多孔介质渗透率的一种新分形模型  

A New Fractal Model for the Permeability of Porous Media

作　　者：王世芳[1] 吴涛[2] 邓永菊[1] 郑秋莎[1] 

机构地区：[1]湖北第二师范学院物理与机电工程学院,湖北武汉430205 [2]武汉工程大学理学院,湖北武汉430074

出　　处：《力学季刊》2016年第2期293-301,共9页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11402081);西南石油大学油气藏地质及开发工程国家重点实验室开放基金项目(PLN1205)

摘　　要：多孔介质的渗流特性是油气藏工程、地下水资源利用、高放废物深地质处置等实际工程领域的热门研究问题.基于分形理论及多孔介质由一束面积大小不等的椭圆形毛细管组成的假设,本文建立了流体在分形多孔介质中渗流时的绝对渗透率及相对渗透率的分形渗透率模型.结果表明,绝对渗透率是最大和最小孔隙面积、分形维数、形状因子ε的函数,且当ε=1时,本文模型可以简化成Yu与Cheng模型;而非饱和多孔介质的相对渗透率与饱和度和多孔介质微结构参数有关.将本文提出的渗透率分形模型预测与实验测量数据及其他模型结果进行对比,显示它们整体吻合很好.Seepage characteristics of porous media has become a hot topic in many practical applications such as oil and gas reservoir engineering, groundwater resources utilization as well as the geological disposal of high-level nuclear waste. Based on the fractal theory, the fractal models for the absolute permeability and relative permeability for both saturated and unsaturated fractal porous media, which are composed of a bundle of elliptical capillaries with different cross-sectional areas, are developed in this paper. Results show that the absolute permeability expression is a function of the maximum and the minimum pore areas, fractal dimensions and the shape factor ε. For ε =1, the absolute permeability model can be simplified as Yu and Cheng＇s model. And the relative permeability for the unsaturated porous media is related to the saturation and micro-structures of porous media. To validate the proposed model, the results from our fractal model are compared with the available experimental data as well as two existing models, and good agreement is achieved between them.

关 键 词：渗透率 相对渗透率 分形理论 饱和度 

分 类 号：O357.3[理学—流体力学]