Potential Of Porous Media Research Articles

3D Forward Modeling of Seepage Self-potential Using Finite-infinite Element Coupling Method

The streaming potential in porous media is one of the main constituents of the self-potential. It has attracted special attention in environmental and engineering geophysics. Forward modeling of streaming potentials could be the foundation of corresponding data inversion and interpretation, and improving the application effect of the self-potential method. The traditional finite element method has a large subdivision area and computational quantity, and the artificial boundary condition is not suitable for complex models. The Helmholtz-Smoluchowski equation is introduced for evaluating the streaming potential. Then three new shape functions of the multidirectional mapping infinite elements are proposed and the finite-infinite element coupling method is deduced for reducing the subdivision scale and improving both the calculation efficiency and accuracy. The correctness and validity of the new coupled method are verified by a resistive model in homogeneous half-space. Besides, a seepage model with complex terrain and a landfill model with dynamic leakages are modeled using the improved coupled method. The results show that the accuracy of the improved coupled method is superior to the unimproved coupled method, and is better than the finite element method. Also, the coupled method has better adaptability to complex models and is suitable for the accurate simulation of dynamic multi-source seepage models.

The temperature dependence of the zeta potential in porous media

The measurements of the zeta potential of five consolidated samples including natural and artificial ceramic rocks saturated with 5.0×10-3 M NaCl electrolyte at different temperatures have been reported. The zeta potential obtained in this work is always negative and increases in magnitude with increasing temperature for all samples (an average increase of the zeta potential of 0.4 mV/ oC in magnitude). The experimental results are in good agreement with previously published data. The experimental data is then explained by a theoretical model. It is shown that the model is able to reproduce the main trend of the experimental data from our work and from published articles.

A fractal model for streaming potential coefficient in porous media

ABSTRACTStreaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid−liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.

Computation of streaming potential in porous media: Modified permeability tensor

We quantify the pressure-driven electrokinetic transport of electrolytes in porous media through a matched asymptotic expansion based method to obtain a homogenized description of the upscaled transport. The pressure driven flow of aqueous electrolytes over charged surfaces leads to the generation of an induced electric potential, commonly termed as the streaming potential. We derive an expression for the modified permeability tensor, K↔eff, which is analogous to the Darcy permeability tensor with due accounting for the induced streaming potential. The porous media herein are modeled as spatially periodic. The modified permeability tensor is obtained for both topographically simple and complex domains by enforcing a zero net global current. Towards resolving the complicated details of the porous medium in a computationally efficient framework, the domain identification and reconstruction of the geometries are performed using adaptive quadtree (in 2D) and octree (in 3D) algorithms, which allows one to resolve the solid–liquid interface as per the desired level of resolution. We discuss the influence of the induced streaming potential on the modification of the Darcy law in connection to transport processes through porous plugs, clays and soils by considering a case-study on Berea sandstone.

Deviation of linear relation between streaming potential and pore fluid pressure difference in granular material at relatively high Reynolds numbers

Abstract We conducted streaming potential measurements on the packing of glass beads, and investigated the deviation of streaming potential from the Helmholtz-Smoluchowski (H-S) equation. The H-S equation was originally derived on the assumption of laminar flows. Studies using a capillary have shown that the H-S equation is valid for turbulent flows in so far as the viscous sublayer is thicker than the electrical double layer and the entrance effect is negligible. Although the streaming potential in porous media has been reported to deviate from the H-S equation for turbulent flows, its mechanism is still poorly understood. We measured the fluid flux and the streaming potential as a function of the pore fluid pressure difference. The fluid flux begins to deviate from Darcy’s law at Reynolds number >3, and the streaming potential begins to deviate from the linear relation at larger Reynolds numbers. When the flow is fast, the fluid inertia separates the boundary layer from the solid surface and induces the counter flows. The fluid in the counter-flow region is separated from the circulating fluid, and ions there cannot contribute to the convection current. We think that this results in a lower streaming potential than expected from the H-S equation.

Ionic transport and membrane potential in porous media with interfacial charges

Electrical conductivity σ of a porous medium, in which the pore-walls carry an electric double layer, is shown to be a nonlinear function of the electrolyte conductivity σ w, which fills the pores. As σ w increases, dominant current paths shift from surface to pore and therefore are subjected to different tortuosities. σ is shown to be a superposition of cation and anion conductivities σ = σ cation + σ anion, and membrane potential is proportional to σ cation/( σ cation + σ anion). The macroscopic conductivities σ cation and σ anion depend on microgeometry of the pore and surface as well as the surface charges. Thus, geometrical effects are similar for membrane potential and conductivity.