Fingering of Dense Nonaqueous Phase Liquids in Porous Media: 2. Analysis and Classification

Abstract

Fingering of dense nonaqueous phase liquids (DNAPLs) as seen in three‐dimensional experirments with saturated, homogeneous porous media was analyzed. A consistent geometrical quantification of finger configurations was obtained using concepts of fractal and multifractal scaling. Fractal patterns that determine the probabilistic distribution of the DNAPL were found to be representative for every experimental combination of sand and DNAPL. These patterns could be attributed to either capillary or viscous fingering regimes. With multifractal formalisms we were able to give a description of the underlying process kinetics. The generalized dimension Dq relates results to diffusion‐limited aggregation (DLA) or invasion percolation type models. The spectrum of singularities ƒ(α) is invariable for cross sections of an experiment and in turn can be used for a classification of the displacement system. The width of the ƒ(α) curve in the range of positive moments quantifies displacement instability. Phase transitions are indicated for the more stable displacement systems.