水力裂缝分形扩展对压裂效果的影响
Influence of Hydraulic Fracture Fractal Propagation on Fracturing Result
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摘要: 为深入认识裂缝分形扩展对压裂效果的影响,研究了裂缝扩展分形性对裂缝延伸净压力及裂缝尺寸的影响规律。分析裂缝分形几何形态及其尖端应力场特征,并应用分形断裂力学理论对线性扩展净压力模型进行修正,得到了分形扩展净压力模型;在此基础上,结合力平衡模型及Sneddon最大裂缝宽度模型,建立了裂缝分形扩展与线性扩展的裂缝高度比模型和裂缝最大宽度比模型。数值分析结果表明:裂缝的分形扩展增加了裂缝高度、最大缝宽以及延伸所需的净压力;当50 m缝长处的裂缝扩展形态的分形维数由1.20增大至1.80,净压力比由1.50增大至6.30。在给定地层力学参数条件下,当分形维数由1.30增大至1.60时,20 m缝长处的裂缝高度比由1.04增大至1.11,裂缝最大宽度比由1.70增大至2.70。研究表明,分形扩展对裂缝几何尺度的影响明显,裂缝分形扩展程度越剧烈,裂缝高度和裂缝最大宽度的增量越大。Abstract: The influence of fracture fractal feature on net propagation pressure and fracture size was studied for better understanding of fracture fractal propagation effect.Based on fractal fracture mechanics,the fractal propagation net pressure model was established through modification of linear propagation net pressure model,and analysis of hydraulic fracture fractal geometry and fractal crack tip stress field features.Then coupled with force equilibrium model and Sneddon maximum crack width model,fracture height ratio model and fracture maximal width ratio model of fractal propagation and linear expansion were built.Analysis results show that net pressure ratio increased from 1.5 times to 6.3 times when the fractal dimension increased from 1.20 to 1.80 under constant fracture length of 50 meters.In addition,fracture height ratio increased from 1.04 times to 1.11 times and fracture maximal width ratio increased from 1.70 times to 2.70 times at given formation mechanical parameters when fractal dimension increased from 1.30 to 1.60 under fracture length of 20 meters.So,fractal propagation influences geometric dimensions of hydraulic fracture significantly and the higher the hydraulic fracture fractal level,the bigger the fracture height increment and maximal width increment.