Acidization is a widely used stimulation technique for carbonate reservoirs aimed at removing formation damage, and if successful, can result in the creation of wormholes of specific lengths and conductivities around the wellbore. The formation of wormholes depends on the injection rate for a particular acid-mineral system and can be predicted through numerical simulations of the reactive phenomenon during acidization. In this paper, the commonly used two-scale continuum model is enhanced to encompass fractured-vuggy porous media. The fractures are characterized by a pseudo-fracture model, while vugs are represented by a cluster of anomalous matrices with high porosity. Moreover, a method for generating random pore-fracture-vuggy models is proposed. The governing equations are discretized by the finite volume method and are solved under three-dimensional linear and radial conditions. Sensitivity analysis of dissolution dynamics with respect to fracture and vug parameters is performed. The simulation results indicate that both fractures and vugs significantly impact wormhole development. Except for fractures perpendicular to the acid flow direction, fractures in other directions play a crucial role in determining the direction of wormhole growth.