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Infiltration into an Analog Fracture

Experimental Observations of Gravity-Driven Fingering

^a Geoscience Dep., Univ. of Nevada, Las Vegas, NV 89122-4010
^b Flow Visualization and Processes Lab., Sandia National Laboratories, Albuquerque, NM

View larger version (139K): [in a new window]   Fig. 1. Cliff face showing an approximately 10-m high exposure of fractured basalt located in southeastern Idaho (Schaefer, 2002). Extensive vertical fractures formed during cooling of the molten lava dominate the fracture network, which also includes a smaller number of less extensive subhorizontal fractures. The horizontal recess is a sedimentary interbed.

View larger version (17K): [in a new window]   Fig. 2. (a) Sketch illustrating the fluid–fluid interface in plan view (not to scale). In-plane curvature, r2, is shown at two different locations, while the inset depicts the approximation of r2 in Eq. [4]. (b) Cross-sectional view along the line A–A' (Fig. 2a) depicts the definition of r1. Inset shows and ß from Eq. [3].

View larger version (22K): [in a new window]   Fig. 3. a) Sketches of our 15- by 30- and 30- by 60-cm test cells in plan and cross-sectional views (not to scale). Each of the textured glass plates is separated from a 19-mm (3/4") glass plate window by a thin rectangular gasket. A needle inserted through the gasket allows pressurization of the intervening space, pushing the two textured plates into close contact. Note that a larger number of bolts than shown were used to assemble the 30- by 60-cm cell. (b) Sketch of our test stand (not to scale). Light intensity is controlled through a feedback circuit. The light box also contains a cooling system to prevent warming the experiment.

View larger version (54K): [in a new window]   Fig. 4. (a) A 3- by 3-cm segment representative of the aperture field formed when one of our textured glass plates is held against a smooth glass plate. Dark regions (small aperture) correspond to raised bumps on the surface of the textured plates. (b) 3- by 3-cm segment representative of the aperture field formed when two of our textured glass plates are held in face-to-face contact. (c) Aperture distributions. (d) Spatial correlation within the aperture field. Note the negative correlation, or hole, in the variogram at separation distances of approximately 0.08 to 0.17 cm (1–2). Measurements were made by Nicholl et al. (1999), using transmitted light imaging techniques developed by Detwiler et al. (1999).

View larger version (60K): [in a new window]   Fig. 5. The formation of gravity-driven fingers following ponded infiltration (Vp = 4.29 cm3) into the initially dry 30- by 60-cm cell at cos = 1.0.

View larger version (74K): [in a new window]   Fig. 6. The effects of pond volume, Vp, on fingers formed in the initially dry 30- by 60-cm cell at cos = 1.0. Image time in seconds after starting the experiment (t) gives an indication of relative velocity. (a) Vp = 4.29 cm3, t = 23 s; (b) Vp = 6.17 cm3, t = 23 s; (c) Vp = 10.23 cm3, t = 23 s; and (d) Vp = 14.06 cm3, t = 15 s.

View larger version (71K): [in a new window]   Fig. 7. The effects of cos on fingers formed following ponded infiltration into the initially dry 30- by 60-cm cell at similar Vp. Image times give an indication of relative velocity. (a) cos = 0.25, Vp = 6.23 cm3, t = 1593 s; (b) cos = 0.50, Vp = 6.10 cm3, t = 63 s; (c) cos = 0.75, Vp = 6.47 cm3, t = 39 s; and (d) cos = 1.0, Vp = 6.17 cm3, t = 23 s.

View larger version (56K): [in a new window]   Fig. 8. Slow growth of a single finger following ponded infiltration (Vp = 6.23 cm3) into the initially dry 30- by 60-cm cell at cos = 0.25. Image times give an indication of relative velocity. (a) t = 39 s; (b) t = 619 s; (c) t = 1211 s; and (d) t = 1518 s.

View larger version (78K): [in a new window]   Fig. 9. Influence of previous events on formation of gravity-driven fingers at cos = 1.0.

