In nitrogen drilling, entrained sand particles in the gas flow may cause erosive wear on metal surfaces and have a significant effect on the operational life of discharge pipelines, especially for elbows. In this paper, computational fluid dynamics (CFD) simulations based code FLUENT is carried out to investigate the flow erosion on a sand discharge pipe in conjunction with an erosion model. The motion of the continuum phase is captured based on solving the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations, while the kinematics and trajectory of the sand particles are evaluated by the discrete phase model (DPM). The flow field has been examined in terms of pressure, velocity, and erosion rate profiles along the flow path in the bend of the simulated discharge pipe. Effects of flow parameters such as inlet velocity, sandy volume fraction, and particle diameter and structure parameters such as pipe diameter and bend curvature are analyzed based on a series of numerical simulations. The results show that small pipe diameter or small bend curvature leads to serious erosion, while slow flow, little sandy volume fraction, and small particle diameter can weaken erosion. The results obtained from the present work provide useful guidance to practical operation and discharge pipe design.