In this paper, a novel fractal model for the invasion depth of fluid through the tortuous capillary bundle with roughened surfaces in porous media is proposed. The capillary pressure effect is considered in the proposed model. The proposed model is expressed as a function of structure parameters of porous media, including the relative roughness, the fractal dimension for pore size distribution, the contact angle, the density, the gravitational acceleration, the tortuosity and porosity. The invasion depth can be quantitatively characterized by the proposed model. By using the fractal theory, the effect of relative roughness on the invasion depth is discussed. It is observed that the invasion depth decreases with increasing the relative roughness of the tortuous capillary bundle with roughened surfaces. In addition, it is found that the invasion depth increases with the increase of the invasion time. The proposed model predictions are in good agreement with the available experimental data. Each parameter in our model has clear a distinct physical meaning, which may contribute to comprehend the better understanding of seepage mechanisms.

中文翻译：

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一种新的分形模型，用于流体通过具有粗糙表面的曲折毛细血管束在多孔介质中的侵入深度

在本文中，提出了一种新的分形模型，用于计算流体通过多孔介质中粗糙表面的曲折毛细管束的侵入深度。在所提出的模型中考虑了毛细压力效应。所提出的模型表示为多孔介质结构参数的函数，包括相对粗糙度、孔径分布的分形维数、接触角、密度、重力加速度、曲折度和孔隙度。入侵深度可以通过所提出的模型进行定量表征。利用分形理论，讨论了相对粗糙度对侵入深度的影响。可以观察到，随着具有粗糙表面的曲折毛细管束的相对粗糙度的增加，侵入深度减小。此外，发现随着侵入时间的增加侵入深度增加。所提出的模型预测与可用的实验数据非常吻合。我们模型中的每个参数都有明确的物理意义，这可能有助于更好地理解渗流机制。