Tracer dispersion in three-dimensional multipole flows

The transit time distribution for the hydrodynamic dispersion of a passive tracer in three-dimensional reservoir configurations of localized sources and sinks is related to the large-scale geometry of the system. Extending previous work on the planar case, we find that the first-passage transit time probability distribution function has a region of power-law decay, depending only on the multipole order of the distribution of fluid sources and sinks, an exponential decay region, whose characteristics are related to stagnation points in the flow field, and a shoulder whose location is related to the system size. Tracer measurements may thus be used as a noninvasive surface diagnostic tool to characterize subsurface reservoirs.