A probability model for solid particle erosion in a straight pipe

• A probability model is developed to predict the penetration rate in a straight pipe.
• Distribution of vortexes is investigated to describe the turbulent flow field.
• Particle motion in the radial direction is regarded as a Markov process.
• The model is well verified by comparing with numerical simulations and experiments.
• The model demonstrates advantages in accuracy and applicability.

Erosion caused by solid particles entrained in pipelines can lead to serious economic loss and potential safety hazards in the oil and gas industry. Long straight pipe is the most common form of pipeline. In the present work, a probability model for particle erosion in a long straight pipe is proposed to predict the overall penetration rate caused by solid particles by analyzing the random movement of a single particle in the turbulent flow field. The model works in two mechanisms. First, the distribution of the characteristic vortex length is deduced to describe the turbulent flow in a pipe based on the energy equilibrium among eddies with different scales and the distribution of fluctuation velocities. Second, the particle motion in the radial direction is regarded as a Markov process which is only influenced by the eddy randomly appearing in the fully developed turbulent flow. Based on the knowledge of the turbulent flow field and the motion of particles, a particle erosion formula is introduced into the probability model to calculate erosion in a straight pipe. By comparing with numerical simulations and experimental data, the present model is well verified and demonstrates advantages in accuracy and applicability.