Upscaling matrix diffusion coefficients for heterogeneous fractured rocks

Mathematics – Logic

Scientific paper

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Hydrology: Groundwater Hydrology, Hydrology: Groundwater Transport, Hydrology: Hydrologic Scaling, Physical Properties Of Rocks: Transport Properties

Scientific paper

The scale dependence of the matrix diffusion coefficient (D m ) for fractured media has been observed at variable scales from column experiments to field tracer tests. In this paper, we derive an effective D m for multimodal heterogeneous fractured rocks using characteristic distributions of matrix properties and volume averaging of the mass transfer coefficient. The effective field-scale D m is dependent on the statistics (geometric mean, variance, and integral scale) of laboratory-scale ln(D m ) and on the domain size. The effective D m increases with the integral scales and is larger than the geometric mean of ln(D m ). Monte Carlo simulations with 1000 realizations of heterogeneous D m fields were conducted to assess the accuracy of the derived effective D m .

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