Pore-network modeling of liquid water transport in gas diffusion layer of a polymer electrolyte fuel cell

A pore-network model is developed to study the liquid water movement and flooding in a gas diffusion layer (GDL), with the GDL morphology taken into account. The dynamics of liquid water transport at the pore-scale and evolution of saturation profile in a GDL under realistic fuel cell operating conditions is examined for the first time. It is found that capillary forces control liquid water transport in the GDL and that liquid water moves in connected clusters with finger-like liquid waterfronts, rendering concave-shaped saturation profiles characteristic of fractal capillary fingering. The effect of liquid coverage at the GDL–channel interface on the liquid water transport inside GDL is also studied, and it is found that liquid coverage at the GDL–channel interface results in pressure buildup inside the GDL causing the liquid water to break out from preferential locations.     

Determination of oxygen effective diffusivity in porous gas diffusion layer using a three-dimensional pore network model

In proton exchange membrane fuel cell (PEMFC) models, oxygen effective diffusivity is the most important parameter to characterize the oxygen transport in the gas diffusion layer (GDL). However, its determination is a challenge due to its complex dependency on GDL structure. In the present study, a three-dimensional network consisting of spherical pores and cylindrical throats is developed and used to investigate the effects of GDL structural parameters on oxygen effective diffusivity under the condition with/without water invasion process. Oxygen transport in the throat is described by Fick's law and water invasion process in the network is simulated using the invasion percolation with trapping algorithm. The simulation results reveal that oxygen effective diffusivity is slightly affected by network size but increases with decreasing the network heterogeneity and with increasing the pore connectivity. Impacts of network anisotropy on oxygen transport are also investigated in this paper. The anisotropic network is constructed by constricting the throats in the through-plane direction with a constriction factor. It is found that water invasion has a more severe negative influence on oxygen transport in an anisotropic network. Finally, two new correlations are introduced to determine the oxygen effective diffusivity for the Toray carbon paper GDLs.     

Pore-Scale Simulation of Drying of a Porous Media Saturated with a Sucrose Solution

This work presents results of Monte Carlo simulations of isothermal drying of a nonhygroscopic porous media initially saturated with a sugar solution. The porous media is represented by a two-dimensional network of cubic pores connected by throats with a given radius distribution. The considered network had just one open side (the three other sides were sealed) from which water evaporation occurred. Water evaporation, hydraulic flow, and diffusivity of sucrose in water are considered in the physical model. It was considered that drying occurred under isothermal conditions (low drying rates) and that the capillary forces surpass the viscous forces, as in invasion percolation. It was also considered that water evaporation inside the network of pores and throats causes solution concentration, which remains at the corners, allowing hydraulic connection throughout the whole network. At each simulation step, a single meniscus moves through a particular pore segment with the higher displacing force. As drying progresses, air replaces the solution. Determination of the mechanism prevailing at any given drying stage requires calculation of evaporation. In other words, each step of the simulation involves finding the solution to three systems of equations: the vapor pressure field in the vapor phase, the pressure field in the liquid phase, and the solutes' concentration in the liquid phase. Herein, we report results of drying curves calculated as a function of the sucrose and water saturation and of the distribution of liquid, sucrose, and vapor as drying advances. The results presented in this work showed that network models are a powerful tool for investigating the influence of the main mechanisms controlling drying at its different stages; that is, from liquid saturation condition to very low saturation (end of drying). Despite the applied simplifications, the model can capture the main aspects of drying of liquids and solutions present in porous media.     

Effect of the coordination number of the pore-network on the transport and deposition of particles in porous media

Effect of the coordination number of the pore-network structure on the transport and deposition of colloidal particles in porous media was investigated. Applying with the orthogonal collocation principle and the pseudo-spectral method based on the Chebyshev polynomial, the complete solutions of the population balance equations describing the deposited particles, the suspended particles and the unblocked pore throats of porous media were obtained for the simple square network and the capillary tube network. It is shown that the network structure of porous media may significantly affect filtration rate, and therefore the effluent concentration and pressure drop. The filter with a capillary tube network structure owns higher filter coefficient than that of the filter with a simple square network structure. Theoretical predictions for different influent concentrations of particles, different flow rates and the case of blocking occurred in the filter bed are in agreement with the available experimental data.     

Two-phase flow in porous media

Two-phase flow in porous media depends on many factors, such as displacement vs steady two-phase flow, saturation, wettability conditions, wetting fluid vs non-wetting fluid is displacing, the capillary number, interfacial tension, viscosity ratio, pressure gradient, uniformly wetted vs mixed-wet pore surface, uniform vs distributed pore throats, small vs large pores, well-connected pores vs pores connected by small throats, etc. These parameters determine how the two fluids are distributed in the pores, e.g. whether they flow in seperate channels or side-by-side in the same channels, either with both fluids being continous or only one fluid being continous and the other discontinuous. In displacement, the capillary number and the viscosity ratio determine whether the displacement front is sharp, or if there is either capillary or viscous fingering.     

