多孔介质中卡森流体的分形分析

Fractal analysis of Casson fluid flow in porous media

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理.

Fractal models for flow rate,velocity,starting pressure gradient and effective permeability for Casson fluid in porous media are proposed based on the fractal properties of porous media and capillary model. The proposed models are expressed as functions of fractal dimension,porosity,maximum pore size and representative length of porous media. All parameters in the proposed expressions have clear physical meaning,and the proposed models relate the properties of Casson fluid to the structural parameters of porous media. The velocity, starting pressure gradient and effective permeability versus different parameters are discussed,and the analytical expressions reveal the physical principles for flow velocity,starting pressure gradient and effective permeability in porous media.