## 3 Field Test Study on Liquid CO2 Phase-Transition Rock Fracturing
### Fracturing Effects
#### 3.3.2 Distribution Characteristics of the Granularity of the Rock after Fracturing  
In the current study, since only the projected areas of the fractured rock blocks could be obtained using the above-mentioned \"UAV camera shooting + MIPS image processing\" method, when the number of rock blocks in each grain size was large enough, the plane  
Figure 6: Schematic diagram of the aerial photography [27]. Figure 7: Original image and processed image. projection sizes (such as the areas or perimeters) of the rock fragments were used as the geometric characteristic quantities in order to detect the granularity after fracturing. It was determined that the plane projection sizes had accurately reflected the actual fracturing effects. There was observed to be a certain quantitative relationship between the planar sizes and the volumes of the rock blocks. At the present time, the following formulas are commonly used [28]:  
\[\left\{ \begin{array}{c}a=\frac{\frac{p}{n}+\sqrt{\frac{p^{2}}{n^{2}}-\frac{4S} {n}}}{2}\\ b=\frac{\frac{p}{n}-\sqrt{\frac{p^{2}}{n^{2}}-\frac{4S}{n}}}{2}\\ D=1.16b\sqrt{1.35\frac{b}{n}}\\ V=D\ \times\ S\end{array} \right. \tag{1}\]  
where \(S\) represents the area of the rock mass; \(P\) is the perimeter of the rock mass; \(D\) indicates the screen size of the rock mass; \(a\) is the maximum radius of the optimal ellipse; \(b\) represents the minimum radius of the optimal ellipse; \(V\) denotes the volume of the rock mass. In the current study, Formula (1) was used for the volume conversion. Figure 8 shows a comparison of the fracturing volumes of the different schemes of liquid CO\({}_{2}\) phase-transition fracturing. The total volume of the several fractured granules was obviously larger than that of the single-hole fracturing. This was mainly due to the different CO\({}_{2}\) storage in the fracturing pipe, and major changes in the released energy. Further, the fracturing volume of the 108-type fracturing test was found to be larger than that of the 95-type fracturing test. Figure 9 shows the granule composition after four tests. According to the comparison of the two several-hole tests, the granularity distribution of the 108-type several-hole test was more uniform, and the boulder content was smaller than that in the 95-type test. At the same time, the fracturing volume of the 108-type several-hole test was observed to be larger than that of the 95-type several-hole test. In summary, the fracturing effects of the 108-type several-hole test were found to be superior to those of the 95-type several-hole test. Further, according to this study's comparison of the two single-hole test results, the 95-type single-hole boulders were found to have a smaller content and better fracturing effects. The reasons for these results were that the rock weathering at the test site of the 95-type single-hole fracturing test was more serious and the rock mass itself was looser. This had reduced the transmission of the energy force and resulted in less effective fracturing. Figure 8: The total volume of fragmentation caused by liquid CO\({}_{2}\) phase-transition rock fracturing. It has been observed that fractured rock blocks have statistical self-similarity in both geometric shape and fractal distribution. The fractal description of the rock mass fracturing process is as follows: A rock mass will be initially broken into a finite number of blocks with similar shapes; some of those blocks will become separately broken into sub-blocks of similar shapes as the original rock mass under load conditions; some of the sub-blocks will become further broken into smaller sized rock blocks with similar shapes; each repetition of the process will produce smaller blocks [29; 30]; therefore, in the present study, the distributions of the fractured rock, which were the result of the liquid CO\({}_{2}\) transition were analyzed from a fractal point of view. The fractal dimensions were used to reflect the distributions of rock granularity, and to quantitatively evaluate the fracturing effects.