A comparison of mathematical model formulations for organic vapor transport in porous media

Investigation of the behavior of volatile organic contamination in unsaturated soils requires a thorough understanding of vapor transport processes. This paper presents a modeling investigation of one-dimensional, transient, binary gas transport in open porous systems. Several model formulations, based on mass and molar balance equations and Fickian-type diffusion expressions are compared to predictions of the full set of the Dusty Gas model (DGM) equations. The DGM is also used to investigate the relative contributions of various mechanisms to predictions of transient transport behavior for a number of diffusing species and porous media. This research reveals that, in general, predictions of a molar-based advection-Fickian-type diffusion model agree more closely with DGM results than mass-based model predictions. A modified definition of tortuosity for use in Fickian-type diffusion models is proposed to reduce model discrepancies in low permeability media. Results also demonstrate that application of a mass-based coupled flow and transport model to non-equimolar species transport can lead to substantial errors in transport predictions, especially under transient conditions in diffusion-dominated systems, due to discrepancies between Darcy and mass average velocities.