Three-dimensional Navier-Stokes flow and transport simulations are conducted for a single pore throat between cubic- packed grains 1-2 mm in diameter to advance our basic understanding of porous media processes. The grains are considered either spherical or ellipsoidal, and flow between the grains at different Reynolds Number is oriented along or across their long axis. Discharge through the pore varied linearly with imposed pressure gradients. Vortices are present near the pore throats, with narrower and deeper pore throats displaying a series of vortices. The vortices drive tailing of solutes resulting in power-law residence time distributions. Different tailing behavior is observed since the vortices are sensitive to grain shape and flow orientation. Tailing becomes more pronounced at higher Reynolds Number although the shape of the vortices remains unchanged.