基于交错网格有限差分算法的页岩声波各向异性校正方法研究

Study on acoustic anisotropy correction method of shale based on staggered grid finite difference

页岩具有层理发育的特征,这会引起强烈的声波各向异性,导致直井与水平井声波测井数据之间差异明显,因此在水平井储层参数计算中无法直接应用基于直井的岩石物理解释模型.为了解决这一问题,本文以页岩波速各向异性实验数据为基础,引入交错网格有限差分算法,首先在直井井孔模型中(VTI介质)模拟了声波的发射和接收,随后通过弹性系数矩阵的Bond变换,模拟了在井斜角不为0的情况下(TTI介质)井孔中的声场传播,以任意井斜角与井斜角为0情况下纵波慢度差值相对值为纵坐标,以相对应的井斜角为横坐标,建立起了纵波各向异性校正公式.模拟与应用结果表明:井孔中波形曲线与实轴积分法(RAI)得到的波形曲线一致,同时利用慢度相似相关算法(STC)得到的地层纵波慢度与给定的实验测量值吻合很好,在28种地层弹性参数的情况下,平均相对误差为2.3%;纵波慢度差值相对值与井斜角关系曲线显示,在井斜角小于30°的条件下,纵波慢度差值相对值变化较小,随着井斜角大于30°后,相对值变化增大,当井斜角为90°也就是水平井模式下,纵波慢度差值相对值达到最大.根据纵波各向异性校正公式,对水平井纵波曲线进行了慢度校正.利用纵波校正前后计算的水平井有效孔隙度与导眼井岩心分析有效孔隙度相对误差分析表明,纵波校正后计算的有效孔隙度计算精度有了明显的提高,证明了该方法具有非常好的应用效果,可用于页岩水平井纵波慢度校正.

The presence of bedding characteristics in shale can lead to pronounced acoustic anisotropy and significant discrepancies logging data obtained from vertical and horizontal wells. Consequently, the petrophysical interpretation model employed for vertical well reservoir calculation cannot be directly extrapolated to horizontal wells. To tackle this challenge, we have introduced the staggered grid finite difference algorithm, based on experimental data on the wave velocity anisotropy of shale. The simulation of acoustic wave transmission and reception is initially conducted in a vertical wellbore model (VTI medium). Subsequently, the propagation of the acoustic field in a wellbore (TTI medium) is simulated by applying bond transformation to the elastic coefficient matrix, assuming non-zero inclination angle of the well. The ordinate represents the relative value of P-wave slowness difference between deviation angle and zero deviation angle, while the abscissa represents the corresponding well deviation angle for establishing an acoustic anisotropy correction formula. The simulation and application results demonstrate that the waveform curve within the borehole aligns with the waveform curve acquired through the Real Axis Integration method (RAI). Furthermore, the slowness similarity correlation algorithm (STC) accurately determines the formation P-wave slowness, exhibiting a strong correlation with experimental measurements. In the presence of 28 formation elastic parameters, it achieves an average relative error of merely 2.3%. The relationship between the relative value of P-wave slowness difference and well inclination angle suggests that minimal changes occur in the relative value of P-wave slowness difference when the well inclination angle is less than 30°. However, beyond an inclination angle of 30°, a rapid increase is observed. In the case of a horizontal well (90°), the relative value of P-wave slowness difference reaches its maximum. The P-wave anisotropy correction formula was employed to rectify the slowness values of the P-wave curve for horizontal wells. The relative error analysis was subsequently conducted on the effective porosity of the horizontal well calculated before and after the P-wave correction, and compared to the effective porosity derived from core analysis of the pilot well. The results indicated a significant enhancement in the accuracy of effective porosity calculation following P-wave correction, thereby demonstrating the efficacy of this method and its applicability for P-wave slowness correction in shale horizontal wells.