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摘要:
渗透率在水资源管理、油气勘探与开采和地质灾害评估中具有重要的作用。而目前渗透率研究多通过间接的方式探究渗透率的影响因素，缺乏直观手段刻画多孔介质与渗透率的关系，渗透率与多孔介质内部孔隙结构的关系尚不清晰。自主研发了一个可控孔隙空间属性的试验系统，探究多孔介质渗透率与孔隙度、孔隙的水平或垂直分布、孔隙排列的规则性和椭圆孔隙长短轴比例的关系。结果表明，多孔介质渗透率与孔隙度呈正相关关系，且圆形颗粒多孔介质基本满足Kozeny-Carman方程；而不同颗粒圆度及排列方式会造成显著的渗透率各向异性，由于多孔介质颗粒横向排列导致流体经过更长的流动路径，与流动方向一致的横向排列渗透率明显高于纵向排列的渗透率；不规则排列的多孔介质渗透率要大于规则排列的多孔介质渗透率，这是因为颗粒的不规则排列会导致在多孔介质中出现一些大的孔隙，这些孔隙可以提供更大的通道，促进流体的渗透，另一种原因是不规则排列会增加多孔介质内的流动路径，使得流体能使用更多的路径通过多孔介质；长短轴长度之比为1的多孔介质渗透率最大。研究结果可为多孔介质渗透率演化及其孔隙空间属性关联性研究提供基础认识。
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关键词:
- 多孔介质 /
- 渗透率 /
- 孔隙结构 /
- Kozeny-Carman方程 /
- 变异性
Abstract:Permeability plays a pivotal role in water resources management, oil and gas exploration and production, as well as geological hazard assessment. Previous studies primarily explores the influencing factors of permeability through indirect methods, and lacks direct means to describe the relationship between porous media and permeability, and the relationship between permeability and the internal pore structure of porous media is still unclear. This study developed an experimental system featuring controllable pore space properties to investigate the relationship between permeability in porous media and factors including porosity, the horizontal and vertical distribution of pores, the regularity of particle arrangements, and the aspect ratio of elliptical pores. The experimental results demonstrate a positive correlation between permeability and porosity in porous media. Circular porous media generally adhere to the Kozeny-Carman equation, while variations in particle circularities and arrangements lead to pronounced permeability anisotropy. Due to the transverse arrangement of porous media leading to the fluid with a long flow path, permeability in horizontally arranged pores aligned with the flow direction is significantly higher than that in vertically arranged pores. Irregularly arranged porous media exhibit higher permeability compared to regularly arranged porous media, because 1) the irregular arrangement of the particles can lead to some large pores in the porous media that can provide large channels to facilitate the penetration of the fluid; 2) the irregular arrangement increases the flow path within the porous medium, leading to more fluid paths in the porous medium. Porous media with an aspect ratio of 1 for the long and short axes exhibits the highest permeability. The findings of this study provide essential insights into the evolution of penetration rates in porous media and their relationship with pore space properties.
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Key words:
- porous media /
- permeability /
- pore structure /
- Kozeny-Carman equation /
- variability
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表 1 样品特征及结构形态各向异性比
Table 1. Sample characteristics and structural morphological anisotropy ratio
编号 样品特征 结构形态各向异性比 A1 规则竖排等轴长椭圆，孔隙度0.3（长短轴比2∶1） 0.6∶1.2=0.5 A2 规则竖排等轴长椭圆，孔隙度0.4（长短轴比2∶1） 0.6∶1.2=0.5 A3 规则竖排等轴长椭圆，孔隙度0.5（长短轴比2∶1） 0.6∶1.2=0.5 A4 规则横排等轴长椭圆，孔隙度0.3（长短轴比2∶1） 1.2∶0.6=2.0 A5 规则横排等轴长椭圆，孔隙度0.4（长短轴比2∶1） 1.2∶0.6=2.0 A6 规则横排等轴长椭圆，孔隙度0.5（长短轴比2∶1） 1.2∶0.6=2.0 A7 不规则排列竖排变轴长椭圆，孔隙度0.4（长短轴比2∶1） A8 不规则排列横排变轴长椭圆，孔隙度0.4（长短轴比2∶1） A9 不规则排列竖排等轴长椭圆，孔隙度0.4（长短轴比2∶1） A10 不规则排列横排等轴长椭圆，孔隙度0.4（长短轴比2∶1） A11 规则排列等径圆，孔隙度0.3 0.786∶0.786=1.0 A12 规则排列等径圆，孔隙度0.4 0.786∶0.786=1.0 A13 规则排列等径圆，孔隙度0.5 0.786∶0.786=1.0 A14 不规则排列等径圆，孔隙度0.3 A15 不规则排列等径圆，孔隙度0.4 A16 不规则排列等径圆，孔隙度0.5 A17 规则横排等轴长椭圆，孔隙度0.4（长短轴比3∶1） 1.47∶0.49=3.0 A18 规则竖排等轴长椭圆，孔隙度0.4（长短轴比3∶1） 0.49∶1.47=0.3 
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表 2 雷诺数计算数据
Table 2. Reynolds number calculation
试验组 流量/（mL·min−1） 密度/（103 kg·m−3） 流速/（10−2 m·s−1） 当量直径/（10−3 m） 黏度/（10−6 kPa·s） 雷诺数 流量1 2.5 1 1.458 1.253 1.01 18.12 流量2 5.0 1 2.916 1.253 1.01 36.24
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表 3 多孔介质渗透率与孔隙度关系
Table 3. Relationship between the permeability and porosity of porous media
多孔介质
孔隙度绝对渗透率/μm2 规则排列
等径圆不规则排列
等径圆规则横排
等轴长椭圆规则竖排
等轴长椭圆0.3 32.62 30.86 39.72 36.80 0.4 81.56 57.67 78.83 73.53 0.5 83.24 107.81 85.12 78.53
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表 4 多孔介质渗透率与颗粒排列形式关系
Table 4. Relationship between porous media permeability and particle arrangement
多孔介质颗粒
排列方式绝对渗透率/μm2 等径圆，
孔隙度0.5竖排等轴长椭圆，
孔隙度0.4横排等轴长椭圆，
孔隙度0.4规则 83.24 73.53 78.83 不规则 107.81 93.24 87.16
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表 5 等轴长椭圆多孔介质渗透率与颗粒长短轴之比
Table 5. The relationship between the permeability of equiaxial elliptical porous media and the ratio of the particle’s major to minor axes
多孔介质颗粒
长短轴之比绝对渗透率/μm2 规则竖排等轴长椭圆 规则横排等轴长椭圆 3∶1 58.30 77.64 2∶1 73.53 78.83 1∶1 81.56 81.56
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表 6 椭圆多孔介质渗透率与颗粒横竖排列关系
Table 6. Relationship between the permeability of elliptical porous media and the horizontal and vertical arrangement of particles
多孔介质颗粒
排列方式绝对渗透率/μm2 规则排列等轴长椭圆 不规则排列等轴长椭圆 不规则排列变轴长椭圆 孔隙度0.3，
长短轴比为2∶1孔隙度0.4，
长短轴比为2∶1孔隙度0.5，
长短轴比为2∶1孔隙度0.4，
长短轴比为3∶1孔隙度0.4，
长短轴比为2∶1孔隙度0.4，
长短轴比为2∶1横 39.72 78.83 85.12 77.64 87.16 65.16 竖 36.80 73.53 78.53 58.30 93.24 71.79
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