﻿ 考虑钻头转速影响的新三维钻速方程

1. 中海油田服务股份有限公司钻井事业部, 河北三河 065201;
2. 中海石油(中国)有限公司深圳分公司, 广东深圳 518067;
3. 中国石油大学(北京)石油工程学院, 北京 102249

A New 3D ROP Equation Considering the Rotary Speed of Bit
Liu Junbo1, Wei Hongshu2, Zhao Jingfang1, Zhang Hui3, Zhang Ripeng3
1. Drilling Division of China Oilfield Services Limited, Sanhe, Hebei, 065201, China;
2. CNOOC (Shenzhen) Company, Shenzhen, Guangdong, 518067, China;
3. College of Petroleum Engineering, China University of Petroleum (Beijing), Beijing, 102249, China
Abstract:In order to fully consider the factors affecting the ROP and improve the accuracy of predicting the ROP and wellbore trajectory, the 3D ROP equation involving the interaction between bit and formation was studied. Considering the effect of rotary speed of the bit, the bit anisotropic index and the formation anisotropic index were redefined. Based on the definition of both anisotropic indexes and the coordinate transformation, a new 3D ROP equation considering the rotary speed of bit and the bit-formation interaction was established. Using the new 3D ROP equation, a practical case was taken to analyze the effect of rotary speed on ROP.It was found that all ROPs in Xd direction, Yd direction and normal Zd direction increased with the increase of rotary speed, but to different extents.ROP in normal Zd direction increased more than that in Xd and Yd directions.The results showed that the new model could be used to predict the change of ROP and wellbore trajectory with the change of rotary speed in drilling operations, and that the wellbore trajectory could be controlled by adjusting the rotary speed, bit anisotropic index, bit mechanical force and other parameters.
Key words: rotary speed of the bit    ROP equation    anisotropic index

1 各向异性指数的定义 1.1 地层的各向异性

1.2 钻头的各向异性

2 考虑钻头转速新三维钻速方程的建立 2.1 坐标系的建立

2.1.1 大地坐标系(O－XYZ)

 图 1 建立的大地坐标系 Fig.1 Established geodetic coordinates
2.1.2 地层坐标系(OXfYfZf)

 图 2 建立的地层坐标系 Fig.2 Established formation coordinates
2.1.3 井底坐标系(O－XdYdZd)

 图 3 建立的井底坐标系 Fig.3 Established bottomhole coordinates
2.1.4 钻头坐标系(O－XbYbZb)

 图 4 建立的钻头坐标系 Fig.4 Established bit coordinates
2.2 坐标系之间的转换关系

 图 5 钻头坐标系和井底坐标系的相对位置关系 Fig.5 Relative position relation of bottomhole coordinates and bit coordinates
2.3 方程的推导

vxdvydvzd分别为井底平面上钻头机械钻速沿XdYdZd方向的分量，FxdFydFzd分别为井底平面上钻头机械力沿XdYdZd方向的分量，由地层各向异性和钻井效率的定义，它们之间的关系可表示为：

3 钻头转速影响机械钻速实例分析

 图 6 钻头转速对井底3个方向机械钻速的影响 Fig.6 Influence of rotary speed of the bit on ROP in three directions at bottomhole

4 结论与认识

1) 建立的新三维钻速方程考虑了钻头转速对机械钻速的影响，这样更符合现场实际情况。对钻头和地层的各向异性指数重新进行了定义，考虑钻头转速因素，避免了因钻头转速改变而导致测出的各向异性指数不同。

2 ) 井底3个方向的机械钻速随钻头转速增加而提高的幅度并不相同，井底法向Zd方向机械钻速的提高幅度要大于井底XdYd方向机械钻速的提高幅度。

3) 新三维钻速方程与BHA力学分析相结合，作为正演模型可以预测钻头转速变化对机械钻速和井眼轨迹的影响，进一步可以通过调节钻头转速、钻头机械力、钻头各向异性指数等参数来控制井眼轨迹；作为反演模型可以进行钻头和地层各向异性参数反演。

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#### 文章信息

Liu Junbo, Wei Hongshu, Zhao Jingfang, Zhang Hui, Zhang Ripeng

A New 3D ROP Equation Considering the Rotary Speed of Bit

Petroleum Drilling Techniques, 2015, 43(01): 52-57.
http://dx.doi.org/10.11911/syztjs.201501009