用特征长度、弯曲度、收缩度和孔隙度描述渗透率
Permeability Description by Characteristic Length, Tortuosity, Constriction and Porosity
摘要：
在这篇文章中，我们研究了达西定律中给出的多孔介质的渗透率。渗透率由多孔介质中的有效水力孔隙半径、局部水力孔隙半径的波动、流线的长度和传导流的体积分数来描述。有效水力孔隙半径与特征水力长度有关，局部水力半径的波动与收缩因子有关，流线的长度以曲折度为特征，从入口到出口的体积分数由有效孔隙度描述。因此，特征长度、收缩因子、弯曲度和有效孔隙度是相对于方向的孔结构的内在描述符。我们表明，我们的孔隙结构描述的综合效果充分描述了多孔介质的渗透性。该理论适用于理想化的多孔介质，在那里它再现达西定律的流体流动来自哈根-Poietille方程。我们还将这一理论应用到枫丹白露砂岩的全网络模型中，在那里我们展示了这种天然多孔介质的孔隙结构和渗透率与孔隙度的相关性。这项工作建立了如何渗透率可以与孔隙度，在Kozeny-Carman的意义上，通过基本的和明确的孔隙结构参数：特征长度，收缩，和曲折。
英文摘要：
In this article we investigate the permeability of a porous medium as given in Darcy's law. The permeability is described by an effective hydraulic pore radius in the porous medium, the fluctuation in local hydraulic pore radii, the length of streamlines, and the fractional volume conducting flow. The effective hydraulic pore radius is related to a characteristic hydraulic length, the fluctuation in local hydraulic radii is related to a constriction factor, the length of streamlines is characterized by a tortuosity, and the fractional volume conducting flow from inlet to outlet is described by an effective porosity. The characteristic length, the constriction factor, the tortuosity and the effective porosity are thus intrinsic descriptors of the pore structure relative to direction. We show that the combined effect of our pore structure description fully describes the permeability of a porous medium. The theory is applied to idealized porous media, where it reproduces Darcy's law for fluid flow derived from the Hagen-Poiseuille equation. We also apply this theory to full network models of Fontainebleau sandstone, where we show how the pore structure and permeability correlate with porosity for such natural porous media. This work establishes how the permeability can be related to porosity, in the sense of Kozeny-Carman, through fundamental and well-defined pore structure parameters: characteristic length, constriction, and tortuosity.
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