Permeability of soft porous media under one-dimensional compaction

Abstract

A novel experimental approach to measure permeability of porous material samples under variable longitudinal compaction has been developed. The material has a non-linear structural behavior and exhibits a small hysteresis during mechanical loading and unloading experiments. The new permeameter includes a piston moving inside a Plexiglas cylinder with controllable speed and a test section where the porous material sample is placed under compaction by two grids with adjustable positions. Time-dependent pressure was recorded at four different locations along the sample together with the velocity of the piston. Experiments with two different sample lengths have been performed at three different Reynolds numbers based on the apparatus diameter. The results show that pressure gradient and permeability data do not depend on initial uncompacted sample length. All experiments included measurements at various compaction ratios of the material followed by measurements during relaxation/expansion of the material. No hysteresis was observed in the pressure gradient and permeability data during compaction and expansion of the material for a wide range of compaction ratio. The effects of small velocity fluctuations due to variable friction of the moving piston with cylinder’s wall were also considered. These velocity fluctuations cause pressure fluctuations within the sample which are high close to the inlet part of the material sample and are reduced almost completely towards its outlet. However these pressure fluctuations when scaled with the corresponding mean pressure retained their time-dependent amplitude and phase unchanged along the material. These relative pressure fluctuations cancelled out the flow velocity fluctuations resulting insignificant fluctuations in permeability. It was found that permeability, which is a material property, is drastically reduced with increased compaction ratio of the material while its solid fraction changes substantially but its porosity remains practically unchanged. A comparison with the Cármán–Kozeny expression for random porous media was also examined. Cármán–Kozeny expression predicts qualitatively the reduction of permeability with compaction. However, the predicted values of permeability are very sensitive to the initial value of porosity.