FLOW RESISTANCE STUDY OF POROUS MEDIA BASED ON FIVE SPHERE MODEL

Flow resistance in porous media has been a challenging research topic. It has extremely important applications in many fields, such as energy, chemical industry, metallurgy, petroleum, materials, and nuclear reactors. However, it is difficult and hot to calculate the flow resistance. This paper presents the innovative five-sphere model by employing the capillary flow, pore-throat, and 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. On the basis of 42 sets of experimental data obtained from the literature, this paper compares and validates the proposed model. When Re<sub>p</sub> < 30, the five-sphere model is compared with the Carman equation and the Ergun and WuJinsui equation; when Re<sub>p</sub> > 30, the comparison is made with the Ergun and WuJinsui equation. Of the 22 data sets with deviations in the range of 0% to 30%, the five-sphere model equation for particles had an average diameter of 0.2 to 56.8 mm, porosity ranging from 0.32 to 0.4174, superficial velocities ranging from 0.000038 to 0.5342 m/s, and Reynolds number ranging from 0.124 to 10,730. Through further analysis of viscous and inertial resistance, it was found that viscous resistance losses from capillary flow and flowing around contribute the most; when Re<sub>p</sub> is < 30, inertial resistance losses from diameter change, and flowing around contribute the most when Re<sub>p</sub> > 150. This further confirms that flowing around occupies an important position in the flow resistance of porous media.