声波测井响应的二维谱与共振特征

在井内液体中激发瞬态振动后, 该振动沿径向传播的分量被井壁无数次反射, 在地层中激发出无数个纵波、横波, 固井Ⅰ界面胶结差时还在套管固体中激发无数个套管模式波, 其沿井轴方向传播时通过边界在井内液体中耦合出声波——耦合波。无数次反射波与耦合波叠加构成声波测井响应, 该测井响应受频率和圆柱形状影响。瞬态振动的频率连续, 其测井响应是频率f和井轴方向波数k的复变函数的双重积分, 用双变量复变函数——二维谱描述。在f-k平面上, 刚性壁圆柱形液体内能够传播的模式波其二维谱的极值呈双曲线分布, 套管模式波和地层内的纵波的二维谱的极值呈斜直线分布。它们通过边界在井内液体中耦合, 双曲线与斜直线相交, 为满足边界条件, 实现声波耦合, 双变量复变函数在交点处没有极值, 交点周围二维谱的极值分布改变: 双曲线和斜直线均断开, 沿斜直线分布的二维谱极值是纵波或套管波的频谱, 靠近双曲线幅度大, 离开则幅度快速减小, 随频率变化构成频谱峰, 在峰值附近频谱断开, 频谱峰形状与套管和地层物理参数有关, 决定首波波形形状, 具有共振特征。在频率域用指数函数的频谱拟合断开的频谱峰形状得到首波的衰减系数, 它是固井质量和地层物理衰减、声速的综合描述, 可用于评价固井质量和非常规油气藏。改变套管井的套管厚度和半径发现, 双曲线被各种方式截断, 形成不同的耦合波, 均具有共振特征。

Transient vibrations excited in the fluid of a well propagate radially and are often reflected many times by the wall of the well.Many P-waves, S-waves, and casing waves exited in the formation or casing well.They propagated in the z-direction, with many corresponding coupled waves in the well's fluid.These coupled waves combine to form an acoustic logging response affected by the well's frequency and its cylindrical shape.The frequency of the transient vibration is continuous, and its logging response is the double integral of the complex variable function of the frequency f and wave number k in the z-direction.The multivariable complex variable function-a two-dimensional (2D) spectrum-was considered.In the f-k plane, the 2D spectral shapes of the acoustic wave that can propagate in the cylindrical fluid are hyperbolic, and the P-wave of the formation (or casing mode wave) is an oblique line.The 2D spectral distribution at the intersection of the hyperbola and oblique lines describes the acoustic wave propagating in the well fluid.It is coupled to the formation or casing well through a borehole wall.The two-variable complex function changed the amplitude and extreme value distribution near the intersection point to satisfy the boundary conditions.The hyperbola and oblique line were cut off, and the 2D spectrum distributed along the oblique line of the p-wave (or casing wave) changed with frequency and was broken near the hyperbola.The closer it was to the hyperbola, the greater its amplitude.When it left the hyperbola, the amplitude decreased rapidly, and a peak was produced in the p-wave or casing wave spectrum.The P-wave or casing wave in acoustic logging is determined by the shape of the peak, which is the resonance.The spectral peak shape to be broken is converted into an attenuation coefficient that describes the physical attenuation and velocity of the formation or casing well and is used to evaluate the cementing quality and unconventional reservoirs.Different amplitudes and extreme value distributions were obtained by varying the casing thickness and radius.The hyperbola was cut in different ways, and coupled waves were formed in the liquid of the well.Their responses exhibited resonant characteristics.