Impact of correlation structure on drainage in open rough walled fractures

The spatial correlation structure of heterogeneous parameters plays an important role in upscaling of many flow and transport processes in porous media and fractures. We analyze upscaling of a slow drainage process in a horizontal open rough walled fracture. The applicability of upscaled continuum models for this kind of flow process is discussed. We consider two different fracture aperture distributions with different spatial correlation properties. One is described by a slowly decaying, the other one by a Gaussian autocovariance. The flow process is modelled using an invasion percolation model, which takes the in plane curvature of the fluid cluster into account. Results are compared to laboratory experiments in artificial plexiglas fractures. Different averaging procedures are tested in order to assess the applicability of continuum models. Independently of the correlation structure of the fracture aperture field, spatial averages do not converge to a continuum formulation. Ensemble averages do converge, however, they only give probabilistic information and are not applicable to model drainage in a fracture.     

Dynamics of the finite SK spin-glass

The dynamical behavior of a Sherrington-Kirkpatrick spin-glass model consisting of a large but finite number of Ising spins with a time evolution given by Glauber dynamics is investigated. Starting from the resummation of a diagrammatic expansion we derive a differential equation for the response function which allows us to handle nonperturbative effects. This enables us to find explicit expressions for the dynamical behavior of response and correlation function on time scales related to those free energy barriers which diverge with system sizeN. For the largest of these barriers we find a behavior proportional toN with =1/3.     

Generalized detection of a turbulent front generated by an oscillating grid

This report presents experimental results on the propagation of a turbulent front induced by an oscillating grid starting from rest. The purpose of this preliminary investigation is to implement and validate detection methods of the turbulent/non-turbulent interface, which are based on flow measurements (velocity and vorticity) and scalar intensity, for oscillating grid turbulence. This is done using particle image velocimetry (PIV) and fluorescent dye visualization, separately. The results of both techniques describe the spreading of the turbulent front, confirming the known dependency of the front location, H, on time, t. It is demonstrated, that the level-based detection of a turbulent front can be applied to an unsteady flow, such as grid turbulence advancing into a fluid at rest.     

Experimental study of aortic flow in the ascending aorta via Particle Tracking Velocimetry

A three-dimensional, pulsatile flow in a realistic phantom of a human ascending aorta with compliant walls is investigated in vitro. Three-Dimensional Particle Tracking Velocimetry (3D-PTV), an image-based, non-intrusive measuring method is used to analyze the aortic flow. The flow velocities and the turbulent fluctuations are determined. The velocity profile at the inlet of the ascending aorta is relatively flat with a skewed profile toward the inner aortic wall in the early systole. In the diastolic phase, a bidirectional flow is observed with a pronounced retrograde flow developing along the inner aortic wall, whereas the antegrade flow migrates toward the outer wall of the aorta. The spatial and temporal evolution of the vorticity field shows that the vortices begin developing along the inner wall during the deceleration phase and attenuate in the diastolic phase. The change in the cross-sectional area is more distinct distal to the inlet cross section. The mean kinetic energy is maximal in the peak systole, whereas the turbulent kinetic energy increases in the deceleration phase and reaches a maximum in the beginning of the diastolic phase. Finally, in a Lagrangian analysis, the temporal evolution of particle dispersion was studied. It shows that the dispersion is higher in the deceleration phase and in the beginning of the diastole, whereas in systole, it is smaller but non-negligible.     

Time-resolved 3D visualization of air injection in a liquid-saturated refractive-index-matched porous medium

The main goal of this work is to implement and validate a visualization method with a given temporal/spatial resolution to obtain the dynamic three-dimensional (3D) structure of an air plume injected into a deformable liquid-saturated porous medium. The air plume develops via continuous air injection through an orifice at the bottom of a loose packing of crushed silica grains. The packing is saturated by a glycerin-water solution having the same refractive index and placed in a rectangular glass container. By using high-speed image acquisition through laser scanning, the dynamic air plume is recorded by sequential tomographic imaging. Due to the overlap between adjacent laser sheets and the light reflection, air bubbles are multiply exposed in the imaging along the scanning direction. Four image processing methods are presented for the removal of these redundant pixels arising from multiple exposure. The respective results are discussed by comparing the reconstructed air plume volume with the injected one and by evaluating the morphological consistency of the obtained air plume. After processing, a 3D dynamic air flow pattern can be obtained, allowing a quantitative analysis of the air flow dynamics on pore-scale. In the present experimental configuration, the temporal resolution is 0.1 s and the spatial resolution is 0.17 mm in plane and about 1 mm out of plane of the laser sheet.     

Three-dimensional saltwater-freshwater fingering in porous media: contrast agent MRI as basis for numerical simulations

This study investigated miscible fingering phenomena in a saturated porous medium due solely to fluid density differences. The objective was to determine dissolved salt concentrations in the porous medium and, thus, local fluid density with high temporal resolution and covering substantial volume. A magnetic resonance imaging method, which can achieve this goal by adding Cu(II)SO(4) to salt solutions, has been developed. This method was applied here to observe and quantify three-dimensional miscible fingering for the initial unstable layering of saltwater above freshwater. Additionally, characteristic properties were defined and evaluated to facilitate a more meaningful comparison with numerical simulations.     

Time-Dependent Measurement of Strongly Density-Dependent Flow in a Porous Medium via Nuclear Magnetic Resonance Imaging

Solute transport in saturated artificial porous media was observed in a series of laboratory experiments using magnetic resonance imaging. The objective was to study a situation of density-dependent flow in three dimensions both qualitatively and quantitatively. The time-dependent measurements visualised inflow from below of dense salt water into a freshwater reservoir, internal density-driven flow and the behaviour of a salt water layer below freshwater flow including plume development by dispersion. The main feature of the flow experiment was the strong tendency for the salt water to remain stagnant and to resist being swept out by the freshwater. Additional measurements were performed to gain information about reproducibility, flow field and breakthrough curves.