# Study of Rock Crack Extension under Liquid Nitrogen Low-Temperature Fracturing
## 5 Effect of In Situ Stress on Crack Propagation  
Given the varying shale physical properties and in situ stress conditions, different fracture forms, including single fracture, complex fractures, and network fractures, may be formed after fracturing [33]. The in situ stress state is an important factor that affects crack initiation and propagation. Accordingly, understanding the influence of in situ stress on crack propagation and predicting and controlling the crack direction to ensure that it can communicate with natural cracks and form complex network cracks are the keys to improving the volume of fracturing. Based on the circular hole model of the horizontal well section, the in situ stress \(\sigma\) (x direction) is set as 6.89 MPa (1000 psi) to study the influence of temperature stress distribution and crack propagation under the liquid nitrogen impact of the circular hole model with different lateral stress coefficients k (k = 0.25, 0.5, 1, 2). The experimental results reported by [PERSON] et al. [16] show that the surface temperature of the borehole decreased to a lower temperature (\(-\)160-170 \({}^{\circ}\)C) after 10 min of a low-temperature and low-pressure injection of liquid nitrogen. After 40 min of impact, the surface temperature of the sample decreased from 20 \({}^{\circ}\)C to \(-\)20 \({}^{\circ}\)C, which is nearly 40 \({}^{\circ}\)C. In combination with the above discussion results and Figure 8, the heat transfer coefficient was preliminarily selected as 500 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\). The other parameters were the same as those of the model experiment in Section 2. The propagation depths of the cracks generated at low temperature in the direction of larger principal stress were longer, as shown in Figure 21. For example, when k = 0.25, that is, the constraint stress k\(\sigma\) in the y direction was 1.7225 MPa, this was much smaller than the constraint stress in the x direction. The maximum main crack propagated along the x direction. When t = 100 s, the propagation length of the main crack could reach 35 mm, while the crack in the y direction was almost invisible to the naked eye. When k = 2, the constraint stress k\(\sigma\) in the y direction was 13.78 MPa, which was much larger than that in the x direction. The maximum main crack propagated along the y direction. When t = 100 s, the propagation length of main crack was about 9 mm, while the propagation length of the crack in the x direction was only 1 mm. This phenomenon mainly occurs because the reaction to the applied temperature load is small when the rock is restricted. Meanwhile, the tensile stress in the restricted direction is small when the liquid nitrogen is cold-shocked. When k < 1, the tensile stress in the y direction of the borehole was less than that in the x direction, as shown in Figure 13. Cracks occurred when the value was greater than the tensile strength of the rock. The cracks in the y direction stopped propagating with the development of time. Meanwhile, the cracks in the x direction continued to develop. However, in the case of k < 1, the constraint stress in the direction of k = 0.25 was smaller  
Figure 20: Failure patterns of shale under the condition of thermal shock by soaking the specimen in liquid nitrogen. (**a**) Test results of Cha [17]; (**b**) test results of Han [32]. than that in the direction of k = 0.5 y, and the restriction was smaller. Although the number of cracks was less, the propagation depth of the main crack was deeper. In this case, the crack was not uniformly distributed, and its length was not similar or graded compared with the crack generated when k = 1. In the actual engineering operation, the above model corresponded to the horizontal well area.