松散砂粒孔隙结构、孔隙分形特征及渗透率研究

A study of pore structure,pore fractal feature and permeability of unconsolidated sand

多孔介质孔隙结构特征是决定流体微观运移机制的重要方面。文章用环氧树脂固结松散石英砂磨制出二维多孔介质薄片,并用孔隙结构图像处理方法提取出孔隙结构参数信息;根据孔隙结构参数,建立描述孔隙结构的分形几何模型,分析松散地层孔隙结构的分形特征;进行多孔介质渗透率的实验测量和分形计算。结果表明:多孔介质的孔隙率和孔径与粒径之间存在线性相关性,拟合度分别达到-0.976 5和0.996 6;在方格边长ε和含有孔隙的格子总数N(ε)的双对数坐标系中,lnε-lnN(ε)数据点近似成直线,且不同样品的孔隙分布分维数值比较接近;而在孔径r与大于该孔径的孔隙总数N(r)的双对数坐标系中,lnr-lnN(r)的数据点必须进行分段回归分析,以便能更好地反映孔隙结构的实际情况;孔隙分布分维数和孔径分维数与粒径也存在较高的对应关系;中砂渗透率的实验测得值是5.19×10-5mm2,孔径分维数分段回归法计算的大孔隙多孔介质渗透率为5.75×10-5mm2,测量值与计算值较为接近,孔径分维数可以计算多孔介质的渗透率。

Pore structure of unconsolidated medium is an important influence on fluid migration. Unconsolidated quartz sand samples are consolidated with epoxy resin and are used to produce thin sections. The parameters of pore structure are obtained from these sections with image processing method. The fractal models of pore structure are used to analyze the fractal feature of unconsolidated porous medium, and the permeability of porous medium is measured and calculated. The results indicate that there is linear dependence among porosity, pore size and grain diameter. The correlation coefficient between porosity and grain diameter is -0.9765, while the correlation coefficient between pore size and grain diameter is 0.9966. In the double logarithmic coordinate system of Ins - InN（ε）, the data points of side length of square （i. e., ε ） and total square numbers （i. e., N（ε）） of having pores are approximately in a line, and the fractal dimensions of pore distribution are very close for different samples. Moreover, in the double logarithmic coordinate system of lnr -lnN（ r）, the data points of pore sizes （i. e., r） and total pore numbers （i. e., N （r）） of pore size that are greater than r are analyzed with the subsection regression method. The results of subsection regression method can reflect the practical situation of pore structure. There are high corresponding relationships between the fractal dimension of pore structure and the fractal dimension of grain diameters. The permeability measured by experiment is 5.19 × 10^-5mm^2 , which is 5.75 × 10^-5mm^2 when calculated with the fractal dimension of bigger grain diameters. The two values are very close. Fractal dimension of grain diameters can be used to calculated the permeability of porous medium.