PEMFC带沟槽气体扩散层内传输特性孔隙网络模拟

采用三维孔隙网络模型计算了不同沟槽参数下气体扩散层(GDL)的液态水突破压力、毛细压力分布、气体扩散率和液相相对渗透率随饱和度变化,并从孔隙尺度角度探究了沟槽的作用机制。研究结果表明:沟槽改变了GDL的毛细压力分布,提供了液态水直接传输路径并优化了GDL内氧气和液态水的分布,从而提高了氧气有效扩散率。沟槽位置对氧气传输有明显影响,对液相传输的影响取决于是否形成贯穿GDL的传输路径;沟槽加深,氧气和液态水传输性能增强,沟槽穿透GDL时传输性能达到最佳;沟槽变宽,液相传输性能增强,氧气传输性能在低饱和度范围内先增强后减弱。综合各因素,给出了氧气和液态水传输性能最优时的沟槽参数。     

Investigation of liquid water in gas diffusion layers of polymer electrolyte fuel cells using X-ray tomographic microscopy

In polymer electrolyte fuel cells (PEFCs), condensation of water within the pore network of the gas diffusion layers (GDL) can influence the gas transport properties and thus reduce the electrochemical conversion rates. The use of X-ray tomographic microscopy (XTM), which allows for a resolution in the order of one micrometer is investigated for studying ex situ the local saturation in GDL's. The strength of XTM is the high spatial resolution with simultaneous contrast for water and carbon, allowing for non-destructive 3D-imaging of the solid and the contained water. The application of this method for imaging the ex situ water intrusion into the porous network of GDLs is explored using absorption and phase contrast methods. It is shown that the inhomogeneous filling behavior of GDL materials can indeed be visualized with sufficient resolution. For Toray paper TGP-H-060 the local saturation was measured as function of the water pressure. The results, evaluated in 1D, 2D and 3D show a liquid water retention effect at the denser layers near the surface. A comparison with established capillary pressure functions is presented. Altogether, the results show the potential of the XTM-method as a tool for studying the liquid water behavior in PEFC on a microscopic scale.     

A method to calculate the multiphase flow properties of heterogeneous porous media by using network simulations

A method is suggested to compute the capillary pressure and relative permeability curves of heterogeneous porous media. The broad pore radius distribution (PRD) and throat radius distribution (TRD) are decomposed into relatively narrow component distribution functions which are used for the computer‐aided construction of pore‐and‐throat networks. The quasi‐static motion of menisci in pores and throats is tracked by accounting for capillary forces. The presence of fractal roughness along pore walls ensures the coexistence of both phases in pores. The calculation of the hydraulic conductance of each phase is based on the concept of constricted unit cell. Simulations in component pore networks constructed from narrow PRD and TRD produce a set of capillary pressure and relative permeability functions, the arithmetic averaging of which yields the corresponding functions for a heterogeneous synthetic pore network. This information is used by a dynamic simulator of drainage in permeability networks to predict experimental results of soil columns. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Effects of sample size on capillary pressures in porous media

Capillary pressure curves and their hystereses depend not only upon the geometry and wetting properties of the individual pores of a porous sample, but also upon the accessibility of these pores from the surface of the sample. Dependence of accessibility on distance from the surface of the sample implies that capillary pressure curves are sensitive to sample size. This sensitivity is investigated by measuring capillary pressure curves for porous samples of varying thickness. A theoretical investigation of sample thickness effects is made through application of the concepts of percolation theory of chaotic media. In the theory presented here, functions describing accessibility and pore size distribution appear in integral equations which account for all prominent features of drainage and imhibition, including threshold pressure, hystereses, residual saturations and dependence of residual saturation on initial saturation. The character and magnitude of sample thickness effects predicted by percolation theory are generally consistent with experimental results.     

Discrete pore network modeling of superheated steam drying

A nonisothermal two-dimensional pore network model is developed to describe the superheated steam drying of a capillary porous medium. The complex void space is approximated by a network of spherical pores interconnected by cylindrical throats. In this model, the condensation of water vapor at the network surface as well as the network drying are taken into account. During the network drying period, the liquid transport is driven by capillary action, whereas vapor transport occurs because of convection. The condensation of water vapor within the pores is modeled based on newly formulated liquid invasion rules. The simulation results, presented as temperature and moisture content profiles over time, indicate qualitative agreement with available experimental observations. The inclusion of the liquid invasion rules is shown to accommodate more of the condensed water mass compared to earlier models, in which condensation is only partly treated. Due to the viscous vapor flow, the vapor overpressure within the network, which is the driving force of vapor transport, is reproduced in these simulations. The influence of vapor overpressure on the disintegration of the liquid phase is also discussed.     

