## 2 Materials and Methods  
### 3D Heterogeneous Aquifer Models and Simulation Conditions  
A total of 1024 heterogeneous aquifers are constructed geost statistically under spatial uncertainty of permeability and porosity. The spatial distribution of these properties is modeled using Petrel (Schlumberger, Houston, TX, USA). Three dimensional unstructuredgrid systems are generated to demonstrate both the upward CO\({}_{2}\) movement and the horizontal flow. Total number of unstructured grids is 22,230 (= 38 \(\times\) 45 \(\times\) 13). The saline aquifer size is (\(x,y,z\)) = (6310 m, 7076 m, 250 m). It is assumed that the impermeable cap rock is located at 840 m true vertical depth. Dykstra-Parsons coefficients (\(v_{DP}\)) measure permeability heterogeneity between 0 and 1 (Equation (1)). \[v_{DP}=\frac{k_{0.5}-k_{0.841}}{k_{0.5}} \tag{1}\]  
In Equation (1), \(k_{0.5}\) is the mean value and \(k_{0.841}\) is the value placed at one standard deviation plus the mean [43,44]. \(v_{DP}\) = 0 means that the medium is homogeneous. The higher the Dykstra-Parsons coefficient is, the more heterogeneous the medium is. The ratio of vertical to horizontal permeability is 0.1 and the permeabilities are isotropic horizontally (\(x\) and \(y\) directions). Table 1 summarizes the input ranges of the spatial properties for constructing 3D heterogeneous aquifers. The stochastic realizations, i.e., geostatistical property modeling, are carried out with the inputs randomly selected (Table 1). The heterogeneous geo-models are made with massive sandstone intercalated with almost impermeable shale (Figure 1). Shale is placed at the bottom of aquifer and interbedded in sandstone; the former is to prevent leakage at the early time and the latter is to demonstrate the realistic heterogeneous aquifers. The shale volume ratio is defined as the ratio of shale volume to the rock volume and represents the effects of shale layers; this is selected between 2 and 20%. The shale porosities (ranging from 0.1 and 0.15) are smaller than those of sandstone. The shale permeabilities (ranging from 0.05 and 0.5 millidarcy) represent almost impermeable barriers. The standard deviations of shale permeability and porosity are negligible compared to sandstone. The end point of relative permeability at the irreducible water saturation (=0.1) is 0.85, while that at the irreducible CO\({}_{2}\) saturation (=0.2) sets as 0.2. Figure 1 illustrates an example of heterogeneous aquifer models with four injectors (namely, I1, I2, I3 and I4). Figure 1 depicts the spatial distribution of permeability and Figure 1 describes that of porosity. The injection wells are installed to evenly divide the entire aquifer; (\(x,y\)) grid positions are as follows, I1 = (10, 12), I2 = (28, 12), I3 = (10, 34), and I4 = (28, 34). The perforation zone in \(z\) direction is from 1032.3 m to 1051.53 m, the lower part of the aquifer. The wells are partially perforated, over the less permeable basement rock (the shale layer), to demonstrate the upward movement of CO\({}_{2}\) plume. MRST (MATLAB Reservoir Simulation Toolbox) is used to simulate CO\({}_{2}\) sequestration in saline aquifers [44,45]. It provides various trapping volumes: a volume of combined structural and residual trapping, a volume of residual trapping, a volume of residual trapping with plume, a volume of structural trapping, and a volume of movable plume, respectively. CO\({}_{2}\) properties are assessed using CO2 Lab module in MRST [44]. The reference pore-pressure is 120 bar and the temperature is 45 degrees Celsius at the top of the aquifer (840 m depth) where the formation fracture pressure is 150 bar. CO\({}_{2}\) viscosity is set as 0.051 centipoise (1 centipoise = 10\({}^{-3}\) Pa\(\cdot\)s) and its density is 675.324 kg/m\({}^{3}\) at the given reference pressure and temperature. Brine density is 975.86 kg/m\({}^{3}\).