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Free-Surface Films
Pages 217-242

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From page 217...
... It is imperative that the acting transport mechanism be identified because fractured vadose sites are being marked for potential toxic waste repositories. A free-surface film may provide a mechanism by which fluids in the unsaturated zone are transported through air-filled fractures much more rapidly than plug flow or porous matrix transport.
From page 218...
... It is imperative that this transport mechanism be identified because fractured vadose sites are being identified for potential toxic waste repositories. Miscalculations regarding fluid transport could have a major impact on the future integrity of any repository.
From page 219...
... However, at low capillary pressures, because pressure equilibrium is required between the fracture and matrix, the largest liquid-filled aperture in the fracture will be on the order of magnitude of the largest pore size that is liquid-filled in the surrounding porous medium. Fractures in arid regions, where the porous medium is at very low saturation and very low capillary pressures, are likely to be saturated only in sections where the aperture is very small, such as where two porous blocks touch.
From page 220...
... , Yucca Mountain, Nevada, a bomb-pulse chlorine-36 signature was found hundreds of feet below surface, even though the bomb-pulse signal is less than 50 years old (FabrykaMartin et al., 1998~. This anomalous rapid transport rate is occurring in an arid region where the vadose zone is highly unsaturated and fractured.
From page 221...
... Furthermore, FIGURE 7-3 Model for flow in unsaturated fractures where fluid flows in the form of free surface films down the fracture walls while sustaining a continuous air phase.
From page 222...
... They established steady-state conditions in which flow delivered to the upper surface of their sample was quickly distributed to both the rock matrix and fracture surface while the metric potential was kept near saturation. Their experiment showed that these free-surface films can generate very high transport rates and velocity while sustaining subatmospheric pressures within the film (see section on Seepage Generated Film Flow below)
From page 223...
... This lack of boundary condition can be resolved by assuming that at steady state the free surface is flat and the film thickness constant (Nusselt, 1916~. As will be shown later, although this assumption is incorrect, it provides a FIGURE 7-4 Geometry used for development of free-surface film mathematical model.
From page 224...
... These solitary waves appear to ride over a thin fluid substrate. They travel faster than the mean film speed, can have amplitudes two to five times the substrate thickness, and appear to trap a recirculating region of fluid (Figure 7-5)
From page 225...
... . vapor phase; the restorative force of surface tension due to the waviness of the surface is included in the fifth boundary condition; and the film is allowed to vary in thickness.
From page 226...
... (7.10) The second boundary condition is no slip at the wall and no matrix absorption, aty=O, v=O; the third boundary condition is the kinematic condition at the free surface, at y = h, v = ht + uhx, where the subscript signifies differentiation with respect to that variable; the fourth boundary condition is balance of shear stresses at the free surface, aty=h, ~ ~ (7.11)
From page 227...
... (7.16) where h is the film thickness and al are the coefficients of the stream function expansion.
From page 228...
... A very important result of this model is the link between the structure of the predicted chaotic disturbance and the shape of the naturally forming solitary wave. Since the attractor exists only for perturbations with celerity less than a specific value, we can hypothesize that the solitary waves forming on the free surface will travel at an approximate speed equal to the product of the transition celerity times the predicted steady-state film speed, UN.
From page 229...
... The development of solitary waves has implications for fracture flow related to transport rate, dispersion of contaminants, solute transfer between matrix and fluid, and sporadic flow behavior. Transport rate will be enhanced by the higher speed of the solitary waves.
From page 230...
... HYDROLOGIC MODEL The mathematical model has permitted determination of key characteristics of the chaotic film that were used to develop a more simplified hydrologic model for fluid transport. The following simple expressions account for the dual-mode transport by a chaotic film: Qsubstrate ~ 0.06 Qsource Qsoliton 0 94 Qsource Usubstra~e ~ 0.16 UN = 0 Source - 30 hSUbstra~e ~ 0~4 hN 0 4( g :~/3 u fir ~ 2.1 UN = 2.1(Q)
From page 231...
... Film thickness was assumed to be that which "almost" saturates the conduit so as to properly compare it to the plug flow model. Both the plug flow and film flow models predict channeling of flow down the fracture; however, a more subdued behavior is predicted by the plug flow model.
From page 232...
... , plug flow model (light grey) , and parallel plate model (dashed line)
From page 233...
... FLOW PARALLEL PLATES FILM 0 0.1 0.2 0.3 0.4 0.5 FILM THICKNESS (mm) FIGURE 7-10 Flow capacity within a fracture for free-surface film model (solid line)
From page 234...
... Local development of a film could drain fluid from higher in the fracture and generate sudden changes in flow rate. These peaks in transport rate would be short lived if the free surface once again became unstable.
From page 235...
... Wan, 1997. Water film flow along fracture surfaces of porous rock.
From page 236...
... where K is the hydraulic conductivity of the porous matrix; A the cross-sectional area of the seepage face; W the lateral width of the seepage wall; and x the vertical distance over which seepage occurs. Although the source flow rate is determined by the hydraulic conductivity of the porous matrix, once the film starts to flow, the film thickness becomes a dynamic variable and different equations apply.
From page 237...
... Film flow rate per unit width below the active seep area can be found by solving Equation 7.29 for x = L, where L is the length of the seep: Qfilm = hNUN = Matrix (7.30) Figure 7-14 shows the relationship between seep matrix hydraulic conductivity and maximum film velocity for a chaotic film.
From page 238...
... CONCLUDING REMARKS Free-surface films have a greater capacity for transporting fluids via unsaturated fractures than plug flow. They are minimally affected by fracture aperture characteristics and as a result do not suffer the capillary and geometric restrictions imposed on standard fracture flow models.
From page 240...
... Even though the free surface of the film would indicate that pressure in the film is atmospheric, tensiometer measurements in the Bishop Tuff experiment indicate that the free-surface film was subatmospheric. The hopscotch potential of a combined fracture-film transport mechanism suggests that dispersion of contaminants in a fractured vadose system may require a different approach than used in standard unsaturated porous transport.
From page 241...
... Wan, 1997. Water film flow along fracture surfaces of porous rock.


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