  The study of flow in fractured porous media is a key ingredient for many
geoscience applications, such as reservoir management and geothermal energy
production. Modelling and simulation of these highly heterogeneous and
geometrically complex systems require the adoption of non-standard numerical
schemes. The Embedded Discrete Fracture Model (EDFM) is a simple and effective
way to account for fractures with coarse and regular grids, but it suffers from
some limitations: it assumes a linear pressure distribution around fractures,
which holds true only far from the tips and fracture intersections, and it can
be employed for highly permeable fractures only. In this paper we propose an
improvement of EDFM which aims at overcoming these limitations computing an
improved coupling between fractures and the surrounding porous medium by a)
relaxing the linear pressure distribution assumption, b) accounting for
impermeable fractures modifying near-fracture transmissibilities. These results
are achieved by solving different types of local problems with a fine
conforming grid, and computing new transmissibilities (for connections between
fractures and the surrounding porous medium and those through the porous medium
itself near to the fractures). Such local problems are inspired from numerical
upscaling techniques present in the literature. The new method is called Local
Embedded Discrete Fracture Model (LEDFM) and the results obtained from several
numerical tests confirm the aforementioned improvements.
