Direct numerical simulation of matrix diffusion across fracture/matrix interface

Accurate descriptions of matrix diffusion across the fracture/matrix interface are critical to assessing contaminant migration in fractured media. The classical transfer probability method is only applicable for relatively large diffusion coefficients and small fracture spacings, due to an intrinsic assumption of an equilibrium concentration profile in the matrix blocks. Motivated and required by practical applications, we propose a direct numerical simulation (DNS) approach without any empirical assumptions. A three-step Lagrangian algorithm was developed and validated to directly track the particle dynamics across the fracture/matrix interface, where particle's diffusive displacement across the discontinuity is controlled by an analytical, one-side reflection probability. Numerical experiments show that the DNS approach is especially efficient for small diffusion coefficients and large fracture spacings, alleviating limitations of the classical modeling approach.