Transport in Porous Media

The flow characteristics in the inertial Reynolds number regime are investigated in a mono-dispersed random pack porous media. Time-resolved particle image velocimetry (PIV) is used to visualize the velocity field in a low aspect ratio bed with 15 mm glass beads. An aqueous solution of Ammunium Thiocynante is used as the working fluid to facilitate matching the solid-fluid refractiveindices. In order to illuminate the inertial regime characteristics, two pore Reynolds number of 100 and 270 are examined. Also, due to the random nature of the packing several pore geometries are compared to identify local scaling used to define the inertial regime effects. Discrete vortical flow structures are evaluated using LES (lowpass filtering) decomposition, in conjunction with criticalpoint analysis of the local velocity gradient tensor. The identified scales associated with the vortical elements are compared based on Reynolds number and pore geometry. Implementing circulation as an integral measure of all vortical structures locally at the pore-scale level demonstrated a linear attitude over the range of Reynolds numbers. Evolution of inertial effects within pore-regions are indicated to be the primary driving mechanism for the emergence of swirling structures passing through the PIV field of view at the onset of turbulence. KEYWORDS Particle image velocimetry (PIV), vortex identification, vorti-cal structure, transition to turbulence, porous media, inertial flow regime, random packed bed, refractive index matched (RIM/MIR) NOMENCLATURE d p [µm] Diameter of PIV tracer particles β [mm] Characteristic length scale of fluid phase n L Liquid refractive index n S Solid refractive index D B [m] Bead diameter D H [m] Hydraulic diameter D tracer [m] Tracer particle diameter L x [mm] Test section width x-direction L y [mm] Test section height y-direction Re p Pore Reynolds number Re P local Local Pore Reynolds number V Darcy [mm/s] Superficial or Darcy velocity V int [m/s] Interstitial velocity Γ 1 [m 2 /s] Vortex center identification scheme Γ [m 2 /s] Circulation λ [nm] Wavelength of light λ ci [1/s] Swirl strength µ [Kg/ms] Dynamic viscosity of fluid phase ν [m 2 /s] Kinematic viscosity of fluid phase φ Porosity ρ [Kg/m 3 ] Density of fluid phase ρ p [gr/cm 3 ] Density of PIV tracer particles rms Root mean square St p The stokes number of PIV tracer particles 1

We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res. 105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.

In a previous study Arns et al. (2004, Transport Porous Media 55, 21–46) we considered the role of topology on drainage relative permeability curves computed using network models derived from a suite of tomographic images of Fontainebleau sandstone. The present study extends the analysis to more complex imbibition displacements where the non-wetting fluid can be disconnected by snap-off as a result of swelling of wetting films in the corners of pores and throats. In contrast to the findings for drainage displacements which showed that relative permeabilities are significantly affected by network topology, the present study shows that the effect of topology on imbibition relative permeabilities depends on the level of snap-off. For strongly wetting conditions where snap-off dominates the displacement the effect of network topology is significantly smaller than for weakly wet conditions where snap-off is suppressed. For contact angles sufficiently large to completely suppress snap-off, the effect of topology on imbibition relative permeabilities is similar to that for drainage displacements. The findings are valid for random networks and for networks displaying short-range pore–throat and longer range spatial correlations.

This work evaluates and improves upon existing effective medium methods for permeability upscaling in fractured media. Specifically, we are concerned with the asymmetric self-consistent, symmetric self-consistent, and differential methods. In effective medium theory, inhomogeneity is modeled as ellipsoidal inclusions embedded in the rock matrix. Fractured media correspond to the limiting case of flat ellipsoids, for which we derive a novel set of simplified formulas. The new formulas have improved numerical stability properties, and require a smaller number of input parameters. To assess their accuracy, we compare the analytical permeability predictions with three-dimensional finite-element simulations. We also compare the results with a semi-analytical method based on percolation theory and curve-fitting, which represents an alternative upscaling approach. A large number of cases is considered, with varying fracture aperture, density, matrix/fracture permeability contrast, orientation, shape, and number of fracture sets. The differential method is seen to be the best choice for sealed fractures and thin open fractures. For high-permeable, connected fractures, the semi-analytical method provides the best fit to the numerical data, whereas the differential method breaks down. The two self-consistent methods can be used for both unconnected and connected fractures, although the asymmetric method is somewhat unreliable for sealed fractures. For open fractures, the symmetric method is generally the more accurate for moderate fracture densities, but only the asymmetric method is seen to have correct asymptotic behavior. The asymmetric method is also surprisingly accurate at predicting percolation thresholds.

In this paper, we address the issue of threshold yield pressure of yield-stress materials in rigid networks of interconnected conduits and porous structures subject to a pressure gradient. We compare the results as obtained dynamically from solving the pressure field to those obtained statically from tracing the path of the minimum sum of threshold yield pressures of the individual conduits by using the threshold path algorithms. We refute criticisms directed recently to our previous findings that the pressure field solution generally produces a higher threshold yield pressure than the one obtained by the threshold path algorithms. Issues related to the solidification of yield stress materials in their transition from fluid phase to solid state have also been investigated and assessed as part of the investigation of the yield point.