A Critical Review of Water Transport Models in Gas ... - CiteSeerX

Proceedings of the Sixth International ASME Conference on Nanochannels, Microchannels and Minichannels ICNMM2008 June 23-25, 2008, Darmstadt, Germany

ICNMM2008-62201 A CRITICAL REVIEW OF WATER TRANSPORT MODELS IN GAS DIFFUSION MEDIA OF PEM FUEL CELL Jacob LaManna [email protected] Mechanical Engineering Department Kate Gleason College of Engineering Rochester Institute of Technology, Rochester, NY USA ABSTRACT Proton Exchange Membrane (PEM) fuel cells are gaining popularity as a replacement to the internal combustion engine in automobiles. This application will demand high levels of performance from the fuel cell making it critical that proper water management is maintained. One of the areas of interest in water management is the transport of water through the Gas Diffusion Medium (GDM) on the cathode side of the cell. Research is currently being conducted to understand how water moves through the porous structure of the GDM. Due to the small scale of the GDM, most work done is analytical modeling. This paper will focus on reviewing current models for water transport within the GDM of a PEM fuel cell to address state of the art and provide recommendations for future work to extend current models. 1 INTRODUCTION Hydrogen fuel cells are gaining viability as replacements for current fossil fuel powered internal combustion engines. This viability is in part due to the efficiency of fuel cells and also their power densities. Proton Exchange Membrane (PEM) fuel cells offer the best chance for internal combustion engine replacement in the automotive sector. Because of the high demand that the automotive sector would place on PEM fuel cells it is imperative to understand the internal operation of the cell completely. Performance of PEM fuel cells is strongly related to the quantity of water within the cell making water management one of the most important areas of current research. There are currently several methods that are being pursued to model the water transport behavior in the Gas Diffusion Medium (GDM), an area vital to proper water management. Extensive research within the past few years has resulted in many models and modeling methods for analyzing the modes of transport of water through the GDM and its effect on fuel cell performance.

Satish G. Kandlikar Mechanical Engineering Department Kate Gleason College of Engineering Rochester Institute of Technology, Rochester, NY USA

One modeling method developed to understand flow in the GDM is the pore network method. Pore network modeling was adapted from soil mechanics and percolation theory [6, 8, 59, 60] where it would track liquid flow in porous soil. One of the first adaptations to fuel cells of the pore network model was performed by Nam and Kaviany [28]. Here the structure for the network was changed to a square grid to represent the structure in the GDM formed by the carbon fibers. Since this adaptation several other models have been developed using this method [10, 11, 24, 39, 45, 46]. Another popular modeling method is the multiphase mixture model (M2) original developed by Wang and Cheng [52]. This model is capable of tracking two-phase flow within a capillary porous media, specifically the GDM of a PEM fuel cell. The M2 model has been implemented in several models since this initial model [7, 12, 16, 20, 32, 34, 48, 61]. Since most models either describe the GDM from the macroscopic level in many two-phase flow models with parameters such as effective porosity and permeability or develop generalized pore structures as in pore network models, work has been performed to use actual GDM structure data. Niu et al. [29] developed a lattice Boltzmann model that tracked the two-phase flow through an X-ray tomography reconstructed model of actual GDM. Schultz et al. [40] used a stochastic approach for reconstructing the form for the GDM. Other modeling approaches have included continuity and energy based models, electrochemical coupled models, and mixed domain models. Continuity and energy based models such as by Matamoros and Brüggemann [25] and Rawool et al. [38] base transport through the GDM on the continuity equation and conservation equations. Electrochemical coupled models such as by Hwang [14], Ju et al. [18], and Sinha et al. [47] account for the electrochemical reactions occurring at the catalyst sites to model the entire fuel cell. This method allows for the construction of an i-V curve to show the effects of twophase flow on performance within the fuel cell. Mixed domain models by Meng [27] and Vynnycky [50] split the fuel cell into

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Copyright © 2008 by ASME

2


110°

Not given

Air Air, water vapor Air, water vapor

2-p flow using full morphology model

2-p flow using multiphase mixture model

2007

Pasaogullari et 2007 al.

Koido et al.

Wang et al.

[54]

[20]

Ju et al.

[16]

2008

2007

2007

Air, water vapor

Air

3-D, multiphase model


Air


[36] Pharoah et al. 2006 2-D Cathode model

[32]

Schulz et al.

[40]

Air

2006

2-p flow using mmrt lattice Boltzmann model

Niu et al.

