This paper mainly investigated the fractal characteristics of crack propagation in hydraulic fracturing and the effect of fractal dimension of induced fractures on the rock breakdown pressure. A series of fracturing experiments with water and nitrogen (N2) as the fracturing fluids were conducted on coal, red sandstone and shale. The injection pressure curves, rock breakdown pressure and macro- and micro-morphologies of the induced fractures were analyzed. A new fractal crack initiation criterion was developed to evaluate the rock breakdown pressure in hydraulic fracturing. The validity of the new criterion was verified by comparing the theoretical and experimental rock breakdown pressures. Further, the difference between the water fracturing and N₂ fracturing was analyzed and the influence of crack fractal effect on the rock breakdown pressure was discussed by considering different initial permeabilities of rocks, injection rates and viscosities of fracturing fluids. The results show: (1) N₂ fracturing may reduce the rock breakdown pressure and induce more tortuous macro-fractures with larger fractal dimension; (2) ignoring the actual fractal dimension of induced fractures would cause the prediction values of the rock breakdown pressure to be larger; and (3) the influence degree of crack fractal dimension on the rock breakdown pressure is related to the initial permeability of rocks, injection rate and viscosity of fracturing fluids. Therefore, we suggest the crack fractal dimension is an important factor that should not be ignored in designing the fracturing operations.

中文翻译：

---

水氮压裂下储层岩石裂缝起裂扩展的分形透视

本文主要研究了水力压裂中裂缝扩展的分形特征以及诱导裂缝分形维数对岩石击穿压力的影响。水氮（N）系列压裂实验2)因为压裂液是在煤、红砂岩和页岩上进行的。分析了注入压力曲线、岩石破裂压力以及诱发裂缝的宏观和微观形貌。开发了一种新的分形裂纹起始准则来评估水力压裂中的岩石破裂压力。通过比较理论和实验岩石破裂压力验证了新准则的有效性。进一步分析了水压和N ₂压裂的区别，并结合岩石初始渗透率、注入速度和压裂液粘度等因素，讨论了裂缝分形效应对岩石破裂压力的影响。结果表明： (1) N ₂压裂可以降低岩石的破裂压力，形成更大分形维数的更曲折的宏观裂缝；(2)忽略诱发裂缝的实际分形维数会导致岩石破裂压力的预测值偏大；(3)裂缝分形维数对岩石击穿压力的影响程度与岩石的初始渗透率、注入速度和压裂液黏度有关。因此，我们认为裂缝分形维数是设计压裂作业时不可忽视的重要因素。