## 4 Results and Discussion
### Simulations of Advective Transport  
Figure 9 shows the particle traces and the associated trace lengths in Case I for three different models. Figure 9a,b show the release locations and the particle traces for the ECPM model. The results for the DFN model are shown in Figure 9e,f, while Figure 9c,d,g,h show the release location and the particle traces for the developed HD model. For comparison purposes, the HD results in Figure 9g,h only show the particles released along the edges of the fractures. In Case I, particles were randomly released on the inlet area, i.e., the specified head on the top boundary. The fracture hydraulic conductivity is four orders of magnitudes higher than the rock matrix. Figure 9a,b show that most particles directly penetrate the F3 and move to the outlet area with relatively small trace lengths in the ECPM model. However, the developed HD model shows that the fast pathway in F3 has significantly controlled the local flow and forced the particles to move along the fracture. No particle trace is shown in the block below the F3 fracture (see Figure 9c,d). All the particles move along the F3 and then follow the flow of the F1 and F2. In the ECPM model, the behavior of particle movement shows that the characteristic of high velocity in F3 is weak because the conductivity values of the F3 are lumped with the rock matrix conductivity in the upscaled  
Figure 7: The steady-state head distributions obtained from the HD, DFN, and ECPM models for Case I: **(a,b)** The solutions for the HD and ECPM models; **(c,d)** The heads obtained from the HD and DFN models for the fractures. cells in the ECPM model. Therefore, the hydraulic conductivity of the cells intersected by F3 might be slightly higher than the rock matrix after the upscaling process. In the ECPM model, the cell sizes intersected by fractures should be smaller than the fracture aperture to resolve the detailed flow behavior. However, it is impractical to consider small cell sizes for large-scale and complex fractured rock systems. Figure 9e,f show the release locations and traces of particles for the DFN model. The boundary condition in the DFN model limited the particles to release on the edges of the intersections between fractures and the domain surface. Note that the particles are restricted to moving in the fractures plates. In Figure 9g,h, the particle traces on the virtual fractures were extracted from the HD model for comparison purposes. There are special trace circulations obtained on the F3, which was recognized as the local flow effect. The local flow effect is a unique feature in the 3D DFN model because of the interplay between fracture geometry and boundary conditions for flow in the fracture plates [47]. The local flow effect has little influence on flow in a 3D DFN but may constitute a mechanism that  
Figure 8: The head distributions obtained from the HD and ECPM models for Case II: **(a,b)** The head solutions on the surfaces of the simulation domain; **(c,d)** The different angle views of heads for the specified profile. contributions to the long breakthrough tails and retardation observed in transport. The results obtained from the developed HD model captured the behavior of the local flow effect. However, the local flow behavior is relatively small as compared with those obtained from the DFN model. Table 2 summarizes the advective transport based on particle tracking applied to different models for Case I. Note that the velocity of each particle could be calculated by the observed trace length and the travel time. In Table 2, the results show that the mean trace length and the standard deviation (STD) and the coefficient of variation (CV) of the HD model are 1.14 times and 2.91 times higher than that of the ECPM model. There is no considerable deviation on the minimum trace length, but the maximum trace length of the HD model is 1.64 times higher than that of the ECPM model.