In fractured media, solute transport is controlled by advection in open and connected fractures and by matrix diffusion that may be enhanced by chemical weathering of the fracture walls. These phenomena may lead to non-Fickian dispersion characterized by early tracer arrival time, late-time tailing on the breakthrough curves and potential scale effect on transport processes. Here we investigate the scale dependency of these processes by analyzing a series of convergent and push-pull tracer experiments with distance of investigation ranging from 4m to 41m in shallow fractured granite. The small and intermediate distances convergent experiments display a non-Fickian tailing, characterized by a -2 power law slope. However, the largest distance experiment does not display a clear power law behavior and indicates possibly two main pathways. The push-pull experiments show breakthrough curve tailing decreases as the volume of investigation increases, with a power law slope ranging from -3 to -2.3 from the smallest to the largest volume. The multipath model developed by Becker and Shapiro (2003) is used here to evaluate the hypothesis of the independence of flow pathways. The multipath model is found to explain the convergent data, when increasing local dispersivity and reducing the number of pathways with distance which suggest a transition from non-Fickian to Fickian transport at fracture scale. However, this model predicts an increase of tailing with push-pull distance, while the experiments show the opposite trend. This inconsistency may suggest the activation of cross channel mass transfer at larger volume of investigation, which leads to non-reversible heterogeneous advection with scale. This transition from independent channels to connected channels when the volume of investigation increases suggest that both convergent and push-pull breakthrough curves can inform the existence of characteristic length scales.