Two-fluid phase configurations in a periodic random close packing of spheres with porosity 0.369. This data set contains equilibrium fluid configurations obtained using the lattice Boltzmann method based on randomly initialized distribution of phases for a variety of fluid saturations. Data sets are labeled with the initial fluid saturation (sw_XX) and the whether a connected (a) wetting phase or (b) non-wetting phase was used to determine the initial fluid configuration. For additional details on the data set, please refer to McClure et al. (2016) (currently under review at Physical Review E). For all data sets, the phases are labeled as: solid (0), Non-wetting (1), and wetting (2).