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arXiv 1808.09804cond-mat.softphysics.chem-phphysics.flu-dyn
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基于孔隙空间可达性和半径分辨饱和度的毛管压力滞后微观理论

Microscopic theory of capillary pressure hysteresis based on pore-space accessivity and radius-resolved saturation

Zongyu Gu, Martin Z. Bazant

摘要:

多孔介质的连续介质模型使用宏观参数和状态变量来捕捉孔隙尺度物理的基本特征。我们提出了一个宏观属性“accessibility”($α$)来表征多孔介质中不同尺寸孔隙的网络连通性,宏观状态描述符“半径分辨饱和度”($ψ_w(F),ψ_n(F)$)来表征流体相的分布。小附着性($α\to0$)意味着不同尺寸孔隙之间的串联连接,而大附着性($α\to1$)对应于更多的平行排列,正如经典毛细血管束模型隐含假设的那样。基于这些概念,我们开发了一个统计理论准静态不混溶排渗在任意周期,并达到简单的代数公式更新$ψ_n(F)$,自然捕获毛细管压力滞后,与$α$控制量的滞后。这些概念可用于解释滞后数据,高档孔隙尺度的观察,并制定新的本构律,通过提供一个简单的概念框架,量化连接性的影响,并可能有更广泛的实用程序在连续建模的运输,反应和相变在多孔介质中。

英文摘要:

Continuum models of porous media use macroscopic parameters and state variables to capture essential features of pore-scale physics. We propose a macroscopic property "accessivity" ($α$) to characterize the network connectivity of different sized pores in a porous medium, and macroscopic state descriptors "radius-resolved saturations" ($ψ_w(F),ψ_n(F)$) to characterize the distribution of fluid phases within. Small accessivity ($α\to0$) implies serial connections between different sized pores, while large accessivity ($α\to1$) corresponds to more parallel arrangements, as the classical capillary bundle model implicitly assumes. Based on these concepts, we develop a statistical theory for quasistatic immiscible drainage-imbibition in arbitrary cycles, and arrive at simple algebraic formulae for updating $ψ_n(F)$ that naturally capture capillary pressure hysteresis, with $α$ controlling the amount of hysteresis. These concepts may be used to interpret hysteretic data, upscale pore-scale observations, and formulate new constitutive laws by providing a simple conceptual framework for quantifying connectivity effects, and may have broader utility in continuum modeling of transport, reactions, and phase transformations in porous media.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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