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近来,Biot理论的研究被拓展到多尺度下岩石的非均匀性。着眼于实验室频段,本文从理论上讨论了双孔波动方程与BISQ方程之间的关系,推导了双孔方程向BISQ方程退化所必须满足的三个条件。引入了与频率相关的动态渗透率、动态流动增量的概念,从而写出了完整格式的动态双孔波动方程。基于窄频近似,提出了动态双孔方程的一种近似模拟方法。最后,基于虚谱法给出了实验室频段(50KHz)的弹性波模拟结果,结果证实了动态双孔方程描述Squirt流机制的可行性以及窄频近似方法的有效性。
Recently, the research of Biot theory has been extended to the heterogeneity of rock under multi-scale. Focusing on the laboratory frequency band, this paper theoretically discusses the relationship between the two-hole wave equation and the BISQ equation and deduces the three conditions that must be satisfied to degenerate the two-hole equation to the BISQ equation. Introduced the concept of dynamic permeability and dynamic flow increment related to frequency, and then wrote a complete format of dynamic two-hole wave equation. Based on narrowband approximation, an approximate simulation method for dynamic two-hole equations is proposed. Finally, the simulation results of the elastic wave in the laboratory frequency band (50KHz) are given based on the virtual spectrum method. The results confirm the feasibility of the dynamic two-hole equation describing the Squirt flow mechanism and the effectiveness of the narrowband approximation method.