Abstract: In this talk an adaptive mixed finite element method will be introduced for the Darcy flow in a two-dimensional fractured porous media. The discrete fracture model (DFM) is applied to model the fractures by one-dimensional fractures in a two-dimensional domain. We derive a robust residual-based a posteriori error estimator for the problem with non-intersecting fractures. Then applying the adaptive algorithm, we will further introduce an efficient upscaling algorithm to compute the effective permeability of the fractured porous media, and a two-scale reduced model for simulating the flow in the porous media with conductive fractures. Several numerical results will be shown to demonstrate the efficiency of the adaptive algorithm and the proposed two-scale model.