An indirect approach for correlation of permeability and diffusion coefficients

Diffusion tests in porous media are quite sensitive and long lasting procedures compared to permeability tests, which are usually more reliable and of shorter duration. Both diffusion and advection phenomena are dependent on the tortuosity of the material tested. A relevant question is to know whether it is possible to correlate permeability tortuosity τp and diffusion tortuosity τd. Several diffusion and permeability tests have been performed on non-uniform sand specimens having different grain size distribution. For each specimen, both the permeability and diffusion coefficients have been measured and two tortuosity factors (permeability and diffusion) have been back calculated. A theoretical model has been proposed to estimate τd from τp for a non-uniform granular material. The maximum particle diameter dmax is used to determine the maximum hydraulic diameter dh₋max using the Hydraulic Radius Theory (HRT) for a 3D arrangement of spheres of same diameter dmax. Then, a filling factor α is applied to dh₋max in order to capture the fact that smaller grains tend to fill the voids present in between the bigger particles. The filling factor is based on the coefficient of uniformity Cᵤ. Relatively good results are obtained so that this model allows estimating the diffusion properties from a simple permeability test rapidly and at a fraction of the diffusion test cost