A method for estimating an upscaled directional permeability of a formation includes: receiving a discrete fracture network (DFN), aligning the DFN in a desired direction; cropping the DFN to a desired size having boundaries. The method further includes identifying a fracture plane or fracture planes that are connected with each other and establish a path between the boundaries of the cropped DFN and creating a pipe model of the identified fracture plane or planes that includes one or more conduits connecting one boundary to another boundary. The method further includes creating a system of equations representing flows through the conduits, applying boundary conditions to the system of equations; solving the system of equations for steady-state flow to estimate the upscaled directional permeability of the formation. The method steps can be iterated for another desired direction if the upscaled directional permeability is wanted for the another desired direction.