ABSTRACT
The effect of permeability heterogeneities and viscosity variations on miscible displacement processes in porous media is examined using high-resolution numerical simulations and reduced theoretical modelling. The planar injection of one fluid into a fluid-saturated, two-dimensional porous medium with a permeability that varies perpendicular to the flow direction is studied. Three cases are considered, in which the injected fluid is equally viscous, more viscous or less viscous than the ambient fluid. In general it is found that the flow in each case evolves through three regimes. At early times, the flow exhibits the concentration evolves diffusively, independent of both the permeability structure and the viscosity ratio. At intermediate times, the flow exhibits different dynamics including channelling and fingering, depending on whether the injected fluid is more or less viscous than the ambient fluid, and depending on the relative magnitude of the viscosity and permeability variations. Finally, at late times, the flow becomes independent of the viscosity ratio and dominated by shear-enhanced (Taylor) dispersion. For each of the regimes identified above, we develop reduced-order models for the evolution of the transversely averaged concentration and compare them to the full numerical simulations.
ABSTRACT
Fluid flowing through a deformable porous medium imparts viscous drag on the solid matrix, causing it to deform. This effect is investigated theoretically and experimentally in a one-dimensional configuration. The experiments consist of the downwards flow of water through a saturated pack of small, soft, hydrogel spheres, driven by a pressure head that can be increased or decreased. As the pressure head is increased, the effective permeability of the medium decreases and, in contrast to flow through a rigid medium, the flux of water is found to increase towards a finite upper bound such that it becomes insensitive to changes in the pressure head. Measurements of the internal deformation, extracted by particle tracking, show that the medium compacts differentially, with the porosity being lower at the base than at the upper free surface. A general theoretical model is derived, and the predictions of the model give good agreement with experimental measurements from a series of experiments in which the applied pressure head is sequentially increased. However, contrary to theory, all the experimental results display a distinct and repeatable hysteresis: the flux through the material for a particular applied pressure drop is appreciably lower when the pressure has been decreased to that value compared to when it has been increased to the same value.
