The interplay of flow-induced, gravitational and mechanical compaction in soft porous media

Flow-induced compaction of soft, elastically deformable porous media occurs in numerous industrial processes. A theoretical study of this problem, and its interplay with gravitational and mechanical compaction, is presented here in a one-dimensional configuration. First, it is shown that soft media can be categorised into two ‘types’, based on their compaction behaviour in the limit of large applied fluid pressure drop. This behaviour is controlled by the constitutive laws for effective pressure and permeability, which encode the rheology of the solid matrix, and can be linked to the well-known poroelastic diffusivity. Next, the interaction of gravitational and flow-induced compaction is explored, with the resultant asymmetry between upward and downward flow leading to distinct compaction behaviour. In particular, flow against gravity – upwards – must first relieve gravitational stresses before any bulk compaction of the medium can occur, so upward flow may result in compaction of some regions and decompaction of others, such that the overall depth remains fixed. Finally, the impact of a fixed mechanical load on the sample is considered: again, it is shown that flow must ‘undo’ this external load before any bulk compaction of the whole medium can occur in either flow direction. The interplay of these different compaction mechanisms is explored, and qualitative differences in these behaviours based on the ‘type’ of the medium are identified.