View larger version (164K): [in a new window]   Fig. 10. Relationship between residual moisture and cos. (a) Satiated condition produced by slow horizontal displacement of air by water in our 15- by 30-cm cell; dark regions are water-filled, light regions air-filled. (b) We then successively tilted the cell to inclinations of 75.5, 60, 41.4, and 0° from vertical. At each step we allowed the cell to drain freely. Capillary fringe at the bottom shows fluid left behind after drainage at vertical (cos = 1.0). Moving upward, the black wavy lines show position of the capillary fringe at cos = 0.75, 0.5, and 0.25. Both the size of fluid blobs left behind and residual saturation increase as cos decreases.

View larger version (65K): [in a new window]   Fig. 11. Formation of gravity-driven fingers following ponded infiltration (Vp = 6.98 cm3) into a uniform initial moisture field at cos = 0.25. Water in the initial moisture field was not dyed, and is nearly transparent.

View larger version (43K): [in a new window]   Fig. 12. Formation of a gravity-driven finger from steady supply (Q = 1.36 cm3 min–1) to a point source at cos = 1.0.

View larger version (49K): [in a new window]   Fig. 13. Effects of cos on finger behavior. Experiments were run at different cos values, but similar Q. Image times give an indication of relative velocity. (a) cos = 1.0, Q = 0.254 cm3 min–1, t = 90 s; (b) cos = 0.50, Q = 0.265 cm3 min–1, t = 200 s; (c) cos = 0.25, Q = 0.247 cm3 min–1, t = 285 s; and (d) cos = 0.125, Q = 0.235 cm3 min–1, t = 375 s.

View larger version (94K): [in a new window]   Fig. 14. (a, b) Slow horizontal (cos = 0.0) invasion of the air-filled 15- by 30-cm cell. Invasion is completely controlled by capillary forces (quasistatic displacement), (c) eventually filling the cell to a satiated condition where air is fully entrapped at a variety of length scales.

View larger version (53K): [in a new window]   Fig. 15. Effect of Q on finger behavior under dry initial conditions at cos = 1.0. Image times give an indication of relative velocity. (a) Q = 13.3 cm3 min–1, t = 32 s; (b) Q = 1.25 cm3 min–1, t = 36 s; (c) Q = 0.254 cm3 min–1, t = 108 s; and (d) Q = 0.0243 cm3 min–1, t = 690 s.

View larger version (48K): [in a new window]   Fig. 16. Macroscopic instability of a gravity-driven finger initiated by steady supply (Q = 2.51 cm3 min–1) to point source at the top of the 15- by 30-cm air-filled cell at cos = 1.0.

View larger version (46K): [in a new window]   Fig. 17. Dendritic secondary finger formed in the 15- by 30-cm cell (cos = 0.50) from steady supply (Q = 0.0254 cm3 min–1) under dry initial conditions.

View larger version (57K): [in a new window]   Fig. 18. Unsteady flow resulting from steady supply to an inclined fracture. (a) Desaturated zone behind a fingertip in the 15- by 30-cm cell at steady supply (Q = 0.025 cm3 min–1) under dry initial conditions (cos = 0.50). (b) Enlargement of the boxed area focuses on a single fluid blob. (c) Dynamic behavior within the boxed area is explored by recording changes in saturation with time. White represents repeated drain and fill cycles (e.g., drip points), while black indicates no change.

View larger version (66K): [in a new window]   Fig. 19. Four different fluid configurations observed within the desaturated zone behind a finger formed from steady supply (Q = 0.0198 cm3 min–1) to a point source. As illustrated in these enlargements, pulsed flow imposed by the desaturated zone led to changes in connection.

View larger version (60K): [in a new window]   Fig. 20. Steady supply from a point source (Q = 0.0639 cm3 min–1) into a structured initial moisture field in the 30- by 60-cm cell at cos = 0.25. The initial moisture field (clear water) is outlined in (a) and (d).

View larger version (73K): [in a new window]   Fig. 21. Comparison of fingers formed under wet and dry initial conditions. (a) Finger to the left followed an existing moisture field, while the one to right invaded the dry portion of the aperture field (see Fig. 20). (b) Binary image marking the area swept by each finger.

View larger version (83K): [in a new window]   Fig. 22. Finger splitting in a uniform initial moisture field. The 30- by 60-cm cell was saturated, then drained to residual moisture content at cos = 0.25. Steady supply (1.79 cm3 min–1) was applied from a point source located to the right of center.

