On the departure from Gaussianity and Fickianity of transport in highly heterogeneous aquifers

The solution of the advective transport problem is difficult because of its intrinsic nonlinearity. The aim of this work is to present a few new results concerning nonlinear transport of passive solutes valid for large conductivity variance. The impact of high heterogeneity is twofold: (i) highly conductive zones may create preferential paths leading to early particle arrival times and large particle displacements; and (ii) the low conductive regions "trap" the solute particles, causing late arrival times and small particle displacements. The combination of the two effects (with the second one prevailing in highly heterogeneous aquifers) leads to continuously increasing values of dispersion coefficients and a departure from the classic Gaussian distribution of trajectories. The effects are larger for the large values of the log-conductivity variance. As a consequence, the transport will seem to be "anomalous" or "non-Fickian" for a long period of time after the injection. Such anomaly is evident, for example, in the tailing of the travel times and the trajectory PDFs.