[29]

Capillary diffusion

Capillary diffusion

Darcy Law flow

Potential driven transport

Capillary transport

Capillary forces

Diffuse interface theory

Comment Does not take actual GDL morphology into account

Results Relative permeability and capillary pressure on heterogeneity of porous material

Model was able to track 2phase interface in 3D GDL structure

Methods for calculating capillary The authors used a good mix 3D reconstruction of pressure and relative permeability of experimental and actual diffusion matched experimental curves well. numerical techniques to media Shows applicability of these verify the models purposed in this paper models

Provides reliable capillary pressure Further evaluation of data that can feed into full cell compression model needed models Anisotropic properties of the GDL Many other models assume Effective Porosity greatly affect the temperature and isotropic properties which can affect the results collected liquid water distributions Anisotropic properties of the GDl can greatly affect effective mass Should be extended into to Effective Porosity diffusivity, thermal conductivity, 3D to show anisotrpoic electron conductivity, and liquid differences in more depth permeability Agrees with NR but shows Model compares well with neutron the weakness of NR in it Effective Porosity radiography data. Shows actual inability to separate anode distribution of water in cell. and cathode water distributions Compared the performance Data shows the importance characteristics of carbon paper of knowing operational Effective Diffusivity and carbon cloth, found that conditions when designing a carbon cloth performs better under cell and selecting between high humidity will carbon paper is cloth and paper.

Stochastic reconstruction of two media

3D reconstruction of Authors show that the mmrt lattice actual diffusion Boltzmann model is effective for media use in GDL 2-phase flow modeling

Further research is needed to Regular cubic Most models most likely over validate the results of network, calibrated estimate gas phase flow possible overestimation to two samples Shows flows governed by capillary Further research needed in Regular cubic the study of mixed wet network, calibrated fingering, thereforce Darcy's Law cannot be used properties to two samples Crossover from fractal fingering to Further Research into mixed Regular cubic stable front morphology occurs wet effects and new network, calibrated with increasing hydrophillic fraction manufacting processes to to two samples supporting the use of Darcy's Law control hydrophillic fraction

Regular square network

GDL characterizing

Table 1: Summary of Selected Articles

162°

110°

92°

120°

60° and 120°

Capillary and viscous forces

Distribution range of 60°120°

Air

Capillary and viscous forces

diffusion

Liquid flow mechanism invasion percolation algorithm w/

110°

[46] Sinha & Wang 2008 Pore network model

100° for SGL and 98° for Toray

Not given

Air

Air

GDL Contact angle

[45] Sinha & Wang 2007 Pore network model

Gostick et al.

[11]

Capillary network model

Gas phase

Air

2007

Markicevic et al.

[24]

Model approach

2007 Pore network model

Year

Author

Ref #

two separate domains. This allows for the removal of complicated boundary conditions between the catalyst layers and the membrane therefore simplifying the model. This article will focus on discussing several pore network and two-phase flow models. A table summarizing selected articles from this review is given in Table 1. NOMENCLATURE GDM – gas diffusion medium CCL – cathode catalyst layer PEM – proton exchange membrane MEA – membrane electrode assembly MPL – microporous layer 2 DISCUSSION 2.1 GOSTICK ET AL. [11] PORE NETWORK MODEL Model Description: Gostick et al. [11] developed a pore network model to investigate the relative permeability of water and gas, and the effective gas diffusivity. The authors modeled the fibrous GDM as regular cubic pores. These cubic pores are interconnected by narrowing throats that are treated as square ducts. The basic framework of the model can be seen below in Figure 1. A Weibull cumulative distribution was used to assign the pore body size distribution as the network was constructed. The throat size is determined by using the diameter of the smallest adjacent pore. Saturation levels were varied from 0 to 1 for liquid water to find the affects on gas transport. Anisotropic properties were analyzed in this article. To account for this in the model, throats were additional constricted in specific directions. This constriction was calibrated to match the porosity of Toray 090 and SGL 10BA.

