A Three-Dimensional Numerical Model for Determining the PressureDrops in Porous Media Consisting of Obstacles of Different Sizes

Abstract

A three-dimensional numerical model is proposed to determine the pressure drops in porous media consisting of obstacles of different sizes. A series of full three-dimensional numerical calculations were performed to reveal complex three-dimensional velocity and pressure fields within three-dimensional porous structures consisting of spheres of different sizes. These numerical results are processed to obtain the macroscopic pressure gradients. An effective diameter concept has been proposed to correlate the resulting macroscopic pressure gradients with the Ergun equation. The most appropriate definition of the effective diameter has been found such that it, when substituted in the Ergun formula, gives the most reasonable estimate on the pressure drop for the given porosity and diameter distribution.