不规则形状垂直井孔中波传播的2.5维边界元模拟

本文给出了求解声波测井工作中具有任意形状的垂直井孔中波传播的波数域边界元公式。我们将问题看成是垂向均匀的二维介质,并沿垂直方向变换到离散波数域。通过与有限差分计算的频散曲线的比较验证了算法和程序的正确性。边界元方法可以处理任意形状的边界,作为初步应用,我们研究了垂向裂纹对井孔中波传播的影响。

2.5D Boundary element simulation of wave propagation in a vertical fluid-filled borehole with irregular shape

In this paper, a boundary element formulation in the wave-number space domain for solving the wave equation for a borehole with arbitrary shape in acoustic logging problems is presented. The problem is treated as a two-dimensional medium with the discrete wave- number method in the vertical direction. The method is validated by comparing the results obtained by this method with those obtained by the finite-difference method. The method is used to study the effect on wave propagation in a vertical borehole of a vertical fracture. For a monopole source, the dispersion curves for Stoneley waves yield three branches. For dipole and quadrupole sources, different orientations of the source yield different results. When the dipole source is orthogonal to the fracture, the dispersion curve is similar to that of the open hole, while the curves are quite different when the source is parallel to the fracture. These characteristics enable us to determine the orientation of the vertical fracture.