Numerical modelling of non-isothermal non-equilibrium mass transfer in the subsurface

William J. Ferguson, A. Kaddouri

    Research output: Contribution to journalArticle

    Abstract

    A three-phase flow and contaminant transport mathematical model for a non-isothermal system is developed and is modelled as a system of six fully-coupled non-linear partial differential equations. The coupled flow of water, air, water vapour and heat is assumed to follow the mechanistic approach of Philip and De Vries. Gravity, viscous and capillary forces are included in addition to non-equilibrium mass transfer (volatilisation and dissolution) based on first-order kinetics. The system of governing equations is solved by employing the finite element numerical solution technique where the modified Galerkin weighted residual method is used for the spatial discretisation whilst the generalised mid-point rule is employed for the temporal discretisation. The non-linearities are handled by both the Newton-Raphson algorithm for the flow equations and the iterative Picard method for the transport and energy equations. The numerical model was validated and verified against several isothermal and non-isothermal analytical and 'benchmark' problems. The effect of a surface temperature variation on the non-equilibrium mass transfer process was investigated and has been shown to have a significant impact on the transport of pollutants in the subsurface.

    Original languageEnglish
    Pages (from-to)1-9
    Number of pages9
    JournalInternational Journal for Engineering Modelling
    Volume19
    Issue number1-4
    Publication statusPublished - 2006

    Fingerprint

    mass transfer
    modeling
    three phase flow
    pollutant transport
    volatilization
    nonlinearity
    water vapor
    surface temperature
    dissolution
    gravity
    kinetics
    pollutant
    air
    energy
    water
    method

    Keywords

    • Finite element
    • Heat transfer
    • Mass transfer
    • Non-equilibrium
    • Non-isothermal
    • Three-phase flow

    Cite this

    @article{ad2f3b4266f44d1fa390e09a0762ba39,
    title = "Numerical modelling of non-isothermal non-equilibrium mass transfer in the subsurface",
    abstract = "A three-phase flow and contaminant transport mathematical model for a non-isothermal system is developed and is modelled as a system of six fully-coupled non-linear partial differential equations. The coupled flow of water, air, water vapour and heat is assumed to follow the mechanistic approach of Philip and De Vries. Gravity, viscous and capillary forces are included in addition to non-equilibrium mass transfer (volatilisation and dissolution) based on first-order kinetics. The system of governing equations is solved by employing the finite element numerical solution technique where the modified Galerkin weighted residual method is used for the spatial discretisation whilst the generalised mid-point rule is employed for the temporal discretisation. The non-linearities are handled by both the Newton-Raphson algorithm for the flow equations and the iterative Picard method for the transport and energy equations. The numerical model was validated and verified against several isothermal and non-isothermal analytical and 'benchmark' problems. The effect of a surface temperature variation on the non-equilibrium mass transfer process was investigated and has been shown to have a significant impact on the transport of pollutants in the subsurface.",
    keywords = "Finite element, Heat transfer, Mass transfer, Non-equilibrium, Non-isothermal, Three-phase flow",
    author = "Ferguson, {William J.} and A. Kaddouri",
    year = "2006",
    language = "English",
    volume = "19",
    pages = "1--9",
    journal = "International Journal for Engineering Modelling",
    issn = "1330-1365",
    publisher = "University of Split",
    number = "1-4",

    }

    Numerical modelling of non-isothermal non-equilibrium mass transfer in the subsurface. / Ferguson, William J.; Kaddouri, A.

    In: International Journal for Engineering Modelling, Vol. 19, No. 1-4, 2006, p. 1-9.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Numerical modelling of non-isothermal non-equilibrium mass transfer in the subsurface

    AU - Ferguson, William J.

    AU - Kaddouri, A.

    PY - 2006

    Y1 - 2006

    N2 - A three-phase flow and contaminant transport mathematical model for a non-isothermal system is developed and is modelled as a system of six fully-coupled non-linear partial differential equations. The coupled flow of water, air, water vapour and heat is assumed to follow the mechanistic approach of Philip and De Vries. Gravity, viscous and capillary forces are included in addition to non-equilibrium mass transfer (volatilisation and dissolution) based on first-order kinetics. The system of governing equations is solved by employing the finite element numerical solution technique where the modified Galerkin weighted residual method is used for the spatial discretisation whilst the generalised mid-point rule is employed for the temporal discretisation. The non-linearities are handled by both the Newton-Raphson algorithm for the flow equations and the iterative Picard method for the transport and energy equations. The numerical model was validated and verified against several isothermal and non-isothermal analytical and 'benchmark' problems. The effect of a surface temperature variation on the non-equilibrium mass transfer process was investigated and has been shown to have a significant impact on the transport of pollutants in the subsurface.

    AB - A three-phase flow and contaminant transport mathematical model for a non-isothermal system is developed and is modelled as a system of six fully-coupled non-linear partial differential equations. The coupled flow of water, air, water vapour and heat is assumed to follow the mechanistic approach of Philip and De Vries. Gravity, viscous and capillary forces are included in addition to non-equilibrium mass transfer (volatilisation and dissolution) based on first-order kinetics. The system of governing equations is solved by employing the finite element numerical solution technique where the modified Galerkin weighted residual method is used for the spatial discretisation whilst the generalised mid-point rule is employed for the temporal discretisation. The non-linearities are handled by both the Newton-Raphson algorithm for the flow equations and the iterative Picard method for the transport and energy equations. The numerical model was validated and verified against several isothermal and non-isothermal analytical and 'benchmark' problems. The effect of a surface temperature variation on the non-equilibrium mass transfer process was investigated and has been shown to have a significant impact on the transport of pollutants in the subsurface.

    KW - Finite element

    KW - Heat transfer

    KW - Mass transfer

    KW - Non-equilibrium

    KW - Non-isothermal

    KW - Three-phase flow

    UR - http://www.scopus.com/inward/record.url?scp=58149173942&partnerID=8YFLogxK

    M3 - Article

    VL - 19

    SP - 1

    EP - 9

    JO - International Journal for Engineering Modelling

    JF - International Journal for Engineering Modelling

    SN - 1330-1365

    IS - 1-4

    ER -