Network models are an effective means of incorporating pore-scale heterogeneity into flow models of porous materials. The drawback to these models used to be the inability to obtain quantitative macroscopic parameters representing larger (experimental-scale) media. However recently developed modeling techniques, combined with more widely available computational resources, make the simulation of macroscopic parameters from a network approach viable. A network model for the slow flow of an incompressible fluid in disordered packed beds is presented Fundamental fluid mechanics equations are solved at the pore scale and then translated to macroscopic behavior using a network approach. The results reproduce experimental permeabilities and show excellent quantitative fits to residence time distributions for mechanical dispersion in real beds. Simulations of the RTD are of special interest because they are definitive links between pore-scale flow behavior and macroscopic responses.