Unni Oxaal

Slow two-phase flow in artificial fractures: Experiments and simulations

The slow displacement of a wetting fluid by a nonwetting fluid in models of a single fracture was studied experimentally and by computer simulations on identical geometries. The fracture was modeled by the gap between a rough plate and a smooth transparent plate, both oriented horizontally. Two different rough plates were used, a textured glass plate and a polymethyl methacrylate plate with a computer-generated pattern. A nonwetting fluid (air) was injected slowly through an inlet into the model and displaced a wetting fluid (water) initially filling the model. The aperture fields of the artifical fractures were measured using a light absorption technique. The experiments were simulated using modified invasion percolation models, making use of the measured aperture fields. The simulation models captured invasion bursts and fragmentation and redistribution of the invading air. Experiments and simulations were compared step by step, and good qualitative and quantitative agreement was found.

Slow Two-phase Flow in Single Fractures: Fragmentation, Migration, and Fractal Patterns Simulated Using Invasion Percolation Models

Abstract—The slow displacement of a wetting fluid by an invading non-wetting fluid in single fractures was studied using experiments and simulations. In the experiments, the fracture aperture was modeled by the gap between a rough plate and a smooth transparent plate. The displacement was simulated using invasion percolation models and two types of self-affine fracture aperture models; model A with an infinite in-plane correlation length, and model B with a finite in-plane correlation length. Simulations were also performed on self-affine models that precisely represented the aperture fields of the experiments. At length scales below the in-plane correlation length, the simulated displacement patterns show scaling properties that may be tuned by changing the characteristics of the underlying geometry. In the experiment-matched simulations, we observed closely corresponding displacement patterns.

Growth Patterns and Fronts: Fluid Flow Experiments

Patterns and fronts arise in most fluid flow situations. Waves, clouds, convection patterns and turbulence are well known examples. In porous media the displacement of one fluid by another fluid-leads to many new, often fractal,[1,2] fronts and patterns. The disorder of the porous matrix plays a key role that is not well understood. Depending on the displacement rates, viscosity ratios, miscibility, interfacial tensions and pore geometry a bewildering variety of displacement fronts arise. Lenormand[3] has studied many of the regimes observed under various conditions during two-fluid displacement processes in micromodels of porous media.

Structure of Miscible and Immiscible Displacement Fronts in Pourous Media

We demonstrate displacement processes of fluids by other fluids in porous and non-porous Hele-Shaw cells. We also demonstrate a new result9 showing the fractal nature of the dispersion front of a tracer when it is abruptly added at the injection site in an experiment where a viscous fluid is pumped into a two dimensional porous medium. The concentration contours of the tracer are self-affine fractal curves with a (local) fractal dimension D ≃ 1.42 ± 0.05. The dispersion front may, on the average, be described by the hydrodynamic dispersion with a longitudinal dispersion coefficient D ∥ = Ud ∥, where U is the average flow velocity and d∥ is a characteristic length of the order of a pore diameter. This result is valid for dispersion at high Peclet numbers Pe = Ud/D m , where D m is the molecular diffusion coefficient of the dye.

Growth and Viscous Fingers on Percolating Porous Media

Growth models and viscous fingers are studied on simple percolation models of porous media. Studies include computer and real experiments on square lattice models, at the percolation threshold, and exact calculations of deterministic flow on non-random fractal models. Crossover away from the threshold is also analyzed, using both computer simulations and scaling theory.