Analysis of permeabilities for slug flow in fractal porous media

Slug flow is one of types of flow in two-phase flow in porous media, and this type of flow widely exists in oil and gas pipelines, underground water reservoirs, and nuclear reactor cooling systems, etc. Study of the mechanisms and characteristics of slug flow in porous media has the great significance in the reservoir engineering, power engineering, aerospace engineering, and chemical engineering etc. In this paper, we propose analytical models for seepage characteristics, both permeabilities and relative permeabilities, for slug flow in a capillary by unit cell approach. Then, we extend the methodology to analyze the seepage characteristics of slug flow in fractal porous media. The proposed relative permeabilities for slug flow in porous media are expressed as a function of micro-structural parameters of porous media and fluid properties, such as maximum and minimum capillary sizes, fractal dimensions, the surface tension, as well as capillary numbers. The parametrical effects on the relative permeabilities are also investigated. The validity of the proposed model for slug flow is verified by comparing the model predictions with the available experimental data.