Microstructure of Gas Diffusion Layers for PEM Fuel Cells

The gas diffusion layer (GDL) is a critical component of a proton exchange membrane fuel cell, and can play a key role in fuel cell performance. In order to design reliable and durable fuel cells, knowledge of the GDL microstructure is necessary. Currently, characterization of GDLs is generally based on porosity measurements to obtain a pore size distribution. However, the pore size distribution in GDLs may not be the only factor that affects the fuel cell performance. Additional microstructural characterization of GDLs manufactured by three different vendors (Toray, SGL, and Freudenberg) has been investigated. In addition to the pore size distribution, other statistical information of GDL microstructure including size, shape, orientation, and distribution of pores have been characterized and compared. Among these GDLs, the Freudenberg sample was found to have the smallest pore size and orientation analysis indicated that the pores were randomly distributed. Pore roundness was the lowest and pore clustering was highest in Toray sample. The effect of threshold setting on pore size data was also studied and found to have negligible influence on the calculated distributions. The microstructures of the GDLs were reconstructed in three‐dimension using computer simulations and good agreement with the two‐dimensional image analysis data was observed. The present work opens new opportunities for experimentalists and modelers in the area of fuel cell research to take into account the statistical characteristics of GDL microstructure.     

石油污染物在地下环境系统中运移的多相流数值模型

在综合考虑有石油污染物在地下环境体系中扩散、吸附解吸、界面间分配以及微生物降解等作用下,建立了有机污染物在多孔介质迁移转化的多相流动力学模型,并采用特征有限差分方法和隐式压力显式饱和度方法对耦合模型进行数值离散,编制了相应的计算程序;利用该程序对石油污染物在地下环境系统中运移机制进行定量化研究.研究结果表明：石油污染物在地表泄漏以后,将在重力和毛细力的作用下,产生水平位移和垂直位移.当污染物迁移到地下毛细管区后,其向下的运动将整体受到毛细张力的阻碍,污染物要想进入毛细饱和带必须克服油-水界面的进气压力,这时污染物在毛细饱和带顶部聚集以期获取压力,同时将产生以水平方向为主的迁移,最终随着污染物的压力超过其进气压力,导致污染物进入毛细饱和带,在地下水水位上形成一个透镜体.数值模拟曲线与实验测试曲线吻合较好,验证了模型的可靠性.这为定量化研究石油污染物在地下环境系统中分配与归宿及污染预测、预报提供了理论依据.     

Mercury porosimetry and the interpretation of pore geometry in sedimentary rocks and artificial models

The major objectives of this paper are to investigate how the form and hysteresis of mercury injection, withdrawal and reinjection capillary pressure curves are affected by the geometry of pores and their connections in samples of sedimentary rocks and also in artificial and theoretical pore-network models.In particular, those aspects of pore systems which may influence trapping of mercury during pressure reduction and withdrawal are considered. These are: pore to throat ratio, throat to pore coordination number or connectivity and the types and extent of random and non-random heterogeneities within the system.These aspects of pore systems influence the threshold pressure and the gradient of injection curves as well as the gradients and degree of hysteresis displayed by withdrawal and re-injection curves. Such curves are useful in interpreting pore geometry and give information which is valuable in assessing multiphase fluid behaviour in oil and gas reservoir rocks. In the case of water displacing oil or gas, in a strongly water-wet system, the trapping of oil or gas is controlled mainly by capillary forces and a direct analogy with the air-mercury system is possible.     

Study on diffusion and flow of benzene, n-hexane and CCl4 in activated carbon by a differential permeation method

In this paper the diffusion and flow of carbon tetrachloride, benzene and n-hexane through a commercial activated carbon is studied by a differential permeation method. The range of pressure is covered from very low pressure to a pressure range where significant capillary condensation occurs. Helium as a non-adsorbing gas is used to determine the characteristics of the porous medium. For adsorbing gases and vapors, the motion of adsorbed molecules in small pores gives rise to a sharp increase in permeability at very low pressures. The interplay between a decreasing behavior in permeability due to the saturation of small pores with adsorbed molecules and an increasing behavior due to viscous flow in larger pores with pressure could lead to a minimum in the plot of total permeability versus pressure. This phenomenon is observed for n-hexane at 30°C. At relative pressure of 0.1-0.8 where the gaseous viscous flow dominates, the permeability is a linear function of pressure. Since activated carbon has a wide pore size distribution, the mobility mechanism of these adsorbed molecules is different from pore to pore. In very small pores where adsorbate molecules fill the pore the permeability decreases with an increase in pressure, while in intermediate pores the permeability of such transport increases with pressure due to the increasing build-up of layers of adsorbed molecules. For even larger pores, the transport is mostly due to diffusion and flow of free molecules, which gives rise to linear permeability with respect to pressure.     

