Resistance to the Flow of Fluids Through Simple and Complex Porous Media Whose Matrices Are Composed of Randomly Packed Spheres

Abstract

Experimental data relating to the flow of fluids through simple and complex porous media whose matrices are composed of randomly packed spheres have been obtained. In this context the term “simple” refers to porous media whose matrices are composed of spheres of uniform diameter, while “complex” refers to matrices composed of spheres having different diameters. It was found that Darcy’s law is valid for simple media within a range of the Reynolds number, Re, whose upper bound is 2.3. The upper bounds of Darcy flow for complex media were found to be consistent with this value. It is shown that the resistance to flow in the Darcy regime can be characterized by taking the Kozeny-Carman constant equal to 5.34 if the characteristic dimension is taken equal to the weighted harmonic mean diameter of the spheres that comprise the matrix. Forchheimer’s equation was found to be valid for simple media within the range 5 ≤ Re ≤ 80. The corresponding bounds for complex media were found to be consistent with this range. It is shown that the resistance to flow in the Forchheimer regime for both simple and complex media can be characterized by adopting the following values of the Ergun constants: A = 182 and B = 1.92. Finally, it is shown that fully developed turbulent flow exists when Re > 120 and that the resistance to flow in the turbulent regime can be calculated using Forchheimer’s equation by adopting the following values of the Ergun constants: A′ = 225 and B′ = 1.61. A simple method for characterizing the behavior of porous media in the transition regions between Darcy and Forchheimer and between Forchheimer and turbulent flow is presented.