Abstract. Fracture transmissivity and detailed aperture fields are measured in analog fractures specifically designed to evaluate the utility of the Reynolds equation. We employ a light transmission technique with well-defined accuracy (---1% error) to measure aperture fields at high spatial resolution (---0.015 cm). A Hele-Shaw cell is used to confirm our approach by demonstrating agreement between experimental transmissivity, simulated transmissivity on the measured aperture field, and the parallel plate law. In the two roughwalled analog fractures considered, the discrepancy between the experimental and numerical estimates of fracture transmissivity was sufficiently large (---22-47%) to exclude numerical and experimental errors (<2%) as a source. We conclude that the threedimensional character of the flow field is important for fully describing fluid flow in the two rough-walled fractures considered and that the approach of depth averaging inherent in the formulation of the Reynolds equation is inadequate. We also explore the effects of spatial resolution, aperture measurement technique, and alternative definitions for link transmissivities in the finite difference formulation, including some that contain corrections for tortuosity perpendicular to the mean fracture plane and Stokes flow. Various formulations for link transmissivity are shown to converge at high resolution (---1/5 the spatial correlation length) in our smoothly varying fracture. At coarser resolutions the solution becomes increasingly sensitive to definition of link transmissivity and measurement technique. Aperture measurements that integrate over individual grid blocks were less sensitive to measurement scale and definition of link transmissivity than point sampling techniques.

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Abstract. We develop and evaluate a modified invasion percolation (MIP) model for quasi-static immiscible displacement in horizontal fractures. The effects of contact angle, local aperture field geometry, and local in-plane interfacial curvature between phases are included in the calculation of invasion pressure for individual sites in a discretized aperture field. This pressure controls the choice of which site is invaded during the displacement process and hence the growth of phase saturation structure within the fracture. To focus on the influence of local in-plane curvature on phase invasion structure, we formulate a simplified nondimensional pressure equation containing a dimensionless curvature number (C) that weighs the relative importance of in-plane curvature and aperture-induced curvature. Through systematic variation of C, we find in-plane interfacial curvature to greatly affect the phase invasion structure. As C is increased from zero, phase invasion fronts transition from highly complicated (IP results) to macroscopically smooth. In addition, measurements of fracture phase saturations and entrapped cluster statistics (number, maximum size, structural complication) show differential response between wetting and nonwetting invasion with respect to C that is independent of contact angle hysteresis. Comparison to experimental data available at this time substantiates predicted behavior.

Experimental evidence demonstrating gravity‐driven wetting front instability in an initially dry natural fracture is presented. An experimental approach is developed using a transparent analog rough‐walled fracture to explore gravity‐driven instability. Three different boundary conditions were observed to produce unstable fronts in the analog fracture: application of fluid at less than the imbibition capacity, inversion of a density‐stratified system, and redistribution of flow at the cessation of stable infiltration. The redistribution boundary condition (analogous to the cessation of ponded infiltration) is considered in a series of systematic experiments. Gravitational gradient and magnitude of the fluid input were varied during experimentation. Qualitative observations imply that finger development is strongly correlated to the structure of the imbibition front at the onset of flow redistribution. Measurements of fingertip velocity are used to develop a first‐order relationship with fingertip length. Measured finger width is compared to theoretical predictions based on linear stability theory.

Experiments and analyses are presented to elucidate the critical control of fracture intersections on the evolution and dynamics of the liquid phase structure within unsaturated fracture networks in impermeable media. Phase structure was visualized within a thick vertical sheet of broken glass where the breaks constituted the fracture network. The critical system parameters, applied flow rate (viscous forces) and initial condition, were varied in a series of experiments. When initially dry, individual fracture intersections acted as capillary barriers and created a repeated dynamic from which a network‐scale “slender‐ladder” phase structure emerges that is composed of pools above each intersection joined by fingers or “tendrils” below. At low‐flow rates, pulsation is found at intersections, within fingers, and along horizontal fractures. In some cases, pulsation extends to larger volume “cascade” events where several intersections act in concert. At higher‐flow rates, viscous forces remove pulsation. Reinvasion upon drainage demonstrates that when initially wet, the capillary barrier behavior of the individual fracture intersections vanishes and intersections are rapidly spanned. This marked hysteretic response tends to guide flow and cause pathway persistence from one event to the next.