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

https://doi.org/10.1016/j.jconhyd.2003.10.014Get rights and content

Abstract

A hysteretic constitutive model describing relations among relative permeabilities, saturations, and pressures in fluid systems consisting of air, nonaqueous-phase liquid (NAPL), and water is modified to account for NAPL that is postulated to be immobile in small pores and pore wedges and as films or lenses on water surfaces. A direct outcome of the model is prediction of the NAPL saturation that remains in the vadose zone after long drainage periods (residual NAPL). Using the modified model, water and NAPL (free, entrapped by water, and residual) saturations can be predicted from the capillary pressures and the water and total-liquid saturation-path histories. Relations between relative permeabilities and saturations are modified to account for the residual NAPL by adjusting the limits of integration in the integral expression used for predicting the NAPL relative permeability. When all of the NAPL is either residual or entrapped (i.e., no free NAPL), then the NAPL relative permeability will be zero. We model residual NAPL using concepts similar to those used to model residual water. As an initial test of the constitutive model, we compare predictions to published measurements of residual NAPL. Furthermore, we present results using the modified constitutive theory for a scenario involving NAPL imbibition and drainage.

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., kSP 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 kSP 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 kSP model for predicting subsurface fluid flow. Modifications to the existing kSP 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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