Abstract Coal seam gas (CSG) is gaining global interests due to its natural abundance and environmental benefits in comparison to more traditional energy sources. However, due to its significant heterogeneity and complex porous structure, it is challenging to characterise and thus predict petrophysical properties. Moreover, the fracture network of coal poses a major challenge for direct numerical simulations on segmented images collected from X-ray micro-computed tomography (μCT). The segmentation of coal images is problematic and often results in misclassification of coal features that subsequently causes numerical instabilities. This paper aims to develop an advanced image analysis method and a novel discrete fracture network model to circumvent these issues. Coal μCT data are utilised for the acquisition of structural parameters and then discrete fracture networks are built to reconstruct representative coal images. The modelling method mimics the cleat formation process and reproduces particular cleat network patterns. The reconstructed network preserves the key attributes of coal, i.e. connectivity and cleat structure, while not being limited in terms of size and/or resolution. Furthermore, direct numerical simulations based on lattice Boltzmann method are performed on the cleat network realisations to evaluate coal permeability. We find that directional permeabilities result in different system scaling effects because of the dependence on the underlying structure of the cleat network. The developed method facilitates the evaluation of the relationship between coal cleat structure and resulting flow properties, which are steps forward in the evaluation of coal petrophysical properties at the core scale.