## 2 Fracturing Tests  
### Rock Specimens and Apparatus  
The experimental specimens were Longmaxi shales collected from outcrops in Changing (labeled as CN-Shale) and Pengshui (labeled as PS-Shale), both located in the Sichuan Basin, China. Figure 1 shows the flow chart of the shale specimen preparation. The prepared specimens were used in hydraulic fracturing experiments to determine the breakdown pressure, and in basic tests to measure the rock's petrophysical and mechanical properties, including bulk density, tensile strength, compressive strength, P-wave velocity, and water content (Table 1). The processing requirements of the shales for these basic tests adhered to International Society of Rock Mechanics standards.  
As shown in Figure 2, the shale specimens used for fracturing had a diameter of 100 mm and height of 200 mm, with a central borehole of 10 mm in diameter and 110 mm in height, leaving an open hole section with a depth of 40 mm. The shale bedding planes were oriented perpendicularly, with the borehole drilled parallel to the bedding planes.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **CN-Shale** & **PS-Sahle** & **Units** \\ \hline Bulk density, \(\rho_{s}\) & 2546 & 2648 & kg/m\({}^{3}\) \\ Elastic modulus, \(E\) & 12.16 & 11.99 & GPa \\ Poisson’s ratio, \(\
u\) & 0.20 & 0.25 & — \\ Tensile strength, \(\sigma_{t}\) & 15.63 & 18.18 & MPa \\ Compressive strength, \(\sigma_{c}\) & 151.55 & 138.45 & MPa \\ P-wave velocity, \(v_{p}\) & 5.00 & 4.47 & km/s \\ Water content, \(w\) & 0.4 & 0.3 & \% \\ Sampling site & Changing & Pengshui & — \\ Bedding orientation & Perpendicular & Perpendicular & — \\ \hline \hline \end{tabular}
\end{table}
Table 1: Average values of basic parameters of shale.  
Figure 1: Flow chart of the shale specimen preparation for the experiments. UCS denotes uniaxial compressive strength. \(\phi 50\,*\,100\) and \(\phi 50\,*\,25\) denote cylindrical specimens with a diameter of 50 mm and heights of 100 mm and 25 mm, respectively. “\(\phi\)” is the symbol that typically represents diameter, and “\(*\)” is a notation for the dimension.  
The packet fixing method for sealing and forming the open hole was described in detail by [PERSON] et al. (2021) and [PERSON] et al. (2022).  
Figure 2 shows the experimental apparatus used for hydraulic fracturing tests, which consisted of six main modules, as follows: (1) gas supply; (2) water supply; (3) axial and confining pressure loading; (4) vacuuming; (5) temperature control; and (6) seepage testing. These modules operate collaboratively to achieve specific functions. Further design and functionality details are available in the work of [PERSON] et al. (2021). This apparatus enables fracturing experiments using various injection fluids on shale under different in situ stress conditions, reservoir temperatures, and flow rates, with real-time data acquisition of injection pressure, axial/confining pressure, temperature, strain, and acoustic emission (AE) signals during the fracturing process, as well as seepage testing when fractures propagate to the end face of the shale specimen. In this study, we merely concentrated on the breakdown pressure for providing experimental data.