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A New Method to Evaluate the Anisotropy of Rock Permeability
DOI: 10.12677/AG.2019.92006, PDF, HTML, XML, 下载: 1,008  浏览: 4,489

Abstract: The permeability of rock is a typical vector, and more and more attention is paid to the testing and evaluation methods of the anisotropy of permeability. Based on traditional permeability anisotropy, evaluation methods cannot fully reflect extreme value point effect, physical meaning is not clear, is not convenient to contrast between the core and classify faults. In order to express the characteristics of anisotropy of permeability of reservoir rock more clearly, a new method of permeability evaluation is put forward based on the study of previous permeability evaluation methods of reservoir rock and the permeability test of reservoir rock of different lithology. The geometric average of the three-dimensional permeability is used to represent the apparent permeability of the core, the relative relationship between the anisotropic permeability and the ratio of the geometric average to the arithmetic average of the three-dimensional permeability is used to quantitatively describe the degree of anisotropy. The results show that the new method can scientifically and comprehensively evaluate the anisotropy of rock permeability.

1. 引言

Figure 1. Ellipsoid diagram of vector permeability

Figure 2. Schematic diagram of permeability anisotropy

$\stackrel{¯}{K}=\frac{{K}_{x}+{K}_{y}+{K}_{z}}{3}$ (1)

${\delta }_{1}={K}_{i}/{K}_{j}$ (2)

${\delta }_{2}=\sqrt{\left({\left(\frac{{K}_{x}-\stackrel{¯}{K}}{\stackrel{¯}{K}}\right)}^{2}+{\left(\frac{{K}_{y}-\stackrel{¯}{K}}{\stackrel{¯}{K}}\right)}^{2}+{\left(\frac{{K}_{z}-\stackrel{¯}{K}}{\stackrel{¯}{K}}\right)}^{2}\right)/3}$ (3)

2. 描述岩石渗透率方向性大小的特征值

${K}_{a}=\sqrt[3]{{K}_{x}{K}_{y}{K}_{z}}$ (4)

Figure 3. Sphere of radius of characteristic permeability Ka

3. 三角网状图法描述储层渗透率方向性

${P}_{x}=\frac{{K}_{x}}{{K}_{x}+{K}_{y}+{K}_{z}}×100%$

${P}_{y}=\frac{{K}_{y}}{{K}_{x}+{K}_{y}+{K}_{z}}×100%$ (5)

${P}_{z}=\frac{{K}_{z}}{{K}_{x}+{K}_{y}+{K}_{z}}×100%$

Table 1. Permeability anisotropy triangulation and its characteristics

Figure 4. Depicts the triangular mesh of permeability directivity of the reservoir

4. 渗透率各向异性程度定量表征

$d=\frac{\sqrt[3]{{K}_{x}{K}_{y}{K}_{z}}}{\frac{1}{3}\left({K}_{x}+{K}_{y}+{K}_{z}\right)}$ (5)

Figure 5. Permeability trigonometric isograms

Table 2. Triangulation and characteristic of permeability anisotropy

5. 渗透率方向性测试分析及应用

5.1. 方向渗透率仪测量各向异性实验

Figure 6. Each rock cube sample

Figure 7. Directional permeability core holder

1-气瓶；2-减压阀；减压阀；3-进气阀；进气阀；4-压力调节器；压力调节器；压力调节器；5，7，9-压力表；压力表；6-立方体岩心夹持器；立方体岩心夹持器；立方体岩心夹持器；立方体岩心夹持器；8-恒压泵；10-皂膜流量计； 皂膜流量计；皂膜流量计；11 -铁架台

Figure 8. Flow chart of permeability anisotropy measurement of cubic rock sample

Table 3. Data of sandstone, carbonate, shale and coal

Figure 9. Permeability histogram of sandstone, carbonate and shale samples

5.2. 渗透率方向性大小和非均质程度评价

Table 4. Calculation table of permeability directivity and heterogeneity indexes of different samples

Figure 10. Different sample permeability trigonometric isograms

6. 结论

1) 综合岩石的三向渗透率大小提取出描述渗透率大小的特征值，可对不同地层条件的储层或相同地层不同层位的储层渗透率大小进行比较判断；

2) 用三角图对岩石渗透率各向异性进行表征，通过对标点位置可以分析出样品渗透性特征；

3) 利用各向异性程度d和渗透率各项异性三角等值线图可以判断各样品的各向异性程度。

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