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摘要:
油气工程中常利用地球物理资料获取地层弹性模量并结合小样本的岩心实验数据进行校正，但这种方法在复杂地质条件下往往表现不佳。为提高岩石弹性模量的预测精度和泛化能力，提出了一种利用基本岩石物性参数的弹性模量智能预测模型。分别采用3种集成学习算法（RandomForest，XGBoost，LightGBM）构建了岩石弹性模量智能预测模型，并采用TPE方法对模型进行超参数优化，最后利用SHAP归因分析探讨了各输入变量对模型的贡献。结果表明：①提出的智能预测模型明显优于传统模型，能够实现弹性模量的精确预测并具有较强的泛化能力，其中XGBoost模型表现最佳（决定系数
R 2=0.87，均方根误差RMSE =6.94，平均绝对误差MAE =4.96）；②横波速度对模型贡献最大，纵波速度次之，密度最小，精确横波波速对弹性模量预测有重要意义。该方法无需对工区及地层进行预先识别即可实现弹性模量的精准预测，研究成果对油气工程设计及实施有重要参考意义。Abstract:Objective Geophysical data is often used to determine the elastic modulus of formations in oil and gas engineering, with experimental data from small core samples used for calibration. However, acquiring core samples from every stratum is impractical and often leads to inadequate performance under complex geological settings. To improve the predictive accuracy and generalizability of the rock elastic modulus, an intelligent prediction model based on fundamental rock physical properties is proposed.
Methods Using 397 sets of core experimental data from diverse sources, with compressional and shear wave velocities and density as input variables, intelligent prediction models for rock elastic modulus were developed based on three ensemble learning algorithms (Random Forest, XGBoost, LightGBM). The TPE method was employed to optimize the models. The dynamic and static elastic modulus regression models were constructed based on current methods used in petroleum engineering to provide a comprehensive assessment of the performance of the intelligent predictive model using statistical indicators. Additionally, the SHAP attribution analysis was utilized to assess the contribution of each input variable to the model.
Results The research findings indicated that: ① The proposed intelligent prediction model using TPE was significantly better than traditional statistical regression models, achieving accurate predictions of the elastic modulus without distinguishing geological layers, with strong generalization ability. Among the three models, the XGBoost model performed the best (
R 2=0.87,RMSE =6.94,MAE =4.96). ②Shear wave velocity made the greatest contribution to the model, followed by compressional wave velocity, with density having the least impact. Accurate shear wave velocity was crucial for predicting the elastic modulus.Conclusion This method allows for the precise prediction of elastic modulus without the need for prior identification of the work area and strata, providing valuable insights for the design and implementation of oil and gas engineering projects.
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Key words:
- elastic modulus /
- TPE /
- ensemble learning /
- SHAP /
- shear wave
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图 1 TPE超参数优化算法流程示意图
$ l(x) $，$ g(x) $分别为损失函数≤${y}^{*} $和＞${y}^{*} $的密度组成；P(x|y)为条件分布概率；EI为期望函数
Figure 1. Schematic workflow of TPE hyperparameter optimization algorithm
图 2 技术路线
RandomForest. 随机森林；XGBoost. 极限梯度提升树；LightGBM. 轻量梯度提升机；下同
Figure 2. Technical roadmap
图 3 变量数据分布特征和相关性
Figure 3. Distribution characteristics and correlation of variable data
表 2 数据分布情况
Table 2. Data distribution
参数 密度/
（g·cm−3）静态弹性模量/
GPa纵波速度/
（km·s−1）横波速度/
（km·s−1）平均值 2.49 26.64 4.13 2.41 标准差 0.25 18.99 1.10 0.58 中位数 2.53 12.00 3.51 2.13 最大值 3.16 93.9 6.57 3.73 最小值 1.18 0.77 1.78 0.90 
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表 3 优化后的超参数
Table 3. Optimized hyperparameters
LightGBM
超参数取值 XGBoost
超参数取值 RandomForest
超参数取值 alpha 11.05 alpha 9.23 max_depth 25 learning_rate 0.19 learning_rate 0.09 n_estimators 1011 max_depth 36 max_depth 35 min_data_in_leaf 16 subsample 0.46 n_estimators 310 n_estimators 163 num_leaves 43 num_leaves 93 reg_lambda 1.71 reg_lambda 2.86 eta 0.02
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表 4 预测模型的性能对比
Table 4. Performance comparison of prediction models
预测模型 RandomForest XGBoost LightGBM 统计回归模型 R2 训练集 0.98 0.98 0.97 0.78 测试集 0.86 0.87 0.86 交叉验证集 0.86 0.86 0.85 RMSE 训练集 2.54 2.70 3.41 9.11 测试集 7.16 6.87 7.14 交叉验证集 6.90 6.94 7.04 MAE 训练集 1.78 1.88 2.27 6.80 测试集 4.93 4.94 5.00 交叉验证集 4.87 4.96 5.19 注：R2. 决定系数；RMSE. 均方根误差；MAE. 平均绝对误差
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