Topological Persistence for Relating Microstructure and Capillary Fluid Trapping in Sandstone

Results from a series of two-phase fluid flow experiments in Leopard, Berea, and Bentheimer sandstones are presented. Fluid configurations are characterized using laboratory-based and synchrotron based 3-D X-ray computed tomography. All flow experiments are conducted under capillary-dominated conditions. We conduct geometry-topology analysis via persistent homology and compare this to standard topological and watershed-partition-based pore-network statistics. Metrics identified as predictors of nonwetting fluid trapping are calculated from the different analytical methods and are compared to levels of trapping measured during drainage-imbibition cycles in the experiments. Metrics calculated from pore networks (i.e., pore body-throat aspect ratio and coordination number) and topological analysis (Euler characteristic) do not correlate well with trapping in these samples. In contrast, a new metric derived from the persistent homology analysis, which incorporates counts of topological features as well as their length scale and spatial distribution, correlates very well (R-2=0.97) to trapping for all systems. This correlation encompasses a wide range of porous media and initial fluid configurations, and also applies to data sets of different imaging and image processing protocols. Plain Language Summary When fluids flow through porous rocks or soils, small bubbles (ganglia) of oil or gas may become trapped in the pore structure of the rock. This occurs during many natural and engineered processes (e.g., rainfall infiltration into soils, enhanced oil recovery, geologic carbon dioxide sequestration, contaminant remediation of pollutants in soils). In this study, we analyze the small-scale 3-D structure (length scales on the order of microns) of sandstone rocks to determine the structural controls on ganglion trapping, and compare to results from a series of fluid flow experiments. The analysis uses a new data/image analysis technique known as persistent homology that can quantify structure in terms of geometry, topology, and spatial distribution. We define a new metric which combines these structural impacts and demonstrate that the new metric provides a universal correlation for ganglia trapping levels for a variety of sandstone types and initial fluid configurations, and also applies to 3-D data sets derived from different imaging and image processing protocols.