A probability model of predicting the sand erosion profile in elbows for gas flow

•A probability model is developed to predict the sand erosion profile in elbows.•The particle stochastic rebound rule is firstly introduced in theoretical analysis.•The second collision behavior of particles is firstly investigated theoretically.•Maximum penetration rates and entire erosion profiles can be directly calculated.•Second collision plays a significant role in forming the erosion profile.

The damage caused by sand erosion is an inevitable problem encountered in the oil and gas transportation system. The elbow is one of most vulnerable fittings of pipelines. For gas flow in elbows, it has been proved that incident solid particles will rebound randomly when they initially impact the wall, and then impact the wall once again with a certain probability, resulting in second collision erosion. In the present work, a probability method is developed to analyze the impact-rebound-impact behavior of sands in elbows for gas flow. First, the Lagrange method is adopted to track motion trajectories of particles, and the motion rules of particles are deduced. First and second collision velocities can then be calculated. Second, by analyzing the probability behavior of a single particle, holistic impact behavior of a large quantity of particles can be characterized. Last, first and second collision-induced erosion rates at specific position are calculated by using erosive correlations, and the three-dimensional erosion profile can then be exhibited over the entire elbow surface. A large number of experimental data are adopted to examine the probability model based on the knowledge of second collision. The erosion profiles along the centerline and on the entire surface of the elbow, which can hardly be measured in experiments, are also calculated and analyzed through the probability model. The present work not only demonstrates the accuracy of the probability model, but also confirms that second collision of solid particles is an important behavior in elbows for gas flow, and plays a significant role in forming the erosion profile.