## 1 Introduction
Also, to further reveal the rock erosion law using the SC-CO\({}_{2}\) jet and establish a theoretical basis for better application of the SC-CO\({}_{2}\) jet in drilling engineering, a large number of rock erosion experiments was conducted by [PERSON] et al. [12]. They found that with the increasing ambient pressure, the rock erosion efficiency of the SC-CO\({}_{2}\) jet can reach the maximum when the ambient pressure is around the critical pressure under constant pressure difference, and the rotary speed of the core sample has no substantial influence on the erosion depth, but has an effect on the average width of eroded grooves. Besides, for the sake of better applying the SC-CO\({}_{2}\) jet in shale gas drilling, the microscopic changes between the original shale samples and the samples eroded by the SC-CO\({}_{2}\) jet were studied by [PERSON] et al. [20]. They found that the surface of the shale sample impacted by the SC-CO\({}_{2}\) jet exhibits a grid-like failure. The sample is broken into layers of large volume overall as a whole. Also, the mechanical strength of the shale sample is reduced by the erosion of shale mineral induced by SC-CO\({}_{2}\). Moreover, to clarify the rock failure mechanism and change of pore structure, rock erosion experiments using the SC-CO\({}_{2}\) jet and SEM observations were carried out on different rocks by [PERSON] et al. [21]. The results showed that rock erosion by SC-CO\({}_{2}\) jet impingement is mainly in the brittle tensile failure mechanism, accompanied with the shear failure in particular locations such as the edge of the jet impinging area. Then, a tangential injection type swirl jet nozzle was used by [PERSON] et al. [22] to investigate the rock erosion characteristics of a SC-CO\({}_{2}\) swirl jet. The results showed that the optimum number of tangential injected entrances to achieve the best rock erosion effect for the jet is three and the optimum standoff distance is twice the nozzle diameter. Similarly, to simultaneously utilize the characteristics of both the swirling jet and conventional round jet, combined swirling and round jet nozzles were designed, and rock erosion experiments using SC-CO\({}_{2}\) combined with swirling and round jets using the nozzles were conducted by [PERSON] et al. [23]. Their experimental results illustrated that the rock erosion efficiency of the SC-CO\({}_{2}\) combined with swirling and round jets is 42.9% higher than that of the conventional water jet, and the combined jet can lead to the occurrence of rock mass breakaway. Simultaneously, to improve the erosion capacity of the SC-CO\({}_{2}\) jet, the influence of nano-silica additive on the rock erosion characteristics was experimentally investigated by [PERSON] et al. [15]. They found that an appropriated amount of nano-silica additive can greatly enhance the erosion ability of the jet, and the effect on the erosion capability largely depends on the operating conditions. On the other hand, for the purpose of figuring out the impact characteristics of the SC-CO\({}_{2}\) jet and the influence of parameters on the impact characteristics, [PERSON] et al. [24] performed a systematical simulation to study the three-dimension flow field of SC-CO\({}_{2}\) jet using a computational fluid dynamic method. They concluded that a SC-CO\({}_{2}\) jet can generate stronger impact pressure than water jet under the same conditions. With the increase of standoff distance, the impact pressure of the SC-CO\({}_{2}\) jet decreases, while the impact scope increases. Similarly, [PERSON] et al. [17] theoretically explored the flow characteristics of a SC-CO\({}_{2}\) jet using the computational fluid dynamics method, and they concluded that the SC-CO\({}_{2}\) jet has a higher impact velocity than that of the water jet under the same conditions and the maximum velocity of the SC-CO\({}_{2}\) jet increases with growing fluid temperature. Besides, a computational fluid dynamics model that includes the real gas effects of CO\({}_{2}\) was used by [PERSON] et al.