A novel description of fluid flow in porous and debris materials
A novel description of fluid flow in porous and debris materials
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DOI：
10.1016/j.enggeo.2015.12.023
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发表时间：
2016-03
影响因子：
7.4
通讯作者：
S. Pudasaini
中科院分区：
文献类型：
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作者：
S. Pudasaini
基于固体颗粒和间隙流体混合物的广义两相质量流模型（Pudasaini，2012），本文推导了固体基质静止的一般多孔介质和碎屑材料中亚扩散和亚平流流体流动的新动力学模型方程。我们构造了新模型的一些精确解析解。导出了完全亚扩散流体流动的完全精确解。比较了经典线性扩散和二次通量子扩散的解，讨论了它们的异同。我们表明，在多孔和碎片材料的亚扩散流体流动的解决方案是从根本上不同的扩散流体流动。在亚扩散过程中，流体在时间上缓慢扩散，因此，流动（物质）较少扩散。进一步地，我们通过将完全的亚扩散和亚平流方程转化为经典的扩散和平流结构，构造了它的一些解析解。给出了完全亚扩散亚平流模型的高分辨率数值解，并与经典扩散亚平流模型的解进行了比较。亚扩散和亚平流模型的解决方案揭示了非常特殊的流动行为，即，由一个逐渐变薄的尾巴，延伸到原来的后方位置的流体，向前平流的前端孔头的演变。然而，对于经典的扩散-平流模型，流体简单地平流和扩散。此外，给出了线性和二次阻力下的完全亚扩散和亚平流模型解，表明广义阻力对亚扩散-平流波的特殊形式和传播速度起着重要作用。我们还表明，通过多孔介质的亚扩散和亚平流流体流动的长时间解决方案在很大程度上是独立的初始流体剖面。这些精确的，解析的和数值的解决方案揭示了许多基本的物理现象，因此可能会发现在建模和模拟环境，工程和工业流体通过一般多孔介质和碎片材料的流动的应用。
Based on a generalized two-phase mass flow model (Pudasaini, 2012) as a mixture of solid particles and interstitial fluid, here, we derive a novel dynamical model equation for sub-diffusive and sub-advective fluid flow in general porous media and debris material in which the solid matrix is stationary. We construct some exact analytical solutions to the new model. The complete exact solutions are derived for the full sub-diffusive fluid flows. Solutions for the classical linear diffusion and the new sub-diffusion with quadratic fluxes are compared, and the similarities and differences are discussed. We show that the solution to sub-diffusive fluid flow in porous and debris material is fundamentally different from the diffusive fluid flow. In the sub-diffusive process, the fluid diffuses slowly in time, and thus, the flow (substance) is less spread. Furthermore, we construct some analytical solutions for the full sub-diffusion and sub-advection equation by transforming it into classical diffusion and advection structure. High resolution numerical solutions are presented for the full sub-diffusion and sub-advection model, which is then compared with the solution of the classical diffusion and advection model. Solutions to the sub-diffusion and sub-advection model reveal very special flow behavior, namely, the evolution of forward advecting frontal bore head followed by a gradually thinning tail that stretches to the original rear position of the fluid. However, for the classical diffusion–advection model, the fluid simply advects and diffuses. Moreover, the full sub-diffusion and sub-advection model solutions are presented both for the linear and quadratic drags, which show that the generalized drag plays an important role in generating special form and propagation speed of the sub-diffusion–advection waves. We also show that the long time solution to sub-diffusive and sub-advective fluid flow through porous media is largely independent of the initial fluid profile. These exact, analytical and numerical solutions reveal many essential physical phenomena, and thus may find applications in modeling and simulation of environmental, engineering and industrial fluid flows through general porous media and debris materials.