## 3 Results and Analysis
### Confined Limestone Sample  
This section studies the effectiveness of the plasma stimulation technique in the confined limestone formations. A cubic limestone sample has the dimensions of a 14-inch side length and a 2-inch wellbore diameter was subjected to confining stresses. The sample was placed inside the tri-axial plasma cell and stresses of 360, 405, and 450 psi were applied in the two horizontal directions and the vertical direction, respectively.  
After the relaxation of the sample under stresses, a sequence of pressure pulses was released inside the wellbore and the sample integrity was examined after each pulse release. The first two plasma pulses were generated using 20-inch Al wire of 22 gauge and energies of 9 kJ. These plasma specifications are the same as those of the confined sandstone experiment presented in this study. Checking the confined limestone sample after each pulse showed that the rock was intact, and the pulses did not grow fractures in the limestone. A third plasma reaction was generated inside the sample wellbore using 20-inch Al wire and 10 kJ electrical energy. The current and volt measurements recorded by the oscilloscopes are shown in Figure 17. The time duration of the pressure pulse applied to the simulation model is taken from the volt and current data measurements. In the third pulse, the limestone developed fractures that propagated from the wellbore towards the sample edges. The results are shown in Figure 18. In the figure, three fractures are developed from the wellbore. One of the fractures grew and reached the outer edge of the sample. However, the other two fractures propagated, to a certain extent, almost half the distance from the wellbore to the edge.  
Figure 16: Simulation results of unconfined limestone experiment: fractured model (**left**) and developed fractures (**right**).  
Figure 17: Volt (yellow) and current (green) waveforms of plasma generated in the confined limestone sample.  
The confined limestone experiment was simulated numerically. A cubic model of the same dimensions as those of the rock sample was built. The simulation process was carried out in two stages. In the first stage, the outer boundaries of the created model were subjected to confining stresses (360, 405 and 450 psi in the three directions) and allowed to relax under the confining stresses. The sudden application of the confining stresses to the outer boundaries generated kinetic energy (vibrations) in the rock. During the relaxation stage, the model was brought to the static state (zero kinetic energy) before the fracturing stage [2]. During this relaxation stage, the inner boundary conditions in the wellbore were atmospheric pressure. In the second stage, the pressure pulses were released inside the wellbore while keeping the outer boundaries subjected to confinement. A similar sequence of pressure pulses to the confined sandstone model was applied to the confined limestone model, and the first two pulses were equivalent to 60 MPa pressure peak. The peak pressure was then raised to 65 MPa in the third pulse. The application of the first 60 MPa pressure pulse did not introduce fractures into the model. The second pulse of 60 MPa pressure was introduced and was able to develop minor fractures around the wellbore, as demonstrated in Figure 19. The third pressure pulse of 65 MPa pressure extended these fractures to reach the model outer boundaries, as given in Figure 20.  
Figure 19: The developed fractures (**left**) and the pressure pulse (**right**)—second pulse.  
Figure 18: Confined limestone sample after the third plasma pulse.