基于等效介质理论的孔隙纵横比分布反演

欧阳芳, 赵建国, 李智, 肖增佳, 贺艳晓, 赵皓, 任静. 2021. 基于等效介质理论的孔隙纵横比分布反演. 地球物理学报, 64(3): 1016-1033, doi: 10.6038/cjg2021O0348
引用本文: 欧阳芳, 赵建国, 李智, 肖增佳, 贺艳晓, 赵皓, 任静. 2021. 基于等效介质理论的孔隙纵横比分布反演. 地球物理学报, 64(3): 1016-1033, doi: 10.6038/cjg2021O0348
OUYANG Fang, ZHAO JianGuo, LI Zhi, XIAO ZengJia, HE YanXiao, ZHAO Hao, REN Jing. 2021. Inversion of pore aspect ratio distribution based on effective medium theories. Chinese Journal of Geophysics (in Chinese), 64(3): 1016-1033, doi: 10.6038/cjg2021O0348
Citation: OUYANG Fang, ZHAO JianGuo, LI Zhi, XIAO ZengJia, HE YanXiao, ZHAO Hao, REN Jing. 2021. Inversion of pore aspect ratio distribution based on effective medium theories. Chinese Journal of Geophysics (in Chinese), 64(3): 1016-1033, doi: 10.6038/cjg2021O0348

基于等效介质理论的孔隙纵横比分布反演

  • 基金项目:

    国家自然科学基金联合基金重点基金(U20B2015),国家自然科学基金项目(41574103,41974120,41804104和U19B6003-04),国家重大专项课题(2016ZX05004-003)和中国石油科技创新基金(2018D-5007-0303)资助

详细信息
    作者简介:

    欧阳芳, 女, 1992年4月生, 博士研究生, 主要从事地震岩石物理学研究.E-mail: FangOuyang92@163.com

    通讯作者: 赵建国, 男, 1976年12月生, 现为中国石油大学(北京)地球物理学院教授, 主要从事地震波传播、数字岩芯、跨频段地震岩石物理实验技术与理论研究.E-mail: zhaojg@cup.edu.cn, jgzhao761215@aliyun.com
  • 中图分类号: P631

Inversion of pore aspect ratio distribution based on effective medium theories

More Information
  • 孔隙纵横比是描述多孔岩石微观孔隙结构特征的重要参数,目前用于获取岩石完整孔隙纵横比分布的经典模型为David-Zimmerman (D-Z)孔隙结构模型,该模型假设岩石由固体矿物基质、一组纵横比相等的硬孔隙以及多组纵横比不等的微裂隙构成,并认为固体矿物基质和硬孔隙均不受压力影响,在此基础上,利用超声纵横波速度的压力依赖性反演岩石硬孔隙和各组微裂隙的孔隙纵横比及孔隙度.该方法的关键点在于以累积裂隙密度为桥梁,借助等效介质理论建立了岩石弹性模量和孔隙纵横比之间的内在联系.但在D-Z模型中,多重孔隙岩石累积裂隙密度的计算直接由单重孔隙裂隙密度公式实现,这种近似导致该模型在许多情况下难以获得良好的反演精度.为了完善经典D-Z模型,本文提出了一种基于虚拟降压的孔隙纵横比分布反演策略,通过多个假想降压过程实现累积裂隙密度的准确计算,并将基于DEM和MT的经典D-Z模型推广到KT和SCA中,结合四种等效介质理论建立了一套完整的反演流程.采用一系列砂岩和碳酸盐岩样品,测试了反演流程在实际岩芯孔隙纵横比提取中的应用效果,研究结果表明:与D-Z模型相比,本文方法的模拟结果与实际数据吻合更好,并同时适用于砂岩和碳酸盐岩;此外,通过分析四种等效介质理论的模拟结果发现,本文方法并不十分依赖于等效介质理论的选择,这些理论获得的孔隙结构参数随压力的变化趋势基本一致,数值上仅存在略微差异,且这种差异随着压力的增大逐渐消失.本文方法是经典D-Z孔隙结构模型的重要补充,对岩石孔隙结构表征、流体饱和岩石速度预测以及孔间喷射流效应的模拟具有十分重要的意义.

