Bulk stress distributions in the pore space of sphere-packed beds under Darcy flow conditions

In this paper, bulk stress distributions in the pore space of columns packed with spheres are numerically computed with lattice Boltzmann simulations. Three different ideally packed and one randomly packed configuration of the columns are considered under Darcy flow conditions. The stress distributions change when the packing type changes. In the Darcy regime, the normalized stress distribution for a particular packing type is independent of the pressure difference that drives the flow and presents a common pattern. The three parameter (3P) log-normal distribution is found to describe the stress distributions in the randomly packed beds within statistical accuracy. In addition, the 3P log-normal distribution is still valid when highly porous scaffold geometries rather than sphere beds are examined. It is also shown that the 3P log-normal distribution can describe the bulk stress distribution in consolidated reservoir rocks like Berea sandstone.