Wave propagation through elastic porous media containing two immiscible fluids
Wave propagation through elastic porous media containing two immiscible fluids
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DOI：
10.1029/2004wr003162
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发表时间：
2005-02
影响因子：
5.4
通讯作者：
W. Lo;G. Sposito;E. Majer
中科院分区：
文献类型：
--
作者：
W. Lo;G. Sposito;E. Majer
近年来，由于人们对地下含水层中孔隙弹性行为的科学认识日益加深，含有多相流体的多孔介质中的声波现象受到了极大的关注。为了提高对这些现象的定量理解，推导了一组描述膨胀波在弹性多孔介质中传播的耦合偏微分方程组。这些方程包含了欧拉参照系中的惯性耦合和粘性阻力，以前的膨胀波传播模型可以作为特例恢复。文中还将两个重要的孔弹性概念--流体含量的线性化增量和孔隙度变化的闭合关系--推广到两流体系统。为了考察相对流体饱和度和波浪激励频率(50、100、150和200赫兹)对松散多孔介质中自由膨胀波行为的影响，对哥伦比亚细砂壤土中含有空气-水和油水混合物的三种可能的波动模式进行了数值模拟。结果表明，传播模式(P1)由固体骨架和两种孔隙流体的同相运动产生，其运动速度等于含流体多孔介质的有效体积弹性模量与有效密度之比的平方根，而与流体饱和度和两种流体混合物的运动速度无关。孔隙流体的性质对P1波的衰减有很大影响。在空气-水体系中，衰减由物质密度差和孔隙流体的相对迁移率控制，而在油水体系中，孔隙流体的有效运动剪切粘度是控制参数。另一方面，两种扩散模式(P2是固体骨架和流体异相运动的结果，P3是毛管压力波动的结果)的速度和衰减与孔隙流体的有效动态剪切粘度密切相关。P2波和P3波也具有相同的品质因数常数值，通过与前人对砂岩中这两种膨胀波模式的研究相比较，发现两者都对多孔介质的固结状态敏感。
Acoustic wave phenomena in porous media containing multiphase fluids have received considerable attention in recent years because of an increasing scientific awareness of poroelastic behavior in groundwater aquifers. To improve quantitative understanding of these phenomena, a general set of coupled partial differential equations was derived to describe dilatational wave propagation through an elastic porous medium permeated by two immiscible fluids. These equations, from which previous models of dilatational wave propagation can be recovered as special cases, incorporate both inertial coupling and viscous drag in an Eulerian frame of reference. Two important poroelasticity concepts, the linearized increment of fluid content and the closure relation for porosity change, originally defined for an elastic porous medium containing a single fluid, also are generalized for a two‐fluid system. To examine the impact of relative fluid saturation and wave excitation frequency (50, 100, 150, and 200 Hz) on free dilatational wave behavior in unconsolidated porous media, numerical simulations of the three possible modes of wave motion were conducted for Columbia fine sandy loam containing either an air‐water or oil‐water mixture. The results showed that the propagating (P1) mode, which results from in‐phase motions of the solid framework and the two pore fluids, moves with a speed equal to the square root of the ratio of an effective bulk modulus to an effective density of the fluid‐containing porous medium, regardless of fluid saturation and for both fluid mixtures. The nature of the pore fluids exerts a significant influence on the attenuation of the P1 wave. In the air‐water system, attenuation was controlled by material density differences and the relative mobilities of the pore fluids, whereas in the oil‐water system an effective kinematic shear viscosity of the pore fluids was the controlling parameter. On the other hand, the speed and attenuation of the two diffusive modes (P2, resulting from out‐of‐phase motions of the solid framework and the fluids, and P3, the result of capillary pressure fluctuations) were closely associated with an effective dynamic shear viscosity of the pore fluids. The P2 and P3 waves also had the same constant value of the quality factor, and by comparison of our results with previous research on these two dilatational wave modes in sandstones, both were found to be sensitive to the state of consolidation of the porous medium.