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

William J. Ferguson, A. Kaddouri

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number1-4
    Publication statusPublished - 2006


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


    Dive into the research topics of 'Numerical modelling of non-isothermal non-equilibrium mass transfer in the subsurface'. Together they form a unique fingerprint.

    Cite this