Conventional sonic logging tools are destined mainly for the determination of elastic waves’ velocities. In this paper, we have considered a different type of sonic logging tool that is destined for the registration of parameters of reflected waves in a borehole. We have calculated the mechanical impedance loading an acoustic source located on the axis of a fluid-filled borehole. The problem was solved for a borehole drilled in a poroelastic formation. The solution was obtained in the framework of the Biot theory of poroelasticity. We have considered two limiting cases with permeable and impermeable (mudcake at the boundary between the borehole and porous rock) borehole wall. We have obtained the frequency dependences of the mechanical impedance. It was shown that the acoustic system ‘logging tool – fluid-filled borehole – porous rock’ presents several resonance frequencies. These resonances’ frequencies are close to the resonance frequencies of a liquid layer between two rigid cylinders with radii equal to the source and borehole radii. The mechanical impedance calculated at the resonance frequency depends on the porosity and permeability that allows one to use impedance measurements in the frequency range near the resonance to determine the filtration properties of highly permeable rocks (of order higher than 10 mD). We have calculated the mechanical impedance in the low-frequency range. The results obtained have shown that the use of low-frequency impedance measurements provides a good way to evaluate the permeability of porous media.

中文翻译：

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对位于流体饱和多孔介质中的钻孔中的声源进行阻抗加载

传统的声波测井工具主要用于确定弹性波的速度。在本文中，我们考虑了一种不同类型的声波测井工具，用于记录钻孔中反射波的参数。我们已经计算了加载位于充满流体的钻孔轴上的声源的机械阻抗。在多孔弹性地层中钻出的钻孔解决了这个问题。该解决方案是在 Biot 多孔弹性理论的框架内获得的。我们已经考虑了可渗透和不可渗透（钻孔和多孔岩石之间的边界处的泥饼）钻孔壁的两种极限情况。我们已经获得了机械阻抗的频率依赖性。结果表明，声学系统“测井工具——充满流体的钻孔——多孔岩石”呈现出几个共振频率。这些共振的频率接近于半径等于源和钻孔半径的两个刚性圆柱之间的液体层的共振频率。在共振频率下计算的机械阻抗取决于孔隙度和渗透率，这使得人们可以在共振附近的频率范围内使用阻抗测量来确定高渗透性岩石（高于 10 mD 的数量级）的过滤特性。我们已经计算了低频范围内的机械阻抗。获得的结果表明，使用低频阻抗测量提供了一种评估多孔介质渗透率的好方法。这些共振的频率接近于半径等于源和钻孔半径的两个刚性圆柱之间的液体层的共振频率。在共振频率下计算的机械阻抗取决于孔隙率和渗透率，这使得人们可以在共振附近的频率范围内使用阻抗测量来确定高渗透性岩石（高于 10 mD 的数量级）的过滤特性。我们已经计算了低频范围内的机械阻抗。获得的结果表明，使用低频阻抗测量提供了一种评估多孔介质渗透率的好方法。这些共振的频率接近于半径等于源和钻孔半径的两个刚性圆柱之间的液体层的共振频率。在共振频率下计算的机械阻抗取决于孔隙率和渗透率，这使得人们可以在共振附近的频率范围内使用阻抗测量来确定高渗透性岩石（高于 10 mD 的数量级）的过滤特性。我们已经计算了低频范围内的机械阻抗。获得的结果表明，使用低频阻抗测量提供了一种评估多孔介质渗透率的好方法。在共振频率下计算的机械阻抗取决于孔隙率和渗透率，这使得人们可以在共振附近的频率范围内使用阻抗测量来确定高渗透性岩石（高于 10 mD 的数量级）的过滤特性。我们已经计算了低频范围内的机械阻抗。获得的结果表明，使用低频阻抗测量提供了一种评估多孔介质渗透率的好方法。在共振频率下计算的机械阻抗取决于孔隙率和渗透率，这使得人们可以在共振附近的频率范围内使用阻抗测量来确定高渗透性岩石（高于 10 mD 的数量级）的过滤特性。我们已经计算了低频范围内的机械阻抗。获得的结果表明，使用低频阻抗测量提供了一种评估多孔介质渗透率的好方法。