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A Mass Conservative Non-Isothermal Subsurface Three-Phase Flow Model: Formulation and Application

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Abstract

The three-phase flow and contaminant transport of NAPL in a non-isothermal system is modelled as a system of six coupled non-linear partial differential equations. The coupled flow of water, air, water vapour and heat is assumed to follow the theory of Philip and De Vries. Gravity, viscous and capillary forces are included in addition to volatilisation and dissolution of NAPL which are based on either local equilibrium or first order kinetics. The modified Galerkin weighted residual method is used in the spacial discretisation while the generalised mid-point rule is employed for time integration. 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. Mass balance errors are minimised by specific treatment of the mass storage coefficients. The model was tested against several isothermal and non-isothermal analytical and `benchmark' problems whenever available. A variety of problems constituting a subset of the general formulation have been simulated. Very good agreements were obtained between this model and the analytical solutions for the case of both one-dimensional and two-dimensional transient heat transfer. Additionally, the analytical results of steady transport in water and gas with and without biodegradation have been very well reproduced. The particular effect of the surface temperature variation on the flow of LNAPL and DNAPL in the subsurface was investigated and it has been shown to have significant impact on both the imbibition and redistribution stages. During the imbibition stage, the quantity of LNAPL or DNAPL contaminating the system is largely affected by the surface temperature. The resulting relative variation of NAPL saturation during the redistribution stage can reach about 30% for the range of surface temperature of 5–30 °C, mainly in the vadose zone near the ground surface.

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Authors and Affiliations

  1. School of the Built Environment, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, U.K.

    W. J. Ferguson & A. Kaddouri

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  1. W. J. Ferguson
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  2. A. Kaddouri
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Correspondence to W. J. Ferguson.

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Ferguson, W.J., Kaddouri, A. A Mass Conservative Non-Isothermal Subsurface Three-Phase Flow Model: Formulation and Application. Water, Air, & Soil Pollution 153, 269–291 (2004). https://doi.org/10.1023/B:WATE.0000019950.92893.65

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