A constitutive model for air–NAPL–water flow in the vadose zone accounting for immobile, non-occluded (residual) NAPL in strongly water-wet porous media
Section snippets
Background
Modeling the subsurface behavior of contaminants can be a cost-effective tool to aid in cleaning up and managing contaminated sites. Before models can be the tools of choice, they must be able to accurately predict contaminant behavior and assess the level of uncertainty associated with the predictions. One shortcoming of multifluid flow and transport codes is their inability to accurately predict the retention of nonaqueous-phase liquid (NAPL) in the vadose zone after long drainage periods.
Conceptual model
Our objective is to improve existing multifluid constitutive theory (i.e., k–S–P relations) so that the effects of entrapped and residual NAPL on subsurface contamination and cleanup can be predicted. However, we first want to give a conceptual understanding of ‘residual’ NAPL, as we will use it in our model.
We hypothesize that NAPL in small pores and small pore wedges can be considered to be immobile because (1) the pore dimensions are small and any advection of NAPL through those spaces would
Model development
We will modify the hysteretic, multifluid k–S–P model of Parker and Lenhard (1987) and Lenhard and Parker (1987), which is valid for air–NAPL–water systems in strongly water-wet porous media where water is the wetting fluid and air and NAPL are nonwetting fluids with NAPL wetting water surfaces relative to air. The intent is to minimize changes to the existing model so that coding the improvements will not be a major undertaking, but the use of the model in flow and transport simulators will
Discussion
Key elements of the proposed model are (1) some portion of the NAPL is predicted to remain in the pore spaces as residual NAPL unless all of it is entrapped by imbibing water, (2) the residual NAPL saturation is a function of the saturation-path history (not a constant), and (3) the NAPL relative permeability (kro) will approach zero as the free-NAPL saturation (Sof) approaches zero. To calculate fluid saturations using the revised constitutive model in numerical models, the apparent
Summary and conclusions
A mathematical model for predicting residual NAPL in three-phase air–NAPL–water fluid systems was developed. The model was incorporated into an existing hysteretic k–S–P model for predicting subsurface fluid flow. Modifications to the existing k–S–P model were minimized to allow easy coding changes. The conceptual model of residual NAPL formation used for the mathematical model is that NAPL becomes immobile when it forms thin films and when it invades small pore spaces, such as pore wedges.
Acknowledgements
This work was supported by the Laboratory Directed Research and Development Program at the Idaho National Engineering and Environmental Laboratory (INEEL). The INEEL is operated for the US Department of Energy (DOE) by Bechtel BWXT Idaho, LLC under DOE's Idaho Operations Office Contract DE-AC07-99ID13727. M. Oostrom was supported by the Groundwater/Vadose Zone Integration Project that is funded by DOE's Richland Operations Office. The authors also want to thank Dr. Paul van Geel for his
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