Pulsed gradient stimulated echo (PGSTE) and microimaging nuclear magnetic resonance (NMR) are used to probe correlations between structure and flow in the void space of a model porous system formed from a packing of 1-mm diameter glass spheres. The pulsed gradient stimulated echo data determine the average propagator and permit the dispersion of the flow to be studied as a function of delay time. Microimaging yields structural information and, specifically, a reduced radial distribution function (rdf) for the structure of the void space. Transition to fully developed dispersive flow is shown to occur on a scale size for which no further correlations in the structure of the void space are observed.