The aim of the present paper is to evaluate and compare the pore level hydrodynamic dispersion and effects of turbulence during flow in porous media. In order to compute these quantities, large eddy simulations of turbulent flow in five unit cells comprised of spherical particles are performed and the results are averaged over the cells. Visualizations of vortical structures reveal that the size of the turbulence structures is of the size of the pores. Investigations furthermore yield that volume-averaged values of the hydrodynamic dispersion are of the same order as the Reynolds stress within the pores. It is also shown that the effect of intra-pore turbulence and hydrodynamic dispersion on the redistribution of macroscopic momentum within the porous medium is negligible compared to Forchheimer term. A discussion is provided on the accuracy of the eddy viscosity hypothesis in the modeling of the volume-averaged intra-pore Reynolds stresses. Finally, the effect of variation in the pore-scale geometry on the turbulence structures and averaged values of hydrodynamic dispersion and Reynolds stress is investigated.