Knudsen and Molecular Diffusion Coefficients for Gas Transport in Unconsolidated Porous Media

Abstract

This study was an assessment of the Knudsen and molecular diffusion coefficients in relation to gas‐phase permeability and air‐filled porosity, respectively, for gas transport in unconsolidated porous media. Single gas flow experiments at various gas pore pressures and equimolar binary experiments were conducted to determine apparent, effective gas permeabilities as well as the Knudsen and molecular diffusion coefficients. Experimental results integrated with data from previous studies showed that for dry porous media, the Knudsen diffusion coefficient value for kaolin with total porosity ranging from 0.675 to 0.85 is on the order of 10−4 m2, while it is at least one order of magnitude greater for sea sand and one order less for silica flour. Additionally, the existing correlations of the Knudsen diffusion coefficient can give lower and upper limits to the order of this coefficient value for porous media with effective gas permeabilities in the order of 10−14 to 10−16 m2 The gas‐phase molecular diffusion coefficient for an unsaturated silica flour sample with total porosity of 0.386 and water saturation levels >50% was measured to be one order of magnitude less than those for the other samples with total porosities ranging from 0.402 to 0.417 at similar air‐filled porosities. The former also had lower gas diffusivity under rewetting than under desaturation conditions. The diffusivity factor values obtained from all of the unsaturated silica flour samples were far less than the predictions from other commonly used diffusivity relationships.