Water Resources Research

A new stochastic particle-tracking approach for fractured sedimentary formations


Corresponding author: M. Willmann, Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Str. 15, CH-8093 Zurich, Switzerland. (willmann@ifu.baug.ethz.ch)


[1] Explicit particle-tracking simulations in both fractures and surrounding sediments are conceptually complex and difficult to implement. This is mainly due to the difference in the nature of the velocity fields in fractures and the matrix. The major problems are (1) to avoid particles in the matrix jumping over fractures and (2) to control particle behavior at the interfaces between fractures and the matrix. We developed a particle-tracking method that models advection and diffusion explicitly in both fractures and the matrix. Analogously to most flow simulations, we conceptualize transport by two separate domains, the fracture and the matrix domains, which exchange particles between them. No a priori assumptions on transport mechanisms in the matrix have to be made. Each individual particle step stops at an interface between two matrix cells, between two fracture cells, or between the matrix and a fracture. Mass exchange at the interface from fractures to the matrix is controlled by the fracture aperture, the matrix flux perpendicular to the fracture plane, the flux within the fracture, and a diffusive component. The method is developed for fractured sedimentary rocks where the advective fluxes in the matrix can be as large as the fracture fluxes. However, it could also be applied to fractured crystalline rocks where the matrix contribution is smaller. Finally, some simple applications to a fractured shale formation in northern Switzerland are included to illustrate the usefulness of this method to investigate transport in fractured sedimentary formations.