基于反射声波测井有限元方法的井旁裂缝分布特征

Near wellbore fracture distribution characteristics based on acoustic reflection logging finite element method

基于声波传播理论,利用声波有限元方法研究存在井旁裂缝情况下的反射波波形特征。以井眼为对称轴,对有声阻抗不连续界面的一侧进行二维轴对称有限元建模,分别建立井旁存在交叉裂缝和弧状裂缝的交叉裂缝反射界面计算模型和弧状裂缝反射界面有限元计算模型。通过对相同源距条件下不同接收点接收的波形数据进行处理,得到反射波波至时间等参数,进而判断出页岩储层井旁裂缝的分布规律。结果表明:反射波的波至时间随声源纵坐标变化而呈现的规律与井旁裂缝的形态表现出了很好的一致性,井旁存在交叉裂缝时,根据波至时间计算得到井旁裂缝倾角为10.13°和20.19°,与解析模型对比的误差率分别为1.31%和0.95%。井旁存在弧状裂缝时,由反射波波至时间得出反射界面的坐标,并与计算模型结果进行对比,得到裂缝中心位置与反射点坐标相对误差为1.70%。声波有限元方法可以有效地反演出井旁裂缝的位置和形态特征。

Based on the theory of acoustic wave propagation,reflected wave characteristics are studied by the finite element method in the presence of well fracture. 2 D axial symmetry finite element modeling is applied on one side of discontinuous acoustic impedance. The models to computing cross fracture reflection interface and arc fracture reflection interface are established for the cases where cross fracture and arc fracture exist on the side of well. Waveform data from the same source received by the different receivers are processed and the parameters（e.g.,reflection phase arrival time） are obtained. The distribution character of wellbore fracture in shale reservoir is obtained accordingly. The results show that the variations in the arrival time of the reflected wave owing to the changes in the vertical coordinates of sound source is consistent with the shape of the wellbore fracture. In the presence of a cross shaped fracture near the wellbore,inclination angles of the side fracture obtained using the arrival time of reflected wave are 10. 13 degrees and 20. 19 degrees,respectively,which are within 1. 31%and 0. 95% of the analytical model. In the case of an arc shaped fracture near the wellbore,the location and shape feature of the wellbore fracture can be effectively derived by the coordinates of the reflecting interface. The relative error between the central position of fracture and the coordinate of reference point is within 1. 70%.It is concluded that the acoustic finite element method can effectively infer the position and morphology of fracture near the wellbore.