用分段回归方法计算孔隙结构的分形维数

Calculation of fractal dimension of pore structure by using subsection regression method

储层岩石的孔隙空间具有良好的分形特征,孔隙结构的分形维数可以用来定量描述孔隙结构的复杂程度。应用分形几何的原理,推导了储层岩石不同孔隙分布和毛细管压力曲线的分形几何模型。根据毛管压力曲线资料,用分段回归的方法计算了不同孔隙结构的分形维数。计算结果表明,用分段回归方法计算孔隙结构的分形维数能更好地反映孔隙结构的实际情况。若孔隙大小相差不大,孔隙结构的分形维数相等或比较接近;若孔隙大小相差较大、非均质性较强,得到的孔隙结构分形维数不同。

The pore spaces in reservoir rocks have fractal property. The fractal dimension of pore structure can be used to quantitatively describe the complexity of pore structure. According to the principle of fractal geometry, the fractal models for describing the pore size distribution and capillary pressure curve were developed. On the basis of the capillary pressure data, the fractal dimension of pore structure was calculated by using subsection regression method. The results obtained by the subsection regression method can really reflect the pore structure in reservoir. If the difference of pore sizes is small, the fractal dimensions of pore structure are equivalent or close. If the difference of pore sizes is big and the inhomogeneity of reservoir is strong, the fractal dimensions are different.