Morphology quantification of three-dimensional fluid invasion patterns

In many situations, patterns of immiscible fluid displacement appear obviously different at first glance, but can hardly be distinguished using the commonly applied quantification by fractal dimension. In this work, we propose the mean finger area of the invading fluid, the average distance of defending fluid elements to the invading fluid as well as a discrete surface area of a coarse grained fluid representation as three alternative methods to characterize fluid displacement patterns in three dimensional permeable media. Applying the proposed methods to X-ray microtomography data of fluid displacement experiments in bead packs of homogeneous and mixed wettability, all of the three methods allow to clearly distinguish between a compact front morphology for wetting invading liquids and a finger-like structure for non-wetting invading liquids. When compared to the fractal dimension of the fluid pattern, all three quantities reveal more details with respect to the structure of the invading liquid. Applying these methods to microtomography data of fluid displacement in heterogeneously wetting bead packs reveal a fingering structure and preferential invasion paths that are controlled by local wettability.