Our Newly Published articles provide view of research, ideas, and discussion in the field of Porous Media.
Rheology of High-Capillary Number Flow in Porous Media
The hydrodynamics of real things very often happens at small scale, i.e. in a porous medium. This is the case in a wide variety of biological, geological and technological systems where there are normally several immiscible fluids present. The challenge of describing such systems in a unified way, however, is largely unsolved. An important reason for this is the lack of a length scale above which the system may be averaged as if it were homogeneous.
We have studied the effective viscosity of immiscible two-fluid flow in porous media in the high capillary number limit where the capillary forces may be ignored compared to the viscous forces. We find that the Lichtenecker–Rother equation describes the effective viscosity well. The exponent depends on the fluid configuration, i.e. the number of bubbles/interfaces in the pores. For small bubbles or many interfaces in the pores, as with the Boltzmann model, we find α = 1, whereas when the bubbles are larger or the interfaces fewer in the pores, we find α = 0.6 in 2D (square and hexagonal lattices) and α = 0.5 in 3D for networks reconstructed from Berea sandstone and sand packs. Our arguments are based on analytical and numerical methods.
Relations between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media
Based on thermodynamic considerations we derive a set of equations relating the seepage velocities of the ﬂuid components in immiscible and incompressible two-phase ﬂow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model. The aim of this paper is to derive a set of equations on the continuum level where differentiation make sense. We define a representative elementary volume
— REV — as a block of porous material with no internal structure filled with two immiscible and incompressible fluids: it is described by a small set of parameters which we will now proceed to define. We illustrate the REV in Fig. 1. Read the paper here.