Effects of surface roughness and derivation of scaling laws on gas transport in coal using a fractal-based lattice Boltzmann method

Abstract

Unconventional energy such as coal seam gas is trapped in a low porosity/permeability environment and poses challenges for production. Of particular interest is the mode of microscale gas transport through so-called coal cleats which form a network of micro-channels/fractures and allow for gas transfer through impermeable coal seams. The problem has attracted interest from many fields such as microstructural characterization, permeability-, porosity-, fluid flow-, diffusion-, adsorption/desorption- and adsorption-induced deformation studies. The main mode of gas flow is supported by the cleat network pattern for which the surface roughness is a very significant property of gas transport. Roughness plays an important role because adsorption is very sensitive to the change in the area. Direct studies on the effects of surface roughness for methane migration in coal by experimental methods are difficult to perform because the micro-scale heterogeneous pore structure and methane sorption properties are difficult to observe and therefore robust numerical simulations provide the most comprehensive method of investigation. In this paper, we develop a numerical model of coal seam gas diffusion and adsorption considering surface roughness based on fractal statistics and the lattice Boltzmann method. The rough surface is characterized by a 3D-Laser profiler and the fractal dimension of the cleat surface is quantified. Generic variants of the measured rough profiles are generated by the Weierstrass-Mandelbrot function through altering the fractal dimension D and length-scale parameter G. The fractal-based lattice Boltzmann method is introduced to solve the governing equations for the gas flow and diffusion processes and scaling laws may be a standardized analysis method and are applied for the non-dimensionalization of gas adsorption. By considering D ranging from 1.5 to 1.8 and G ranging from 1 to 20 it is found that the fractal dimension D has a small effect on the flow but a significant effect on the gas diffusion. In addition, the length-scale parameter G significantly affects gas transport through varying characteristic cleat aperture, and gas diffusion and adsorption by changing the contact area. The data rescaled by scaling laws provide a better analysis of gas adsorption through simplifying the assessment of the effects of multiple variables. Results of this work allow direct quantification of the effect of surface roughness on gas diffusion and adsorption in coal cleats and can provide an improved assessment of the effect of microscopic mechanisms of gas transfer/adsorption in coal on the overall large recovery of gas in the reservoir.