幂律流体在椭圆井眼同心环空中螺旋层流流动压降

Flow pressure drop of laminar helical flow of power-law fluid in concentric annulus of elliptical wellbore

环空压降的准确预测是精准控制井底压力的基础,能够有效防止井漏、溢流,甚至井喷等井下复杂和事故。常规环空压降预测多以圆形井眼为基础,未考虑井眼形状不规则的影响;由于岩石力学特性参数和地应力的非均质性,易形成椭圆形井眼。以流体动力学为基础,建立椭圆井眼中幂律流体螺旋层流流动压降数值模型,利用流体力学仿真结果和实验结果对数值模型进行验证;以数值模型为基础,开展流动压降影响因素分析,明确不同参数对流动压降的影响规律;采用最小二乘法建立无量纲压力梯度拟合模型。研究结果表明,数值模型与仿真模拟和实测结果误差介于±5%。压力梯度随流体稠度系数的增加呈线性增大,随流体流性指数和环空内外径比率增大呈指数数型增大,随轴向平均速度增大呈对数型增大,随椭圆长短轴之比和内管转速增大呈指数型降低。无量纲压力梯度几乎不随流体稠度系数的变化而变化,拟合模型与数值模型误差仅为±5%。适用参数范围为0.8 m/s≤v_x≤1.4 m/s,40 r/min≤ω≤120 r/min,0.5≤K_d≤0.8,1.0≤η≤1.2和0.5≤n≤0.8。椭圆井眼同心环空螺旋层流无量纲压力梯度拟合模型能够实现流动压降的准确便捷预测。

Accurate prediction of annular pressure drop provides the foundation for precisely controlling bottom hole pressure and effectively preventing complex downhole incidents such as wellbore leakage,overflow,and even blowout.The conventional prediction method of annular pressure drop is usually based on circular wellbores,without considering the influence of irregular borehole shapes.Owing to the heterogeneity of mechanical rock parameters and in-situ stress,elliptical wellbores are easily formed.Based on fluid dynamics,a numerical model for the pressure drop of power-law fluid in laminar helical flow in elliptical wellbores was established,and was further verified by fluid mechanics simulation results and experimental data.Using the numerical model,the influencing factors of flow pressure drop were analyzed to clarify the effects of different parameters on flow pressure drop.A dimensionless pressure gradient fitting model was established by the least square method.The results show that the numerical model has an error within±5%when compared with simulation and measured results.The pressure gradient increases linearly with the increase of fluid viscosity coefficient,increases exponentially with the increase of flow behavior index and the ratio of inner and outer diameters,and increases logarithmically with the increase of average axial velocity;however,it decreases exponentially with an increase in the ratio of major and minor axes of the ellipse and the inner tube rotational speed.The dimensionless pressure gradient shows little variation with the change of fluid viscosity coefficient.The fitting model has an error of only±5%when compared to the numerical model.The applicable parameter ranges are as follows:0.8 m/s≤vx≤1.4 m/s,40 r/min≤ω≤120 r/min,0.5≤Kd≤0.8,1.0≤η≤1.2 and 0.5≤n≤0.8.The dimensionless pressure gradient fitting model established for concentric annular laminar helical flow in elliptical wellbore enables accurate and convenient prediction of flow pressure drop,thus laying a theoretical foundation for the fundamental study of wellbore hydraulics.