We present a set of single-well injection withdrawal tracer tests in a paleoreef porous reservoir displaying important small-scale heterogeneity. An improved dual-packer probe was designed to perform dirac-like tracer injection and accurate downhole automatic measurements of the tracer concentration during the recovery phase. By flushing the tracer, at constant flow rate, for increasing time duration, we can probe distinctly different reservoir volumes and test the multiscale predictability of the (non-Fickian) dispersion models. First we describe the characteristics, from microscale to meter scale, of the reservoir rock. Second, the specificity of the tracer test setup and the results obtained using two different tracers and measurement methods (salinity-conductivity and fluorescent dye­optical measurement, respectively) are presented. All the tracer tests display strongly tailed breakthrough curves (BTC) consistent with diffusion in immobile regions. Conductivity results, measured over 3 orders of magnitude only, could have been easily interpreted by the conventional mobile-immobile (MIM) diffusive mass transfer model of asymptotic log-log slope of 2. However, the fluorescent dye sensor, which allows exploring much lower concentration values, shows that a change in the log-log slope occurs at larger time with an asymptotic value of 1.5, corresponding to the double-porosity model. These results suggest that the conventional, one-slope MIM transfer rate model is too simplistic to account for the real multiscale heterogeneity of the diffusion-dominant fraction of the reservoir.