Abstarct: In the oil industry, millions of dollars are spent annually on managing and overcoming sand control issues. Extracting hydrocarbons from sandstone reservoirs often encounters problems such as erosion, reduced well productivity, and pipeline blockage. In this study, fundamental and preliminary models for single-phase and two-phase fluid flow were used to validate the simulations, and the results were consistent with analytical solutions. We then examined the fluid flow around a spherical particle, particle fall, particle submersion, particle ingress and egress, and particle motion near the free surface in single-phase and two-phase environments using the discrete element method. After comparison with other models, we observed that the employed models were highly accurate and reliable. In the discrete element method, each solid particle is modeled individually, and their interactions and the forces imposed on them are simulated using motion equations. Furthermore, by simulating the movement of one particle, six particles, and forty-eight particles inside a pipe, we observed that the results are consistent with previous studies. The discrete phase method was also used to track the path of particle motion within the pipe and elbow to observe the erosion rate. In the discrete phase method, solid or liquid particles are modeled as a discrete phase, and their movement path in the fluid environment is tracked and calculated. Therefore, firstly, the erosion model due to particle collision in an elbow was examined, and it was noted that the erosion rate increases with the flow velocity and particle size and decreases by changing the particle shape from sharp to more rounded. Moreover, we investigated the erosion rate due to particle collision in two elbows placed in series and noted that parameters such as increased connection length between elbows and increased curvature radius help reduce the erosion rate in both elbows. The simulations conducted can serve as an effective tool for reducing erosion in oil and gas industry pipelines.