数字岩心孔隙结构的分形表征及渗透率预测

The fractal characterization of pore structure for some numerical rocks and prediction of permeabilities

基于多孔介质孔隙结构的分形理论,对9种数字岩心样品的孔隙相和固体相结构进行了分形表征。计算结果表明固体相的分形维数通常要大于孔隙相的分形维数,其分形标度区间的宽度要小于孔隙相的标度区间宽度。这表明数字岩心是一种近似两相分形多孔介质。在此基础上,对9种数字岩心样品的孔隙度、体积分数和渗透率进行了预测。预测结果表明数字岩心孔隙结构的分形理论在描述介质的孔隙度和渗透率方面是有效的。而且在近似两相分形介质中,对固相的分形描述似乎更加有效。当用分形理论对数字岩心样品的渗透率进行预测时,其准确地确定最大孔隙尺寸至关重要。最后,通过对比发现,在预测渗透率方面,采用的FT方法要比目前国际上通用的PNEM方法更加准确,也更加具有普适性和计算成本更低。

This paper uses the fractal theory of pore structures for porous media to study the fractal characterization of pore structure for nine numerical rocks.The results show that the fractal dimension of solid phase is usually greater than the pore fractal dimension,and its fractal scaling regions is less than the one of pore phase.This indicates that the numerical rock is an approximate two-phase fractal porous media.The porosities,volume fractions and permeabilities of nine numerical rocks are predicted.The results show that the fractal theory about pore structures of numerical rocks is effective in describing the porosity and permeability.Moreover,it seems to be more effective for solid phase in approximate two-phase fractal porous media.When predicting permeability using the fractal theory,it is very important to accurately determine the maximum pore size and the range of statistical self-similarity.By comparing the two kinds of predicted permeabilities,it is found that the FT method used by this paper is more accurate,more general and less computational cost than the PNEM method which has been worldwide used.