Acidizing in un-fractured carbonate reservoirs has been well studied through modeling and simulation. Since carbonate reservoirs are often naturally fractured, fractures should be modeled for realistic acidizing operations. We present adaptive enriched Galerkin (EG) methods to simulate acidizing in fractured carbonate reservoirs. We adopt a two-scale continuum model for the acid transport. The coupled flow and reactive transport systems are spatially discretized by EG methods. Fractures are introduced using local grid refinement (LGR) technique. Adaptive mesh refinement (AMR) is implemented around wormhole interfaces. Simulation results show that acidizing in fractured carbonate reservoirs is largely dependent on the fracture system while acidizing in unfractured carbonate reservoirs is mainly determined by operation parameters such as acid injection rate. Computationally, the proposed EG scheme has less numerical dispersion and grid orientation effects than standard cell center finite difference/volume methods. AMR is very efficient to track the wormhole growth and speed up acidizing simulations.