Porosity-Tortuosity Relations in Complex Porous Media Using Pore-Scale Numerical Simulation

Diffusive transport is an important mechanism of mass transfer in gas or liquid phases in porous media. The continuous presence of solids in porous media causes the diffusion paths to deviate from straight lines, and this behavior is descried as the tortuosity of porous media. In this contribution, the porosity-tortuosity relations were studied using a random walk particle tracking (RWPT) code for three-dimensional complex porous medium geometries. The RWPT code was massively parallelized and has been tested on Titan (Cray XK7) at the Oak Ridge National Laboratory and on Mira (IBM Blue Gene/Q) at the Argonne National Laboratory with up to 16,384 cores. The porous medium geometries were synthetically created based on Voronoi tessellations, and include homogeneous fibrous/tubular/granular geometries as well as heterogeneous (vuggy) tubular/granular geometries. Simulation results show that the homogenous granular geometry is the least tortuous, the homogeneous tubular geometry is intermediately tortuous, and the homogeneous fibrous geometry is the most tortuous. For homogeneous granular and tubular geometries, as porosity increases, the difference between the tortuosity of tubular geometry and that of granular geometry decreases. The vuggy porosity increases the tortuosity, due to the fact that mass "particles" trapped in a vug cannot exit the vug except along specific directions where the vug has narrow openings. The size of vugs relative to the size of inter-vug pores also affects tortuosity: the larger the vug size relative to the inter-vug pores, the higher the tortuosity, because in smaller vugs (with the same vuggy porosity and total porosity) the chance is higher for mass "particles" to diffuse into the exiting cylindrical pores. To test the effect of vuggy porosity and tortuosity on permeability, three vuggy geometries were set up with the same vuggy porosity, but different vug sizes. It is found, interestingly, that they have the same dimensionless permeability ks2, where s is the specific surface area of the medium. Although larger vugs increase the tortuosity of the medium, they also reduce the specific surface area and therefore the skin friction. The effects of tortuosity and specific surface area therefore cancelled out.