2D benchmark experiments and simulations of density coupled flow problems

Variations of fluid densities can alter flow patterns and transport processes, if solute concentration differences are high enough to cause relevant density contrasts. Since numerous environmental problems are related to these phenomena, the need for accurate process description and modeling continues to increase. The numerical simulation of such processes is challenging due to the strong non-linear coupling of flow and transport processes. Therefore, experimental studies are required to elaborate the basic principles and to test numerical codes in order to provide reliable tools for water resources management and planning. In this thesis, density-coupled flow processes under the influence of geometrical boundary conditions are studied and numerical codes are tested against high resolution experimental data.
Photometric methods were further developed to increase the accuracy of measurements in flow tank experiments. They directly related digitally measured intensities of a tracer dye to solute concentrations. This enabled an effective processing of a large number of images in order to compute concentration time series at various points of the flow tank and concentration contour lines. Perturbations of the measurements were lens flare effects and the image resolution. Transmissive and reflective intensity measurements were compared. The reflection images were more homogeneous in spatial illumination than the transmission images. Major perturbations of the transmissive images were lens flare effects and light dispersion within the bead-water-Plexiglas system which smeared the front of the plume. Based on the conducted evaluation of transmissive and reflective intensity measurements, the reflection data delivered more reliable intensity values to derive solute concentrations in intermediate scale flow tank experiments. The newly developed resistivity measurement system used two different input voltages at gilded electrode sticks to enable the measurement of salt concentrations from 0 to 300 g/l. The method was highly precise and the major perturbations were caused by temperature changes, which can be controlled in the laboratory. The two measurement approaches, photometric and resistivity methods, were compared with regard to their usefulness in providing data for benchmark experiments. Due to the unknown measurement volume of the electrodes, the photometric method was better to determine experiments in a series of laboratory-scale 2D porous medium tank experiments.
Various density-driven flow problems were investigated using well-defined experimental parameters and boundary conditions. The experiments were carried out both in a rectangular flow tank (158×100×4 cm3) and in a more complex geometrical setup aiming to study variable density flow in geological formations of aquifers and aquicludes connected via fault zones. An impermeable layer within the porous medium tank forced the solutes to pass through a channel to reach the outlet of the tank. The porous medium was homogeneous in both cases. The image analysis technique deliverd 2, 10, 50 and 80% salt concentration isolines at distinct times and breakthrough curves of the dyed saltwater. The experimental data were presented as benchmark problems to evaluate numerical codes. A numerical model based on Mixed Finite Elements for the fluid flow problem and a combination of Discontinuous Galerkin Finite Element and Multi-Point Flux Approximation methods for the transport turned out to be adequate for the simulation of the physical experiments. The high data availability made the proposed benchmark experiments a valuable tool for assessing the performance of density-coupled flow models. Heterogeneous porous medium experiments were conducted with a low permeability zone in the centre of the tank. Three different boundary conditions, corresponding to different localizations of the inflow and the outflow openings at the opposite edges of the tank, were applied and different flow scenarios are observed in the heterogeneous tank. The numerical model used for the simulations was based on efficient advanced approximations for both spatial and temporal discretizations. The Method Of Lines (MOL) was used to allow higher-order temporal discretization and the model adapted in both the order of approximation and time step to provide the necessary accuracy. The model was able to reproduce the experiments. The numerical results were improved by assuming a non-Fickian dispersivity for high density experiments.