形状差异的岩屑颗粒沉降规律及曳力系数模型

王贵; 谭凯; 曹成

doi:10.12358/j.issn.1001-5620.2022.06.007

形状差异的岩屑颗粒沉降规律及曳力系数模型

doi: 10.12358/j.issn.1001-5620.2022.06.007

西南石油大学石油与天然气工程学院, 成都 610500

基金项目: 国家自然科学基金“裂缝性漏失桥接堵漏颗粒动力学行为细观模拟研究”(51604237)

详细信息

作者简介:
王贵，博士，副教授，1982年生，主要从事复杂深井及非常规油气钻井液理论与技术、油气井工程流-固耦合数值模拟技术研究工作。E-mail：wanggui@swpu.edu.cn

中图分类号: TE254
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出版历程
- 收稿日期: 2022-06-08
- 修回日期: 2022-07-19
- 刊出日期: 2022-11-30

Settling Behavior and Drag Coefficient Model of Rock Cuttings of Varied Shapes

Petroleum Engineering School, Southwest Petroleum University, Chengdu，Sichuan 610500

摘要

摘要: 油气钻井中，岩屑颗粒在井筒中自由沉降会引起沉砂卡钻等问题。为了探究岩屑颗粒沉降规律，开展了模拟岩屑颗粒自由沉降实验。利用沉降实验数据和图像处理技术，计算出10种不同形状颗粒在9种非牛顿流体中的沉降末速度与曳力系数，研究了颗粒形状和流变性对沉降的影响规律，并探究了现有曳力系数模型对非球形颗粒在非牛顿流体中的适用性。结果表明，颗粒偏离球形程度越大，在流体中越难沉降。流体黏度增加可有效抑制沉降的发生，且流体非牛顿性越强，对沉降的抑制作用越明显。现有曳力系数模型不适合描述非牛顿流体中非球形颗粒沉降规律，因此，构建了一种新的形状因子，并结合该形状因子建立了新的曳力系数模型。误差分析结果显示，新模型对沉降实验测量数据具有良好的拟合性，决定系数R²大于0.99。较现有模型预测精度提高了50.5%，预测真实岩屑颗粒曳力系数的误差在15%以内，可较好地描述不同形状岩屑颗粒的沉降曳力系数规律，对提高钻井过程中颗粒流体稳定性具有重要理论和现实意义。
- 油气钻井 /
- 岩屑颗粒 /
- 自由沉降 /
- 形状因子 /
- 曳力系数模型
Abstract: In oil and gas drilling, free settling of drilled cuttings along the wellbore may cause pipe sticking. To investigate the settling behavior of the cuttings particles, laboratory experiment was performed to simulate the free settling of drilled cuttings. Using the data collected in the experiment and image processing technology, the final settling velocities and drag coefficients of 10 kinds of particles of varied shapes in 9 non-Newtonian fluids were calculated and the effects of the particle shape and rheology of the fluids on the settling behavior of the particles were investigated. The adaptability of the existing drag coefficient models to the settling of non-spherical particles in non-Newtonian fluids was also studied. The results of the studies show that the higher the non-sphericity of the particles, the more difficult for them to settle in the fluids. Increase in the viscosity of the fluid can effectively hinder the settling of the particles, and the stronger the non-Newtonian property of the fluids, the stronger the hindrance of the fluids on the settling of the particles. The existing drag coefficient models are not suitable for describing the settling behavior of non-spherical particles in non-Newtonian fluids. To solve this problem, a new shape factor is presented to build a new drag coefficient model. Results of the error analyses of the model show that the new model has excellent fit to the data measured in settling experiment; the coefficient of determination R² is greater than 0.99. Compared with the existing model the prediction accuracy of the new model is increased by 50.5%, and errors in predicting the drag coefficient of real rock particles are less than 15%. This new model can be used to better describe the settling drag coefficient of rock particles of varied shapes, and has both theoretical and practical significance to improving the stability of rock particles in drilling fluid during drilling operation.
- Oil and gas drilling /
- Rock particles /
- Free settlement /
- Shape factor /
- Drag coefficient model

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图 1 不同实验溶液的流变曲线

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图 2 3D打印树脂颗粒实物图

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图 3 不同溶液实测曳力系数与有效黏度的变化关系

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图 4 不同形状颗粒的沉降末速度

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图 5 不同形状颗粒的雷诺数与实测曳力系数变化关系

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图 6 实测曳力系数与不同模型预测的曳力系数对比

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图 7 新模型下岩屑曳力系数预测值与实测值对比

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表 1 实验溶液组分和密度

溶液	ρ/(kg·m⁻³)	溶液	ρ/(kg·m⁻³)
清水	998.7	0.08%GUAR	1026
0.4%CMC	1025.0	0.12%GUAR	1027
0.6%CMC	1026.0	0.2%PAM	1025
0.8%CMC	1027.0	0.4%PAM	1026
0.04%GUAR	1025.0	0.6%PAM	1027

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表 2 实验流体流变参数

溶液	n	K/(Pa·sⁿ)	溶液	n	K/(Pa·sⁿ)
清水	1.000	0.001 08	0.08%GUAR	0.646	0.025 37
0.40%CMC	0.622	0.254 00	0.12%GUAR	0.711	0.023 44
0.60%CMC	0.551	0.734 70	0.20%PAM	0.557	0.032 75
0.80%CMC	0.499	1.654 00	0.40%PAM	0.523	0.051 04
0.04%GUAR	0.629	0.025 09	0.60%PAM	0.542	0.052 55

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表 3 不同形状颗粒形状因子计算结果

颗粒形状	投影面最长轴长度/m	投影面中间轴长度/m	投影面最短轴长度/m	球形度$\varPhi $	扁平度F_c	新的形状因子${\varPhi _F}$
球状	0.0112	0.0112	0.0112	1.000	1.000	1.000
椭球状1	0.0105	0.0105	0.0105	0.993	1.000	0.996
椭球状2	0.0100	0.0100	0.0100	0.972	1.000	0.986
椭球状3	0.0097	0.0097	0.0097	0.971	1.000	0.985
八面体状	0.0164	0.0164	0.0164	0.854	1.000	0.924
类盘状1	0.0200	0.0100	0.0050	0.803	0.354	0.533
类盘状2	0.0250	0.0080	0.0050	0.789	0.354	0.528
类盘状3	0.0500	0.0040	0.0050	0.784	0.354	0.526
类圆柱状1	0.0128	0.0100	0.0040	0.639	0.354	0.476
类圆柱状2	0.0166	0.0030	0.0025	0.634	0.354	0.474
圆柱状	0.0200	0.0200	0.0010	0.471	0.050	0.153
盘状	0.0100	0.0100	0.0010	0.471	0.100	0.217

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表 4 新的形状因子进行多元非线性拟合结果

a	b	c	d	e	R²
15.6	0.763	0.267	5904	0.046	0.993

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表 5 曳力系数模型预测误差结果

经验模型	预测误差
经验模型	r	s₁	s₂
Haider模型	52.41%	41.44	5.52
Ganser模型	46.72%	33.18	3.068
新的曳力系数模型	22.10%	6.55	1.59

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