基于分形几何的非饱和多孔介质热流映射关系

Mapping Correlation Between Heat Conduction and Fluid Flow Through Unsaturated Porous Media

基于分形几何建立了非饱和多孔介质热传导和气液两相渗流的孔隙尺度模型,研究并提出了传热与渗流的映射关系。结果表明非饱和多孔介质的热流特性取决于介质孔隙率、孔隙尺度限、孔隙分形维数、迂曲度分形维数和液相饱和度。孔隙结构固定时,液相相对渗透率与有效热导率均随着液相饱和度的增加而提高,气相相对渗透率则随着饱和度的增加而降低,因此液相和气相相对渗透率与有效热导率分别呈正相关和负相关;液相饱和度不变且孔隙结构发生变化时,液相和气相相对渗透率与有效热导率分别呈负相关和正相关。非饱和多孔介质的相对渗透率与有效热导率满足二次函数关系,热流映射关系对于理解其传热传质机理和预测输运特性具有重要的意义。

Pore-scale models for heat conduction and multiphase fluid flow in unsaturated porous media are developed based on fractal geometry, and the mapping correlation between thermal conductivity and permeability is also explored and discussed accordingly. The results show the predicted effective thermal conductivity and relative permeability both depend on the porosity, pore scale, pore and tortuosity fractal dimensions, and liquid saturation of porous media. The relative permeability of liquid phase and effective thermal conductivity increase with the increment of liquid saturation,when the pore structure is fixed. Oppositely, the relative permeability of gas phase decreases with the increase of liquid saturation. And thus, at variable liquid saturation and fixed pore structures,the relative permeability of liquid and gas phases are positively and negatively correlated with the effective thermal conductivity, respectively. While the relative permeability of liquid and gas phases are negatively and positively correlated with the effective thermal conductivity when the liquid saturation is constant and pore structure varies. The fitting results indicate that the mapping correlation between the effective thermal conductivity and relative permeability obey quadratic function. The present work is of great significance for understanding the mechanisms of heat transfer and fluid flow,and provide theoretical basis for predicting and verifying the heat and flow properties of unsaturated porous media.