页岩孔隙结构的分形表征及渗透率预测

Fractal Characterization of Pore Structure for Shale and Prediction of Permeability

基于SEM二维页岩切片图像,采用MATLAB图像处理技术并结合多孔介质分形理论,对页岩二维切片图像的原始二值图像和重建二值图像中孔隙结构进行了分形表征,得到了页岩原始二值图像和重建二值图像的孔隙半径分维数,分析了页岩孔隙结构多重分形的原因。基于分形理论并利用毛细管束模型和Hagen-Poiseuille方程推导了页岩渗透率与孔隙半径分维数的关系式。MCMC方法重建的数字岩心能较好地体现原图的性质;最大孔隙半径、拐点半径、孔隙半径分维数和迂曲度分维数均对页岩渗透率有较大影响,页岩渗透率与最大孔隙半径和拐点半径呈明显的正相关性,与孔隙半径分维数和迂曲度分维数呈明显的负相关性,与孔隙半径分维数的相关性较小。

Based on two-dimensional SEM image of shale and image processing technology of MATLAB and combining with the fractal theory of porous media,given is the fractal characterization of the original binary image and the reconstruction binary image of shale respectively,and obtaining the fractal dimensions of them and analyzing the reasons of the multifractal of pore structure of shale.Then based on the fractal theory,we get shale permeability model by using the capillary bundle model and Hagen-Poiseuille equation.The results show that the digital cores,reconstructed by using MCMC method,can better reflect the nature of the original image;the maximum of pore radius,the corner radius,fractal dimension of pore and the fractal dimension of tortuosity have a great influence on permeability of shale,the permeability of shale has a positive correlation with the maximum of pore radius and the corner radius,the permeability of shale has a negative correlation with fractal dimension D1 and the fractal dimension of tortuosity,the correlation with D2 is small.