Abstract A mixed discretization approach is propsed to adequately resolve fracture system while accurately and efficiently modeling both flow and geomechanics. An extended finite element method (XFEM) is applied to approximate the geomechanics, and an embedded-discrete-fracture model (EDFM) is used to model the multiphase flow equations. The two schemes are fully coupled, and the time discretization for flow is fully-implicit. Moreover, a hybrid fracture representation concept is employed where the dual porosity approach is used in conjunction with the embedded discrete representation in order to capture small-scale fracture networks efficiently.