Analysis of fluid flow in shale gas reservoir is challenging as a variety of flow mechanisms are involved at different pore scales.In this study,the porous structures of Australian shales are characterised by a new image technology combining X-ray micro-CT and Focused Ion Beam/Scanning Electron Microscopes (FIB/SEM).The obtained porous structure is divided into two subdomains: nano-pores and micro-pores,where LBM and FEM are applied respectively to numerically simulate the continuum and non-continuum flows.Then the resulted diffusivity tensors at each representative elementary volume (REV) are used to calculate the permeability tensors for the samples,which will be finally validated by transient pressure test in the laboratory.