Gas transport equation based on fractal characterization of rough micro-nano pores

In order to reveal the effect mechanism of rough microstructures of the inner surface of coal pores on gas transport and accurately study the law of gas transport in rough pores,the precise mathematical expressions of effective average height and effective radius of rough elements in micro-nano pore were derived based on fractal theory of self-similarity. Optical Tensiometer was used to quantitatively analyze the 3D morphology and structure of inner surface wall. The key parameters obtained from analysis were substituted into the expression of relative roughness,and the cor- responding value is 0. 352. Combining with the slip flow effect of fluid velocity and molecular diffusion transport mech- anism,the modified gas slip flow transport flux equation and molecular diffusion transport flux equation of discontinu- ous flows in rough micro-nano-pore were deduced,and then the apparent permeability model in micro-nano-pore is de- veloped in rough micro-channel by the principle of equivalent conversion. Considering that it is difficult to accurately measure and characterize the nano-pore of coal,and avoid the influence of pore connectivity on gas transport,the nano- porous anodic alumina film with regular circular holes were selected as the carrier of gas flow channel. Based on the experimental principle of gas pressure differential penetration,the permeability experiment of nano-film were carried out by using PMI micro-permeability equipment,and the permeability data measured from the experimental results were compared with the calculated values of the theoretical model in this paper. Results show that the gas transport e- quation based on fractal characterization of rough pore is reasonable and reliable. The effect of pore roughness should and must be considered in gas transport. The formula of relative roughness of pore expressed by fractal theory is more accurate than the empirical formula proposed by predecessors. In the field of fractal topology,the fractal characteriza- tion of relative roughness will provide an important theoretical support for the simulation of gas flow in self-affine rough micro-channels.