The hierarchical fracture modeling approach is extended to a loosely coupled strategy in order to enhance its efficiency for highly conductive fractures and to easily integrate it into the iterative Multiscale Finite Volume (i-MSFV) framework. The fracture and matrix equations are decoupled and a sequential implicit approach is used to solve them. The i-MSFV method is then introduced for the efficient solution of the matrix equation which also involves fracture terms. Very important it that only one degree of freedom per connected fracture network appears in the coarse multiscale operator. This results in very efficient simulations for realistic problems, and also ensures total mass balance for each fracture network during the iterations. Local fracture functions are introduced in order to capture the fractures at the coarse scale accurately; similar to the complex well functions developed by Jenny and Lunati (2009). Numerical results show that the i-MSFV is an efficient conservative multiscale solver for simulations of flow in fractured porous media.

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