## Numerical Examples
### The Conceptual Models of the Test Cases
The domain size is \(8~{}\mathrm{m}~{}\times~{}8~{}\mathrm{m}~{}\times~{}16~{}\mathrm{m}\) in x-, y- and z-directions, and the cylinder DH has 8 m in height and 1.75 m in diameter. There are three fracture plates in the simulation domain, i.e., F4 to F6. The sizes for F4 and F5 are 6 m \(\times\) 6 m and the area for the F6 is 5 m \(\times\) 14 m. The apertures for the fractures are 0.1 m. Two intersected fractures cut the DH, i.e., F4 and F5 (see Figure 4b). In this case, the specified hydraulic stress is the same as that in Case I (i.e., the hydraulic head of \(\mathrm{H_{in}}\) = 4 m and \(\mathrm{H_{out}}\) = 1 m are assigned on the inlet and outlet areas, respectively). Note that three fractures have no contact with any domain boundaries, which means that the specified boundary conditions on the inlet and outlet areas need to be on the cell faces. Therefore, the DFN model was excluded in Case II because of the special setting of the conceptual model. The condition has shown the limited features of the DFN models that focus on the fractures only. Table 1 also lists the hydraulic properties and the convergence criteria for the simulation cases. In Case II, the DH hydraulic conductivity is the same as that in the rock matrix. For most practical problems, the hydraulic conductivity of DH should be lower than 1.0 \(\times\) 10\({}^{-12}\) m/s to avoid a high corrosion rate and a possible release of radionuclides. The DH hydraulic conductivity value of 1.0 \(\times\) 10\({}^{-10}\) m/s in this study could be a worse scenario for the DH design. The concept was proposed by studies of the case in Sweden [45]. In this case, we had made the ECPM model capture the flow and transport influenced by the fracture geometries. Therefore, the fracture aperture was assumed as 0.1 m to reduce the total computational grid in the ECPM model. Based on the safety assessment report proposed by Sweden and Finland, i.e., the well-experienced countries that provide the general disposal concept for spent nuclear fuel, there are three potential pathways for releasing radionuclides if the canister in the DH is destroyed by corrosion or shear movement [6; 46]. One of the potential and high probability pathways is the Q1 path, which is a concept for radionuclides released through the intersection point between a fracture and a DH. The intersection point usually has the highest velocity, one of the key input parameters for the corrosion calculation. Typical approaches consider the intersection points to release particles for evaluating the Q1 pathways. These released particles are in the highest velocity grid centers or nodes at the intersections to assess the possible pathways. In Case II, the particle release followed the concept of the Q1 path. In this study, the HD model could search for the highest velocity near the intersections between DH and fractures and release a particle to track the particle movement. It is interesting to obtain the intersection position, the highest velocity, and the overall transport behavior in different models. In addition, there were 48 particles released along the intersections between fractures and the DH to assess the variations of the particle movements in the case.