Upscaling matrix diffusion coefficients for heterogeneous fractured rocks

Abstract

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 .