A new correlation for predicting solid particle erosion caused by gas-sand flow in elbows

The current work presents a new correlation for estimating solid particle erosion under gas-sand flow conditions in standard elbows. To develop this correlation, in the first step, a dimensional analysis was performed to obtain dimensionless groups that governed the erosion phenomenon in standard elbows. Then, a power-law correlation was established among the extracted governing dimensionless groups. In the next step, effect of target wall material on erosion was investigated to include a material factor in the correlation. In the final step, an empirical factor to account for sand particle shape was included in the correlation. Dimensionless erosion number was calculated for different flow conditions, sand sizes and densities, and pipe diameters. It was shown that the dimensionless groups and their exponents provide insight into the importance of different parameters on erosion. The resulting erosion ratio (in mm/kg) was compared to experimental data collected from the literature. It was found that, the dimensionless erosion number correlation follows the trend of the experimental data, and good agreement between the correlation's predictions and the experimental data was observed. The proposed correlation is an effective tool that enables the users to estimate erosion under gas-sand flow conditions in just several minutes. More importantly, unlike the existing empirical correlations that do not account for many of the parameters affecting erosion and have been developed based on a limited number of experimental data, the correlation proposed accounts for all flow and particle parameters.