## 3 Results and Analysis
### Natural Fractured Rock Simulation  
The numerical rock model developed here is used to simulate naturally fractured rock. The 2-D square model dimensions are 2 m side length and 10 cm wellbore diameter. The natural fractures in the rock are simulated as material inclusions of different properties from the rock matrix. Three fractures are introduced into the rock model and each natural fracture has a length of 1 m and a width of 1 mm, as given in Figure 21. The matrix properties along with the properties of natural fractures are listed in Table 3.  
A pressure profile of 100 MPa peak is applied to the model wellbore to simulate plasma stimulation pulse. The pressure increases exponentially to reach its peak and then decreases exponentially to one atmospheric pressure, as in Figure 22. The sample outer sides are subjected to free boundary conditions. The application of the pressure profile results in the fractures shown in Figure 23. A threshold is used to develop the results graphs after the  
Figure 21: Squared rock model with three natural fractures. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Matrix Value** & **Natural Fracture Value** & **Unit** \\ \hline Density & 2700 & 2500 & kg/m\({}^{3}\) \\ Young’s modulus & 30 & 10 & GPa \\ Poisson’s ratio & 0.27 & 0.35 & \\ Friction factor & 0.6 & 0.5 & \\ Shear strength & 10 & 2.5 & MPa \\ Tensile strength & 2 & 0.5 & MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties of matrix and natural fractures. Figure 20: The developed fractures (**left**) and the pressure pulse (**right**)—third pulse. fracturing process. The threshold used here is of a value of 0.5. The fractures developed in the rock can be scaled from 0 to 1. The zero value means that no fractures are propagated, and the rock is intact. However, the value of one means that the rock is fractured, and the fracture is completely open (the finite elements are fully separated). In Figure 23, the first graph to the left shows the sample after fracturing, where all fractures are depicted. In the middle, the major fractures of a width greater than the 0.5 threshold are illustrated. However, the minor fractures that represent improvements in permeability are shown in the figure to the right. The threshold is a value used in result visualization, where the width of the developed fractures is normalized between zero and one. Zero means that the rock is intact and one is for a fully open fracture. The results in Figure 23 show that the plasma stimulation pulse affects the whole model. Major fractures (shown in the middle graph) propagate from the wellbore and reach the model's outer boundaries. One also can observe that the natural fractures arrest the plasma-developed fractures. However, new plasma fractures grow from the tips of the natural fractures. Moreover, the plasma stimulation method develops minor fractures in the rest of the rock model as shown in the graph to the right. These minor fractures are interpreted as enhancement in the rock permeability. The improvement in permeability obtained by plasma stimulation is verified experimentally by [PERSON] et al. [3]. The main fractures (wider than a specific threshold) are given in Figure 24 for different thresholds, where 0.5, 0.7, 0.9, and 1 are shown. The threshold of one shows the fractures that are completely opened, where the elements are completely separated. In the results, on the one hand, one can observe that the pulse fractures propagate from the wellbore toward the boundaries. The presence of the natural fractures restricts the fracture growth to the boundaries, where the natural fractures arrest the pulsed fractures. However, on the  
Figure 23: Fractures developed in naturally fractured rock: all fractures (**left**), major fractures (**middle**), and minor fractures (**right**). Fractures are green (major) and greenish blue (minor), intact rock is in light blue, and natural fractures are in red. Figure 22: Pressure pulse used for the natural fractured rock.