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.

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This paper presents the results of an experimental investigation that is a sequel to a previously published study of the flow of fluids through porous media whose matrices are composed of randomly packed spheres. The objective of the previous study was to accurately determine the ranges of the Reynolds number for which Darcy, Forchheimer and turbulent flow occur, and also the values of the controlling flow parameters—namely, the Kozeny-Carman constant for Darcy flow and the Ergun constants for Forchheimer and turbulent flow—for porous beds that are infinite in extent; that is, practically speaking, for sufficiently large values of the dimension ratio, D/d, where D is a measure of the extent of the bed and d is the diameter of a single spherical particle of which the porous matrix is composed. The porous media studied in the previous and present experiments were confined within circular cylinders (pipes), for which the dimension D is taken to be the diameter of the confining cylinder. The previous study showed that the flow parameters are substantially independent of the dimension ration for D/d ≥ 40. For D/d < 40, the so-called “wall effect” becomes significant, and the flow parameters become functionally dependent upon this ratio. The present paper presents simple empirical equations that express the porosity and the flow parameters as functions of D/d for 1.4 ≤ D/d < 40. Transitions from one type to another were found to be independent of D/d and occur at values of the Reynolds number identical to those reported in the previous study.

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