The multiscale pore structure of a natural shale is obtained by three distinct imaging means. First, micro-tomography image data are extended to provide the spatial arrangement of the minerals and pores observable with a voxel size of 700 nm (denoted here as the macroscopic scale). Second, FIB/SEM provides a 3D representation of the porous clay matrix on the so-called mesoscopic scale (10-20 nm); a connected pore network, devoid of cracks, is obtained for two samples out of five, while the pore network is connected through cracks for two other samples out of five. Third, the nanometric pore network is characterized with tomographic STEM. Using these experimental pore structure data, permeability calculations are performed by the Lattice Boltzmann Method on the nanoscale, on the mesoscale, and on the combination of the two. Upscaling is finally done (by a finite volume approach) on the larger macroscopic scale. Calculations show that, in the absence of cracks, the contribution of the pore structure at the nanoscale, on the overall permeability, is similar to that of the mesoscale. The impact of the most recent tomographic STEM measurements on the overall transport properties is discussed.