## 1. Introduction

[2] Most research on transport in fractured media has focused on crystalline rocks [e.g., *National Research Council*, 1996; *Neuman*, 2005; *Davy et al*., 2006; *Bourbiaux*, 2010]. Those formations are characterized by such small flow velocities in the background matrix that successfully transport calculations focused on the fractures only. The matrix contribution is either completely ignored, and only particles within a discrete fracture network (DFN) are calculated, or the matrix contribution is approximated as a delay/retention mechanism such as matrix diffusion [*Neretnieks*, 1980; *Carrera et al*., 1998]. Matrix diffusion leads to a power law tail of −3/2 in the breakthrough curves, which was often observed in crystalline rocks [e.g., *Hadermann and Heer*, 1996]. However, even for crystalline rocks, different slopes of breakthrough curve tails were observed [*Becker and Shapiro*, 2000], indicating that other effects like advective heterogeneity [e.g., *Zinn et al*., 2004; *Willmann et al*., 2008] control large-scale behavior.

[3] In fractured sedimentary formations the matrix contribution to flow and transport can be much stronger and cannot be ignored or approximated. Here the most common approach is the opposite; the fracture contribution is approximated, while the matrix is modeled. One approach is to map the fracture permeability into the permeability of the background matrix [e.g., *Jackson et al*., 2000; *Lee et al*., 2001; *Svensson*, 2001; *Botros et al*., 2008; *Roubinet et al*., 2010a], conserving the overall flux through the formation. However, as the matrix blocks are much larger than the fractures, the fractures are smeared out to match the matrix geometry. In order to conserve the fracture transport velocities one needs to decrease the porosities in the respective blocks. Those matrix blocks are much larger than the fractures, but the fracture properties dominate its transport behavior and any fracture-matrix exchange is not well represented.

[4] Explicit particle tracking in a hybrid fracture-matrix system where particles move in both discrete fractures and the background matrix is complicated due to the different nature of matrix and fracture flow. Matrix flow is continuous in the entire domain (3-D), while fracture flow only takes place within the discrete fractures (2-D). A problem is that in many particle-tracking approaches the particles do not move continuously but jump from position to position. This leads to two apparent problems: first, particles transported in the matrix may jump across existing fractures instead of being transported within the fracture. Second, it is unclear how a particle, once moved into a fracture, can leave the fracture again. Also, it has to be determined what a deterministic particle does at any fracture intersection where flow is distributed to different paths. Recently, *Roubinet et al*. [2010b] developed a particle-tracking method that allows particles to jump from one fracture to another one depending on the homogeneous matrix diffusion parameters and the fracture proximity. However, advection within the matrix cannot be adequately represented.

[5] Our objective is to develop a particle-tracking method to model hybrid fracture-matrix transport where advection and diffusion within both the fractures and the matrix are accounted for explicitly.