شبیه سازی CFD و مدل سازی دو بعدی فرسایش ذرات جامد در جریان حلقوی CFD simulation and 2-D modeling of solid particle erosion in annular flow

۱٫ INTRODUCTION Predicting solid particle erosion in multiphase flow is difficult as so many factors are involved in the problem. Currently, both experimental and numerical approaches can be applied to investigate the phenomenon of multiphase flow erosion. Several experimental studies were conducted at the University of Tulsa Ersoion/Corrosion Resesrch Center (E/CRC) to measure erosion in multiphase flow (Dosila, 2008; Vieira, 2015; Parsi; 2015; Fan, 2010). However, there are still many questions unanswered and especially modelling of multiphase flow erosion has not been extensively studied. This is especially the case for annular flow commonly found in oil and gas production. Dosila (2008) found through experimentation that for annular flow the erosion rate can decrease when liquid flow rate increases above a critical value.2 Fan (2010) also observed the same behavior even for large pipe diameters.3 Vieira (2015) studied the effect of elbow orientation on erosion in annular flow. He found that erosion in a vertical-horizontal elbow was significantly higher than that in a horizontal-horizontal elbow. He improved a 1-D simplified model by increasing the initial particle tracking velocity. The factor was obtained empirically through flow experimental data4 . Computational Fluid Dynamics (CFD) is another approach to investigate erosion in multiphase flow. But, the application of this approach to study annular flow erosion is relatively new and literature on this topic is extremely limited. A typical CFD-based  erosion model can be divided into three parts: flow modeling, particle tracking and erosion calculation. Parsi (2015) investigated CFD erosion prediction for slug/churn flows. An Eulerian-Eulerian approach with Multi-Fluid VOF (Volume of Fluid) model was employed and multiphase flow particle tracking was achieved by utilizing local mixture velocity.5 The CFD simulation demonstrated that sand concentration is proportional to local liquid hold-up. Also, the obtained erosion trend showed good agreement when compared with experimental data. In the present work, CFD is utilized to investigate erosion rates in annular flow and the results are used to obtain the necessary information and to improve a simplified 2-D model for predicting erosion rates in annular flow. ۵٫ CONCLUSIONS An Eulerian-Eluerian with Multi-Fluid VOF model is successfully applied to model annular flow. Particle tracking in the resulting flow field offers good erosion prediction results. Compared to the VOF model, it is less time-consuming and can effectively resolve interfacial flow field. Both of the models can obtain comparable erosion results and show good agreement with experimental data. Investigation of annular flow by the Eulerian-Eulerian with Multi-Fluid VOF model reveals that the liquid film can effectively reduce erosion for elbows. However, for all annular flow conditions, the liquid film does not always exist continuously over the elbow. It is dependent on superficial gas and liquid velocities and other factors. Further stability analysis can be carried out to determine the criteria for a stabilized continuous liquid film over the elbow which will shed more light on annular flow erosion modeling. A 2-D mixture model is evaluated to predict erosion for annular flow conditions. Results show that the 2-D mixture model can significantly over predict erosion for some cases. For the 2-D mixture model, the effect of liquid film on erosion is not considered which may be one of the reasons causing large deviations from experimental data. Considering the effect of both superficial gas and liquid velocity, a 2-D ad-hoc model is implemented. It is an empirical model based on collected experimental data. Results from this 2-D ad hoc model show improvement compared with the mixture model but further refinement is desired for some cases. Finally, even though CFD produces good results for erosion prediction, the flow modeling results are still not physical as no entrainment is observed in the gas core which needs to be further investigated. But, it can provide liquid film distribution information over the elbow which can be utilized to develop a flow regime dependent 2-D annular flow model.