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A New Method of Porosity Automatic Extraction and Calculation Based on Electrical Imaging Logging Image
DOI: 10.12677/JOGT.2021.432016, PDF , HTML, XML, 下载: 271  浏览: 458

Abstract: The pore structure of tight carbonate reservoir is complex and there are many types of development, so it is difficult to accurately predict the porosity. Through the processing of electrical imaging logging image, the image processing threshold segmentation technology is used to correct the deviation of image acquisition, and a new calculation method is proposed to extract the gray value of image, and the advantages of different algorithms are evaluated by the correlation between gray value and conventional logging electrical parameters. Finally, the regression model is established according to the correlation between gray value and measured porosity. The model is used to predict the porosity of tight carbonate rocks in a section. The results show that the scatter fitting method has strong adaptability to the characteristics of strong structural heterogeneity and diverse reservoir types of tight carbonate rocks, and it is superior to other algorithms in porosity extraction. This method can not only predict more accurately and compactly, but also complete porosity interpretation efficiently, which provides a new way for porosity prediction of tight carbonate reservoir.

1. 引言

2. 常规电成像测井孔隙度计算

2.1. 电成像测井

2.2. 孔隙度分布谱的计算

${R}_{i}=\frac{\stackrel{¯}{\sigma }}{{\sigma }_{i}}{R}_{LLS}$ (1)

${\phi }^{m}{R}_{xo}=\frac{ab{R}_{mf}}{{S}_{xo}^{n}}$ (2)

${\phi }_{i}=\sqrt[\begin{array}{l}m\\ \end{array}]{\frac{{\sigma }_{i}}{\stackrel{¯}{\sigma }}}×{\phi }_{0}$ (3)

3. 电成像测井图像矫正

3.1. 电成像测井成像原理

Figure 1. Schematic diagram of electrical imaging principle

Figure 2. Determination of segmentation for graphics interval

3.2. 井眼基准线拟合

Figure 3. Image of datum line fitting

3.3. 正弦矫正计算法则

$A=\alpha ×L×\frac{{90}^{\circ }}{{360}^{\circ }}×\mathrm{tan}\left({90}^{\circ }-\mathrm{arctan}\left(k\right)\right)$ (4)

$\left\{\begin{array}{l}{\Delta }_{y}=A×\mathrm{sin}\left(w\cdot x+b\right)\\ x=\frac{{180}^{\circ }}{{360}^{\circ }}×L,{\Delta }_{y}=0\\ x=0,{\Delta }_{y}=0\end{array}$ (5)

3.4. 应用效果

Figure 4. Comparison of electrical imaging data before and after sine correction in a logging

4. 电成像测井图像孔隙度提取算法及评价方法

4.1. 电成像测井图像数据标准化

Figure 5. Gray value frequency distribution curve of each logging

4.2. 实验环境

4.3. 灰度值提取算法

1) 算术平均法

$\stackrel{¯}{x}=\frac{1}{z}\underset{i=1}{\overset{{z}_{1}}{\sum }}\underset{j=1}{\overset{{z}_{2}}{\sum }}{x}_{ij}$ (6)

2) 加权平均法

$\stackrel{¯}{x}=\underset{i=1}{\overset{{z}_{2}}{\sum }}\underset{j=1}{\overset{{z}_{1}}{\sum }}{\omega }_{ij}\cdot {x}_{ij}$ (7)

3) 标准差法

$\sigma =\sqrt{\frac{1}{Z}\underset{i=1}{\overset{Z}{\sum }}{\left({x}_{i}-\mu \right)}^{2}}$ (8)

4) 散点拟合法

$M=\underset{k=1}{\overset{m}{\sum }}\underset{i=1}{\overset{n}{\sum }}\left[{\left({z}_{i}-{z}_{ik}\right)}^{2}+{\left({y}_{i}-{y}_{ik}\right)}^{2}\right]$ (9)

$\left\{\begin{array}{l}\frac{\partial M}{\partial {z}_{i}}=2\underset{k=1}{\overset{m}{\sum }}\left({z}_{i}-{z}_{ik}\right)=0\\ \frac{\partial M}{\partial {y}_{i}}=2\underset{k=1}{\overset{m}{\sum }}\left({y}_{i}-{y}_{ik}\right)=0\end{array}$ (10)

$\left\{\begin{array}{l}{z}_{i}=\frac{1}{m}\underset{k=1}{\overset{m}{\sum }}{z}_{ik}\\ {y}_{i}=\frac{1}{m}\underset{k=1}{\overset{m}{\sum }}{y}_{ik}\end{array}$ (11)

$\stackrel{¯}{z}=\frac{1}{n}\underset{i=1}{\overset{n}{\sum }}{z}_{i}$ (12)

4.4. 计算方法评价

4.4.1. 皮尔森相关系数

${P}_{XY}=\frac{\mathrm{cov}\left(X,Y\right)}{{\sigma }_{X}{\sigma }_{Y}}=\frac{E\left(X-{\mu }_{X}\right)\left(Y-{\mu }_{Y}\right)}{{\sigma }_{X}{\sigma }_{Y}}$ (13)

4.4.2. 斯皮尔曼秩相关系数

${S}_{XY}=1-\frac{6\underset{i=1}{\overset{n}{\sum }}{\left({p}_{i}-{q}_{i}\right)}^{2}}{N\left({N}^{2}-1\right)}$ (14)

4.4.3. 结果分析

Table 1. The influence of extraction distance interval on correlation coefficient in each gray value extraction method

4.5. 孔隙度预测及应用实例

Figure 6. Interpretation results of Logging porosity of Deng’er member of Dengying Formation in E area

5. 结束语

1) 本文研究用不同算法对灰度值进行提取，在各类提取算法中散点拟合法对灰度值进行提取能取得较高的相关系数，不同提取距离间隔上呈现不规律差异，不具有明显关系。

2) 通过对比常规测井孔隙度解释成果，本文章算法无论在精度和速度上都优于常规处理手段，更能反映地层孔隙结构的真实情况。

3) 研究表明，本文章算法对致密碳酸盐岩储层预测和评价具有指导意义，并具有显著的准确性及普及性，具有广阔的应用前景。

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