## 1 Introduction  
The application of supercritical carbon dioxide (SC-CO\({}_{2}\)) has achieved obvious progress during the last few decades, stimulated by the demand of a wide range of industries that have recognized the incomparable advantages of SC-CO\({}_{2}\) fluid [1]. SC-CO\({}_{2}\) is an intermediate state between gas and liquid for carbon dioxide when the pressure and temperature are both above the critical point (\(P_{\rm c}\) = 7.38 MPa and \(T_{\rm c}\) = 304.13 K, respectively; the subscript \"\(c\)\" indicates the critical value.) [2]. It has many unique properties, such as high density, high diffusivity, low viscosity, high absorptive capacity by rock substances and so on, which make SC-CO\({}_{2}\) very suitable for the exploitation of oil and gas reservoirs as a working fluid [3; 4; 5; 6]. In more specific terms, high density can provide enough power for downhole drilling tools. Low viscosity can reduce the friction loss during the drilling fluid circulation. High diffusivity can improve the rock erosion efficiency. Furthermore, high absorptive capability by rock substances can lead to greater extraction of hydrocarbons and enhance recovery. In addition,using SC-CO\({}_{2}\) as a working fluid in drilling and completion engineering will contribute to reducing greenhouse gas emissions and pollution of water resources [7; 8]. To make better use of SC-CO\({}_{2}\) fluid in the field of oil and gas development, different kinds of technologies using SC-CO\({}_{2}\) fluid have been invented, like SC-CO\({}_{2}\) flooding, SC-CO\({}_{2}\) fracturing, SC-CO\({}_{2}\) coiled tubing drilling, SC-CO\({}_{2}\) jets, and so on. Among them, the SC-CO\({}_{2}\) jet, which can be more efficient in eroding rocks than the water jet under the same conditions, has been the subject of numerous studies [9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. The most attractive point of this novel jet technology is that by taking full advantage of the high diffusivity of SC-CO\({}_{2}\), it can produce an effective jet with a strong ability to erode rock without using any devices for increasing the inlet pressure in the drilling systems. Simultaneously, the jet medium, SC-CO\({}_{2}\), can play a role in protecting reservoirs and enhance recovery during the drilling process. In the late 1990s, [PERSON] [19] first experimentally studied the rock erosion characteristics of the SC-CO\({}_{2}\) jet, for the purpose of overcoming the technical problems encountered in water jet assisted coiled tubing drilling. He found that the SC-CO\({}_{2}\) jet will cut hard shale, marble and granite at much lower pressure than a water jet. In more specific terms, the SC-CO\({}_{2}\) jet threshold pressure is 2/3 that of water jet in the granite and less than half that of water jet in the shale. Moreover, the rate of penetration in the Mancos Shale with SC-CO\({}_{2}\) was 3.3 times the rate using water and the drilling specific energy is only about 20% that observed while drilling with water. Then, based on this study, to make a better use of the SC-CO\({}_{2}\) jet by maximally enhancing the erosion capability, many researchers are focusing on the rock erosion characteristics, jet types, and flow field of the SC-CO\({}_{2}\) jet as well as the impacting characteristics, aiming at optimizing the operating conditions and revealing the rock erosion mechanism. For instance, an experimental study was performed by [PERSON] et al. [9] to understand the relationship of the rock erosion performance of the SC-CO\({}_{2}\) jet with the various influencing factors by the use of a well-designed experimental setup. They concluded that there exist optimal standoff distance and nozzle diameter to achieve the strongest rock erosion capability for the SC-CO\({}_{2}\) jet. The increase in inlet pressure can significantly improve the rock erosion capacity of the SC-CO\({}_{2}\) jet. It should be noted that standoff distance, \(S\), was defined as the distance from the exit of the nozzle to the surface of the specimen.