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  • 图 1 

    扁圆椭球状孔隙

    Figure 1. 

    The oblate-ellipsoid pore

    图 2 

    受压后岩石内部硬孔隙和微裂隙的形态变化示意图

    Figure 2. 

    Schematic diagram of stiff pores and micro-cracks in rock at different hydrostatic pressures

    图 3 

    增压过程中岩石内各组微裂隙的形态变化示意图

    Figure 3. 

    The change of each group of micro-cracks in rock during pressure increasing

    图 4 

    基于虚拟降压的孔隙纵横比反演流程图

    Figure 4. 

    Inversion workflow of aspect ratio distribution based on a thought unloading method

    图 5 

    硬孔纵横比反演流程图

    Figure 5. 

    Inversion workflow for aspect ratio of the stiff pores

    图 6 

    砂岩样品(a-b)和碳酸盐岩样品(c-f)的孔隙结构特征

    Figure 6. 

    Pore structure characteristics of the sandstone (a-b) and carbonate (c-f) samples

    图 7 

    干燥岩芯样品的纵横波速度-压力曲线

    Figure 7. 

    Velocity versus confining pressure for dry rock samples

    图 8 

    基于4种等效介质理论反演的不同有效压力下砂岩(a-b)和碳酸盐岩(c-d)样品的累积裂隙密度分布

    Figure 8. 

    Cumulative crack density distribution as a function of the aspect ratio calculated by different effective medium theories at different pressures for sandstone (a-b) and carbonate samples (c-d)

    图 9 

    基于4种等效介质理论反演的不同有效压力下砂岩(a-b)和碳酸盐岩(c-d)样品的微裂隙孔隙度

    Figure 9. 

    Crack porosity as a function of the aspect ratio calculated by different effective medium theories at different pressures for sandstone (a-b) and carbonate samples (c-d)

    图 10 

    基于不同等效介质理论的模型反演结果与实际测量结果对比

    Figure 10. 

    Comparison of the measured velocities and the results inverted using different effective medium theories

    图 11 

    本文方法和D-Z方法基于DEM理论反演的干燥岩石弹性模量对比

    Figure 11. 

    Elastic Moduli of dry rock calculated with DEM by using our method and D-Z method

    图 12 

    本文方法和D-Z模型反演结果对比

    Figure 12. 

    Comparison of our method and D-Z method

    表 1 

    砂岩和碳酸盐岩样品的基本参数

    Table 1. 

    Physical properties of the sandstone and carbonate samples

    编号 岩石类型 孔隙度 干燥密度 矿物成分
    S1 纯净砂岩 4% 2.54 g·cm-3 石英(100%)
    S2 泥质砂岩 23.9% 2.02 g·cm-3 石英(66%),
    长石(17%),
    粘土(15%),
    黄铁矿(1%),
    菱铁矿(1%)
    C1 孔洞型碳酸盐岩 3% 2.59 g·cm-3 方解石(100%)
    C2 裂缝型碳酸盐岩 0.6% 2.66 g·cm-3 方解石(100%)
    下载: 导出CSV

    表 2 

    基于不同等效介质理论反演的硬孔隙纵横比

    Table 2. 

    Inversion results of the characteristic aspect ratio for the stiff pore obtained from different effective medium theories

    岩芯样品 KT SCA MT DEM
    S1 硬孔纵横比αs 0.39 0.37 0.38 0.42
    平均误差ε 0.18% 0.34% 0.18% 0.19%
    S2 硬孔纵横比αs 0.14 0.29 0.10 0.15
    平均误差ε 4.31% 3.36% 2.74% 2.05%
    C1 硬孔纵横比αs 0.17 0.18 0.17 0.18
    平均误差ε 0.17% 0.27% 0.19% 0.21%
    C2 硬孔纵横比αs 0.95 1.00 0.96 0.95
    平均误差ε 4.96% 4.60% 4.96% 4.97%
    下载: 导出CSV
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收稿日期:  2020-09-11
修回日期:  2020-12-08
上线日期:  2021-03-10

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