Retardation of sorbing solutes in fractured media

Abstract

Sorption of a reactive solute during transport in a fractured geologic medium is analyzed under the assumption that within each fracture, retardation varies in proportion to the product of a surface distribution coefficient and the specific surface area of the fracture (i.e., its surface area‐to‐volume ratio). This approach is analogous to the KD model commonly adopted for granular porous media. Numerical migration experiments in discrete fracture networks show that at the plume scale, retardation is both nonuniform and anisotropic. Different segments of the plume, or equivalently different breakthrough fractions at a downstream boundary, are retarded to a different degree. The degree to which various breakthrough fractions are retarded varies as a function of the orientation of the mean hydraulic gradient relative to the orientation of the fracture sets. This variation can be described in the form of a retardation ellipse. The mean arrival time is the only breakthrough fraction that is consistently described by a uniform, isotropic retardation factor. The degree of nonuniformity and anisotropy in the retardation factor is controlled largely by the difference in the mean apertures of each fracture set, the standard deviation in fracture aperture, and the orientation of the fracture sets relative to the mean hydraulic gradient. A larger variability in fracture aperture, or in the orientation of fractures within each set, promotes nonuniform retardation while reducing the degree of anisotropy in the retardation factor. Our results suggest that a transport model based on the conventional advection‐dispersion equation, using a uniform retardation factor, may be conceptually incorrect, even for a dense fracture network. While the effects of nonuniform retardation modify the dispersive flux in a way that could be described by “effective” dispersion coefficients, it is our opinion that a model formulation is needed that clearly separates chemical effects from those due to hydrodynamic dispersion.

Simulation and analysis of solute transport in 2D fracture/pipe networks: The SOLFRAC program

“…In this case, mass sharing depends on the configuration of inlet and outlet fluxes at the node. The streamtube model has been used by Robinson and Gale (1990), Wels and Smith (1994), Parney and Smith (1995), among others. The diffusional-mixing model, recently developed by Park and Lee (1999), is an alternative mixing rule between the perfect mixing model and the streamtube model.…”

From conservative to reactive transport under diffusion‐controlled conditions

“…Transit time distributions obtained from conservative tracer testing are often used to predict chemically active transport [e.g., Becker and Shapiro , ; Charbeneau , ; Cirpka and Kitanidis , ; Ginn , ; Hadermann and Heer , ; Haggerty et al ., ; LeBlanc et al ., ; Ptak and Schmid , ]. Conservative transport models are then coupled to simple chemical models to investigate contaminant fate involving kinetically degrading compounds [ Bohlke , ; Green et al ., ; Heße et al ., ], radioactively decaying species [ Cvetkovic et al ., ; Neretnieks , ], or sorbing solutes [ Brusseau , ; Vereecken et al ., ; Wels and Smith , ]. Reactivity can be straightforwardly inferred for linear approximation of reactivity, a case for which transport and chemical operators commute [ Bahr and Rubin , ; Michalak and Kitanidis , ; Valocchi , ], as well as for more involved biogeochemical hysteretic cases through exposure time concepts [ Ginn , ; Murphy and Ginn , ].…”

Quantitative mapping and statistical evaluation of fracture minerals in the granitic bedrock at Forsmark, Sweden

“…These processes are often parameterised by the surface related sorption partitioning coefficient K a (m); the effective diffusivity D e (m 2 /s); the volumetric sorption partitioning coefficient K d (m 3 /kg); and penetration depth L (m), e.g. (Neretnieks 1980;Wels and Smith 1994). There are also attempts to describe retardation by way of cation exchange, surface complexation models, precipitation, co-precipitation, etc.…”