We study macroscopic (centimeter scale) dispersion using pore-scale network simulation. A Lagrangian-based transport model incorporating flow and diffusion is applied in a diamond lattice of throats with square cross section whose radius distribution is the same as computed for Berea sandstone. We use physically consistent rules using a combination of stream-tube routing and ideal mixing to transport particles across pore junctions. The influence of both heterogeneity and high Peclet numbers results in asymptotic behavior only being seen after movement through many throats. A comprehensive comparative study of longitudinal dispersion with experiments in consolidated and unconsolidated media indicates that the model can quantitatively predict the asymptotic macroscopic dispersion coefficient over a broad range of Peclet numbers, 0 400.