Multiscale image-based fractal characteristic of shale pore structure with implication to accurate prediction of gas permeability

The heterogeneities of shale are manifested in the complex pore spatial configurations and the wide distribution of pore sizes. The recent advances of high-resolution imaging techniques such as Scanning Electron Microscope (SEM) and Focussed Ion Beam Scanning Electron Microscopes (FIB-SEM) enable accurate characterization of shale pore structure in the limited imaging area. Due to the nature of multiscale pore size, image-based petrophysical properties are highly dependent on the selection of image resolution. Fractal theory proves to be an effective approach to characterize pore structure as well as calculate fluid transport properties. In this study, the image-based fractal characteristic of shale pore structure at multiscale resolutions is investigated and its impact on the accurate prediction of gas permeability is analyzed. The fractal dimensions of pore phase in 100 SEM images at resolutions ranging from 15.5 nm to 420 nm are calculated by the box counting method and Sierpinski carpets analytical solution. The real gas permeability model in consideration of second order slip is derived based on the fractal theory. Two groups of gas permeabilities at different resolutions are estimated respectively based on the fractal dimensions obtained from the box counting method and Sierpinski carpets analytical solution. The results found that fractal dimensions obtained from the box counting method at different resolutions are more close to the exact fractal dimension compared with that obtained from the Sierpinski carpets analytical solution at low resolutions and gas permeabilities calculated at different resolutions based on the box counting estimated fractal dimensions are more close to the exact gas permeability. The image resolution for accurate calculation of shale pore structure properties and gas permeability should be less than 50 nm based on our analysis results.