Upscaling matrix diffusion coefficients for heterogeneous fractured rocks

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.