Acoustic field simulations of logging while drilling by cylindrical finite difference with variable grids

柱坐标变网格有限差分方法的随钻声波测井模拟

This study proposes an elastic finite difference(FD)time domain method with variable grids in three-dimensional cylindrical coordinates.The calculations will diverge and become less accurate by conventional cylindrical FD as the grid size gradually becomes more extensive with the increasing radius.To prevent grids from being too coarse in far fields,we compensate for the grid cell infl ation by refi ning the grid step in the azimuthal direction.The variable grid FD in the cylindrical coordinate systems has a higher effi ciency in solving acoustic logging while drilling(LWD)problems because the grid boundaries are consistent with those of the drill collar and the borehole.The proposed algorithm saves approximately 94%of the FD grids,80%of the computation time,and memory with a higher calculation accuracy than the FD on rectangular grids for the same models.We also calculate the acoustic LWD responses of the fl uid-fi lled borehole intersecting with fractures.Refl ections are generated at the fractures,which can be equivalent to an additional scattering source.The mode conversions between the collar and the Stoneley waves are revealed.The Stoneley spectra are more sensitive to the fracture.Finally,the logs in a heterogeneous formation with two refl ectors far from the borehole are modeled,and a means of estimating the azimuth of geological interfaces from refl ections is proposed.

本文提出了三维柱坐标中的变网格有限差分(FD)算法。传统的柱坐标FD算法计算时,随着径向距离增大,单元网格在方位方向上会发生线性膨胀,导致计算发散、准确性降低。为了防止计算远场时网格过于粗糙,我们在特定的径向位置处将方位步长减半来补偿这种效应。在随钻声波测井(ALWD)的数值模拟研究中,考虑到井孔和随钻仪器组合的多层柱状分层结构、以及井外复杂的地质构造,柱坐标变网格FD计算这类问题时具有更高的效率与精度。对比直角坐标系FD算法,当计算相同模型时,本文提出的算法能够节省约94%的计算网格、约80%的计算时间和内存,而且计算精度更高。另外,计算了ALWD充液井孔与裂缝相交情况下的声场,裂缝处产生的反射波可以等效为一个新的散射源。研究表明,钻铤波和斯通利波之间发生了模式转换,且斯通利波的谱对裂缝更加敏感。最后,讨论了井外不同方位上存在两个地质异常体的情况,能够利用反射波幅度同时对井外两个界面的方位进行准确地测量。