Pride Steven R, Berryman James G
Géosciences Rennes, Université de Rennes 1, 35042 Rennes Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036604. doi: 10.1103/PhysRevE.68.036604. Epub 2003 Sep 9.
For the purpose of understanding the acoustic attenuation of double-porosity composites, the key macroscopic equations are those controlling the fluid transport. Two types of fluid transport are present in double-porosity dual-permeability materials: (1) a scalar transport that occurs entirely within each averaging volume and that accounts for the rate at which fluid is exchanged between porous phase 1 and porous phase 2 when there is a difference in the average fluid pressure between the two phases and (2) a vector transport that accounts for fluid flux across an averaging region when there are macroscopic fluid-pressure gradients present. The scalar transport that occurs between the two phases can produce large amounts of wave-induced attenuation. The scalar transport equation is derived using volume-averaging arguments and the frequency dependence of the transport coefficient is obtained. The dual-permeability vector Darcy law that is obtained allows for fluid flux across each phase individually and is shown to have a symmetric permeability matrix. The nature of the cross coupling between the flow in each phase is also discussed.
为了理解双孔隙复合材料的声衰减，关键的宏观方程是控制流体传输的方程。双孔隙双渗透率材料中存在两种类型的流体传输：（1）一种标量传输，它完全发生在每个平均体积内，当两相之间的平均流体压力存在差异时，该传输解释了多孔相1和多孔相2之间流体交换的速率；（2）一种矢量传输，当存在宏观流体压力梯度时，该传输解释了穿过平均区域的流体通量。两相之间发生的标量传输会产生大量的波致衰减。利用体积平均论证推导了标量传输方程，并得到了传输系数的频率依赖性。所得到的双渗透率矢量达西定律允许流体分别穿过每个相，并显示具有对称的渗透率矩阵。还讨论了各相流动之间交叉耦合的性质。
