Effect of rough fractal pore-solid interface on single-phase permeability in random fractal porous media
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Single-phase permeability k has intensively been investigated over the past several decades by means of experiments, theories and simulations. Although the effect of surface roughness on fluid flow and permeability in single pores and fractures as well as in a network of fractures was studied previously, its influence on permeability in a random mass fractal porous medium constructed of pores of different sizes remained as an open question. A fractal medium is one whose pore space and solid matrix can be characterized by statistical self-similarity and described by a fractal dimension Dm. Specifically, in a random mass fractal, each iteration of construction of the medium is composed of identical-size particles and pores of different sizes that are distributed randomly within (Hunt et al. 2014). This thesis contains the research into the effect of rough pore-solid interface on single-phase flow and permeability in fractal porous media. Using fractal geometry, randomly generated three-dimensional Menger sponges were created to model porous media with a range of mass fractal dimensionalities Dm between 2.579 and 2.893. This dimensionality characterizes both the solid matrix and the pore space of the media. The pore-solid interface of the media is subsequently roughened using the Weierstrass-Mandelbrot approach and controlled primarily by the surface fractal dimension Ds and root-mean-square of roughness height σ. The permeability was calculated for all the roughened media using the lattice-Boltzmann method using D3Q19 geometry and Bhatnagar-Gross-Krook (BGK) collision model. The LBM simulations calculated the single-phase permeability based on Darcy’s Law. Results indicate that permeability decreases sharply with increasing Ds from 1 to 1.1 regardless of Dm value, and remains relatively constant as Ds increases from 1.1 to 1.6. Furthermore, while creating the media, a lower bound for the percolation threshold appeared to be around 29.8% for randomized Menger sponges. When fitted to the percolation model presented in Larson et al. (1981) with an upper limit of 0.36 from Kim et al. (2011), the parameters from a least squares fit point to a critical porosity ϕc of 30% and a percolation exponent t between 3.1 and 3.3. Future research should investigate the effect of the percolation threshold for these simulated porous media and the effect surface roughness would have on this threshold. Finally, future research should expand into two-phase flow and investigate the effects of surface roughness on relative permeability and capillary pressure in simulated fractal porous media.