The transport properties of a natural fracture crossing a limestone block of 36 cm x 26 cm x 60 cm is studied using positron emission projection imaging. This non-invasive technique allows to measure the spatial distribution of the activity of a radioactive solution ( here irradiated-copper-EDTA solution) within the fracture. The fracture aperture is measured from the spatial distribution of the activity as the fracture is completely filled with the tracer. The experiment consists in injecting the tracer at a constant flow rate in the plane of the fracture filled with an identical non-radioactive solution. Every 10 min, a two-dimensional grey scale image of the concentration field is recorded. The heterogeneity of the tracer distribution increases with time in relation with the spatial heterogeneity of the aperture field, and favours only slightly the region of larger aperture. The correlation length of the aperture distribution is larger than the correlation length of the concentration distribution of the tracer within the sample. Consequently, the concentration distribution cannot be modelled using a classical advection-dispersion equation; the mixing process has not reached a stationary Fickian dispersion regime in the finite size domain of the experiment. Nevertheless, the transversally averaged concentration profiles (c) over bar (x) evaluated along the flow direction x rescale adequately with an advective variable x/(U) over bart, where (U) over bar is the mean velocity and t the time. This result is explained in the context of the geometrical dispersion regime where the mixing dispersion zone grows proportionally with time. Different approaches are proposed to characterise this anomalous dispersion regime.