CFD Simulation and Prediction Model of Annular Frictional Pressure Drop with Combined Effects of Drillpipe Rotation Speed and Eccentricity
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摘要:
深井钻井时，准确预测环空摩擦压降是保证井筒压力预测精度的关键，钻井液流速、钻杆转速及环空偏心度是影响环空摩擦压降的重要因素。为研究多种因素耦合作用下环空摩擦压降的变化规律，建立了水平井环空钻井液流动模型，对幂律流体在层流和湍流条件下的流动特性开展了数值模拟。模拟结果表明：层流状态下，偏心度和钻杆转速单独作用时，都会导致环空摩擦压降减小；偏心度和钻杆转速共同作用时，环空摩擦压降随偏心度先增大后减小，这与偏心环空中惯性效应对螺旋流的破坏作用有关。湍流状态下，钻杆转速对同心环空的摩擦压降几乎没有影响；偏心环空中，随着钻杆转速增大，不同偏心度下的环空摩擦压降值逐渐增加，且都逐渐趋近于同心环空摩擦压降。基于数值模拟数据，建立了层流和湍流条件下考虑钻杆转速和偏心度耦合作用的环空摩擦因子预测模型，该模型对模拟数据的最大拟合误差为9.18%，对试验数据的最大预测误差为8.33%。研究结果可为深井钻井时井筒压力控制和水力参数优化提供参考。
Abstract:Accurate prediction of annular frictional pressure drop is the key to ensuring the accuracy of bottomhole pressure prediction during deep well drilling. The flow rate of the drilling fluid, drillpipe rotation speed, and the annular eccentricity are important factors affecting the annular frictional pressure drop. To investigate the change in annular frictional pressure drop with the combined effects of various factors, a drilling fluid flow model in the annulus of a horizontal well was developed, and the flow characteristics of power-law fluids under laminar and turbulent flow conditions were numerically investigated. The results show that: 1) under the laminar flow condition, annular frictional pressure drop decreases when the eccentricity or the drillpipe rotation speed increases separately. However, when these two parameters increase simultaneously, the annular frictional pressure drop increases first and then decreases as eccentricity increases. This is due to the destruction of helical flow by the inertia effect in the eccentric annulus. 2) Under the turbulent flow condition, drillpipe rotation speed has almost no effects on the frictional pressure drop in the concentric annulus. In the eccentric annulus, with the drillpipe rotation speed increasing, the frictional pressure drop under different eccentricities increases gradually and converges to the frictional pressure drop in the concentric annulus. Based on the numerical simulation data, the prediction model for annular frictional coefficient with the combined effects of drillpipe rotation speed and eccentricity under laminar and turbulent flow conditions are developed. The maximum fitting error of the model to the simulated data is 9.18%, and the prediction error for experimental data is no more than 8.33%. The results of this study could provide reference for wellbore pressure control and hydraulic parameter optimization during deep well drilling.
