## 1 Introduction
Simultaneously, the flow field of a SC-CO\({}_{2}\) jet was studied using the computational fluid dynamic method, by [PERSON] et al. [24]. The results showed that the SC-CO\({}_{2}\) jet has a stronger impact pressure and a higher velocity than a water jet does, when under the same conditions. They also claimed that the maximum velocity and impact pressure of the SC-CO\({}_{2}\) jet, increase with the increasing nozzle pressure drop. Moreover, the increasing fluid temperature has almost no effect on the impact pressure, but can increase the maximum velocity. Also, [PERSON] et al. [25] numerically investigated the impinging flow field in the bottom hole. Their results illustrated that the increasing inlet temperature can increase the axial velocity, and reduce both the mass flow rate and the impingement of the SC-CO\({}_{2}\) jet. To further study the dynamic flow characteristics of a SC-CO\({}_{2}\) jet at the bottom hole, [PERSON] et al. [26] conducted a series of simulations and experiments to understand the bottom hole temperature and pressure distributions of SC-CO\({}_{2}\) fluid. The results showed that the bottom hole impact pressure and temperature, increase with increasing nozzle diameter. When the standoff distance increases, the bottom hole temperature decreases, while the bottom hole pressure initially rises, before dropping. Additionally, the bottom hole pressure and temperature both increase with the ascent of inlet pressure. Moreover, by combining the method of computational fluid dynamic (CFD) and lab experiments, [PERSON] et al. [27] investigated the influence of ambient pressure and standoff distance on the impinging pressure and perforation performance of a SC-CO\({}_{2}\) jet. The results showed that, when the inlet pressure is constant, the effective impact pressure and erosion depth notably decrease, with increasing ambient pressure. When the nozzle pressure drop is constant, the erosion depth increases at first, but then decreases with increasing ambient pressure. In spite of the many works that have been completed on the effects of thermodynamic conditions and operating parameters on the rock erosion capacity of a SC-CO\({}_{2}\) jet, a study that associates the rock erosion events with an appropriate amount of proper additive, has not yet been pursued. It is commonly known that various additives have been applied in water jet technology, in order to enhance the cleaning, crushing, and erosion capacity. For instance, experimental studies were performed by [PERSON] et al. [28], to provide a quantitative assessment of the effect of additives on the erosion capacity of a water jet. The results indicated that both the erosion surface quality, and the erosion depth of the specimen, are greatly enhanced by this method. This suggests that a proper additive is able to alter the jet flow field, and subsequently, changes the erosion characteristics of a water jet. Similarly, [PERSON] et al. [29] experimentally investigated the effect of additives on the erosion quality of marble cut by an abrasive water jet, concluding that a certain fraction of additive can improve the erosion quality. Therefore, it is reasonable to speculate that a proper additive should also have great effects on the erosion characteristics of a SC-CO\({}_{2}\) jet. Moreover, nano-silica is an appropriate kind of additive for improving the filtration properties of drilling fluid and enhancing the well bore stability, especially under high temperature and pressure conditions [30; 31; 32; 33]. Also, [PERSON] et al. experimentally investigated the effect of CO\({}_{2}\) fracturing, influenced by a nano-silica additive, and concluded that the effect of nano-silica causes a decrease in CO\({}_{2}\) fingering and an increase in the drainage area. Additionally, the argued that the CO\({}_{2}\) fracturing effect can be enhanced by the nanoparticles [34].