水力裂缝平面应变假设的适用条件与解析修正

Applicable conditions and analytical corrections of plane strain assumption in the simulation of hydraulic fracturing

鉴于平面应变假设在模拟水力裂缝周围应力、位移分布的模型中得到了广泛应用,通过对比椭圆裂缝解和平面应变解,探讨了平面应变假设的适用条件并给出了修正方法。在前人研究的基础上推导、补充并修正了扁平椭圆裂缝的应力、位移场表达式,与平面应变假设条件下的计算结果进行了比较,结果表明:若在缝高方向考虑平面应变假设,长高比大于10后,平面应变解与椭圆裂缝解之间的差异可以忽略,而在主要受缝面法向正应力控制的问题中,平面应变解的适用条件可以放宽到长高比大于5;当长高比满足适用条件时应用平面应变假设具有较高精度,长高比较小时需要对平面应变解进行修正。给出了不同长高比条件下裸眼水平井起裂附加应力和单条裂缝宽度的平面应变解修正图版,发现拟三维模型的缝宽更易于修正。

Plane stain assumption is widely used in the simulation of the distribution of stress and displacement around hydraulic fractures. According to the comparison of the solutions of elliptical fracture and plane stain fracture, the applicable conditions of plane strain assumption were discussed and the correction method was put forward. On the basis of the past research, a classical stress and displacement solution around a fiat elliptical fracture was deduced, fulfilled and corrected. In comparison with the plain strain fracture solution, simulating results show that if taking plane strain assumption into consideration in the fracture height profile, the difference between the elliptical fracture solution and plane strain solution is negligible when the ratio between fracture length and fracture height is larger than 10, and the above critical value could be relaxed to 5 in some simulations which normal stress perpendicular to fracture face plays a decisive role. The plane strain fracture solution is accurate enough when the above critical value is satisfied, the correction of the plane strain fracture solution is needed when the length-height ratio is small. The correction charts of the additional initial stress of the horizontal well with an open-hole and the width of a single fracture were drawn under different length-height ratios. The fracture width of pseudo three dimension propagation models is easier to be modified by the correction charts.