﻿ 非均质储层三维水平井轨道设计研究与应用
 西南石油大学学报(自然科学版)  2018, Vol. 40 Issue (2): 151-158

3D Well-path Design for Horizontal Wells in Heterogeneous Reservoirs
YAN Jizeng
Research Institute of Engineering Technology of Huabei Branch, Sinopec, Zhengzhou, He'nan 450006, China
Abstract: The design and practical application of three-dimensional horizontal wells were studied to solve the problem of three-dimensional horizontal well construction using conventional directional equipment and to reduce costs. After analyzing the three-dimensional trajectory design models and comparing their advantages and disadvantages, the optimal constant tool face angle model was selected. Focusing on the six sections that make up a typical well-path (vertical, increasing, twisting, stable, increasing, and horizontal) and starting with the basic equation with the A target as the constraint, an initial azimuth model was established. After obtaining the build-up rate and the tool face angle based on the initial azimuth, the remaining trajectory parameters were calculated to complete the design of the three-dimensional horizontal well trajectory. This method was applied in the JH17P36 well using conventional equipment to obtain the following results:the vector hit the target, the coincidence rate of the actual trajectory and the design trajectory were high, and the technical indicators were excellent. The drilling example results indicated that the calculation model and the design method were accurate, reasonable, and feasible and also demonstrated the superiority of the constant tool face angle model.
Key words: heterogeneous reservoir     constant tool face angle     horizontal well     well-path     target

1 轨道设计模型优选

2 三维水平井井眼轨道设计 2.1 井眼轨道类型

$\Delta {{N}_{i}}$, ($i=1, 2, 3, 4$)—斜井段“增—扭—稳—增”处北坐标增量，m；

$\Delta N$$A靶点的北坐标，m。 在钻井实践中，为减少起下钻次数，保持施工连续性，提高钻井效率，通常在二维造斜段和三维扭方位段使用同一钻具组合，因此，钻具造斜率是一样的。因此，根据式(2)\sim式(6)以及圆弧模型相关方程，可得  \dfrac{1-\cos {{\alpha }_{1}}}{K}\sin {{\phi }_{1}} +\Delta L\sin {{\alpha }_{2}}\sin {{\phi }_{2}}+\\ \frac{\int_{{{\alpha }_{1}}}^{{{\alpha }_{2}}}{\sin \alpha \sin }\left[\tan \omega \ln \dfrac{\tan (0.5\alpha )}{\tan (0.5{{\alpha }_{1}})}+{{\phi }_{1}} \right]}{K\cos \omega }{\rm d}\alpha+ \\ \dfrac{\cos {{\alpha }_{2}}-\cos {{\alpha }_{A}}}{K}\sin {{\phi }_{2}}=\Delta E (7)  \dfrac{1-\cos {{\alpha }_{1}}}{K}\cos {{\phi }_{1}}+\Delta L\sin {{\alpha }_{2}}\cos {{\phi }_{2}}+\\ \frac{{\int}_{{{\alpha }_{1}}}^{{{\alpha }_{2}}}{\sin \alpha \cos }\left( \tan \omega \ln \dfrac{\tan (0.5\alpha )}{\tan (0.5{{\alpha }_{1}})}+{{\phi }_{1}} \right){\rm d}\alpha} {K\cos \omega }+ \\ \dfrac{\cos {{\alpha }_{2}}-\cos {{\alpha }_{A}}}{K}\cos {{\phi }_{2}}=\Delta N (8) 式中： \Delta L—稳斜段段长，m； {{\alpha }_{A}}$$A$靶点的井斜角，rad。

 $\left( 1-\cos {{\alpha }_{1}} \right)\cos {{\phi }_{1}}\cos \omega \left( {{\phi }_{1}} \right)+N\left( {{\phi }_{1}} \right)+\left( \cos {{\alpha }_{2}}-\cos {{\alpha }_{A}} \right)\cos {{\phi }_{2}}\cos \omega \left( {{\phi }_{1}} \right)+ \\{\kern 40pt}K\left( {{\phi }_{1}} \right)\cos \omega \left( {{\phi }_{1}} \right)\left( \Delta L\sin {{\alpha }_{2}}\cos {{\phi }_{2}}-\Delta N \right)=0$ (9)
 $K\left( {{\phi }_{1}} \right)=\dfrac{E({{\phi }_{1}})+\left( 1-\cos {{\alpha }_{1}} \right)\sin {{\phi }_{1}}\cos \omega \left( {{\phi }_{1}} \right)+\left( \cos {{\alpha }_{2}}-\cos {{\alpha }_{A}} \right)\sin {{\phi }_{2}}\cos \omega \left( {{\phi }_{1}} \right)}{\left( \Delta E-\Delta L\sin {{\alpha }_{2}}\sin {{\phi }_{2}} \right)\cos \omega \left( {{\phi }_{1}} \right)}$ (10)
 $N\left( {{\phi }_{1}} \right)\!=\!{\int}_{{{\alpha }_{1}}}^{{{\alpha }_{2}}}{\sin \alpha \cos }\left[\tan \omega \left( {{\phi }_{1}} \right)\ln \dfrac{\tan (0.5\alpha )}{\tan (0.5{{\alpha }_{1}})}+{{\phi }_{1}} \right]{\rm d}\alpha$ (11)
 $E\left( {{\phi }_{1}} \right)={\int}_{{{\alpha }_{1}}}^{{{\alpha }_{2}}}{\sin \alpha \sin }\left[\tan \omega \left( {{\phi }_{1}} \right)\ln \dfrac{\tan (0.5\alpha )}{\tan (0.5{{\alpha }_{1}})}+{{\phi }_{1}} \right]{\rm d}\alpha$ (12)
 $\omega \left( {{\phi }_{1}} \right)=\arctan \dfrac{{{\phi }_{2}}-{{\phi }_{1}}}{\ln \dfrac{\tan (0.5{{\alpha }_{2}})}{\tan (0.5{{\alpha }_{1}})}}$ (13)

