裂缝性地层水力裂缝非平面延伸模拟

受天然裂缝作用影响，裂缝性地层的水力裂缝可能延伸为多分支、非平面的复杂裂缝体系，这与均质地层压裂产生的对称双翼平面裂缝具有巨大的差异。由于常规水力裂缝延伸模型无法用于模拟裂缝性地层中水力裂缝非平面延伸的裂缝形态和裂缝几何，为此，基于水力裂缝相交天然裂缝转向延伸路径的等效平面裂缝思想，建立了水力裂缝非平面转向延伸的数学模型，并推导了相应的数值求解方法。模拟计算表明，当水力裂缝沿天然裂缝转向延伸时，水力裂缝缝宽在延伸路径上表现为非连续分布，在转向延伸段突变减小，受缝宽减小节流效应影响，井底流体压力升高。影响因素分析表明，水平地应力差和逼近角越大，转向延伸段缝宽越小，对支撑剂输送限制越大；施工排量和压裂液黏度越高，包括转向延伸段在内，整个延伸裂缝段的缝宽越大，支撑剂在裂缝内的运移越容易，压裂施工风险越低。研究为认识裂缝性地层水力裂缝非平面延伸特征提供了思路和方法，为裂缝性地层压裂设计提供了理论依据，具有重要的理论价值和现实意义。

Numerical Simulation on Non-planar Propagation of Hydraulic Fracture inNaturally Fractured Formations

Complex propagation system of multi-branched，non-planar fractures in naturally fractured formations commonlyoccurs due to the effect of natural fractures，which greatly differs from bi-wing，symmetric and planar fracture generated in thehomogeneous formations. Therefore，the conventional hydraulic fracture extending model is no longer adaptable，and there’s anurgent need to develop a new model to simulate the propagation pattern and geometry of induced fracture in naturally fracturedformations when hydraulic fracture extends along natural fractures. Based on the equivalent planar fracture of propagationpathway of hydraulic fracture re-orientating along natural fractures，this paper established the mathematical model of hydraulicfracture non-planar re-orientation propagation and provided corresponding numerical solution. The calculation results showthat the induced fracture width at re-orientation propagation section reduces apparently and the treating pressure increases whenhydraulic fracture extends along natural fractures. Analysis of influence factors shows that the larger differential horizontal stressand approaching angles are，the more the fracture width at re-orientation propagation section reduces；the higher volumetricrate and fracturing fluid viscosity are，the larger the whole extension fracture width including re-orientation propagation sectionis. It is clear that differential horizontal stress and approaching angles are negative factors but volumetric rate and fracturingfluid viscosity are positive factors for that proppant transports along hydraulic induced fracture. For this purpose，raisingvolumetric rate and fracturing fluid viscosity can reduce fracturing risk in naturally fractured formations. This research in thispaper realizes non-planar extending features of hydraulic fracture and offers a theoretical basis for fracturing design in naturallyfractured formations. Therefore，it has importantly theoretical value and practical significance.