Abstract Multiphase flow in unsaturated porous media exhibiting hysteretic phenomenon is of great significance to oil and gas recovery, agriculture, and hydrology etc. Water retention curve (WRC) and relative hydraulic conductivity function (RHC) as well as relative air permeability function (RAP) are usually employed to characterize the transport properties of porous media. A new fractal capillary model accounting for the hysteresis effect is developed in this paper for the multiphase flow in unsaturated porous media. The analytical expressions for WRC, RHC and RAP under drying and wetting paths are derived accordingly. The proposed fractal capillary model shows good consistent with available experimental results. It has been found that the pore-throat structure in the proposed fractal capillary model takes an important influence on the hysteresis effect and fluid flow, especially for the non-wetting phase. The present work may be helpful for understanding the complex mechanisms of hysteresis effect and transport processes in unsaturated porous media.

中文翻译：

---

具有滞后效应的多孔介质中多相流动的分形毛细管模型

摘要 不饱和多孔介质中表现出滞后现象的多相流动对油气回收、农业、水文等具有重要意义。 保水曲线（WRC）和相对水力传导函数（RHC）以及相对透气度函数（RAP）通常用于表征多孔介质的传输特性。本文针对非饱和多孔介质中的多相流开发了一种新的分形毛细管模型，该模型考虑了滞后效应。相应地推导出干燥和润湿路径下的 WRC、RHC 和 RAP 的解析表达式。所提出的分形毛细管模型与可用的实验结果显示出良好的一致性。已经发现，所提出的分形毛细管模型中的孔喉结构对滞后效应和流体流动具有重要影响，特别是对于非润湿相。目前的工作可能有助于理解不饱和多孔介质中滞后效应和输运过程的复杂机制。