Analysis Of Resistance For Flow Through Porous Media

Porous media widely exist in nature, engineering materials, organs, oil and water reservoirs etc. Due to the complexity of porous media, it is usually difficult to find an analytical solution for resistance of flow through porous media. This paper contains two major works:Firstly, a new model for resistance for flow through porous media is developed based on the average hydraulic radius model and on the contracting-expanding channel model. This model indicates that the resistance of fluid flow in porous media is determined by viscous energy loss and kinematic energy loss. The obtained model is expressed as a function of tortuosity, porosity, ratio of pore diameter to throat diameter and fluid properties. The results show that the model predictions are in good agreement with those from the existing experimental data and Ergun equation.Secondly, A fractal mode for resistance of flow through porous media is developed based on the fractal characters of porous media and on the pore-throat model for capillary. The proposed model is expressed as a function of the pore-throat ratio, porosity, fluid property, pore/capillary and particle sizes, fluid velocity (or Reynolds number) and fractal characters of porous media. There is no empirical constant and every parameter has clear physical meaning in the proposed model. The proposed model is shown to be more fundamental and reasonable than Ergun equation. The model predictions are compared with experiment data, and good agreement is found between them.In conclusion, the two model indicate that pressure drop is mainly determined by the viscous energy loss in low Reynolds number, at high speed (or at high Reynolds numbers) the flow may become turbulent and the irregularity of porous shape has the significant influence on the flow resistance and the kinetic/local energy loss dominates the pressure drop.