改进HB模型与液滴动力学耦合的垂直气井流动特性模拟

Simulation of Flow Characteristics in Vertical Gas Wells Coupling Improved HB Model and Droplet Dynamics

摘要: 针对气井积液诊断中井筒压力及微观液滴行为预测的难点，提出一种基于宏观-微观单向耦合的数值模拟方法。采用考虑加速压降项与算术平均粘度的改进Hagedorn-Brown (HB)模型计算垂直井筒气液两相宏观流动参数；基于Hinze湍流破碎理论与Saffman湍流碰撞聚合理论，建立沿井筒高度分布的液滴破碎与聚并动力学模型。利用文献实验数据验证了压力预测模型的准确性，相对误差在3%以内。参数敏感性分析表明：管径增大导致产能非线性剧增，进而显著提高井筒内流体湍流强度，使液滴平均直径有减小的趋势；井壁粗糙度增加会限制产能，由于流速降低导致的湍流耗散减弱效应超过了粗糙度增加带来的湍流增强效应，使液滴直径有增大的趋势；井口回压升高会产生“背压限制”与“气体压缩”双重效应，致使流速大幅下降，使液滴直径有显著的增大趋势。研究揭示了宏观工况通过改变产能进而影响微观流场剪切强度的物理机制。

Abstract: To address the challenges in predicting wellbore pressure and microscopic droplet behavior for liquid loading diagnosis in gas wells, a numerical simulation method based on macro-micro one-way coupling is proposed. An improved Hagedorn-Brown (HB) model, incorporating the acceleration pressure drop term and arithmetic mean viscosity, is adopted to calculate the macroscopic flow parameters of gas-liquid two-phase flow in vertical wellbores. Furthermore, based on the Hinze turbulence breakup theory and the Saffman turbulence collision-coalescence theory, a dynamics model for droplet breakup and coalescence distributed along the wellbore depth is established. The accuracy of the pressure prediction model is validated using experimental data from the literature, with relative errors controlled within 3%. Parameter sensitivity analysis indicates that increasing the tubing diameter leads to a non-linear surge in productivity, which significantly enhances the turbulence intensity of the fluid and consequently causes a decreasing trend in the average droplet diameter. Conversely, increasing wellbore wall roughness limits productivity; the effect of weakened turbulent dissipation caused by reduced flow velocity outweighs the turbulence enhancement effect brought by increased roughness, resulting in an increasing trend in droplet diameter. Additionally, elevated wellhead back pressure induces a dual effect of “back-pressure constraint” and “gas compression”, causing a substantial drop in flow velocity and a significant increase in droplet diameter. This study elucidates the physical mechanism by which macroscopic operating conditions regulate the shear strength of the microscopic flow field by altering gas production capacity.