粒子群寻优支持向量机在储层类型预测中的应用Application of Particle Swarm Optimization Support Vector Machine in Reservoir Prediction

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In view of the problem that it is difficult to predict reservoirs in tight sandstone reservoirs of Enping formation in area of Zhu I depression, SVC is used to predict porosity of reservoirs by logging interpretation. The correctness of the model is improved by combining SVC with particle swarm optimization. The reservoir types of Enping formation are classified by typical well test and production test analysis. 80% of the samples of each type of reservoir are selected as modeling data, and random cross validation is carried out in each type of reservoir to get the cross-validation score of the model. Then the particle optimization method is used to improve the cross-validation score of the model to get the best prediction model. Then the prediction model is tested with the samples that are not involved in the modeling. From this model, the well log interpretation map can be made, that is, the location of the well section where the effective reservoir is located can be directly seen and the thickness of effective reservoir can also be calculated conveniently.

1. 引言

2. 原理分析

2.1. 支持向量分类原理

$\left\{{x}_{1},{y}_{1},{x}_{2},{y}_{2},\cdots ,{x}_{i},{y}_{i}\right\},\left(i=1,2,\cdots ,n\right)$ (1)

$f\left(x\right)=\left(w\cdot x\right)+b$ (2)

$\mathrm{min}\frac{1}{2}\left(w\cdot w\right)+C{\sum }_{i=1}^{n}\left({\xi }_{i}+{\xi }_{i}^{*}\right)$ (3)

$\text{s}.\text{t}.\left\{\begin{array}{c}{y}_{i}-\left(w\cdot {x}_{i}\right)-b\le \epsilon +{\xi }_{i}\\ \left(w\cdot {x}_{i}\right)+b-{y}_{i}\le \epsilon +{\xi }_{i}^{*}\\ \epsilon \ge 0,i=1,2,\cdots ,n\end{array}$ (4)

$\left\{\begin{array}{c}\mathrm{max}\phi \left(a\right)={\sum }_{i=1}^{n}\left({a}_{i}-{a}_{i}^{*}\right){y}_{i}-\frac{1}{2}{\sum }_{i,j=1}^{n}\left({a}_{i}-{a}_{i}^{*}\right)\left({a}_{j}-{a}_{j}^{*}\right)\left({x}_{i}\cdot {x}_{j}\right)\\ \text{s}.\text{t}.{\sum }_{i=1}^{n}\left({a}_{i}-{a}_{i}^{*}\right)=0\\ {a}_{i},{a}_{i}^{*}\ge 0\end{array}$ (5)

$f\left(x\right)={\sum }_{i=1}^{n}\left({a}_{i}-{a}_{i}^{*}\right)K\left({x}_{i},x\right)+b$ (6)

$K\left({x}_{i},x\right)=\mathrm{exp}\left\{-\frac{{\left({x}_{i}-x\right)}^{2}}{2{\sigma }^{2}}\right\}$ (7)

$f\left(x\right)={\sum }_{i=1}^{n}\left({a}_{i}-{a}_{i}^{*}\right)\mathrm{exp}\left[-\frac{{\left({x}_{i}-x\right)}^{2}}{2{\sigma }^{2}}\right]+b$ (8)

2.2. 粒子群寻优原理

${v}_{id}^{k+1}=\omega {V}_{id}^{k}+{c}_{1}{r}_{1}\left({P}_{id}^{k}-{X}_{id}^{k}\right)+{c}_{2}{r}_{2}\left({P}_{gd}^{k}-{X}_{id}^{k}\right)$ (9)

${X}_{id}^{k+1}={X}_{id}^{k}+{V}_{id}^{k+1}\text{\hspace{0.17em}}\left(i=1,2,\cdots ,m;d=1,2,\cdots ,D\right)$ (10)

3. 改进支持向量回归预测模型

3.1. 数据标准化

${y}_{ij}=\frac{{x}_{ij}-{x}_{i}}{{s}_{i}}$ (11)

3.2. 样本分类与选择

3.2.1. 储层下限分类

Table 1. Reservoir classification and evaluation of Enping formation in Zhu I depression

3.2.2. 样本选取

Table 2. Sample distribution of Enping formation in well E2

3.3. 模型建立

Figure 1. Establishment process of Enping prediction model

3.4. 预测结果及分析

Figure 2. Process chart of particle swarm optimization

Figure 3. Comparison of the relationship between the measured core and the predicted reservoir type porosity and permeability in Enping formation of well E2

Table 3. Statistical table for prediction accuracy of reservoir type of measured samples in well E2

Figure 4. Reservoir type prediction map of Enping formation in well E2

4. 结论

1) 粒子群寻优的收敛速度快，与传统网格搜索法相比，具有速度快、准确率高的特点 [18]。将其运用到对支持向量机回归模型的参数c和 ${\delta }^{2}$ 的寻优中，可以得到相对误差较低，精确度较高的预测模型。

2) 根据储层下限对实测样本进行分类，可以在建立预测模型时确保建模样本的多样性。在检验模型时，对测试样本正确率进行分类统计，可以看出模型对于每类储层的预测精确度，对模型精确度不高的储层可以适量增加该类储层在建模样本中所占的比例。

3) 将模型运用于检验井恩平组全段砂岩的储层类型预测，可以较为准确的得到优质储层所在位置及优质储层的厚度。

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