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基于多变量小样本的渗流代理模型及产量预测方法

曹冲 程林松 张向阳 贾品 时俊杰

曹冲, 程林松, 张向阳, 贾品, 时俊杰. 基于多变量小样本的渗流代理模型及产量预测方法. 力学学报, 2021, 53(8): 2345-2354 doi: 10.6052/0459-1879-21-155
引用本文: 曹冲, 程林松, 张向阳, 贾品, 时俊杰. 基于多变量小样本的渗流代理模型及产量预测方法. 力学学报, 2021, 53(8): 2345-2354 doi: 10.6052/0459-1879-21-155
Cao Chong, Cheng Linsong, Zhang Xiangyang, Jia Pin, Shi Junjie. Seepage proxy model and production forecast method based on multivariate and small sample. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2345-2354 doi: 10.6052/0459-1879-21-155
Citation: Cao Chong, Cheng Linsong, Zhang Xiangyang, Jia Pin, Shi Junjie. Seepage proxy model and production forecast method based on multivariate and small sample. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2345-2354 doi: 10.6052/0459-1879-21-155

基于多变量小样本的渗流代理模型及产量预测方法

doi: 10.6052/0459-1879-21-155
基金项目: 国家自然科学基金资助项目(U1762210, 51774297)和中国石油科技项目重大项目(ZLZX2020-02-04)资助
详细信息
    作者简介:

    程林松, 教授, 主要研究方向: 油气田开发理论与系统工程. E-mail: lscheng@cup.edu.cn

    贾品, 副教授, 主要研究方向: 油气田开发理论与系统工程. E-mail:pjia@cup.edu.cn

  • 中图分类号: TE328

SEEPAGE PROXY MODEL AND PRODUCTION FORECAST METHOD BASED ON MULTIVARIATE AND SMALL SAMPLE

  • 摘要: 多孔介质渗流过程中存在的多尺度、多变量、多物理场耦合的非线性渗流问题给复杂渗流机理的表征及数学模型求解提出了巨大的挑战, 综合考虑地下多孔介质耦合渗流过程中关键力学问题的渗流模型往往需要在计算效率和计算精度之间权衡. 近年来, 基于油田多数据的渗流代理模型为高效求解多变量非线性渗流问题提供了思路, 而渗流代理模型在实际油田中的应用往往由于记录不全, 操作不当等因素受到小样本数据的限制. 针对这一问题, 本文提出了一种基于地质−油藏−工艺的多数据小样本渗流代理模型的产量预测方法. 通过填补缺失值, 独热编码分类数据, 数据对数化及标准化等一系列数据预处理方法, 形成了油田产量预测数据库; 经过随机劈分数据集、十折交叉验证, 测试了三种渗流代理模型的预测效果. 结果表明, 三种代理模型的决定系数均超过0.8, 模型预测结果与实际数据较为吻合; 对于小样本多变量的油田数据, 合适的数据预处理方法对模型预测效果影响显著; 经过数据标准化后, 随机森林算法表现最好, 能快速准确预测石油产量(均方误差0.12, 决定系数0.87).

     

  • 图  1  数据建模技术预测油气产量的一般流程

    Figure  1.  A general flow of data modeling techniques for predicting oil and gas production

    图  2  油田数据库的建立

    Figure  2.  Establishment of oilfield database

    图  3  随机森林预测产量示意图

    Figure  3.  Schematic diagram of random forest forecast oil production

    图  4  转换前数据分布(以孔隙度为例)

    Figure  4.  Data distribution before transformation (taking porosity as an example)

    图  5  转换后数据分布(以孔隙度为例)

    Figure  5.  Data distribution after transformation (taking porosity as an example)

    图  6  产量影响因素分析

    Figure  6.  Analysis of factors affecting oil production

    图  7  随机森林模型标准化对比

    Figure  7.  Standardization comparison of random forest models

    图  8  XGBoost模型标准化对比

    Figure  8.  Standardization comparison of XGBoost models

    图  9  人工神经网络模型标准化对比

    Figure  9.  Standardization comparison of artificial neural network models

    图  10  随机森林目标值与预测值交会图

    Figure  10.  Cross plot of target and predicted values of random forest

    图  11  XGBoost目标值与预测值交会图

    Figure  11.  Cross plot of target and predicted values of XGBoost

    图  12  人工神经网络目标值与预测值交会图

    Figure  12.  Cross plot of target and predicted values of artificial neural networks

    表  1  产量数据库统计分析

    Table  1.   Statistical analysis of oilfield database

    StatisticsφK (10−3μm3)SwSh
    mean11.85.148.725.7
    std2.89.08.08.4
    min5.20.00.07.4
    25%10.61.045.019.3
    50%11.52.948.924.9
    75%12.75.852.630.4
    max47.074.673.854.0
    StatisticsRhperf/mh/mpwf
    mean20.03.412.47.3
    std7.31.25.52.4
    min6.11.14.11.3
    25%14.32.98.55.3
    50%20.13.310.76.5
    75%24.74.015.79.3
    max45.310.027.115.0
    StatisticsΔP/MPaPositionVfrac/m3Q6−m/(t·d−1)
    mean10.7 0.3 62.4 3273
    std5.2 0.5 32.5 2190
    min2.0 0 5.3 0
    25%6.3040.72019
    50%10.0 057.6 3102
    75%14.31.078.04095
    max23.7 1.0 178.9 16 146
    下载: 导出CSV

    表  2  模型参数优化结果

    Table  2.   Model parameter optimization results

    Seepage proxy modelOptimal model structure
    random forestnumber of estimators =150
    min samples split = 2
    XGBoostnumber of estimators = 120
    learning rate = 0.05
    subsample = 0.8
    max depth = 5
    artificial neural networkshidden layers = 2
    first layer = 200 neurons
    second layer = 10 neurons
    activation function = ReLU
    下载: 导出CSV

    表  3  渗流代理模型结果对比

    Table  3.   Comparison of results of seepage proxy model

    Seepage proxy modelDatasetEmsR2
    random foresttrain (70%)0.070.93
    test (30%)0.280.71
    total0.120.87
    XGBoosttrain (70%)0.110.70
    test (30%)0.300.89
    total0.170.83
    artificial neural networkstrain (70%)0.080.92
    test (30%)0.450.54
    total0.200.80
    下载: 导出CSV
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  • 收稿日期:  2021-04-14
  • 录用日期:  2021-07-03
  • 网络出版日期:  2021-07-04
  • 刊出日期:  2021-08-18

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