## 4 Results  
### Block Areas Assuming Persistent Versus Non-Persistent Fractures  
For each of the more than 600 simulations, block areas of the DFN were calculated and statistically evaluated. Generally, the block area analyses show cumulative distributions, which are typically gained when the fracture frequency follows a negative exponential probability distribution. Exemplarily, Figure 4 shows block area distribution simulations based on three different input scenarios. Simulation scenario A is based on a mean angle between the two fracture sets of 85.6\({}^{\circ}\), a frequency and trace length of set #1 of 3.4 m\({}^{-1}\) and 10.0 m, and a frequency and trace length of set #2 of 2.8 m\({}^{-1}\) and 13.5 m, respectively. For simulation scenario B, a mean angle between the two fracture sets of 61.6\({}^{\circ}\), a frequency and trace length of set #1 of 0.9 m\({}^{-1}\) and 5.0 m, and a frequency and trace length of set #2 of 2.9 m\({}^{-1}\) and 7.7 m was implemented. For simulation scenario C, the mean angle between the two fracture sets were further reduced to 27.5\({}^{\circ}\). The frequency and trace length of set #1 was set to 1.1 m\({}^{-1}\) and 2.1 m and of set #2 to 1.0 m\({}^{-1}\) and 7.2 m, respectively. The shape of the cumulative block area distribution curves is similar for non-persistent and persistent fractures, although the slopes of the distribution curves for non-persistent fractures are marginally less steep for all simulations (Figure 4). Depending on the implemented fracture network geometry, the simulated mean block areas based on non-persistent fractures are between 1.1 to 6.2 times larger than the corresponding block areas, which were estimated by Equation (1) and the Monte Carlo approach. In contrast to the suggestions by [12] for the calculation of the total interconnectivity index (\(I_{i}\)), a new factor termed as the geometric mean interconnectivity factor (\(I_{g}\)) was defined, which was averaged from the two interconnectivity indexes \(I_{12}\) and \(I_{21}\). \[I_{g}=\frac{I_{12}+I_{21}}{2} \tag{12}\]  
This modification was done because it allows making correlations with only one interconnectivity factor instead of two. The difference between the simulated mean block areas with non-persistent fractures (\(A_{b}\)) and the mean block areas (\(A_{0}\)), assum  
Figure 4: Selected examples of block area simulations, assuming non-persistent fractures (solid lines) and block area distributions, assuming persistent fractures (Monte Carlo simulation based on Equation (1), dashed lines). ing persistent fractures (see Equation (1)) for a given fracture network, was determined. Figure 5 illustrates a clear correlation between the mean A\({}_{0}\)/A\({}_{b}\) ratio and the geometric mean interconnectivity factor (\(I_{g}\)). Remarkably, the mean A\({}_{0}\)/A\({}_{b}\) ratio does not converge towards 1, even for high values of the interconnectivity factor. Consequently, the simulated block areas (\(A_{b}\)) are larger than those that were obtained by the simplified calculation according to equation (1), even for very long fracture dimensions. All geometric mean interconnectivity factors greater than approximately 20 result in an \(A_{0}\)/\(A_{b}\) ratio of approximately 0.65-0.85, indicating that \(A_{b}\) is 15-35% smaller than A\({}_{0}\) for the analyzed DFN simulations. An empirical relationship based on non-linear curve fitting (Figure 5) was obtained between the mean \(A_{0}\)/\(A_{b}\) ratio and the geometric mean interconnectivity factor (\(I_{g}\)). Curve fitting according to a power law showed the best fit to the data set, resulting to the empirical Equation (13):  
\[\frac{A_{0}}{A_{b}}=a\cdot I_{g}^{b}+c \tag{13}\]  
For this simulation, empirical fitting parameters of \(a=-0.9001\), \(b=-0.8012\), and \(c=0.8283\), as well as a coefficient of determination of \(R^{2}=0.9902\) are determined.