Knudsen diffusion, gas permeability, and water content in an unconsolidated porous medium

Abstract

The Knudsen diffusion coefficient was measured at different levels of water saturation for an unconsolidated porous medium consisting of silt-sized particles. The Knudsen diffusion coefficient was found to increase from 4.4 × 10-3 cm2/s to 1.0 × 10-1 cm2/s as water saturation decreased from 82% to 54%. A comparison between the experimental Knudsen diffusion coefficients and predicted values of the corresponding effective binary diffusion coefficients indicated that diffusion at high saturations (>64%) were in the transition regime between Knudsen diffusion and molecular diffusion. The results suggest that Knudsen diffusion has significant implications for the prediction of organic vapor transport in partially saturated silts and in less permeable soils. An expression was developed for the influence of water saturation on Knudsen diffusion coefficients, using the Brooks-Corey capillary pressure saturation relationship. Data from previous studies were also combined with results from this study to develop a correlation between the gas phase permeability and the Knudsen diffusion coefficient for variably saturated porous media. For permeabilities less than 10-10 cm2, the new correlation begins to deviate significantly from an existing correlation for dry porous media.