Micro-CT scans with QEMSCAN mapping provide visualization of core samples to quantify heterogeneous physical properties important for subsurface flow including, as examples, pore size distribution and connectivity, mineral compositions, porosity and permeability, amongst many others. 3D high-resolution micro-CT scans can deliver a very high level of microstructures detail, which also implies enormous numerical data sets and associated computational processing load. It is, therefore, important to understand (1) the voxel resolution of micro-CT scans required to retain physical structure fidelity (e.g., mineral compositions, pore size and throats, and porosity and tortuosity), (2) the sensitivity of individual mineral property and voxel resolution on the directional permeability, and (3) the smallest sample size that provides reliable and representative transport calculations (e.g., directional permeability and connectivity). The lattice Boltzmann method is capable of simulating flow in both open pore spaces and porous media and is used here to allow for flow in multiple matrices (quartz aggregate and low-permeable clay matrix). As an application example, a permeability study of the Precipice Sandstone from the Chinchilla 4 well in the Surat Basin has been conducted. Regarding the Chinchilla sample, we established that (1) the composition ratio is relatively sensitive to voxel resolution: higher resolution imaging is required to retain narrow pore throats and excessively coarsened voxel resolutions result in severe loss of internal microstructures information; (2) both voxel resolutions and individual mineral properties affect flow dynamics, and the clay permeability slightly affects the whole permeability at nD scale; (3) it is not feasible to define the accurate ratio of lattice nodes versus pore apertures for meeting the grid independence due to the complex sample tortuosity; and (4) the directional permeability approaches a constant value as the sample size increases to its representative elementary volume scale size (10 mm in this case). Significantly smaller sample sizes cannot retain the representative physical structure fidelity even using higher resolution imaging.