In this study, the erosion rate of an elbow in a Natural gas pipeline in the dense phase, pseudo-dense phase, and vapor phase were analyzed through a combination of computational fluid dynamics and the discrete element approach. The erosion rate of the Natural gas pipeline in the three phases was evaluated at different particle mass flow rates, Reynolds numbers, particle diameters, and curvature radii. Results showed that the erosion rate for all three phases increased with Reynolds number, particle diameter, and particle mass flow rate while decreasing as the curvature radius increased. The maximum erosion rate (MER) at a Reynolds number of 1,000,000 in the dense phase was 80% and 23% lower than the vapor phase and pseudo-dense phase, respectively. At a Reynolds number of 10,000,000, the MER in the dense phase was 59% and 16% lower than the vapor phase and pseudo-dense phase, respectively. At different particle mass flow rates and particle diameters with a constant Reynolds number for Natural gas flow, the MER in the dense phase was almost 63% and 20% lower than the vapor phase and pseudo-dense phase, respectively. The Reynolds number had a more significant effect on the erosion rate compared to particle mass flow rate, particle diameter, and curvature radius. Additionally, as the curvature radius increased, the reduction in erosion rates in the dense and pseudo-dense phases was greater than in the vapor phase.