## 2 Liquid CO\({}_{2}\) Phase-Transition Rock Fracturing
### Principle of the CO\({}_{2}\) Phase-Transition Fracturing  
The core of CO\({}_{2}\) phase-transition fracturing technology is the liquid-gas conversion of CO\({}_{2}\). It is essentially a typical physical blasting technology. During the fracturing operations, liquid CO\({}_{2}\) is injected into the tube using special filling equipment, and the gas pressure is maintained at between 8 and 10 MPa. The heater has been made to generate large amounts of heat, and the liquid CO\({}_{2}\) in the tubes enters a supercritical state. Supercritical CO\({}_{2}\) is a special phase state. Its molecular diffusion coefficient is large and close to a gas and has a high density, which is close to the fluid density. When the pressure is higher than 7.38 MPa, and the temperature is higher than 31.4 \({}^{\circ}\)C, the CO\({}_{2}\) will be transformed into a supercritical state [24]. The phase transition process of the CO\({}_{2}\) is shown in Figure 2. At that time, the pressure levels in the pipes will rise sharply. When the pressure reaches the ultimate strength of the constant pressure shear sheets, the SC-CO\({}_{2}\) will break through the constant pressure shear sheets and be released from the energy releasers (Figure 3). High-pressure jets act on the rock masses and generate stress waves with energy levels far greater than the dynamic compressive strength of the rock mass. As a result, crushed areas of compressive damages will be produced around the boreholes, and the rock mass in the far areas will produce radial fracturing and tangential tension cracks. At the same time, the pressure will gradually decrease, and the outer boundaries of SC-CO\({}_{2}\) jets will become gasified. The volume will rapidly expand by 500 to 600 times. Then, under the effects of the gas wedges, the cracks will continue to expand until the stress intensity factors at the crack tips become less than the fracture toughness of the rock. During the entire fracturing process, the stress wave action times will be very short. Meanwhile, the gas CO\({}_{2}\) action times will be longer and reach up to 10 to 30 ms, which will result in the cracks becoming fully expanded, extended, and penetrated within the rock masses [14; 16; 25; 26].  
Figure 1: (1) Riser; (2) firing head; (3) heater; (4) fracturing tube; (5) constant pressure shear sheet; (6) energy releaser. The structure of CO\({}_{2}\) blasting device [13; 1; 23]. (a) Photograph of CO\({}_{2}\)-Frac. (b) Sketch of CO\({}_{2}\)-Frac system.  
Generally speaking, the entire liquid CO\({}_{2}\) phase-transition fracturing process mainly includes two stages: the dynamic actions of the stress waves, and the quasi-static actions of the gas expansion. The stress wave actions mainly form the micro-cracks in the crushed zone, and the gas expansion actions are the main driving forces for the radial and circumferential cracks in the fracture zones. The results of this study's experiments are shown in Figure 4. It is not difficult to conclude from the figure that the CO\({}_{2}\) rock-breaking processes were a combination of tensile failures and compressive failures.  
Figure 3: Working principal diagram of liquid CO\({}_{2}\) phase-transition rock fracturing: (1) riser; (2) heater; (3) CO\({}_{2}\)-Frac; (4) constant pressure shear sheet; (5) energy release; (6) gaseous CO\({}_{2}\).  
Figure 2: Phase transformation diagram of CO\({}_{2}\).