Modeling Gravity-Driven Fingering in Rough-Walled Fractures Using Modified Percolation Theory

by Robert J. Glass, Sandia Natl Lab, Albuquerque, United States,

Document Type: Proceeding Paper

Abstract: Pore scale invasion percolation theory is modified for imbibition of wetting fluids into fractures. The effects of gravity, local aperture field geometry, and local in-plane air/water interfacial curvature are included in the calculation of aperture filling potential which controls wetted structure growth within the fracture. The inclusion of gravity yields fingers oriented in the direction of the gravitational gradient. These fingers widen and tend to meander and branch more as the gravitational gradient decreases. In-plane interfacial curvature also greatly affects the wetted structure in both horizontal and non-horizontal fractures causing the formation of macroscopic wetting fronts. The modified percolation model is used to simulate imbibition into an analogue rough-walled fracture where both fingering and horizontal imbibition experiments were previously conducted. Comparison of numerical and experimental results showed reasonably good agreement. This process oriented physical and numerical modeling is a necessary step toward including gravity-driven fingering in models of flow and transport through unsaturated, fractured rock.

Subject Headings: Percolation | Cracking | Hydraulic fracturing | Numerical models | Curvature | Physical models | Fluid flow | Groundwater flow

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