2.4 其他参数计算模型

 $L={{L}_{1}}+\dfrac{\alpha -{{\alpha }_{1}}}{K\left( {{\phi }_{1}} \right)\cos \omega \left( {{\phi }_{1}} \right)}$ (14)

 $D={{D}_{1}}+\dfrac{\sin \alpha -\sin {{\alpha }_{1}}}{K\left( {{\phi }_{1}} \right)\cos \omega \left( {{\phi }_{1}} \right)}$ (15)

$D_1$—起点垂深，m。

 $\phi ={{\phi }_{1}}+\tan \omega \left( {{\phi }_{1}} \right)\ln \dfrac{\tan 0.5\alpha }{\tan 0.5{{\alpha }_{1}}}$ (16)

 $S={{S}_{1}}+\dfrac{\cos {{\alpha }_{1}}-\cos \alpha }{K\left( {{\phi }_{1}} \right)\cos \omega \left( {{\phi }_{1}} \right)}$ (17)

$S$—水平投影长度，m；

$S_1$—起点水平投影长度，m。

2.5 轨道设计步骤

 图3 井眼轨道设计 Fig. 3 Design and calculation of wellpath
3 应用实例

3.1 轨道设计

JH17P36井地质设计水平段长750.00 m，$A$靶点垂深1 476.86 m，东坐标171.94 m，北坐标571.11 m；$B$靶点垂深1 468.86 m，东坐标171.94 m，北坐标1321.11 m。经简单计算，水平段方位为0，$A$靶点方位为16.76°、井斜角为90.57°。

 图4 JH17P36井初始定向方位角 Fig. 4 Initial azimuth angle of JH17P36
 图5 JH17P36井造斜率 Fig. 5 Build-up rate of JH17P36

JH17P36井眼轨道设计三维坐标图见图 6；轨道设计与实钻对比见图 7，井眼轨道参数见表 2

 图6 三维井眼轨迹图 Fig. 6 3D well trajectory
 图7 实钻轨迹与设计对比三维坐标图 Fig. 7 Comparison of 3D drilling trajectory and design

3.2 现场施工

3.3 实施效果

JH17P36井$A$靶点顺利着陆，实现矢量中靶，最大横偏移3.12 m，最大纵偏移0.77 m，中靶精度高；实钻轨迹与设计轨道基本重合，符合率非常高(图 7)，井眼轨迹控制效果良好。

JH17P36井施工时间和机械钻速图分别见图 8图 9

 图8 JH17P36井各井段施工时间 Fig. 8 Construction time of each section in JH17P36
 图9 JH17P36井各井段机械钻速 Fig. 9 ROP of each section in JH17P36

JH17P36井完钻井深2 604 m，水平段长750 m，钻井周期21.20 d(图 8)，平均机械钻速11.09 m/h(图 9)；其钻井周期较该油田二维水平井平均值缩短29.53%，机械钻速提高11.23%。完钻后电测顺利，油层套管一次性安全下入到底，固井质量良好，投产后日产油8.3 t，地质效果显著。

4 结论

(1) 基于典型六段制轨道和恒工具面角模型，给出了初始定向方位角计算模型，其函数特性是关于初始定向方位角的一元非线性函数，易于编程实现。

(2) 根据初始定向方位角、造斜率和工具面角，求取其他轨道参数，形成了比较完整的三维水平井轨道设计方法和步骤，可广泛应用于各三维水平井道设计中。

(3) 利用恒工具面角模型设计的井眼轨道，井眼曲率和工具面角是常数，适合采用常规钻井装备施工，现场易于定向操作，减少了起下钻更换钻具组合次数，提高了效率。

(4) JH17P36井的现场应用表明，通过“螺杆+MWD测量系统”进行定向施工，实钻井眼轨迹与设计符合率高，各技术指标优秀，表明计算模型和设计方法是正确、合理和可行的，也验证了恒工具面角模型具有的优越性，对其他油田进行类似三维水平井设计与施工具有借鉴意义。

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