﻿ 法面扫描井间距离的解析算法

1. 中国石化石油工程技术研究院, 北京 100101;
2. 大庆油田有限责任公司第一采油厂, 黑龙江大庆 163000

Analytical Algorithm for Normal-Plane Scanning of Interwell Distance
Liu Xiushan1, Qi Shangyi1, Liu Ziheng2
1. Sinopec Research Institute of Petroleum Engineering, Beijing, 100101, China;
2. No.1 Oil Production Plant of Daqing Oilfield Company, Daqing, Heilongjiang, 163000, China
Abstract:Normal plane scanning is an important method in interwell relationship analyses such as drilling trajectory deviation, adjacent well anti-collision and directional well targeting. However, the conventional method has two major defects:(1) it can determine whether normal plane has an intersection with comparison well by identifying whether both ends of comparison well section are on the different sides of the normal plane, which may omit danger points of adjacent well anti-collisions;(2) the iteration method can be used for solving the intersection between normal plane and comparison well but needs complicated calculations in the track interpolation, resulting that the convergence is usually poor. Therefore, a method is developed based on the spatial arc model of well tracking to determine whether the normal plane is intersected with the comparison. An analytical method is proposed to solve the intersection. It does not need interpolation for the comparison well but can obtain accurate calculation results by using a design track node or drilling track measuring point data of the comparison well, thus greatly reducing calculations. Its applicabilities have been verified by application examples.
Key words: directional drilling    well trajectory    wellbore quality    adjacent well anti-collision    normal-plane scanning

1 传统方法的局限性

 图 1 法面扫描原理 Fig. 1 Principle of normal plane scanning

 图 2 传统判别方法的异常情况分析 Fig. 2 Abnormal condition analysis of the conventional judgment method

2 比较井段与法面的相对姿态表征

c=0表明比较井段的始点位于法面内。

3 求解比较点的位置

4 法面扫描的技术流程

 图 3 比较井段上是否存在比较点的判别流程 Fig. 3 Process to judge if a comparative point is available in comparison well section

5 应用实例

 井深/m 井斜角/(°) 方位角/(°) 北坐标/m 东坐标/m 垂深/m 0 0 0 0 0 1 360.00 0 (0) 0 0 1 360.00 1 540.00 42.00 0 63.07 0 1 524.31 1 685.00 42.00 0 160.10 0 1 632.06 1 820.00 86.00 0 278.47 0 1 689.80 2 380.00 86.00 0 837.11 0 1 728.86

 井深/m 井斜角/(°) 方位角/(°) 北坐标/m 东坐标/m 垂深/m 0 0 0 0 0 1 400.00 0 (90.00) 0 0 1 400.00 1 560.00 50.00 90.00 0 65.49 1 540.45 1 720.00 50.00 90.00 0 188.06 1 643.30 1 920.00 106.00 90.00 0 376.00 1 683.24 2 000.00 88.00 90.00 0 455.07 1 673.53 2 100.00 76.00 90.00 0 553.92 1 687.43 2 350.00 80.00 90.00 0 798.41 1 739.39

 图 4 参考井和比较井的三维视图 Fig. 4 3D views of reference wells and comparison wells
 图 5 不同法面与比较井的相交情况分析 Fig. 5 Analysis on intersection between different normal planes and comparison wells

 参考井 井间距离 比较井 LP/m αP/(°) φP/(°) ρPC//m θPC /(°) 高边距离/m 右向距离/m LC /m αC/(°) φC/(°) 1 893.00 86.00 0 207.89 278.86 32.01 -205.41 1 754.13 59.56 90.00 1 893.25 86.00 0 201.08 278.13 28.44 -199.06 1 761.42 61.60 90.00 1 893.50 86.00 0 193.72 277.37 24.86 -192.12 1 769.24 63.79 90.00 1 893.75 86.00 0 25.87 34.14 21.41 14.52 1 980.76 92.32 90.00 1 894.00 86.00 0 26.00 313.31 17.84 -18.92 1 947.11 99.90 90.00 1 894.25 86.00 0 38.73 291.58 14.24 -36.02 1 929.63 103.83 90.00 1 894.50 86.00 0 50.50 282.20 10.67 -49.36 1 915.82 104.83 90.00 1 894.75 86.00 0 65.98 276.16 7.08 -65.60 1 899.18 100.17 90.00 1 895.00 86.00 0 149.31 88.66 3.50 149.27 2 117.18 76.27 90.00 1 895.25 86.00 0 164.13 90.03 -0.09 164.13 2 132.47 76.52 90.00 1 895.50 86.00 0 179.26 91.17 -3.67 179.22 2 147.97 76.77 90.00
 图 6 应用实例的法面扫描图 Fig. 6 Normal plane scanning diagram of application examples

6 结 论

1) 当比较井段不平行于法面时，无论比较井段的两端点位于法面的同侧还是异侧，比较井段都有可能与法面相交。此时，无需考虑比较井段两端点位于法面的同侧或异侧问题，可直接求解比较井段与法面的交点，若有解且该交点位于比较井段内，就存在比较点。

2 ) 基于井眼轨迹的空间圆弧模型，得到了比较井段与法面交点的解析算法，具有计算过程高效、计算结果准确等优点。

3) 任一参考点法面可能会与比较井的多个井段相交，因此对于每个法面都必须扫描比较井的每个井段。当某个参考点法面与比较井的多个井段相交时，基于防碰考虑应选取距离参考点最近者作为比较点。

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#### 文章信息

Liu Xiushan, Qi Shangyi, Liu Ziheng

Analytical Algorithm for Normal-Plane Scanning of Interwell Distance

Petroleum Drilling Techniques, 2015, 43(02): 8-13.
http://dx.doi.org/10.11911/syztjs.201502002