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图 1 水平井筒环空模型及横截面网格划分示意
Figure 1. Horizontal wellbore annulus model and cross-section meshing
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图 2 单位长度环空摩擦压降与总网格数的关系曲线
Figure 2. Relationship between annular frictional pressure drop per unit length and total mesh number
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图 4 钻杆不旋转时不同入口速度下单位长度环空摩擦压降随偏心度的变化
Figure 4. Variation of annular frictional pressure drop per unit length with eccentricity at different inlet velocities when drillpipe is not rotating
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图 5 钻杆不旋转时不同偏心度条件下的环空出口钻井液速度云图
Figure 5. Velocity contours of drilling fluid at annulus outlet with dfferent eccentricities when the drillpipe is not rotating
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图 6 同心环空（e=0）中不同入口速度下单位长度环空摩擦压降随钻杆转速的变化
Figure 6. Variation of annular frictional pressure drop per unit length with drillpipe rotation speed at different inlet velocities in a concentric annulus (e=0)
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图 7 同心环空（e=0）中不同钻杆转速下的钻井液表观黏度
Figure 7. Apparent viscosity of drilling fluid under different drillpipe rotation speeds in a concentric annulus (e=0)
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图 8 层流下不同钻杆转速时单位长度环空摩擦压降随偏心度的变化
Figure 8. Variation of annular frictional pressure drop per unit length with eccentricity at different drillpipe rotation speeds under laminar flow condition
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图 9 层流状态下钻杆旋转时同心环空与偏心环空中流体流线对比
Figure 9. Comparison of fluid streamline between concentric annulus and eccentric annulus during drillpipe rotation under laminar flow condition
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图 10 湍流状态下不同入口速度时环空摩擦压降随偏心度的变化曲线
Figure 10. Change curve of annular frictional pressure drop with eccentricity at different inlet velocities under turbulent flow condition
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图 11 环空中层流和湍流状态下出口处钻井液速度分布
Figure 11. Velocity distribution of drilling fluid at the outlet under laminar and turbulent flow conditions in the annulus
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图 12 湍流状态下不同入口速度时同心环空摩擦压降随钻杆转速的变化曲线
Figure 12. Change curve of concentric annular frictional pressure drop with drillpipe rotation speed at different inlet velocities under turbulent flow condition
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图 13 湍流状态下不同偏心度条件下单位长度环空摩擦压降随钻杆转速的变化
Figure 13. Variation of annular frictional pressure drop per unit length with drillpipe rotation speed under different eccentricity conditions and turbulent flow condition
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图 14 层流状态下钻杆不旋转时摩擦因子随偏心度的变化
Figure 14. Variation of frictional coefficient with eccentricity when drillpipe is not rotating under laminar flow condition
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图 15 层流状态下钻杆旋转时摩擦因子随泰勒数的变化
Figure 15. Variation of frictional coefficient with Taylor number when drillpipe is rotating under laminar flow condition
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图 16 湍流状态下钻杆不旋转时雷诺数与摩擦因子之间的关系
Figure 16. Relationship between Reynolds number and frictional coefficient when drillpipe is not rotating under turbulent flow condition
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图 17 湍流状态下钻杆旋转时泰勒数与摩擦因子之间的关系
Figure 17. Relationship between Taylor number and frictional coefficient when drillpipe is rotating under turbulent flow condition
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图 18 层流和湍流情况下摩擦因子预测值与模拟值的对比
Figure 18. Comparison between simulated and predicted frictional coefficients under laminar and turbulent flow conditions
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图 19 层流和湍流情况下环空摩擦压降预测值与试验数据的对比
Figure 19. Comparison between experimented and predicted annular frictional pressure drop under laminar and turbulent flow conditions
表 1 网格无关性分析结果
Table 1 Mesh independence analysis
网格划分
方案网格数 总网格数 单位长度环空摩擦
压降/（Pa·m−1）轴向 径向 周向 1 180 8 24 34 560 759.77 2 240 10 32 76 800 730.67 3 360 10 40 144 000 720.51 4 480 16 48 368 640 719.56 5 500 20 52 520 000 718.78 
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表 2 数值模拟方案
Table 2 Scheme of numerical simulation
稠度系数/
（Pa·sn）流性指数 入口速度/
（m·s−1）偏心度 钻杆转速/
（r·min−1）0.10 0.50 层流：0.10, 0.15,
0.20, 0.25, 0.30
湍流：1.00, 1.20,
1.40, 1.60, 1.800, 0.2, 0.4,
0.6, 0.80, 50, 100, 150 2.10 0.38 层流：1.00
湍流：4.000.4 0, 100 0.83 0.56 0.37 0.59 0.25 0.61
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表 3 偏心度与公式（16）中a1和a2的关系
Table 3 The relationship between Reynolds number and a1, a2 in Eq. 16
e a1 a2 0 0.08017 −1.00121 0.2 0.07819 −0.99010 0.4 0.07179 −0.96671 0.6 0.06114 −0.97408 0.8 0.05223 −0.97522
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表 4 R.M.Ahmed等人和M.Sorgun等人在试验中的环空尺寸及钻井液流变性参数
Table 4 Annulus dimensions and rheological properties of drilling fluids in experiments of R.M.Ahmed and M.Sorgun
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