基于分形几何的多孔介质电导率与渗透率关系数值模拟

Numerical simulation of the relationship between conductivity and permeability of porous media based on fractal geometry

多孔介质的渗透率模拟,一直以来都是油气勘探、储层划分和甜点区预测等实际工程领域的热门研究问题。分析了原始KC模型和改进后的KC模型,根据分形几何理论利用COMSOL Multiphysics建立了管状孔隙模型和谢尔宾斯基地毯模型,并在模型上计算了电势分布、电流密度分布以及流体流速分布,以此为基础通过两种KC模型计算出渗透率,与通过达西定律计算出来的渗透率做对比,揭示了孔隙曲折度对原始和改进的KC模型的影响,比较和评价了原始和改进的KC模型的应用效果。结果显示,孔隙曲折度越大,通过KC模型求得的渗透率值越小。改进后的KC模型求出的渗透率明显与达西公式计算出的渗透率更加接近,为进一步改进渗透率模型提供了参考。

Permeability simulation of porous media has always been a hot research topic in practical engineering fields such as oil and gas exploration,reservoir division and dessert area prediction.In this paper,the original and improved KC models are analyzed.Multiphysics is used to establishe the tubular pore and the Shelpinski carpet models,and to calculate the potential distribution,current density distribution and fluid velocity distribution on the model.Based on this,the permeability was calculated by two kinds of KC models.Compared with the permeability calculated by Darcy's law,it was revealed that the pore tortuosity and particle surface roughness had an effect on the original and improved KC models.The application effect of the original and improved KC models is compared and evaluated.The results show that the larger the tortuosity of pores,the smaller the permeability value obtained by KC model,and the larger the surface roughness of particles,the greater the permeability obtained.The permeability calculated by the improved KC model is obviously closer to that calculated by Darcy formula,which provides a reference for how to improve the permeability model.