Numerical Simulation of the Effects of Eccentric Rotation of the Drill String on Annular Frictional Pressure Drop
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摘要:
准确预测钻柱偏心旋转工况下的环空摩阻压降是复杂结构井控压钻井的重要理论基础，但常规钻井液环空摩阻压降计算方法无法直接计算复杂结构井的环空摩阻压降。为此，应用数值模拟方法，分析了偏心度（0～67.42%）和钻柱转速(0～114.65 r/min)对典型环空（ϕ127.0 mm钻杆和ϕ215.9 mm井眼）中摩阻压降梯度的影响。分析结果表明：偏心度小于45.00%时，转速和偏心度对摩阻压降梯度影响较弱，摩阻压降梯度随转速增大略有降低，随偏心度增大而增大；偏心度大于45.00%时，低转速（<60 r/min）下摩阻压降梯度随偏心度增大而降低，高转速（≥60 r/min）下摩阻压降梯度随偏心度增大而略有增大。基于数值模拟结果，建立了偏心度分类的无因次偏心环空摩阻压降梯度预测模型，计算了南海某水平井ϕ215.9 mm井段的ECD，并与PWD测试结果进行了对比，平均相对误差为0.45%，表明该模型具有较好的准确性。研究结果表明，无因次偏心旋转环空摩阻压降计算模型可以精细描述环空压力场和准确计算ECD，为控压钻井水力参数优化提供指导。
Abstract:Accurate prediction of the annular frictional pressure drop under eccentric rotation of drill string is an important theoretical basis for managed pressure drilling (MPD) in complex structure wells. However, the conventional calculation methods for the annular frictional pressure drop of drilling fluid cannot be directly applied to calculating the annular frictional pressure drop in complex structure wells. For this reason, the influences of eccentricity (0−67.42%) and the rotational speed (0−114.65 r/min)of the drill string on the frictional pressure drop gradient in a typical annulus (created by a ϕ127.0 mm drill pipe and a ϕ215.9 mm wellbore) were analyzed. The results show that when the eccentricity is lower than 45.00%, the rotational speed and eccentricity have a weak influence on the frictional pressure drop gradient. Specifically, the frictional pressure drop gradient decreases slightly with the increase of rotational speed but increases with the increase of eccentricity; when the eccentricity is higher than 45.00%, the frictional pressure drop gradient decreases with the increase of eccentricity at low rotational speed（<60 r/min）, and the friction pressure drop gradient increases slightly with the increase of eccentricity at high rotational speed (>60 r/min). According to the numerical simulation results, a dimensionless frictional pressure drop gradient prediction model with eccentricity classification was built. The equivalent circulating density (ECD) of ϕ215.9 mm section of a horizontal well in the South China Sea was calculated by the proposed model. The results were then compared with the pressure-while-drilling (PWD) test results, with an average relative error of 0.45%, indicating that the proposed model has favorable accuracy. This study concludes that the proposed calculation model of the dimensionless annular frictional pressure drop under eccentric rotation can precisely describe the annular pressure field and ECD, and provide guidance for the hydraulic parameter optimization of MPD.
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图 1 22.47%偏心度下偏心环空物理模型与网格划分
Figure 1. Physical model and meshing of eccentric annulus with the eccentricity of 22.47%
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图 4 轴向流速沿高边方向线分布
Figure 4. Axial velocity distribution along the high-sidedirection line
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图 5 切向流速沿高边方向线分布
Figure 5. Tangential velocity distribution along the high-side direction line
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图 6 钻井液静压力沿宽流域中心线的分布
Figure 6. Static drilling fluid pressure distribution along the center line of wide flow domain
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图 7 偏心环空摩阻压降梯度与钻柱偏心度的关系曲线
Figure 7. Variation of frictional pressure drop gradient ineccentric annulus with eccentricity of drill string
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图 8 偏心环空摩阻压降梯度与钻柱转速的关系曲线
Figure 8. Variation frictional pressure drop gradient in eccentric annulus with rotational speed of drill string
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图 9 南海某水平井ϕ215.9 mm井段当量循环密度计算值与实测值对比
Figure 9. Comparison between calculated and measured values of ECD in ϕ215.9 mm section of a horizontal well in the South China Sea
表 1 偏心环空摩阻压降梯度数值模拟计算结果
Table 1 Numerical computation results of frictional pressure drop gradient in eccentric annulus
偏心度，% 不同钻柱转速下的摩阻压降梯度/（Pa·m−1） 0 r/min 19.11 r/min 38.22 r/min 57.32 r/min 76.43 r/min 95.54 r/min 114.65 r/min 0 898.91 898.69 898.73 898.80 898.91 899.03 899.18 22.47 921.99 919.85 916.67 915.89 915.74 914.72 912.90 26.97 930.93 927.63 922.68 921.31 921.12 919.76 917.43 31.46 939.65 934.85 927.73 925.76 925.82 924.38 921.85 35.96 946.11 939.65 930.41 928.23 929.19 928.37 926.25 40.45 947.04 939.42 929.21 927.89 931.11 932.09 931.20 44.94 938.21 931.38 923.14 924.87 932.38 936.60 937.83 49.44 916.31 914.30 912.82 920.49 934.65 943.11 946.98 53.93 882.02 890.43 901.17 917.22 939.97 952.41 958.70 58.43 841.34 865.33 892.13 916.90 948.91 964.11 971.14 62.92 800.91 842.91 886.76 917.93 957.17 974.83 977.08 67.42 763.60 820.64 879.73 913.85 956.12 977.72 968.23 
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表 2 无因次偏心环空摩阻压降梯度数值模拟结果
Table 2 Numerical simulation results of dimensionless eccentric frictional pressure drop gradient
偏心度，% 不同钻柱转速下的无因次偏心环空摩阻压降梯度 0 r/min 19.11 r/min 38.22 r/min 57.32 r/min 76.43 r/min 95.54 r/min 114.65 r/min 0 1.0000 0.9998 0.9998 0.9999 1.0000 1.0001 1.0003 22.47 1.0257 1.0233 1.0198 1.0189 1.0187 1.0176 1.0156 26.97 1.0356 1.0320 1.0264 1.0249 1.0247 1.0232 1.0206 31.46 1.0453 1.0400 1.0321 1.0299 1.0299 1.0283 1.0255 35.96 1.0525 1.0453 1.0351 1.0326 1.0337 1.0328 1.0304 40.45 1.0535 1.0451 1.0337 1.0322 1.0358 1.0369 1.0359 44.94 1.0437 1.0361 1.0270 1.0289 1.0372 1.0419 1.0433 49.44 1.0194 1.0171 1.0155 1.0240 1.0398 1.0492 1.0535 53.93 0.9812 0.9906 1.0025 1.0204 1.0457 1.0595 1.0665 58.43 0.9360 0.9626 0.9925 1.0200 1.0556 1.0725 1.0804 62.92 0.8910 0.9377 0.9865 1.0212 1.0648 1.0845 1.0870 67.42 0.8495 0.9129 0.9787 1.0166 1.0636 1.0877 1.0771
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