## 1. Introduction

[2] The efficiency of a rock formation as a transport barrier depends not only on the fluid flow in the rock but also on the degree to which contaminants are retained in the rock due to a variety of physical and chemical processes. Open fissures or fractures in the rock provide pathways through which water and tracers may travel. Although most tracers of interest such as radionuclides have a strong tendency to sorb to mineral grains in the rock, tracers first have to diffuse from fractures into the rock matrix in order to access the extensive pool of sorption sites [*Neretnieks*, 1980]. Diffusion in turn depends not only on mass transfer properties of the rock matrix, but also on the structural and hydrodynamic properties of the fracture system, emphasizing the interaction between water flow, advective transport and retention processes.

[3] Flow and transport through individual fractures, as well as fracture networks, has been studied extensively over the past years both experimentally and using simulations. Studies of transport through discrete fracture networks have often been limited to nonreactive particle transport [*Smith and Schwartz*, 1984; *Shapiro and Andersson*, 1985; *Andersson and Dverstorp*, 1987; *Cacas et al.*, 1990; *Nordqvist et al.*, 1992; *Berkowitz and Scher*, 1997; *Margolin et al.*, 1998]. Although understanding nonreactive transport is a prerequisite for quantifying reactive transport in fracture networks, retention of tracers adds further challenges for modeling which have received comparatively little attention in the literature.

[4] Models of retention in fracture networks are derived from models of retention in single fractures. The most basic result was obtained by *Carslaw and Jaeger* [1959] for heat diffusion into semi-infinite domains. Their solution was adopted by *Neretnieks* [1980] for crystalline fractures assuming plug flow. *Tang et al.* [1981] generalized the model of *Neretnieks* [1980] for single fractures by including dispersion. *Maloszewski and Zuber* [1990] extended the model of *Neretnieks* [1980] by including kinetic sorption in the matrix and postulating the applicability of the single fracture model to a network of fractures where effective aperture is implied. The approach of *Maloszewski and Zuber* [1990] was adopted by *Shapiro* [2001] for interpreting environmental tracer data, where instead of aperture, fracture density and flow porosity were used as effective parameters.

[5] Transport with retention in a discrete fracture network was investigated by *Sudicky and McLaren* [1992] in a deterministic framework. A first attempt to account for randomness of discrete fracture networks in retention modeling was made by *Moreno and Neretnieks* [1993] using a channel (or pipe) network model, where fluid flow was resolved on the basis of mass balance, i.e., without resolving three-dimensional flow dynamics. *Cvetkovic et al.* [1999] were the first to account for effects of flow dynamics on tracer retention in single heterogeneous fractures, introducing a random (Lagrangian) variable β [T/L]. Analytical results on the β statistics for fracture networks were provided by *Painter et al.* [1998] and *Painter and Cvetkovic* [2001] by extending the channel concept of *Neretnieks* [1980]. Results on the statistics of β in fracture networks where flow dynamics is resolved, were presented by *Painter et al.* [2002] using generic DFN simulations. Site-specific DFN simulations on a 1000 m scale were presented recently [*Outters and Shuttle*, 2000; *Cvetkovic et al.*, 2002], where the flow field was simplified as a branching pipe network [*Dershowitz et al.*, 1998].

[6] In this paper, we present a systematic study of radionuclide transport and retention in a discrete fracture network where flow dynamics is honored and randomness of fracture properties is accounted for. Transport is studied in a generic rock volume that is a statistical replica of one of the most thoroughly characterized crystalline rock domains to date, on approximately 100m scale at the Äspö Hard Rock Laboratory in southern Sweden [*Forsmark and Rhen*, 2001]. The dual-porosity modeling concept is implemented using the stochastic framework of *Cvetkovic et al.* [1999], here extended to fracture networks. The emphasis is on the hydrodynamic control of retention by means of two random (Lagrangian) variables, τ [T] and β [T/L]. We first summarize the conceptual framework and present relatively simple transport measures for randomly fractured porous media which take advantage of analytical solutions. The proposed measures couple hydrodynamics of fracture flow with microscopic retention processes while explicitly accounting for prediction uncertainty associated with large scale (and unobservable) fluctuations in groundwater velocity. We assess the significance of different modeling concepts for discrete fracture networks, in particular, the impact of different intersection rules (full mixing and streamline routing), and different hydraulic laws (the relationships between fracture transmissivity and aperture).