斯通利波在渗透地层和裂缝带的反射及透射:解析和数值方法模拟对比

Stoneley wave reflection and transmission across permeable formations and fractured zones:Comparison of analytical and numerical modeling results

声波测井常用斯通利波来评价储层渗透性能和识别地层裂缝,描述声波在渗透性地层中的传播需要求解Biot孔隙弹性波动方程.本文采用有限差分方法来求解测井斯通利波在渗透地层和裂缝带的反射及透射问题.综合利用有限差分法和一维等效波数法研究和分析了不同层厚、孔隙度和渗透率下单个和多个渗透地层的斯通利波反射及透射系数以及变化规律,两种方法计算结果对比验证了一维等效波数法在0~2 kHz范围内的可靠性.对于等效波数法难以模拟、更为复杂的裂缝带模型,利用有限差分方法分析和研究了在不同渗透率、轴向和径向延伸长度下裂缝带的斯通利波反射和透射系数及其变化特征.本文结果表明:斯通利波在渗透裂缝带中激发的流体渗流是一种穿透深度有限的趋肤效应,因此要达到0.1 m以上的探测深度,需要使用较低的激发频率(0~2 kHz),低频段内的斯通利波反射和透射系数对井壁附近裂缝带的渗透性能均有响应.随着渗透率升高,斯通利波反射系数在低频明显升高,透射系数在高频降低显著;在高于Biot特征频率的频段,反射和透射系数曲线随渗透率升高呈复杂变化,与孔隙流体从渗流到波动的变化相关.本文的方法和结果有助于分析和解释斯通利波在裂缝型渗透地层的传播特征,为识别此类地层和评价其渗透性能奠定理论基础.

Borehole Stoneley waves are commonly used to evaluate reservoir permeability and identify formation fractures.The propagation of acoustic waves in permeable formations requires solving the Biot′s poro-elastic wave equations.In this study,the finite-difference method is used to solve the problem of Stoneley wave reflection and transmission across permeable formations and fractured zone.Firstly,the finite-difference method and one-dimensional effective wavenumber method were collectively applied to study and analyze the Stoneley wave reflection and transmission coefficients and their variation characteristics with different thickness,permeability and porosity of single or multiple permeable formations.The results verify the reliability of the effective wavenumber method at the range of 0~2 kHz.An advantage of the finite-difference method is to solve the more complex fractured zone problem that is difficult for the wavenumber method to handle,analyzing and studying the Stoneley wave reflection and transmission coefficients of the fractured zone with different permeability,porosity,axial and radial extension length parameters.The results of this paper show that the Stoneley-wave induced fluid flow in the fractured zone is a skin effect having a limited depth of penetration.Thus,to measure the fluid flow effect beyond a radial depth of,say 0.1 m,one should use a low-frequency excitation band of 0~2 kHz,in which both the Stoneley wave reflection and transmission coefficients are sensitive to the fluid transport property of the fractured zone in the borehole vicinity.In general,the Stoneley-wave reflection coefficient increases significantly at low frequencies,and the transmission coefficient decreases with increasing frequency.However,when the wave frequency is close to Biot characteristic frequency,the reflection and transmission coefficients show complicated variation trend with increasing frequency and permeability,due to dynamic fluid flow characteristics in the fractured zone.The methods and results in this paper are helpful to analyze and interpret the propagation characteristics of Stoneley waves in permeable fractured formations,and it lays a theoretical foundation for identifying such formations and evaluating their permeable properties.