Finn Boger

Microstructural sensitivity of local porosity distributions

The recently introduced concept of local porosity distributions for the geometric characterization of arbitrary porous media is scrutinized using computer generated pore space images. The paper presents the first direct determination of local porosity distributions from digital images. Pore space images with identical two point correlation functions are employed to analyse the geometrical sensitivity of the local porosity concept. The main finding is that local distributions can be used to discriminate between images which are indistinguishable using standard correlation functions. We also discuss the question of length scales associated with the local porosity concept.

Dynamics and Structure of Viscous Fingers in Porous Media

The displacement of a high viscosity fluid by a low viscosity fluid in a porous medium is a process of both scientific and practical importance. It has recently been shown by Chen and Wilkinson1 and by Maloy et al.2 that viscous fingering in a random porous medium at high capillary numbers, Ca > >10−4, generates structures with a fractal3 geometry. This fractal structure closely resembles that obtained from the diffusion limited aggregation (DLA) model of Witten and Sander4. Similar structures have also been obtained by fluid-fluid displacement in radial HeleShaw cells using non-Newtonian viscous fluids5. The relationship between fluid-fluid displacement in porous media and DLA was first discussed by Paterson6 and a more detailed analysis has been presented by Kadanoff7.

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.

Dynamics of Invasion and Dispersion Fronts

The displacement of one fluid by a another fluid in a porous medium is a process of both scientific and practical importance. Depending on the displacement rates, viscosity ratios, irascibility, interfacial tensions and pore geometry a bewildering variety of displacement front behaviors arises. Lenormand1–4 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.