Dynamics of diffusive and convective transport in porous media: A fractal analysis of 3-D images obtained by laser technology

Abstract

The objective of this paper was to use laser imaging technique to visualize the diffusion controlled mass transfer process in porous media. Cubical models made of different materials (oil-wet plexiglass and water wet glass) and filled with 1mm and 4mm glass beads and different types of oils were used to visualize the -Fickian- diffusion of solvent with different densities and viscosities. 3-D visualization technique with laser sheet scanning of refractive index matched glass-bead-pack model was used to study the effect of permeability, solvent density, viscosity and boundary effect on mixing by diffusion. Three types of solvents were used: (1) solvent with density higher than oil but low viscosity, (2) solvent lighter than oil but has high viscosity, and (3) solvent lighter but less viscous than oil.It was observed through 3-D images obtained from the experiments that the width (area) of the solvent swept region and fingering depended on the density of the solvent and the speed of the process was higher in the high permeability porous media (4mm glass beads). Wider fingers and swept areas were observed for less viscous solvent. Solvents 1 and 2 slowly mixed and rose to the top of the model filling most of the pores in the model, and then diffused into the unswept region. Solvent 3 reached the top of the model in an extremely short time along the boundary with thin fingering and displaces downward afterwards. The frontal progresses of solvent-oil interfaces (mixing zone) were analyzed quantitatively through the change of the fractal dimension during the process. The fractal dimension increased before the solvent reached at the top of the model. For solvents 1 and 2, the fractal dimension decreased afterward. For solvent 3, the value declined rapidly because the solvent took time to spread along the top of the model due to its extremely low viscosity and density.