This thesis relies on a Langrangian framework used for conservative tracer transport simulations through 2-D heterogeneous porous media. Conducted numerical simulations enable large sets of concentration values in both spatial and temporal domains. In addition to the advection, which acts on all scales, an additional mechanism considered is local scale dispersion (LSD), accounting for both mechanical dispersion and molecular diffusion. The ratio between these two mechanisms is quantified by the Peclet (Pe) number. In its base, the thesis gives answers to contaminant concentration features when influenced by: i) different log-conductivity variance; ii) log-conductivity structures defined by the same global variogram but with different log conductivity patterns cor-related; and iii) for a wide range of Peclet values. Results conducted by Monte Carlo (MC) analysis show a complex interplay between the aforementioned pa-rameters, indicating the influence of aquifer properties to temporal LSD evolu-tion. A stochastic characterization of the concentration scalar is done through moment analysis: mean, coefficient of variation (CVC), skewness and kurtosis as well as through the concentration probability density function (PDF). A re-markable collapse of higher order to second-order concentration moments leads to the conclusion that only two concentration moments are required for an accurate description of concentration fluctuations. This explicitly holds for the pure advection case, while in the case of LSD presence the Moment Deriv-ing Function (MDF) is involved to ensure the moment collapse validity. Fur-thermore, the expected mass fraction (EMF) concept is applied in groundwater transport. In its origin, EMF is function of the concentration but with lower number of realizations needed for its determination, compared to the one point PDF. From practical point of view, EMF excludes meandering effect and incorporates information about exposure time for each non-zero concentration value present. Also, it is shown that EMF is able to clearly reflect the effects of aquifer heterogeneity and structure as well as the Pe value. To demonstrate the uniqueness of the moment collapse feature and ability of the Beta distribution to account for the concentration frequencies even in real cases, Macrodisper-sion Experiment (MADE1) data sets are used. / <p>QC 20131104</p>