Effective dispersivities for a two-dimensional periodic fracture network by a continuous time random walk analysis of single-intersection simulations

Fracture networks are of major importance for transport problems in hydrolo gy. Their inclusion in models requires assumptions about both the single fr acture and the network structure. This paper focuses on the macroscopic eff ect of microscopic mixing conditions in intersections within a periodic fra cture network. Mixing is characterized by the transition probabilities for particles to move from one fracture to another or to stay in the same fract ure. A periodic network is used, which excludes stochastic effects and also single-fracture dispersion. The periodic network can be solved analyticall y and is applicable to a variety of network, structures. We find that for t his type of network, effective dispersivities in the sense of asymptotic va lues for long times and large scales do usually exist (i.e., the asymptotic dispersion is Gaussian). For the particular case of a quadratic network, p article transition probabilities at an intersection have been obtained by m icroscopic lattice Boltzmann simulations of flow and transport in addition to the assumptions of complete mixing and stream routing. The resulting dis persivities show that complete mixing is not a low Peclet number limit in t he presence of regions of immobile water volumes. Dispersivities depend str ongly on the direction between flow and network and on the mixing model; di spersivities are large for high Peclet numbers and flow parallel to the net work. Especially for these cases, we also find a scale dependence up to som e orders of magnitude, which has serious implications for the interpretatio n of simulations and measurements. Since these results also appear in stoch astic network simulations, they are therefore not specific to the periodic structure of the fracture network.