考虑液滴形状影响的气井临界携液流速计算模型

A calculation model of critical liquid-carrying velocity of gas wells considering the influence of droplet shapes

为了判断气井是否积液同时优化气井配产,基于气流中液滴总表面自由能与气相总湍流动能相等的关系,建立了考虑液滴直径、液滴变形及变形对液滴表面自由能影响的气井临界携液流速计算模型(以下简称新模型):基于椭球体假设,通过分析液滴变形对液滴表面积及表面自由能的影响,建立起液滴最大迎风面直径的计算公式;考虑液滴变形对液滴所受曳力的影响,提出针对椭球形液滴的临界携液流速表达式;考虑液滴变形和液滴内部流动的影响,将Brauer模型基于圆球体的曳力系数计算值增大20%作为变形椭球体的曳力系数;基于能量守恒原理提出液滴变形参数与临界韦伯数函数关系式,并将计算结果下调10%;采用考虑气井压力和温度影响的表面张力计算公式。将新模型与Turner模型、李闽模型、王毅忠模型、王志彬模型和熊钰模型进行对比,并在44口气井开展了现场验证。结果表明,新模型的预测结果与气井的实际状况吻合最好。结论认为,新模型可用于对气井积液的判断。

To clarify the existence of liquid loading and optimize the production allocation in gas wells, we constructed a model for calculating the critical liquid-carrying velocity based on the equal relationship between the total surface free energy of droplets and the total turbulent kinetic energy of gas and considering the droplet size, droplet deformation and the influence of droplet deformation on surface free energy. Based on the ellipsoid hypothesis and by analyzing the influence of droplet deformation on the surface area and free energy of droplets, the equation for calculation of the maximum diameter of windward surface of droplets was developed. With consideration to the influence of droplet deformation on drags, the expression for the critical liquid-carrying velocity of ellipsoid droplets was clarified. With consideration to the influence of deformation and internal flow of droplets, the drag coefficient of the ellipsoid droplets was determined to be 20% higher than that of the Brauer Model for spheroid. A functional relationship between the deformation parameter K and the critical Weber number Wec was established based on the energy conservation law. In addition, the calculation results were reduced by 10%. During the course, the impacts of gas-well pressure and temperature on surface tension were taken into account. The proposed model was compared with the models developed by Turner, Li Min, Wang Yizhong, Wang Zhibin and Xiong Yu, and on-site verification was conducted in 44 gas wells. The results show that the proposed model provides the prediction results in best coincidence with the actual performance of gas wells. In conclusion, the proposed model can be used to predict liquid loading in gas wells effectively.