SUMMARY

While the frequency-dependence of permeability under fully saturated conditions has been studied for decades, the corresponding characteristics of partially saturated porous media remain unexplored. Notably, it is not clear whether the use of effective pore fluid approaches under such conditions is valid. To address this issue, we propose a method that allows us to obtain dynamic permeability functions for partially saturated porous media. To this end, we conceptualize the considered pore space as a bundle of capillary tubes of different radii saturated by two immiscible fluid phases. We then solve the Navier–Stokes equations within the pore space and define a capillary pressure–saturation relationship, which permits to obtain saturation- and frequency-dependent effective permeability estimates. The application of this method to a realistic model of an unconsolidated granular sediment demonstrates that dynamic effective permeability functions for wetting and non-wetting fluid phases exhibit distinct characteristics, thus rendering effective pore fluid approaches inadequate. Finally, we explore the capability of the seminal dynamic permeability model developed by Johnson et al.[J. Fluid Mech. 176, 379 (1987)] to account for the effects of partial saturation. We find that the frequency scaling proposed by Johnson et al. prevails in partially saturated scenarios. However, the parameters associated with this model need to be redefined to account for saturation-dependent effects.

中文翻译：

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部分饱和多孔介质的动态渗透率函数

概要

尽管已经研究了在完全饱和条件下渗透率的频率依赖性，但数十年以来，仍未探索部分饱和多孔介质的相应特征。值得注意的是，在这种条件下使用有效的孔隙流体方法是否有效尚不清楚。为了解决这个问题，我们提出了一种方法，可以使我们获得部分饱和的多孔介质的动态渗透率函数。为此，我们将考虑的孔隙空间概念化为一束不同半径的毛细管，该毛细管被两个不混溶的流体相饱和。然后，我们在孔隙空间内求解Navier-Stokes方程，并定义毛细压力-饱和度关系，从而可以获取依赖于饱和度和频率的有效渗透率估计值。该方法在未固结颗粒状沉积物的真实模型中的应用表明，用于润湿和非润湿流体相的动态有效渗透率函数表现出明显的特征，因此使有效的孔隙流体方法不足。最后，我们探讨了Johnson等人开发的精动力动态渗透率模型的能力。流体机械。176，379（1987）]来解释部分饱和的影响。我们发现Johnson等人提出的频率缩放。在部分饱和的场景中占优势。但是，需要重新定义与此模型关联的参数，以解决饱和度相关的影响。