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The analysis of the trajectory's scaling properties of tracer particles and preliminary valuations on their relation to experimentally determined dispersion coefficient tensor components in a saturated porous medium are presented. The matching index technique is used to assure optical access inside a three-dimensional laboratory model of a porous medium. In this way it is possible to determine the trajectories of the tracer particles. Using the methods suggested by PIV (Particle Image Velocimetry), the test section is illuminated with a light sheet and images are acquired and digitalized by means of an acquisition apparatus. A Lagrangian description of the motion is carried out and the statistical analysis performed on the experimental field allows for the estimation of velocity probability density functions, velocity components correlation functions and components of the mechanic dispersion coefficient tensor. The statistical analysis results are briefly recalled. The reconstructed tracer trajectories are analysed to verify the self-similarity or the self-affinity properties. The results show self-affine characteristics of the trajectories confirming the anisotropy of the pollutant plume. A relation between the two components of the dispersion coefficient determined by the scaling analysis of the tracer particles is derived.