## 2 Methodology  
The experimental work conducted for this study was carried out using a plasma apparatus that is composed of several components. As in Figure 1, these components include two capacitors (each can store electrical energy of 10 kJ), a stainless steel cell to host the rock sample (the cell was manufactured to adapt a cubic rock model of 14 inches in size and to apply tri-axial stresses (using hydraulic pumps) to the sample in the cartesian coordinates), two oscilloscopes for recording pressure, volt and current measurements, and two electrodes that can be connected with a thin electrically conductive wire and immersed in water-filled wellbore for plasma generation. The plasma equipment is connected to a computer for monitoring the experiment and recording the data. The capacitors are connected with the electrodes that are immersed in the water-filled sample wellbore. The hydraulic pumps are connected with the cell, where the sample is accommodated for stress application. The oscilloscopes are wire-connected with the capacitors (for volt and current measurements) and the sample wellbore (for pressure measurements), and wireless-connected with a computer for data display. The rock sample is fractured by pressure pulses generated with the plasma stimulation apparatus. A pressure pulse is generated when an electrical energy flows through a thin and high-resistivity wire (connects the two electrodes) immersed in a water-filled wellbore. This results in a plasma reaction that develops the pressure pulse. The technique relies on a release of the electrical energy stored in the capacitors through a thin conductive wire that connects the two electrodes. The two electrodes are immersed inside a conductive electrolyte (water) filling the sample wellbore. The sudden release of the electrical current allows the wire to burn, and plasma reaction occurs and develops a pressure pulse that propagates fractures in the rock sample. For the simulation work carried out in this study, the hybrid multi-physics software package HOSS(r) (Hybrid Optimization Software Suite [[https://www.lanl.gov/orgs/ees/hoss/index.shtml](https://www.lanl.gov/orgs/ees/hoss/index.shtml)]([https://www.lanl.gov/orgs/ees/hoss/index.shtml](https://www.lanl.gov/orgs/ees/hoss/index.shtml)) accessed on 1 January 2024) is used to perform the calculations. The model is assumed to be non-porous and does not account for fluid flow. The assumptions are reasonable as the plasma stimulation technique develops fractures within a microsecond timescale that does not give a chance for the fluid to affect the fractures development. The package is developed to model high-strain-rate cases, such as fractures developed by plasma pressure pulse inside wellbore of rock sample. HOSS(r) uses the finite-discrete element method that combines the finite element method and discrete element method and assumes a continuous rock body. The fractures developed in the rock model propagate when the failure model is met. The general equation controls the system is solved in the finite-discrete element method and follows the conservation of mass and momentum in a solid-mechanics way and is presented as [26; 27]  
\[M\ddot{x}+C\dot{x}=f \tag{1}\]  
where \(M\) is lumped mass matrix, \(C\) is damping matrix, \(x\) is displacement vector, and \(f\) is equivalent force vector acting on each node. The integration of Equation (1) with respect to time gives the transient changes of the model over time. The element interfaces of the finite elements used as a numerical method for solving the system-governing equations are connected by non-linear springs. However, the finite  
Figure 1: Plasma stimulation equipment: (**A**) two capacitors, (**B**) stainless-steel cell, (**C**) electrodes connected with 22-gauge Al wire, (**D**) hydraulic pumps, and (**E**) oscilloscopes. elements that construct the rock model can be deformed in the form of translation, rotation, and stretch.