Flow of fluids through porous mediums

Abstract

This paper is a preliminary report on the flow of heterogeneous fluids in porous permeable mediums as a sum of energy terms, which can be evaluated either by experiment or straightforward calculation. From experiments with air-water interfaces moving through simple synthesized permeable specimens we concluded that a driving agency must supply a characteristic minimum energy per unit volume of fluid injected. This minimum energy is quantitatively equal to the sum of a series of individually measured terms of the form γnΔAn, where γn is the surface energy per unit area of the nth interface and ΔAn is the change in area of the nth interface. The values of γ for water displacing air on Teflon specimens and water displacing air on glass were +46 ergs/cm2 and −30 ergs/cm2, respectively. The energy required for the alternate expansion and contraction of the air-water interface during its transit through passages of varying cross section was shown to be conserved within the experimental error of 10%. Volumes of individual pores were measured and pore volume frequency histograms constructed. A pore could be characterized in terms of volume and energy. Pore shapes were estimated from the data. The method and apparatus have yielded data reproducible within ±10% for specimens with individual pore volumes of the order of 10−5 cm3 and larger. The apparatus can be refined and the range over which smaller pores can be detected can be extended.