Experiments in porous media suffer from preferential flow along apparatus walls-called the wall effect-which results from higher porosity and therefore higher permeability near the walls. Through a theoretical analysis of porosity in a three-dimensional rectangular apparatus containing spherical beads with hexagonal close packing, this study shows that porosity, and therefore wall effects, exhibits different behavior along each of the orthogonal walls. This study also experimentally evaluates two techniques for mitigating wall effects in experiments of solute transport in porous media using monodisperse, spherical beads in hexagonal close packing as the bulk porous medium. The first mitigation technique adds a sublayer of smaller beads of one third of the diameter of the primary beads between the wall and the bulk media. The second mitigation technique applies a half-bead-diameter-thick layer of silicone to the wall and embeds one layer of beads into the silicone, creating a wall of hemispheres. Both techniques seek to impose more uniform porosity up to the wall. Velocity profiles indicate that both techniques eliminate preferential flow along the wall and therefore are effective at mitigating the wall effect.