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流体饱和的多孔圆柱形岩石的弹性模量和声衰减的实验室测量结果,常常受到岩石样品边界条件的影响,即圆柱样品的表面是对空气开放还是完全封闭。本文就此问题推导了拉伸、扭转和弯曲振动模式的解析结果,并计算了几个例子。结果说明存在由开放孔边界条件引起的“人为”衰减,对拉伸振动模式,其驰豫频率与岩石的渗透率成正比,与孔中流体的粘滞系数及样品半径的平方成反比。此种衰减存在于拉伸和弯曲振动模式中,而不存在于扭转振动模式中。
Laboratory measurements of the elastic modulus and acoustic attenuation of fluid saturated porous cylindrical rocks are often influenced by the boundary conditions of the rock samples, ie whether the surface of the cylindrical sample is open to the air or completely closed. In this paper, the analytical results of tensile, torsional and flexural vibration modes are derived and several examples are calculated. The results show that there is a “man-made” attenuation caused by open pore boundary conditions. For tensile modes, the relaxation frequency is proportional to rock permeability and inversely proportional to the viscosity of the fluid in the pores and the square of the sample radius. Such attenuation exists in tensile and flexural vibration modes, but not in torsional vibration modes.