Micro Scale Analysis Of Fluid Flow And Diffusion In Coarse Grained Porous Media

Abstract

X-ray computed tomography and finite element analysis were used to visualize the internal geometry of porous media and calculate the hydraulic conductivity and the diffusion of a dissolved species through the media. The results were compared to laboratory generated results. The calculated hydraulic conductivity showed good agreement with the laboratory results, over-predicting the laboratory results with only 12.5%. Comparison of the calculated results with the Kozeny-Carman equation showed that the Kozeny-Carman equation over-predicted the laboratory results between 62% and 740% depending on the formulation used. The tortuosity and specific surface area showed the highest correlation in predicting the difference between the Kozeny-Carman equation and the modeling results, while the porosity showed the greatest influence in determining the magnitude of the hydraulic conductivity as calculated by the Kozeny-Carman equation. The calculation of the diffusion of potassium iodide through ceramic disks and sandstone showed accurate prediction of the concentration in the receiving cell for the length of the experiment (35 days) for one of the ceramic disks and the sandstone. The other ceramic disk showed accurate prediction up to 20 days, after which it deviated. The results from the study indicate that the diffusional tortuosity and the hydrodynamic tortuosity differ in magnitude, and that they can not be used interchangeably, since (1) the ceramic disks showed the closest prediction to the laboratory results when the diffusional tortuosity is used, rather than the hydrodynamic tortuosity, and when it enters the equation to the first power; and (2) the sandstone showed the closest prediction to the laboratory results when the diffusional tortuosity is used, and when it enters the equation to the second power. Broadly speaking, the results from this study show that the micro scale analysis of porous media allows the accurate calculation of macro scale parameters.