Electrokinetic and electroosmotic couplings can play important roles in water and ions transport in charged porous media. Electroosmosis is the phenomena explaining the water movement in a porous medium subjected to an electrical field. In this work, a new model is obtained through a new up-scaling procedure, considering the porous medium as a bundle of tortuous capillaries of fractal nature. From the model, the expressions for the electroosmosis pressure coefficient, the relative electroosmosis pressure coefficient, the maximum back pressure, the maximum flow rate, the flow rate-applied back pressure relation and the product of the permeability and formation factor of porous media are also obtained. The sensitivity of the relative electroosmosis pressure coefficient is then analyzed and explained. The model predictions are then successfully compared with published datasets. Additionally, we deduce an expression for the relative streaming potential coefficient and then compare it with a previously published model and experimental data from a dolomite rock sample. We find a good agreement between those models and experimental data, opening up new perspectives to model electroosmotic phenomena in porous media saturated with various fluids.

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多孔介质中的电渗耦合，一种基于分形放大过程的新模型

电动和电渗耦合可以在带电多孔介质中的水和离子传输中发挥重要作用。电渗是解释水在受电场作用的多孔介质中运动的现象。在这项工作中，通过新的放大程序获得了一个新模型，将多孔介质视为一束具有分形性质的曲折毛细血管。从模型中还得到了电渗压力系数、相对电渗压力系数、最大背压、最大流速、流速-施加的背压关系以及多孔介质渗透率与地层因子的乘积的表达式获得。然后分析和解释相对电渗压力系数的敏感性。然后将模型预测成功地与已发布的数据集进行比较。此外，我们推导出相对流势系数的表达式，然后将其与先前发布的模型和白云岩岩石样品的实验数据进行比较。我们发现这些模型与实验数据之间具有良好的一致性，为模拟充斥各种流体的多孔介质中的电渗现象开辟了新的视角。