基于有限差分方法的溶洞地层井孔声波数值模拟

Finite-difference modeling of borehole acoustic logging in formations with caves

单极子声源有限差分方法建立了直角坐标系,数值模拟了溶洞地层全波列声波的传播,研究了地层溶洞对纵、横波首波以及散射波的影响。结果表明:当溶洞距井壁的距离超过单极子测井的最大探测距离后,它对井孔声波的影响很小。当溶洞的位置不超过声波测井的最大探测距离且径向排列时,纵波的初至时间和首波幅值的变化与溶洞的半径、数量呈正相关。横波首波的衰减与溶洞的半径线性相关。在单极子声源的探测距离内,溶洞的数量越多,横波的衰减程度越大。当地层横波遇到含水溶洞时,随着源距的增加,转换横波和转换纵波会逐渐分离,横波首波的衰减先增大然后逐渐减小至平稳。横波对地层的溶洞更敏感。溶洞距井壁的距离对声波的影响较复杂,当溶洞距井壁的距离达到一定数值时,纵、横波首波幅值变化最大。散射波能量由溶洞的半径、位置和数量共同决定。一般情况下,溶洞的数量越多,散射波能量越强。

This paper illustrates the results of finite-difference simulations to estimate the response of full-wave acoustic logging in formations where caves are present.The analyses were carried out considering a monopole source which was simulated in a Compute Unified Device Architecture in a rectangular coordinate system.The results showed that the borehole acoustic wave was only slightly affected by caves when the distance between the cave and the borehole wall exceeded the maximum detection depth.If the caves were located within the detection depth,the variation and first arrival of P-waves were positively correlated with the cave radius and number when the caves were arranged radially.The attenuation of S-waves was linearly related to the radius of the cave,and was positively correlated with the number of caves.When the S-wave encountered a water-bearing cave,the converted S-waves and P-waves gradually separated.With an increasing distance from the source,the attenuation of the S-waves first increased,and then gradually decreased to reach a stable value.The S-waves were more sensitive to the presence of caves than the P-waves.The complex effects of the distance to a cave on the acoustic wave were evaluated.In fact,the amplitude of P-and S-waves changed substantially only with a certain distance from the borehole wall.The scattered wave energy was found to be controlled by the radius,position,and number of caves.In general,as the number of caves increased,so did the scattered wave energy.