Permeability Description by Characteristic Length, Tortuosity, Constriction and Porosity
Permeability Description by Characteristic Length, Tortuosity, Constriction and Porosity
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DOI：
10.1007/s11242-014-0307-6
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发表时间：
2014-07-01
影响因子：
2.7
通讯作者：
Berg, Carl Fredrik
中科院分区：
文献类型：
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作者：
Berg, Carl Fredrik
在本文中，我们研究了达西定律中给出的多孔介质的渗透率。渗透率通过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、流线长度和传导流动的体积分数来描述。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，流线长度由曲折度表征，从入口到出口的导流体积分数由有效孔隙率描述。因此，特征长度、收缩因子、曲折度和有效孔隙率是孔隙结构相对于方向的内在描述符。我们表明，我们的孔隙结构描述的综合效应充分描述了多孔介质的渗透率。该理论应用于理想化的多孔介质，再现了从哈根-泊肃叶方程导出的流体流动达西定律。我们还将这一理论应用于枫丹白露砂岩的完整网络模型，其中我们展示了孔隙结构和渗透率如何与此类天然多孔介质的孔隙度相关。这项工作通过基本且明确的孔隙结构参数（特征长度、收缩度和弯曲度），建立了 Kozeny-Carman 意义上的渗透率与孔隙度的关系。
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.