基于黏弹性介质波动理论的页岩超声波数值模拟

Shale ultrasonic numerical simulation based on the viscoelastic medium wave theory

利用超声波透射法来研究页岩的超声波响应特征,是页岩气开发过程中利用测井资料解决地质和工程问题的基础,而目前对于以页岩地层声波测井为目的的声学响应研究成果则鲜有报道且相关研究将页岩当作弹性介质来处理,未考虑页岩的黏弹性特征。为此,基于黏弹性介质波动理论,结合超声波透射实验背景,构建初始条件、振源条件、边界条件和稳定性条件,采用交错网格有限差分法模拟不同层理角度页岩的超声波透射实验。研究结果表明:①数值模拟计算和物理实验所得到的页岩声波特性变化趋势相互吻合;②基于理想和真实岩心的数值模拟计算和物理实验所得到的页岩衰减系数随测试频率、层理角度变化的规律均一致;③在层理尺度和密度恒定的条件下,随着层理角度的增大,波速呈幂函数递减,衰减系数呈线性增加。结论认为:①基于黏弹性介质声波波动理论,结合高阶交错网格差分技术建立的模拟页岩超声波透射实验的数值计算方法计算科学合理,具有较强的适应性;②利用该数值模拟方法可以从微观角度分析页岩层理特征对超声波传播特性的影响规律;③新方法拓展了层理性页岩地层声学研究的思路、避免了人为误差、节约了实验成本,具有重要理论价值和实际意义。

Using the ultrasonic transmission method to study the ultrasonic response characteristics of shale is the basis for the use of logging data to solve geological and engineering problems in shale gas development. However, among few literatures about such related research by present, shale has been only regarded as an elastic medium with its viscoelastic characteristics being unfortunately ignored. In view of this, based on the theory of viscoelastic medium waves, combined with the ultrasonic penetration experiments, we simulated an initial and vibration sources environment as well as boundary and stability conditions. On this basis, we made the ultrasonic transmission experiments of shale with different bedding angles by the staggered grid finite difference method. The following findings were obtained.(1) The waveform trend obtained by numerical simulation is coincided with the physical experiment result.(2) The rules of shale attenuation coefficients varied along with the test frequencies and the bedding angles obtained by numerical simulation calculation and physical experiment based on ideal and real cores agree well with each other.(3) Under a certain constant bedding size and density, the wave velocity declined in power function and the attenuation coefficient increases linearly. In conclusion, this numerical computation method proposed in this paper is scientific and reasonable and is of strong adaptability and can not only be used to analyze the influence of shale bedding characteristics on ultrasonic propagation characteristics from a microscopic point of view, but avoid human errors and save the experimental cost, therefore it is of important theoretical and practical significance.