基于高斯过程回归和高压压汞测定致密砂岩渗透率：以鄂尔多斯盆地长7段致密砂岩为例

王伟; 许兆林; 李维振; 侯涛; 李亚辉; 白云云; 朱玉双

doi:10.19509/j.cnki.dzkq.2022.0117

基于高斯过程回归和高压压汞测定致密砂岩渗透率：以鄂尔多斯盆地长7段致密砂岩为例

doi: 10.19509/j.cnki.dzkq.2022.0117

1.
榆林学院化学与化工学院, 陕西榆林 719000
2.
长庆油田分公司第一采油厂, 陕西延安 716000
3.
西北大学地质学系, 西安 710069

基金项目:

榆林学院高层次人才科研启动基金项目 18GK22

国家自然科学基金 41904128

国家自然科学基金 42062011

陕西省科技厅项目 2021SF-495

详细信息

作者简介:
王伟(1988-), 男, 讲师, 主要从事油气田开发地质研究。E-mail: 283465227@qq.com

通讯作者:
朱玉双(1968-), 女, 教授, 主要从事油气田开发地质与油层物理研究。E-mail: yshzhu@nwu.edu.cn

中图分类号: TE311
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- 被引次数: 0
出版历程
- 收稿日期: 2021-01-08
- 网络出版日期: 2022-09-07

Determination of permeability in tight sandstone reservoirs using Gaussian process regression and high-pressure porosimetry: A case study of the Member-7 of Yanchang Formation in the Jiyuan area of the Ordos Basin

1.
School of Chemistry and Chemical Engineering, Yulin University, Yulin Shaanxi 719000, China
2.
Oil Production Plant No.1 of Changqing Oilfield Company, PetroChina, Yan'an Shaanxi 716000, China
3.
Department of Geology, Northwest University, Xi'an 710069, China

摘要

摘要:
致密砂岩由于滑脱效应的存在, 其气测渗透率存在一定误差, 测定绝对渗透率对明确致密砂岩渗流特征有重要意义。高斯过程回归方法是目前最先进的机器学习算法, 在处理石油领域非线性和多维数复杂问题具有优势。以鄂尔多斯盆地姬塬地区长7段致密砂岩为研究对象, 将平方指数(SE)和马特恩(Matern)函数作为高斯过程回归模型中两个协方差函数, 通过高压压汞测试的孔隙度、未饱和汞体积比、门槛压力和分形维数来预测致密砂岩的绝对渗透率, 并结合误差分析来研究不同协方差模型预测渗透率的效果。结果表明, 马特恩协方差(Matern)模型的相对误差均值(MMRE)、均方根误差(RMSE)、标准偏差(STD)分别为32%, 0.16和0.57, 准确度较高, 尤其当渗透率小于0.1×10^-3 μm²时, 马特恩协方差(Matern)模型精度明显好于平方指数协方差(SE)模型和Winland经验公式。致密砂岩用马特恩模型预测渗透率精度更高。此外, 敏感性分析表明孔隙度对渗透率正影响最大, 门槛压力对渗透率负影响最大; 杠杆值和标准化残差证明高斯过程回归模型预测渗透率的有效性。综上, 马特恩协方差(Matern)模型对渗透率小于0.1×10^-3 μm²致密砂岩适用性好, 对微纳米级孔喉发育的致密砂岩勘探评价有重要意义。
- 渗透率测定 /
- 致密砂岩 /
- 高斯过程回归 /
- 高压压汞 /
- 分形维数 /
- 鄂尔多斯盆地
Abstract:
Because of the Klinkenberge effect in tight sandstones, errors exist forusing air permeability to reflect its reality, and it is thus important to determine the absolute permeability of tight sandstone.The Gaussian process regression (GPR), a state-of-the-art machine learning algorithm, has advantages in dealing with nonlinear and multidimensional complex problems in the petroleum industry. In this paper, the tight sandstone of the Member-7 of Yanchang Formation in the Jiyuan area of the Ordos Basin was taken as a sample to adopt the GPR model. In the model, the squared exponential and Matern covariance functions were taken as two covariance functions. The absolute permeability of tight sandstone was predicted by parameters including the porosity, volume ratio of unsaturated mercury, displacement pressure and fractal dimension measured by high-pressure porosimetry experiments, and the precision of different GPR models in predicting permeability were studied in combination with error analysis. The results indicate that GPR with Matern gives high precision with a mean magnitude relative error (MMRE), root mean square error (RMSE) and standard deviation (STD) equal to 32%, 0.16 and 0.57, respectively. Particularly, if the permeability is less than 0.1×10^-3 μm², the precision of the Matern model is obviously better than that of the squared exponential model and Winland model, so the Matern model has higher precision for permeability prediction of tight sandstones. In addition, sensitivity analysis reveals that porosity and displacement pressure have the highest and lowest absolute impact values on permeability estimation. The applicability and effectiveness of the GPR model are also demonstrated by means of leverage values and standardized residuals. Therefore, the Matern model can better predict tight sandstone reservoirs with permeabilities less than 0.1×10^-3 μm², and this model plays an important role in the exploration and evaluation for tight sandstone reservoirs.
- permeability determination /
- tight sandstone /
- Gaussian process regression /
- high-pressure porosimetry /
- fractal dimension /
- Ordos Basin

HTML全文

图 1 研究区位置及长7段油层组特征(研究区构造位置据文献[15]修改，地层柱状图据文献[16]修改)

Figure 1. Location of the study area and characteristics of the reservoir of the Member-7 of the Yanchang Formation

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图 2 GPR模型误差参数统计

Figure 2. Statistics of errors in GPR models

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图 3 GPR模型实验值和预测值的逐点对比图

Figure 3. Point-by-point comparison of the experimental and estimated data for GPR methods

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图 4 GPR模型实验值与预测值散点图

Figure 4. Cross plots of experimental and estimated data of GPR model

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图 5 GPR模型的相对偏差分布图

Figure 5. Relative deviation distribution of the GPR model

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图 6 GPR模型与经验公式计算渗透率比较

Figure 6. Comparison of the permeabilities calculated by the GPR models with empirical-formula based models

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图 7 Matern模型各参数的敏感性分析

Figure 7. Sensitivity analysis of the input parameters in the Matern model

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图 8 GPR模型杠杆值与残差分布图

Figure 8. Distributions of leverage values and standardized residuals of the GPR model

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表 1 致密砂岩样品参数统计表

Table 1. Statistics of the parameters of tight sandstone samples

参数	最小值	最大值	平均值	标准偏差
孔隙度/%	7.92	17.10	11.37	2.50
未饱和汞体积比/%	1.07	37.18	11.30	5.3
分形维数	2.30	3.05	2.68	0.16
门槛压力/MPa	0.28	2.91	1.91	0.59
渗透率/10^-3 μm²	0.008	1.579	0.286	0.343

下载: 导出CSV

表 2 GPR模型与经验公式误差统计

Table 2. Statistics of errors of the GPR models and empirical-formula based models

模型	MMRE	RMSE	STD
平方指数协方差	0.75	0.29	3.02
Matern协方差	0.32	0.16	0.57
Winland经验公式	1.03	0.16	0.80

下载: 导出CSV

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