## 3 Results and Analysis
### Sandstone Sample 2  
A sandstone sample was used to study plasma fracturing under confining stresses. The dimensions of the rock sample are the same as the unconfined case, which are 14-inches for the cube side length, 2-inches for the wellbore diameter, and 10-inches for the wellbore height. The vertical confining stress is 3 MPa, and the horizontal stress values are 2.7 MPa and 2.4 MPa. The wire used between the electrodes is Al of 22 gauge.  
Four plasma pulses were released inside the sample wellbore. The results showed that the confined sandstone sample was intact after the first three pressure pulses. The first  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Value** & **Unit** \\ \hline Poisson’s ratio & 0.24 & \\ Young’s modulus & 12.1 & GPa \\ Friction angle & 41.5 & Degrees \\ Tensile strength & 2.5 & MPa \\ Shear strength & 1.25 & MPa \\ Density & 2600 & kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical properties of sandstone for simulation.  
Figure 8: Fracture development by applying second pulse: fracture element (**left**) and fracture sample (**right**).  
Figure 7: Fracture development by applying first pulse: fracture element (**left**) and fracture sample (**right**).  
two pulses used 9 kJ electrical energy and a 20-inch wire length. In the third pulse, the energy increased to 10 kJ and the wire length was 20-inches-long. The energy released for the fourth pulse was 10 kJ and the wire length was 25-inches. The fourth pressure pulse was able to develop minor fractures in the rock as given in Figure 9.  
A numerical model was created to simulate the confined sandstone experiment. The sandstone properties listed in Table 1 are used in the numerical simulation. Since the energy and the wire length used in the confined sandstone experiment are higher than those of the unconfined case, a higher pressure pulse is used. The peak values of the four pressure pulses applied to the confined case are 60, 60, 65, and 70 MPa in order. The pressure pulse profiles are given in Figure 10.  
The four pressure profiles are applied in succession to the model wellbore. The numerical model was intact after the application of the first pressure pulse. However, the sample experienced fractures in the following three pulses. The results from the last three pulses are given in Figures 11-13. The fractures developed in the second and third pulses  
Figure 10: Pressure pulses of the confined sandstone sample. The peak pressure is 60 MPa in the first two pulses, 65 MPa in the third pulse, and 70 MPa in the fourth pulse.  
Figure 9: Confined sandstone sample.  
The experimental limestone fracturing process was simulated using HOSS(r). The material properties of limestone were taken as given in Table 2. A 14-inch cubic model with a circular wellbore that is 2-inches in diameter and 10-inch height was created. In Figure 15, a pressure profile of 50 MPa peak pressure was used to mimic the pulse generated by the 6 kJ and 5-inch wire. The pressure pulse was applied inside the model wellbore, while the outer sides were kept unconfined (free to move during the application of pressure pulse). The pressure pulse application resulted in the fractures shown in Figure 16. The figure shows that multiple fractures developed to match the experimental results given in Figure 14.