Probability Analysis Of Flow Field In Pipelines And Its Application To Solid Particle Erosion

As important parts of the flow assurance, the flow pattern analysis of annular flow and prediction of solid particle erosion in the pipelines are of great concerns in the oil and gas industry. The phase distributions and mechanical properties of annular flow have great influences on the conveying efficiency of the oil and gas and the structural stabilities of the pipelines. Erosion caused by solid particles entrained in pipelines reduces the operational reliability, increases the risk of failure and may even result in danger to the personnel and environment. Hence the understandings of the two questions above are essentially significant for theoretical developments and engineering applications. In the present work, the probability models are respectively developed to analyze the flow pattern of annular flow and predict the solid particle erosion in the pipelines.Firstly, the particle movement in turbulent flow field is described based on probability analysis. The probability distribution of some characteristic parameter in time and space is defined as Probability Field of the parameter, to inspect the random variation of the turbulent flow field in the long straight pipe. The Probability Field of the characteristic length, life time and charatersitic velocity of the vortex can be solved based on the energy equilibrium among vortexes with different scales and the distribution of fluctuation velocities. Then the Probability Field of particle pulsation can be solved by analyzing the particle movement in vortexes with different scales. The deposition process of particles can be tracked based on the knowledge of the particle pulsation in radial direction and the spatial distribution of particles. It can be proven that the deposition process has little influence on the particle movement along the axial direction, and then the axial velocity of particle can unlimitedly close to the conveying velocity. Furthermore, the Probabilty Field and tracing method of particles are applied to the flow pattern analysis of the annular flow and the prediction of the solid particle erosion in pipelines to solve the relevant engineering problems.Secondly, a probability model is established to analyze the flow pattern of the upward annular flow, and the effects of many parameters on the morphological characteristics and physical properties of the annular flow are inspected in detail based on the probability analysis. The probability model works in three mechanisms. First, a vortex generation theory on energy transfer from vortexes to droplets is supposed to describe the atomization process. Second, a random walk theory is applied to track the droplet deposition on the liquid film. Third, the atomization and deposition rates are respectively related to the probabilities of droplet generation and elimination by analyzing the interaction between the vortexes and droplets. Based on the knowledge of dynamic equilibrium between the atomization and deposition processes, a balance equation is established to close the equation set and the representative parameters of annular flow can be solved. The proportional parameters can be obtained by calculating the possibilities of the relevant random events, and the morphological parameters are regarded as the statistical results of abundant samples in the probability model. The characteristic parameters, such as droplet entrainment, atomization rate, film thickness, mean droplet size and interfacial shear stress, are well verified by comparing with the experimental data available in the literature. The generation and elimination processes of the droplet with any scale are discussed in detail by analyzing the interactions between the droplet and the vortex and among the droplets. Furthermore, three phenomena observed in experiments can be explained by the probability model. First, the droplet entrainment cannot increase without a limit and cannot make the film thickness equal to zero. Second, the droplet size distribution is an incomplete Gamma distribution. Third, the interfacial friction factor is a linear function of the film thickness.Finally, a probability model is established to predict the solid particle erosion in pipelines, and the effects of many parameters on the penetration rates are inspected in detail based on the probability analysis. The erosion that occurred in straight pipes is due to the random impact of particles on the pipe wall caused by turbulent fluctuations. Based on the spatial distribution and radial movement of particles, the overall penetration rate caused by solid particles can be solved by analyzing the random movement of a single particle in the turbulent field. The erosion observed in the gas bend is caused by the direct impact of particles on the pipe wall, while the combination of the direct and random impacts leads to the solid particle erosion in liquid bend. The particle erosion in the gas bend can be solved by relating the impact position to the entry postion. The particle movements in the liquid bend are decomposed into a deterministic two-dimensional motion on the symmetrical plane of bend and a random one-dimensional motion perpendicular to the symmetrical plane. Then the distribution of the impact position can be used to calculate the particle erosion in the liquid bend. By comparing with the experimental data, the present model is well verified and demonstrates advantages in accuracy and applicability in the straight pipe and gas bend, but the prediction results are little bigger than the measured data for the cases in the liquid bend.