Flow Dimension and Anomalous Diffusion of Aquifer Tests in Fracture Networks

Abstract

Characterization and modeling of aquifers is particularly challenging in fractured media, where flow is concentrated into channels that are poorly suited to traditional approaches to analysis. The generalized radial flow model is an alternative method for hydraulic test interpretation that infers an additional parameter, the flow dimension n, to describe the flow geometry. This study was a Monte Carlo analysis of numerical models of aquifer tests in two‐dimensional fractured media, with the objective of understanding the relationships between the parameters of a discrete fracture network (DFN) with lengths distributed as a power law, the flow dimension, and the regime of hydraulic diffusion (e.g., Fickian or non‐Fickian). The diffusion regime of each realization was evaluated using 〈R2〉 ∼ tk, where t is time, 〈R2〉 is the mean squared radius of hydraulic diffusion, and an apparent value of k = 1 indicates normal (Fickian) diffusion and k < 1 indicates anomalous (non‐Fickian) diffusion. For the DFN model, the apparent flow dimension and exponent k depend on both the density and the power of the fracture length distribution, and thus also on the connectivity regime of the fracture network system. Depending on the connectivity regime, the apparent flow dimension stabilizes to less than the Euclidean dimension and the apparent value of k < 1 indicates that hydraulic diffusion is non‐Fickian. These results suggest that the flow dimension and the exponent k may be useful for characterizing flow and transport in fractured media.

Representation of water abstraction from a karst conduit with numerical discrete-continuum models

“…11a). Additional analysis can be applied for further model evaluation like flow dimension analysis as indicated by, for example, Walker et al (2003), Maréchal et al (2008), and Cello et al (2009).…”

Influence of fracture scale heterogeneity on the flow properties of three‐dimensional discrete fracture networks (DFN)

“…DFNs mimic natural fractured media by representing each fracture individually. They have first been designed toward homogenizing fractured media [ Long et al , 1982], and further applied to understanding the flow structures of complex fracture networks [ Davy et al , 2006a; de Dreuzy et al , 2001b, 2001c, 2002, 2004a; Le Goc et al , 2010; Leung and Zimmerman , 2010], permeability and dispersivity upscaling [ Baghbanan and Jing , 2007; Charlaix et al , 1987; de Dreuzy et al , 2001a, 2010; Frampton and Cvetkovic , 2007, 2009; Mettier et al , 2006; Park et al , 2001; Snow , 1969] and, more generally, the definition of the right modeling approach [ Cello et al , 2009; Davy et al , 2006a; Ji et al , 2011; Jourde et al , 2007; Long and Witherspoon , 1985; Painter and Cvetkovic , 2005; Sahimi , 1993]. As a further interest, DFNs can extract key information on flow properties from the large geological and geophysical data available on fracture media [ Bonnet et al , 2001; Davy et al , 2010].…”

Fractional flow in fractured chalk; a flow and tracer test revisited

“…Several authors have demonstrated that fractal fracture networks give rise to fractional flow (Acuna and Yortsos 1995, Doughty and Karasaki 2002, de Dreuzy and Davy 2007, Cello et al 2009). In non-fractal fracture networks both Euclidean and fractional flow can occur.…”