基于三维重正化近似方法的等效渗透率计算

Calculation of effective permeability based on approximation of 3D renormalization

基于二维重正化方法的近似关系推导出三维重正化的近似计算关系。首先,基于岩样孔隙结构CT图像进行网格剖分;其次,在每个剖分网格单元用等效介质模型计算其等效渗透率;再次,基于剖分单元的等效渗透率分布,综合应用二维电网络模型的解析关系与重正化方法导出三维介质的近似计算关系,并选用一个理想多孔介质模型及2块岩心样本CT成像数据进行测试。另外,用重正化渗透率近似方法对3块数字岩心进行等效渗透率计算,并与用格子玻尔兹曼得到的绝对渗透率进行对比。结果表明:重正化渗透率近似计算方法在简单模型上与理论值误差小于10%;对于砂岩岩样,与实验测试结果误差小于25%,而且计算结果显示出弱各向异性;重正化近似方法得到的等效渗透率计算结果均在可以接受的范围内。

In this study, we derive the approximation of 3D renormalization based on that of 2D. First, we divide CT image into mesh grids according to the pore structure from samples. Next, effective permeabilities of each block are calculated from different equivalent medium models. Third, on the basis of the effective permeability of each grid cell, we apply the similarly analytic expression of the 2D electric network and the renormalization group formula for 2D CT image to derive the approximation equation of effective permeability in 3D media. The validity and accuracy of the proposed method are checked against known results of one idealized porous media models, which have analytic expressions and two rock samples which include both experimental permeability values and CT images. In addition, we apply the approximation of 3D renormalization to compute the effective permeabilities for three digital rocks from Imperial College London and then compare with absolute permeabilities calculated by the lattice Boltzmann method. Test results show that the relative errors deduced from the renormalization group method for simple models and the sandstone samples are within 10% and 25%, repsectivley.The magnitudes in three directions show weak anisotropy,and the effective permeabilities calculated by the approximation of 3D renormalization are in an acceptable range.