Influence of the boundary conditions on capillary flow dynamics and liquid distribution in a porous medium

After depositing a wetting liquid onto a porous medium surface, and under the influence of the capillary pressure, the liquid is imbibed into the porous medium creating a wetted imprint. The flow within the porous medium does not cease once all the liquid is imbibed but continues as a secondary capillary flow, where the liquid flows from large pores into small pores along the liquid interface. The flow is solved using the capillary network model, and the influence of the boundary condition on the liquid distribution within the porous medium is investigated. The pores at the porous medium boundaries can be defined as open or closed pores, where an open pore is checked for the potential threshold condition for flow to take place. In contrast, the closed pore is defined as a static entity, in which the potential condition for flow to take place is never satisfied. By defining the pores at distinct porous medium boundaries as open or closed, one is able to obtain a very different liquid distribution within the porous medium. The liquid saturation profiles along the principal flow direction, ranging from constant to steadily decreasing, to the profile with a local maximum, are found numerically. It is shown that these saturation profiles are also related to the geometrical dimension that is perpendicular to the flow principal direction, and changing the boundary type from open to closed allows the liquid distribution within the porous medium to be controlled. In addition to the liquid distribution, the influence of the boundary conditions on capillary pressure and relative permeability is investigated, where both parameters are not influenced by variation of the boundary condition types. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Effects of wettability and pore geometry on mobilization of oil and gas in physical models and application to water-alternating-gas (WAG) injections

Experiments in capillary tubes show that the mobilization of discontinuous oil and/or gas in a hydrophobic (oil-wet) system requires a pressure gradient of about 6 to 7 times larger than for a comparable water-wet system. The mobilization pressure is directly proportional to the contact angle hysteresis and interfacial tension and inversely proportional to tube radius. For experiments in glass micromodels, where pores were ～ 3 times as large as connecting throats, mobilization pressures for oil-wet systems were only ～ 1.7 times as large as for equivalent water-wet systems and pore geometry had more effect on mobilization pressure than did differences in wettability. These pore-level events are thought to affect mobility within WAG banks used to stabilize gas drives.     

Prediction of convective transport within unsaturated concrete utilizing pore size distribution data

The durability of concrete structures is often compromised by physical and chemical interaction with the external environment that leads to ongoing maintenance and, in the worst cases, can lead to reduced structural integrity and consequent asset replacement. Concrete is a porous material and most field-exposed concrete is partially saturated with water. Where the concrete is unsaturated and there is no external water pressure acting on a concrete surface, the primary mechanisms of transport into concrete are convective-diffusion ingress (i.e. uptake of water and water-borne agents due to capillary attraction). This paper assesses capillarity and outlines a predictive model of the uptake of water by concrete based on analysis of the pore size distribution. It is acknowledged that concrete has a multitude of internal pores with a broad range of lengths and cross-sectional shapes, surface roughness, tortuosities, random meeting and divergence with adjacent pores, microcracks and fractures, and variable pore-water chemical composition, however the prediction model shows reasonable agreement with water sorptivity test data.     

NMR relaxation of molecules confined inside the cement paste pores under partially saturated conditions

Nuclear Magnetic Resonance (NMR) relaxation studies of liquids confined inside cement samples mostly refer to water molecules and saturated pores. Here we extend these studies to the ethanol and cyclohexane molecules partially saturating a white cement paste. The two filling liquids were selected as representatives of polar and nonpolar molecules which should experience different interactions with the surface containing OH groups. The results on these two molecules are compared with those obtained on water filled sample. The transverse relaxation measurements, performed at different saturation degrees, clearly revealed three pore reservoirs in cement paste: intra-C-S-H sheet pores, inter-C-S-H gel pores and capillary pores. A two phase exchange model, describing the effective relaxation rate under partially saturated conditions, is also considered. The model allows finding of a relationship between the relaxation time distribution, the filling degree of the pores and the liquid morphology inside these pores.     

Liquid water transport in a mixed-wet gas diffusion layer of a polymer electrolyte fuel cell

After PTFE treatment, a gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC) features mixed wettability, which substantially impacts liquid water transport and associated mass transport losses. A pore-network model is developed in this work to delineate the effect of GDL wettability distribution on pore-scale liquid water transport in a GDL under fuel cell operating conditions. It is found that in a mixed-wet GDL liquid water preferentially flows through connected GDL hydrophilic network, and thereby suppresses the finger-like morphology observed in a wholly hydrophobic GDL. The effect of GDL hydrophilic fraction distribution is investigated, and the existence of an optimum hydrophilic fraction that leads to the least mass transport losses is established. The need for controlled PTFE treatment is stressed, and a wettability-tailored GDL is proposed.