Correlation-Optimized Modeling Algorithm for Rate of Penetration
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摘要: 针对复杂地层钻井过程中钻速（ROP）预测精度低、参数间存在非单调、非线性强耦合的难题——传统Pearson/Spearman等相关系数主要衡量线性或单调关系，难以有效刻画此类复杂依赖，易导致关键特征被低估.旨在开发一种动态最优相关性建模算法，以提升钻速预测的准确性和工程适用性. 基于10口油气井的21 912组工程数据，综合采用中位数填充、IQR离群值处理和Savitzky-Golay滤波进行数据预处理；通过对比Pearson、Spearman、Kendall和Chatterjee四种相关性理论，识别影响钻速的关键参数（如钻井液密度、固相含量和井深）；引入滑动窗口技术（窗口大小400、步长100）实现局部动态建模，并以随机森林模型为核心进行回归预测.实验表明，以Chatterjee算法选取排名前5的特征时表现最优，结合滑动窗口与随机森林的架构在第10口测试井中窗口测试集平均R2达0.985，较全局静态建模（R2=0.96）显著提升.得到的最优相关性钻速建模算法能自适应地层突变，有效捕捉参数间的局部关联，为钻速实时优化提供高精度解决方案，为钻井工程从经验试错向数据驱动决策的转变提供有效技术支撑.Abstract: Aiming at the problems of low prediction accuracy of rate of penetration (ROP) during drilling in complex formations and strong non-monotonic, nonlinear coupling among parameters: traditional correlation coefficients such as Pearson and Spearman mainly measure linear or monotonic relationships, which cannot effectively characterize such complex dependencies and tend to result in underestimation of key features, this paper aims to develop a dynamic optimal correlation modeling algorithm. This approach is designed to enhance both the accuracy and engineering applicability of ROP prediction. Using 21, 912 data sets from ten oil and gas wells, we performed data preprocessing including median imputation for missing values, IQR-based outlier removal, and Savitzky-Golay smoothing. By comparing four correlation theories: Pearson, Spearman, Kendall, and Chatterjee: key parameters affecting ROP (such as mud density, solid content, and well depth) were identified. A sliding window technique (window size: 400, step size: 100) was introduced to achieve local dynamic modeling, with a Random Forest model serving as the core for regression prediction. Experimental results demonstrate that the Chatterjee algorithm performed best in screening the top 5 features. The architecture combining the sliding window technique with the Random Forest model achieved an average R2 of 0.985 on the window test set of the 10th test well, representing a significant improvement over global static modeling (R2=0.96). The resulting optimal correlation ROP modeling algorithm can adapt to abrupt formation changes and effectively capture local correlations between parameters. This provides a high-precision solution for real-time ROP optimization and it provides effective technical support for the transformation of drilling engineering from empirical trial-and-error to data-driven decision-making.
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图 3 高、中、低相关性参数所占比例
a.Pearson算法；b. Spearman算法；c. Kendall算法d. Chatterjee算法
Fig. 3. The proportions of parameters with high, medium, and low correlations
图 4 高中低相关性参数个数对比图
Fig. 4. Comparison chart of the number of parameters with high, medium, and low correlations
图 5 多层感知机和随机森林模型性能
a. 多层感知机训练集；b. 多层感知机测试集；c. 随机森林训练集；d. 随机森林测试集
Fig. 5. Performance of multilayer perceptron and random forest models
图 7 基于多层感知机的动态选择
a. Pearson算法；b. Spearman算法；c. Kendall算法；d. Chatterjee算法
Fig. 7. Dynamic selection based on multilayer perceptron
图 8 基于随机森林的动态选择
a. Pearson算法；b. Spearman算法；c. Kendall算法；d. Chatterjee算法
Fig. 8. Dynamic selection based on random forest
图 10 窗口测试集R2运算结果
a. 窗口测试集R2；b~e. 窗口优于全局比例，依次为Pearson/Spearman/Kendall/Chatterjee
Fig. 10. R2 calculation results of the window test set
表 1 相关性系数绝对值
Table 1. Absolute value of the correlation coefficient
算法参数 Pearson Spearman Kendall Chatterjee 算法参数 Pearson Spearman Kendall Chatterjee 井深 0.70 0.74 0.52 0.37 稠度系数 0.12 0.30 0.22 0.47 井径 0.66 0.70 0.57 0.34 氯离子含量 0.05 0.15 0.10 0.19 钻压 0.04 0.03 0.02 0.07 钙离子含量 0.02 0.01 0 0.11 大钩载荷 0.66 0.60 0.42 0.33 膨润土含量 0.46 0.44 0.31 0.30 回转转速 0.30 0.27 0.18 0.24 固相含量 0.70 0.77 0.56 0.59 扭矩 0.69 0.66 0.50 0.36 含砂量 0.17 0.26 0.18 0.13 立管压力 0.13 0.08 0.06 0.11 地震速度 0.39 0.33 0.23 0.33 泵量 0.69 0.75 0.54 0.49 孔隙压力 0.71 0.75 0.53 0.41 钻头工作时间 0.22 0.13 0.11 0.12 破裂压力 0.64 0.71 0.50 0.37 泵工作时间 0.35 0.29 0.21 0.12 上覆压力 0.68 0.73 0.51 0.39 钻井液进口比重 0.71 0.78 0.56 0.55 岩性编号 0.23 0.20 0.14 0.11 钻井液出口比重 0.71 0.78 0.56 0.54 喷嘴数量 0.01 0 0 0.01 钻井液入口温度 0.12 0.06 0.05 0.14 等效直径 0.58 0.56 0.40 0.38 钻井液出口温度 0.19 0.17 0.12 0.12 内排磨损 0 0 0 0 屈服值 0.59 0.56 0.39 0.40 外排磨损 0.20 0.24 0.19 0.14 钻井液密度 0.72 0.79 0.58 0.57 液力提速马达 无 无 无 0 马氏漏斗粘度 0.46 0.42 0.29 0.30 水力脉冲 无 无 无 0 塑性粘度 0.60 0.65 0.46 0.40 钻头齿形 无 无 无 0 3转读数 0.57 0.63 0.46 0.30 稠度系数 0.12 0.30 0.22 0.47 6转读数 0.58 0.64 0.46 0.32 氯离子含量 0.05 0.15 0.10 0.19 10 s静切力 0.50 0.53 0.37 0.28 钙离子含量 0.02 0.01 0 0.11 10 min静切力 0.55 0.61 0.43 0.36 膨润土含量 0.46 0.44 0.31 0.30 滤失量 0.70 0.66 0.46 0.46 固相含量 0.70 0.77 0.56 0.59 泥饼厚度 0.61 0.55 0.44 0.24 含砂量 0.17 0.26 0.18 0.13 pH 0.62 0.65 0.49 0.34 流性系数 0.01 0.03 0.02 0.33 
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表 2 各方法性能统计汇总
Table 2. Statistical summary of performance of various methods
算法 窗口大小 特征数量 测试集均值 测试集标准差 最佳测试R2 Pearson 800 15 0.973 8 0.026 7 0.998 8 Spearman 800 15 0.973 9 0.026 2 0.998 6 Kendall 800 15 0.971 6 0.027 4 0.998 6 Chatterjee 400 5 0.979 0 0.020 8 0.999 1
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