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Effective matrix diffusion in kilometer‐scale transport in fractured crystalline rock

Allen M. Shapiro
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Abstract

Concentrations of tritium ( 3 H) and dichlorodifluoromethane (CFC‐12) in water samples taken from glacial drift and fractured crystalline rock over 4 km 2 in central New Hampshire are interpreted to identify a conceptual model of matrix diffusion and the magnitude of the diffusion coefficient. Dispersion and mass transfer to and from fractures has affected the 3 H concentration to the extent that the peak 3 H concentration of the 1960s is no longer distinguishable. Because of heterogeneity in the bedrock the sparsely distributed chemical data do not warrant a three‐dimensional transport model. Instead, a one‐dimensional model of CFC‐12 and 3 H migration along flow lines in the glacial drift and bedrock is used to place bounds on the processes affecting kilometer‐scale transport, arid model parameters are varied to reproduce the measured relation between 3 H and CFC‐12, rather than their spatial distributions. A model of mass exchange to and from fractures that is dependent on the time‐varying concentration gradient at fracture surfaces qualitatively reproduces the measured relation between 3 H and CFC‐12 with an upper bound for the fracture dispersivity approximately equal to 250 m and a lower bound for the effective matrix diffusion coefficient equal to 1 m 2 yr −1 . The diffusion coefficient at the kilometer scale is at least 3 orders of magnitude greater than laboratory estimates of diffusion in crystalline rock. The large diffusion coefficient indicates that diffusion into an immobile fluid phase (rock matrix) is masked at the kilometer scale by advective mass exchange between fractures with large contrasts in trarismissivity. The measured transmissivity of fractures in the study area varies over more than 6 orders of magnitude. Advective mass exchange from high‐permeability fractures to low‐permeability fractures results in short migration distances of a chemical constituent in low‐permeability fractures over an extended period of time before reentering high‐permeability fractures; viewed at the kilometer scale, this process is analogous to the chemical constituent diffusing into and out of an immobile fluid phase.

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Allen M. Shapiro. 2001. Effective matrix diffusion in kilometer‐scale transport in fractured crystalline rock. https://doi.org/10.1029/2000wr900301

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