砂岩微观孔隙分形特征与宏观渗透性能的相关性  

Theoretical research on correlation between microscopic fractal characteristics and macroscopic permeability of sandstone

作　　者：连会青[1,2] 冉伟[2] 夏向学[2] 

机构地区：[1]中国矿业大学(北京)资源与安全工程学院,北京100083 [2]华北科技学院安全工程学院,河北三河065201

出　　处：《辽宁工程技术大学学报（自然科学版）》2017年第6期624-629,共6页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金(41072188);新世纪优秀人才支持计划(NCET-11-0838);"十二五"国家科技支撑计划(2012BAK04B04)

摘　　要：为探索砂岩孔隙微观特征与宏观渗透性能的相关性,针对酸刺沟煤矿3个钻孔不同深度9个砂岩样本的SEM图像(放大1 000倍)进行统计分析,SEM图像中孔隙"周长-面积"具有较好的分形特征,分形维数值取1~1.3.之后,借鉴宏观砂岩孔隙中水体渗流的不等径毛束管模型,建立了基于微观孔隙分形特征的渗流不等径毛束管理论模型,推导了微观尺度下渗透系数和渗透率的计算理论模型,计算了各样本的渗透率和渗透系数,取值范围分别在0.002~0.09 m D和1.2~24.4 m/s.为验证理论模型的计算结果,对相同岩芯样本的渗透率进行了中尺度下的实测,实测值取值范围0.34~0.59 m D.最后经相关分析,建立了微观尺度和中尺度下渗透率的相关关系式,相关系数为0.7.可以得出结论,所建立砂岩孔隙微观尺度下渗透率计算的理论公式有一定的合理性,其与中尺度的渗透率存在一定的相关性.To explore the correlation between microscopic characteristics and macroscopic permeability of sandstone interspace, this paper statistically analyzed nine sandstone samples＇ SEM images （magnified 1000 times） of three drillings from different depths in Suancigou mine. The ＂perimeter - area＂ of interspace in SEM image has a good fractal characteristics with fractal dimension between 1 and 1.3. After drawing lessons from water seepage theoretical model of unequal diameter hank tube in macroscopic sandstone interspace, this study established a model based on fractal characteristics of microscopic interspace, deduced computational theory model of permeability coefficient and permeability in microscopic scales, and calculated permeability and permeability coefficient of each samples, which ranges respectively 0.002-0.09mD and 1.2-24.4m/s. In order to verify the theoretical model calculations, permeability of the same core samples under mesoscales was measured with values range of 0.34-0.59mD. Finally, after correlation analysis, a correlative equation of permeability between micro-scale and mesoscales with correlation coefficient of 0.7 was established. It can be concluded that the permeability theoretical formula which is established under sandstone interspace micro-scale has certain rationality, and there is a certain correlation between permeability under mesoscale.

关 键 词：微观孔隙 分形特征 中尺度 渗透率 SEM图像 

分 类 号：P641[天文地球—地质矿产勘探]