In the present study, two-phase flow simulations using SedFoam (an open-source multi-dimensional Eulerian two-phase solver based on OpenFOAM) are employed to investigate the scour phenomenon around pipelines in the vicinity of the seabed. A complete transport profile from the immobile bed, to slowly moving quasi-static bed and upper transport layers can be captured by the present model. The fluid Reynolds stress is modeled using the two-phase k-ε model. The particle stresses due to binary collisions and enduring contacts are modeled by kinetic theory for granular flow and a phenomenological frictional model, respectively. The model is first validated through a two-dimensional (2D) simulation of scour around a single pipeline near the seabed. The predicted time-dependent scour profiles as well as the scour depth are compared with the simulation results of Lee et al. (2016) and the experimental data reported by Mao (1986). A numerical experiment is then carried out to investigate the scour around the piggyback near the seabed. The effects of different locations of the small pipeline on the scour depth are studied.