## 5 Conclusions  
1. This study conducted repair and PR experiments using a single CaCO\({}_{3}\)/Fe(OH)\({}_{3}\) precipitate or a mixed precipitate with different molar ratios of the two on the same fracture. The Fe(OH)\({}_{3}\) colloid encapsulated CaCO\({}_{3}\) crystals in a mixed precipitate,  
Figure 8: Comparison of PR curves between Stage II of the added schemes and Scheme 1.  
Figure 7: Comparison of PR curves between the added schemes and their corresponding schemes: (a) comparison between added Scheme 1 and Schemes 1 and 2; (b) comparison between added Scheme 2 and Schemes 1 and 4; (c) comparison between added Scheme 3 and Schemes 1 and 5. Note: Similar to Figure 4, the vertical coordinates in the figures are all expressed on a logarithmic scale. To better compare the curves, not all of the longer-span curves in Schemes 4 and 5 are presented.  
reducing the overall structural stability of the mixed precipitate and restricting repair and PR efficiency. The Fe(OH)\({}_{3}\) precipitate had better PR efficiency in the initial stage of the experiment. Therefore, a new fracture repair experiment using a mixed precipitate and a single CaCO\({}_{3}\) precipitate in two stages was conducted to obtain a reasonable scheme with excellent fracture repair efficiency.
2. In the experiment, the fractured rock specimen's PR curves showed different trend characteristics due to the difference in the adsorption and consolidation degree of the precipitates in the fractures. There were three main trends: a steady PR trend, a flat permeability trend, and a fluctuating/oscillating PR trend. The PR trend caused by the single CaCO\({}_{3}\) precipitate was stable and fast, while those caused by the mixed precipitate and single Fe(OH)\({}_{3}\) precipitate tended to frequently fluctuate/oscillate and persist for a long period. Instability in precipitate structures caused by hydraulic erosion is the main reason for this phenomenon. Under our experimental conditions, the strength of the mixed precipitate against hydraulic erosion was about 0.1 MPa, while that of the Fe(OH)\({}_{3}\) precipitate was about 0.2 MPa.
3. Within the first 4 h of the initial stage, the repair efficiency of the single CaCO\({}_{3}\) precipitate on fractures was always the lowest among the schemes. Further experiments showed that a mixed Fe(OH)\({}_{3}\) and CaCO\({}_{3}\) precipitate with a molar ratio of about 1:4 in the early stage (the duration should be more than 2 h) and a single CaCO\({}_{3}\) precipitate in the later stage should be the relatively optimal scheme for WCF repair.
4. The PR law of chemical precipitates in repairing WCFs is a complex problem under the comprehensive influence of multiple factors. This study only examined a sandstone sample under specific fracture development conditions. For other lithological rock samples with different fracture development characteristics, these PR laws require further study. The time boundary setting for using different precipitates to repair fractures in stages will also be the focus of subsequent research.  
Conceptualization, J.J.; writing--original draft preparation, J.J.; writing--review and editing, C.W. and Y.F.; methodology, J.J. and Q.L.; validation, J.J. and Q.L.; formal analysis, J.J., Q.L. and C.W.; data curation, J.J., C.W. and Y.F.; project administration, J.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant number: 42477497) and the National Key Research and Development Program of China (grant number: 2021 YFC2902104).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.  
The authors acknowledge [PERSON] for his help in sample testing.  
The authors declare no conflicts of interest.