Flow resistance study of porus media based on five-sphere model

Flow resistance in porous media has been a challenging research topic in engineering and flow mechanics, plays an crucial role in industrial production and daily life. This paper presents the innovative five-sphere model by employing the capillary flow, pore-throat, flowing around models. The flow resistance of the five-sphere model incorporates capillary flow resistance, local resistance caused by the changes of pore-throat, and flowing around resistance of fluids around the filling material, which is summarized to derive a formula for the flow resistance of porous media without empirical parameters. Based on 42 sets of experimental data obtained from literature, this paper compares and validates the proposed model. When ,the five-sphere model is compared with the Carman equation, Ergun and WuJinsui equation; when , the comparison made with the Ergun and WuJinsui equation. Out of the 22 sets of data with deviations in the range of 0-30% of the five-sphere model equation for particles with an average diameter of 0.2 mm up to 56.8 mm; porosity ranging from 0.32 to 0.4174, superficial velocities ranging from 0.000038 m/s to 0.5342 m/s; and Reynolds number ranging from 0.124 to 10730. By further analysis of viscous and inertial resistance, it is found that viscous resistance losses from capillary flow and flowing around occupy the main part; when Rep < 30; inertial resistance losses from diameter change and flowing around occupy the main part when Rep > 150. This further confirms that flowing around occupies an important position in the flow resistance of porous media.