Macrodispersion by Point-Like Source Flows in Randomly Heterogeneous Porous Media

A pulse of a passive tracer is injected in a porous medium via a point-like source. The hydraulic conductivity K is regarded as a stationary isotropic random space function, and we model macrodispersion in the resulting migrating plume by means of the second-order radial spatial moment Xrr . Unlike previous results, here Xrr is analytically computed in a fairly general manner. It is shown that close to the source macrodispersion is enhanced by the large local velocities, whereas in the far field it drastically reduces since flow there behaves like a mean uniform one. In particular, it is demonstrated that Xrr is bounded between X∞ corresponding to the short-range (far field), and X0 pertaining to the long-range (near-field) correlation in the conductivity field. Although our analytical results rely on the assumption of isotropic medium, they enable one to grasp in a simple manner the main features of macro-dispersion mechanism, therefore providing explicit physical insights. Finally, the proposed model has potential toward the characterization of the spatial variability of K as well as testing more general numerical codes.