , xi )
    Proof: For a real mixture: dGi = RTd ln fˆi (1)
    For a pure component: dGi = RTd ln f i (2)
    From (1) and (2): Gi − Gi = RT ln( fˆi / fi ) (3)
    Giid = Gi + RT ln yi  Giid − Gi = RT ln yi (4)
    From (3) and (4): Gi − Gi = RT ln( fˆi / yi f i )
    id

    For an ideal solution : Gi − Giid = 0, hence : fˆi id = yi f i


    In general : fˆ = y ˆ P  ˆ = fˆ / y P
    i i i i i i

    So : ˆiid = fˆi id / yi P; But , fˆi id = yi f i


    ˆ
    Thus:  = y f / y P = f / P = 
    id
    i i i i i i

    For an ideal solution : ˆi = i


    Hydrocarbon Mixtures
    For hydrocarbon mixtures one may assume ideal solution
    behaviour for both phases, in which case (by Lewis Randall
    Rule, see last page for detailed proof):

    fˆiV (T , P, yi ) = yi fiV (T , P)
    ˆf V / y P = y f V / y P
    i i i i i

    ˆf V / y P = f V / P
    i i i

    Thus, ˆid = 
    i i
    Contd…

    With : ˆiid = i

    y i ˆiL i (T , P ) fi L (T , P) / P
    L

    Ki = = V = V =
    xi ˆi i (T , P ) iV (T , P )

    Pi satisat (T , Pi sat ) Vi L ( P − Pi sat )


    Ki = exp[ ]
    Pi (T , P)
    V
    RT

    Thus Ki above is a function of T & P only, not composition. It is


    computed using suitable EOS for the vapour phase and saturation
    fugacity and plotted as nomographs in the form of De Priester charts
    High Pressure Hydrocarbons VLE: De Priester Nomograms

    Ki = yi / xi = f (T , P)

    Use Raoult’s Law algorithms


    • For solving Bubble point calculations one uses:

     y = K x
    i
    i
    i
    i i =1

    • For solving Dew point calculations one uses:


    yi
    i xi =i K = 1
    i

    • Ki as function of T and P can be estimated using the De-


    Preister nomograph
    General High Pressure VLE Calculations

    fˆiV = fˆi L
    y ˆV P = x ˆ L P
    i i i i

    yiˆiV = xiˆiL
    ˆ ˆ
    yi / xi = i / i = Ki (T , P, yi , xi )
    V L
    Bubble Pressure Calculation at high pressures using Cubic EOS (Note that
    this may be rewritten for Bubble T, and Dew T & P with suitable changes)
    Read T, xi
    physical constants, Print P, yi
    estimates of P and yi
    If ΣKixi > 1
    then Yes
    P (new)=P(old)/ ΣKixi
    Estimate species No
    fugacity coeff. If ΣKixi < 1 Is ΣKixi=1
    for both phases and Ki then
    P(new)=P (old)ΣKixi

    Calculate ΣKixi No
    {iV }

    Calculate all Yes


    Has ΣKixi changed?
    yi=Kixi/ΣKixi

    Recalculate all species


    fugacity coeff, and
    {Ki}, ΣKixi
    END

    You might also like