Visual studies of flow in a regular array of spheres

Recirculation zones induce non-Fickian transport in three-dimensional periodic porous media

In this work, the influence of pore space geometry on solute transport in porous media is investigated performing computational fluid dynamics pore-scale simulations of fluid flow and solute transport. The three-dimensional periodic domains are obtained from three different pore structure configurations, namely, face-centered-cubic (fcc), body-centered-cubic (bcc), and sphere-in-cube (sic) arrangements of spherical grains. Although transport simulations are performed with media having the same grain size and the same porosity (in fcc and bcc configurations), the resulting breakthrough curves present noteworthy differences, such as enhanced tailing. The cause of such differences is ascribed to the presence of recirculation zones, even at low Reynolds numbers. Various methods to readily identify recirculation zones and quantify their magnitude using pore-scale data are proposed. The information gained from this analysis is then used to define macroscale models able to provide an appropriate description of the observed anomalous transport. A mass transfer model is applied to estimate relevant macroscale parameters (hydrodynamic dispersion above all) and their spatial variation in the medium; a functional relation describing the spatial variation of such macroscale parameters is then proposed.

Transition from creeping via viscous-inertial to turbulent flow in fixed beds

This review is concerned with the analysis of flow regimes in porous media, in particular, in fixed beds of spherical particles used as reactors in engineering applications, or as separation units in liquid chromatography. A transition from creeping via viscous-inertial to turbulent flow is discussed based on macro-scale transport behaviour with respect to the pressure drop-flow rate dependence, in particular, the deviation from Darcy's law, as well as direct microscopic data which reflect concomitant changes in the pore-level hydrodynamics. In contrast to the flow behaviour in straight pipes, the transition from laminar to turbulent flow in fixed particulate beds is not sharp, but proceeds gradually through a viscous-inertial flow regime. The onset of this steady, nonlinear regime and increasing role of inertial forces is macroscopically manifested in the failure of Darcy's law to describe flow through fixed beds at higher Reynolds numbers. While the physical reasons for this failure still are not completely understood, it is not caused by turbulence which occurs at Reynolds numbers about two orders of magnitude above those for which a deviation from Darcy's law is observed. Microscopic analysis shows that this steady, nonlinear flow regime is characterized by the development of an inertial core in the pore-level profile, i.e., at increasing Reynolds number velocity profiles in individual pores become flatter towards the center of the pores, while the velocity gradient increases close to the solid-liquid interface. Further, regions with local backflow and stationary eddies are demonstrated for the laminar flow regime in fixed beds. The onset of local fluctuations (end of laminar regime) is observed at superficial Reynolds numbers on the order of 100. Complementary analysis of hydrodynamic dispersion suggests that this unsteady flow accelerates lateral equilibration between different velocities in fixed beds which, in turn, reduces spreading in the longitudial (macroscopic flow) direction.

Flow and dispersion through a close-packed fixed bed of spheres

Fluid flow through a close-packed fixed bed of spheres in a face-centered cubic arrangement is investigated in numerical simulations using a lattice-Boltzmann formulation. The dispersion of a tracer gas is studied both experimentally and numerically. At low Reynolds numbers, Re</=14, the flow is steady with a distribution of normalized local kinetic energies that follows a power law over roughly three orders of magnitude. Consequently the "stagnant" zones play a significant role in determining transport through the packed bed in contrast with the dangling ends for the analogous electrical transport problem, where the distribution of local currents is log binomial. At higher Reynolds numbers transitions to time-oscillatory and chaotically (turbulently) varying flows are predicted to occur with a crossover to a log-normal distribution of local kinetic energies. At the onset of transverse velocity fluctuations the simulated trajectories of tracer particles can cross planes of symmetry, resulting in an abrupt enhancement of dispersion. The dispersion of tracer particles in the time-oscillatory and chaotic varying flows is predicted to be Fickian in the far field. Model predictions for dispersion in a chaotic flow with Re approximately 100 are shown to be in good agreement with experiment.