Fractures are widely developed in various reservoirs, where they provide not only migration pathways but also additional storage space for oil and gas. With the improvement of exploration and development in recent years, the study of fractures has become one of the key factors for high production in reservoirs, and the accurate identification of fracture distribution is of great significance for the exploration and development of many reservoirs. Outcrop, core observation, well logging, and imaging analysis all show that various types of fractures are widely developed in the Ordovician carbonate reservoir in the Shunbei area of the Tarim Basin, with horizontal fractures and low-angle oblique fractures being the main types. To strengthen the further study of fractures in this area, we improve the commonly used ratio of the range to standard deviation (R/S) analysis method. We combine numerical analysis of R(n)/S(n) curves and the existing core data to predict fracture development zones in the Ordovician reservoirs north of the Shunbei no. 5 fault zone. Validated by fractures observed in the core, our results indicate that the R/S analysis is able to predict fractures in the carbonate reservoir. By adding a second derivative term, we are able to reduce the false positives suffered by the traditional R/S method. Fracture prediction is more automated, more accurate, and precise, with accurate identification approaching 68%. We also examine the ability of different log curves for fracture identification, and we determine that the RD and AC curves are the most effective. Our findings indicate that the R/S analysis method using conventional log curves holds great promise in fracture prediction for areas lacking core and image log data.