The Active Fracture Model: Its Relation to Fractal Flow Patterns and an Evaluation Using Field Observations

Abstract

The active fracture model (AFM) (Liu et al., 1998) has been widely used in modeling flow and transport in the unsaturated zone of Yucca Mountain, Nevada, a proposed repository of high‐level nuclear wastes. This study presents an in‐depth evaluation of the AFM, based on both theoretical arguments and field observations. We first argue that flow patterns observed from different unsaturated systems (including the unsaturated zone of Yucca Mountain) may be fractals. We derive an interesting relation between the AFM and the fractal flow behavior, indicating that the AFM essentially captures this important flow behavior at a subgrid scale. Finally, the validity of the AFM is demonstrated by the favorable comparison between simulation results based on the AFM and 14C age and fracture coating data collected from the unsaturated zone at Yucca Mountain. These data sets independently provide important insight into flow and transport processes at the Yucca Mountain site. Potential future improvements of the AFM include expanding it to consider film flow and multifractal concepts.

A Conductivity Relationship for Steady‐State Unsaturated Flow Processes under Optimal Flow Conditions

“…The ARM is an extension of the active fracture model developed for modeling unsaturated water in fractured rock (Liu et al, 1998). Both the active fracture model and the ARM have been evaluated with a variety of experimental data and remarkable agreements between the models and the data have been observed (Liu et al, 1998, 2003, 2005; Sheng et al, 2009); however, the ARM has been tested only for soils that are relatively homogeneous (e.g., Sheng et al, 2009). The ARM assumes a flow domain to be divided into an active region (fingering flow zone) and an inactive region.…”

“…Because of fingering flow, water propagates quickly to significant depths while bypassing large portions of the vadose zone, and solute travel times from a contamination source (located on the soil surface or in the vadose zone) to the groundwater are shorter than a priori expected. As a result of the important effects of this flow process on groundwater contamination (an important issue for water resources management), preferential flow has been a major research area in the vadose zone hydrology community for a number of years and considered probably the most frustrating processes in terms of hampering accurate predictions of contaminant transport in the vadose zone (e.g., Glass et al, 1988; Flury and Flühler, 1995; Liu et al, 2003; Šimůnek et al, 2003; Nimmo, 2010).…”

Modeling Unsaturated–Saturated Flow and Nickel Transport in Fractured Rocks

“…The water relative permeability coefficient k r (ψ) in Eq. [1] is defined as Some researchers (Liu et al, 2003; Seol et al, 2006) have advocated that the water saturation must be replaced by the “effective” water saturation in the retention curves of a fractured outcrop in order to consider the effective “active” fractures during water infiltration. Furthermore, it should be noted that the field saturated permeability of the outcrop, k fs [L 2 ], is related to the saturated permeability of the fracture, , and consequently to the mean fracture aperture, by means of both the permeability of the rock matrix, k m [L 2 ], and the mean spacing between fractures, s [L], at the outcrop (see Fig.…”

The Impact of Fracture–Matrix Interaction on Thermal–Hydrological Conditions in Heated Fractured Rock

“…We evaluated additional sensitivity cases using a range of interface reduction formulations as listed in Table 2 These include constant‐factor reductions using values of 0.1, 0.01, and 0.002, as well as cases where the interface reduction was calculated from the active fracture model. The γ values used, 0.3 and 0.569, are based on calibration to Yucca Mountain field measurements (Liu et al, 2003; Bechtel SAIC Company, 2004b). The resulting interface reduction factors of all cases are plotted as a function of saturation in Fig.…”

“…The improved approaches adjust the interface area between fractures and matrix, depending on the flow characteristics in the fractures. The adjusted interface area represents the fraction of the full geometric interface that actively participates in fluid and solute exchange (e.g., Ho, 1997; Doughty, 1999; Liu et al, 1998, 2003). Different approximate formulations were proposed for fracture–matrix interface reduction, including, for example, multiplication with a constant factor, with a power function of fracture liquid saturation, or with fracture relative permeability, summarized in Doughty (1999), as well as multiplication with a factor derived from the active fracture model developed by Liu et al (1998)…”