Macrodispersion by Diverging Radial Flows in Randomly Heterogeneous Porous Media

Radial flow takes place in a heterogeneous porous formation where the transmissivity T is modelled as a stationary random space function (RSF). The steady flow is driven by a given rate, and the mean velocity is radial. A pulse-like of a tracer is injected in the porous formation, and the thin plume spreads due to the fluctuations of the velocity which results a RSF as well. Transport is characterized by the mean front, and by the second spatial moment of the plume. We are primarily interested in tracer macrodispersion modelling. With the neglect of pore-scale dispersion, macrodispersion coefficients are computed at the second-order of approximation, without neglecting the head gradient fluctuations. Although transport is non ergodic at the source, it is shown that ergodicity is achieved at small distances from the source. This is due to the fact that close to the source local velocities are quite large, and therefore solute particles become uncorrelated very soon. Under ergodic conditions, we compare macrodispersion mechanism in radial flows with that occurring in mean uniform flows. At short distances the spreading effect is highly enhanced by the large variability of the flow field, whereas at large distances transport exhibits a lesser dispersion due to the reduction of velocities. This supports the explanation provided by Indelman and Dagan (1999) to justify why the macrodispersivity is found smaller than that pertaining to mean uniform flows. The model is tested against a tracer transport experiment (Fernàndez-Garcia et al., 2004) by comparing the theoretical and experimental breakthrough curves. The accordance with real data, that is achieved without any fitting to concentration values, strengths the capability of the proposed model to grasp the main features of such an experiment, the approximations as well as experimental uncertainties notwithstanding.