Upscaling matrix diffusion coefficients for heterogeneous fractured rocks

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

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