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Fractured media are heterogeneous systems in which water flows primarily across rock fractures. Flow dynamics and transport of dissolved substances are controlled by the topological distribution and hydraulic properties of the fracture network (including aperture , hydraulic conductivity K and porosity). These topological and hydrodynamic properties are usually insufficiently characterized in field applications, generating uncertainty in the predictions of flow and solute transport. This paper explores a possible application of the concept of geological entropy, in particular the entrogram, as an approach to describe and potentially predict flow and transport in fractured media. In porous media, the entrogram was proven to be an effective approach to represent the spatial persistence and connectivity of high K patterns, enabling predictions for solute transport when proper correlations are established. Given the similarities between high K patterns in porous media and water-bearing fractures in fractured media, preliminary tests were realized to evaluate an idealized two-dimensional fractured system with regular distribution of two sets of fracture networks, one with a more persistent spatial distribution of fractures than the other. A multiphase flow model based on discrete fracture network is used to simulate a tracer test during which a conservative species displaces an immiscible one injected through a well. The analyses of the breakthrough curves (BTCs) of the relative saturation of each phase at another well allows evaluating the relationship between entrogram metrics and the shape of the BTCs. The initial results are promising and push for a more rigorous evaluation of the link among the metrics. This would require primarily the reproduction of more realistic fracture network including multidimensional systems.