# Study of Rock Crack Extension under Liquid Nitrogen Low-Temperature Fracturing
## 4 Numerical Simulation of Liquid Nitrogen Low-Temperature Fracturing
### Discussion of Engineering Measures to the Improve Heat Transfer Coefficient  
In summary, a high heat transfer coefficient has an important effect on the temperature and stress distribution in a rock. The greater the heat transfer coefficient is, the greater the temperature gradient generated by the liquid nitrogen cold shock and the higher the corresponding temperature stress will be. However, the insulating gas layer will be formed at the contact interface when liquid nitrogen enters the rock due to the influence of the Lyton Frost effect, thereby hindering the decrease in surface temperature, which is also the reason for the low heat transfer coefficient of liquid nitrogen. When it impacts low-permeability gas reservoirs (such as shale gas reservoirs), it may not produce a large number of cracks, as expected due to the small stress variation. Accordingly, physical tests may require longer liquid nitrogen freezing times, multiple freezing cycles, or a higher liquid nitrogen impact pressure (Figure 20) to observe obvious cracks on the sample surface. The influence of the Lyton Frost effect must be eliminated, and the heat transfer coefficient must be improved to increase the degree of rock fracturing. Common engineering measures include increasing the liquid nitrogen flow rate and liquid nitrogen pressure. The Lyton Frost effect occurs at relatively high temperatures with the increase in pressure. [PERSON] et al. (2016) showed that the temperature drop on the sample surface will increase with the increase in liquid nitrogen flow rate. Nitrogen fixation and fracturing proppant as solid suspension in liquid nitrogen can also be used. Such a mechanism helps in reducing the Lyton Frost effect, and proppant particles embedded in shale rock plates affect the conductivity of supporting fractures ([PERSON] et al., 2017), which is conducive to maintaining the opening of fractures.  
Although the liquid nitrogen transformation of shale gas reservoirs has good prospects, some oil and gas exploitations used as fracturing fluids have shown good results in the expansion of main cracks and the manufacturing of secondary cracks. However, many technical barriers need to be overcome because the current research is still in the stage of theoretical research and process design. Moreover, the transformation of fracturing fluid from water to liquid nitrogen involves commercial costs, even though this process is more economical and effective for the development of shale gas, and rigorous trade-offs and comparisons are still needed.  
Figure 20: _Cont._  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coefficient of Heat Transfer** & \begin{tabular}{c} **H = 100** \\ **W**\(\cdot\)**m\({}^{-2}\cdot\)**K\({}^{-1}\)** \\ \end{tabular} & \
\begin{tabular}{c} **H = 500** \\ **W**\(\cdot\)**m\({}^{-2}\cdot\)**K\({}^{-1}\)** \\ \end{tabular} &
\begin{tabular}{c} **H = 1000** \\ **W**\(\cdot\)**m\({}^{-2}\cdot\)**K\({}^{-1}\)** \\ \end{tabular} \\ \hline Stop extension time/s & 1800 s & 2000 s & 2340 s \\ Damage rate at 100 s/\% & 0.430 & 0.695 & 0.841 \\ Final destruction rate/\% & 2.096 & 2.677 & 3.089 \\
100 s failure rate ratio/\% & 20.51 & 25.97 & 27.23 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Failure rate of rocks with different heat exchange coefficients.