## 2 Preparation for the Numerical Analysis
### Construction of the Numerical Model  
A numerical study was conducted to evaluate the effect of enhanced buffer materials on the arrangement of disposal tunnels and deposition holes. This study employed COMSOL Multiphysics 5.5 [PERSON] (2013), which is a commercial program based on the theory of continuum mechanics and FEM, to investigate the thermal behavior of a deep geological system. The program has a built-in module for solving the heat transfer mechanisms, which occur during the operation of the disposal system. In thermal analysis, heat conduction in the entire disposal system component was considered while implementing the heat transfer module in COMSOL Multiphysics. The governing equation for the module is expressed as follows [PERSON] et al. (2013):  
\[-\lambda_{i}\cdot(\frac{\partial^{2}T}{\partial x^{2}}+\frac{\partial^{2}T}{ \partial y^{2}}+\frac{\partial^{2}T}{\partial z^{2}})+\rho_{i}\cdot c_{i}\cdot \frac{\partial T}{\partial t}+q_{i}=0\ \ (i=x,y,z) \tag{2}\]where \(T\) is the temperature of the porous medium as a dependent variable, \(\lambda\) is the thermal conductivity of the medium, \(\rho\) is the density, \(c\) is the specific heat capacity, and \(q_{i}\) denotes the internal heat generation. The numerical model was established based on the design concept of the improved Korean Reference Disposal System (KRS\({}^{+}\)) proposed to dispose of the PWR spent nuclear fuel generated in Korea. This is also called the Regular-Spent Nuclear Fuel (R-SNF) disposal system, which has a 40 m distance between the disposal tunnels and a distance of 7.5 m between the deposition holes to satisfy the upper temperature limit of 100 \({}^{\circ}\)C at the buffer surface facing a canister [25]. A 3D finite element model, including the components of the disposal system (backfill, buffer, canister, and rock), was constructed assuming that the disposal system was located at a depth of 500 m. Figure 3 shows the geometry and domain size of the numerical model, and Table 1 presents the input data for the properties of each component of the system. The concept of a DEM described in Section 2.1 was used to validate the input data for the buffer. Figure 3: Geometry of 3D finite element model and generated mesh. Figure 2: Discrete element method (DEM) modelling for bentonite and graphite mixed particles with bulk dry density of 1.67 g/cm\({}^{3}\). In the R-SNF disposal system, the used fuel is stored in a canister after a temporary storage period of 45 years in a temporary storage tank [25]. The decay heat from the spent nuclear fuel is used as the heat source for the canister in the simulation. The heat output from a canister of the Korean reference used fuels can be calculated using the following equation [25,26]:  
\[\mathrm{Y=y0+A1\times exp\left(-\frac{t\times x0}{t1}\right)+A2\times exp\left( -\frac{t-x0}{t2}\right)+A3\times exp\left(-\frac{t-x0}{t3}\right)} \tag{3}\]  
where Y is the decay heat (W) varying with the elapsed time from the reactor per unit weight (1 tU) of the reference PWR used fuels, and \(t\) is the time released from the reactor. Other coefficients, including x0, y0, A1, A2, A3, t1, t2, and t3, are constants, and their values are listed in Table 2.  
A symmetry condition was chosen for the side surfaces as the boundary condition for the model. For the entire domain, a thermal gradient of 3 \({}^{\circ}\)C/100 m and a ground surface temperature of 10 \({}^{\circ}\)C were applied to the initial conditions to consider the temperature variations with respect to the underground depth. To consider the accuracy and efficiency of the analysis simultaneously, a fine mesh was formed in the canister and buffer near the heat source. The host rock far from the heat source was formed coarsely using a built-in function in COMSOL. Free tetrahedral-type 101,831 elements were formed with 10 nodes. The average mesh element quality, defined as the ratio of the element width and height, was 0.6403 for better convergence of the numerical analysis (Figure 3).