Fractures are important in tight formations because they can constitute major paths for fluid flow and increase drainage surface area in oil and gas systems. The natural heterogeneity of subsurface formations is largely simplified or homogenized in practical applications. However, detailed rock characterization of natural discontinuities and planes of weakness can play a decisive role in judging fracture-matrix interaction and the effective properties of tight reservoir formations. We show the results of X-ray microtomography on coal cores with natural and induced fractures accompanied by digital image analyses for fracture discretization and numerical simulation of compressible fluid flow from an adsorptive medium to discrete fractures. Reconstructed tomographic images provide evidence of a complex network of open and mineralized fractures that interacts with induced shear fractures. Mineralized veins occupy from zero to up to 6% volume fraction in some bedding layers. Open fracture porosity is generally lower than 1% except upon shear and dilation. Natural fracture patterns can drastically change in less than 1 cm in direction perpendicular to bedding indicating strong lamination. X-ray microscopy can help assess brittleness during failure, the role of preexistent fracture tips on induced fractures, and potential for fines production. Digital image analysis based on the Hough transform yields meaningful results locating and characterizing a large number of fractures automatically along the core. Numerical simulation results show that desorption times can be more than two orders of magnitude faster in fractured coal than in the intact coal matrix. The use of tracers helps observe and model fluid flow and uptake in fracture-matrix systems. Altogether, combined X-ray tomography, image processing, and numerical simulation help visualize and quantify the complexity and heterogeneity of naturally fractured geological samples in views of applications to integrated reservoir petrophysical and geomechanical characterization. (C) 2015 Elsevier B.V. All rights reserved.