View larger version (17K): [in a new window]   Fig. 23. The length of individual fingertips (Ltip) in the redistribution experiments are shown as a function of infiltration length (Li) for experiments run under dry initial conditions.

View larger version (16K): [in a new window]   Fig. 24. The average velocity (v) of individual fingers in the redistribution experiments are shown as a function of infiltration length (Li) for experiments run under dry initial conditions.

View larger version (18K): [in a new window]   Fig. 25. The average width (W) of individual fingers in the redistribution experiments are shown as a function of infiltration length (Li) for experiments run under dry initial conditions. The solid line represents m/2 from Eq. [9].

View larger version (14K): [in a new window]   Fig. 26. The length of individual fingertips (Ltip) initiated from a point source are shown as a function of supply rate (Q) for experiments run under dry initial conditions.

View larger version (18K): [in a new window]   Fig. 27. The average velocity (v) of individual fingers initiated from a point source are shown as a function of supply rate (Q) for experiments run under dry initial conditions.

View larger version (17K): [in a new window]   Fig. 28. The average width (W) of individual fingers initiated from a point source are shown as a function of supply rate (Q) for experiments run under dry initial conditions.

View larger version (44K): [in a new window]   Fig. 29. Saturated fingertip and desaturated zone in an otherwise air-filled fracture.

View larger version (20K): [in a new window]   Fig. 30. Scaled finger tip length (Ltipcos) is shown as a function of scaled finger velocity (v* = v/Kskrcos). Data from both the redistribution and point source experiments under dry initial conditions are shown, along with two simple models representing Eq. [20] and [27].

View larger version (57K): [in a new window]   Fig. 31. Scaled finger width (Wcos) is shown as a function of scaled finger velocity (v* = v/Kskrcos). Data are shown from the redistribution and point source experiments under dry initial conditions and point source experiments with a uniform initial moisture field. Data are also shown for point source experiments in the smooth-textured aperture field. Lines represent Eq. [23], [24], [25], and [28]. (upper) Full data set. (lower) Range of the y axis (Wcos) is reduced to show more detail at small Wcos.

View larger version (47K): [in a new window]   Fig. 32. Comparison between (a, c) fingers formed in our primary aperture field and (b, d) the smooth-textured variant. Note that the smaller aperture of the smooth-textured field leads to a lower optical contrast between air and water. (a) Primary aperture field, Q = 0.0256 cm3 min–1. (b) Smooth-textured aperture field, Q = 0.0221 cm3 min–1. (c) Primary aperture field, Q = 0.572 cm3 min–1. (d) Smooth-textured aperture field, Q = 0.579 cm3 min–1.

View larger version (125K): [in a new window]   Fig. 33. Finger formed under dry initial conditions in the sandblasted aperture field at cos = 1.0. Steady supply of Q = 0.0236 cm3 min–1 is comparable to that for the images shown in Fig. 32a and 32b. The sandblasted plates diffused a significant amount of light, reducing contrast in the images.

View larger version (137K): [in a new window]   Fig. 34. Ponded infiltration (Vp = 13 cm3) into a 32- by 66-cm natural fracture at cos = 1.0. Dye stains (dark) show a transition from stable infiltration to gravity-driven fingers. Unlike our analog, the natural fracture does not allow us to observe the development of fingers, only the end result following disassembly. Because the dye permanently stains the rock, internal flow structure is obscured and we can only see the area wetted by infiltration. The fracture was collected from an outcrop of densely welded volcanic ash located near Los Alamos, NM (from Nicholl et al., 1994).

View larger version (94K): [in a new window]   Fig. 35. Development of a gravity-driven finger in an analog fracture–matrix system. The darkest zones mark a gravity-driven finger moving downward through the fracture. The somewhat lighter fringe shows matrix wetting (from Glass and Tidwell, 1991).

View larger version (68K): [in a new window]   Fig. 36. Buoyant air invasion into a 15- by 30-cm vertical analog fracture saturated with deionized water. (a) Portions of the analog fracture swept by rising air bubbles are shown in black, while the speckled gray zones remained water saturated (from Glass and Nicholl, 1995). (b–d) This sequence shows the growth and fragmentation of an air finger within the boxed region of (a).