Fractal and prefractal geometric models have substantial potential for contributing to the analysis of flow and transport in porous media such as soils and reservoir rocks. In this study, geometric and hydrodynamic parameters of saturated 3D mass and pore-solid prefractal porous media were characterized using the lattice Boltzmann model (LBM). The percolation thresholds of the 3D prefractal porous media were inversely correlated with the fraction of micro-pore clusters and estimated as 0.36 and 0.30 for mass and pore-solid prefractal porous media, respectively. The intrinsic permeability and the dispersivity of the 3D pore-solid prefractals were larger than those of the 3D mass prefractals, presumably because of the occurrence of larger solid and pore cluster sizes in the former. The intrinsic permeability and dispersivity of both types of structure increased with increasing porosity, indicating a positive relationship between permeability and dispersivity, which is at odds with laboratory data and current theory. This discrepancy may be related to limitations of the convection dispersion equation at the relatively high porosity values employed in the present study.