The porosity and the in situ concentration of tracer testing through different heterogeneous carbonate cores were performed using X-ray computed tomography. The results were interpreted using three approaches: the convection-diffusion equation, the arrival time moments and the stratified model. The results showed that (i) the Fickian approach led to a dispersion coefficient varying along each sample (ii) the statistical approach led to a power law of the variance of the arrival time as a function of the distance and (iii) the stratified model allowed quantification of the heterogeneity factor, which also appeared to be a power function of the distance. These data suggest that the temporal moments approach and the stratified model, but not the classical Fickian approach, are suitable for describing tracer transport through heterogeneous media at the core scale.