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We investigate a series of well tests (WT) in tight sand and shale, dry gas, naturally fractured reservoirs that were conducted for long durations. Surprisingly, the transient pressure analysis signature of these reservoirs is similar to the signatures from lean gas reservoirs. Our primary investigation has explored the possible causes related to, geology, and specific well conditions that could result in the ambiguous WT response. However as the WT response has been found repeatedly in a variety of regions around the world, it cannot be related to any of these. We have considered the possible impact of the scale-dependency of the properties of fracture networks on the WT response. It is argued that the anomalies in the WT response may reflect a step in the scale-dependent properties of the fracture network. It is known that in both dry and lean gas examples the anomalous response is caused by a change in permeability. In the lean gas this is caused by the condensate bank region that induces change in the permeability of the system. However, this cannot be the explanation in the dry gas example. We suggest that the response reflects the scale-dependence of the intrinsic permeability of the fracture network.