The authors selected a method to describe how the nonwetting phase (water) would move through the diffusion media. This simulation began with low capillary pressure and the network was analyzed to find any pores that could be penetrated. Then the throats that are connected to these pores are counted and all are marked as open (available for nonwetting phase). The algorithm then increases the capillary pressure and repeats the procedure. Two limiting cases were developed to analyze the twophase transport within the porous material. The first case stipulates that once a pore is penetrated by liquid water, the pore is no long capable of accepting the gas phase. The second case allows the wetting phase to maintain connections with neighboring pores as the current pore is penetrated. Case 1 was designed to give the worst case for gas transport. Model Results: The model was used to calculate the relative permeabilities of each phase. This relative permeability accounted for the interaction between phases. Relative permeability was calculated in the x, y, and z directions to determine what the anisotropic effects were. It was found that there is a preferential spreading of water in the in-plane direction at the surface of the GDM. This spreading of liquid water can greatly reduce the available area for through-plane diffusion of the reactant gases. The authors found that current models most likely overestimate the amount of gas phase transport that occurs and suggested new models that agree with their results. Overestimation of the gas phase transport within the cell results in underestimation of the quantity of water saturation within the GDM. This can result in much lower current densities being calculated due to the fact that a dry GDM can support much higher current densities than a saturated GDM. Need for Future Work: The authors, Gostick et al. [11] call for an urgent need for experimental research into the effects of water saturation on water permeability and gas diffusion. This need is to verify the results of this experiment since it claims that most models overestimate the gas phase transport. Also this model could be extended to the actual topology of the GDM, which could lead to results that better represent the actual physical structure within a fuel cell. 2.2 SINHA AND WANG [45], [46] PORE NETWORK MODEL

Figure 1: Pore network used by Gostick et al. [5] Capillary pressure was modeled using the Young-Laplace equation due to the choice of modeling the pores as square cross-sections. A uniform contact angle of 115° was chosen for the entire network.

Model Description: Sinha and Wang [45] developed a pore network model based on the frame work as determined by Nam and Kaviany [28]. This method models the GDM as randomly stacked regular fiber screens that form cubic pore shapes and square cross-sectional throats; this can be viewed below in Figures 2 and 3. A cut-off log normal distribution was selected to represent the pore size distribution. The authors assume that only one fluid can inhabit a throat at a time. The algorithm selected begins with the pore network saturated with air with a liquid water reservoir at the inlet face. The authors also account for land regions and only allow water to leave the GDM in areas that reside above channels. The

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Young-Laplace equation is used to govern liquid water movement. Liquid water injection rate is equivalent to the water production at 2.0 A cm-2.

within the GDM and that this must be taken into account. Darcy’s law is applicable in cases where there is compact invasion at high capillary numbers and therefore cannot describe the fractal capillary fingering at low capillary numbers described in this model. They suggest that modeling methods need to be developed that are capable of applying this knowledge to the typical macroscopic descriptions used for fuel cells.

Figure 2: Pore Network Development by Nam and Kaviany [28]. Figure 4: Example of Results from Sinha and Wang [45].

Figure 3: Methods of Diffusion [28] Model Results: The authors, Sinha and Wang [45] found that with the fractal capillary fingering transport of water through the GDM that there is no surface coverage by the water on the inlet side. Water moves in several clusters due to the fractal nature of transport. These two effects can be seen below in Fig. 4. Because capillary pressure determines the direction of the flow, areas of dead ends are formed. These dead ends occur when water contacts a throat where the capillary pressure to invade is too high for the water to continue forward motion. To determine the active pore for water transport, the authors graphed only the pores with non-zero volumetric flow rates (Fig. 5). This shows that the vast majority of the water within the GDM is non-transporting and only blocks gas flow. Saturation levels for liquid water were determined based on capillary number and varied from 0-0.95. Sinha and Wang found that water flow through a homogeneously hydrophobic GDM is governed by fractal capillary fingering due to the extremely low capillary numbers encountered in fuel cells. The authors conclude that two-phase Darcy’s law cannot properly describe the conditions occurring

Figure 5: Steady State Flow Clusters [45] Model Description: Later, Sinha and Wang [46] extended the model described above to investigate the effects of mixed-wet properties within a GDM. This mixed-wet model combines areas that are hydrophobic with areas that are hydrophilic. The distribution of hydrophilic regions is assumed in this analysis since no method of calculating the actual distribution currently exists. The authors assumed a random distribution for the contact angle assigning larger diameter pores larger contact angles. Assigning smaller contact angles to the smaller pores approximates what could occur during actual teflonation process since PTFE may not actually coat small diameter pores which leaves them hydrophilic. Model Results: The authors Sinha and Wang [46] accounted for the effect of hydrophilic/hydrophobic interfaces within a pore. They

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found that water takes preference towards the hydrophilic areas within the GDM. As the concentration of hydrophilic regions increase the movement of water shifts from a finger-like structure to more cylindrical-like structures. This results in more localized flow which goes against the current model of finger-like distribution since the flow transitions to a stablefront morphology (Fig. 6). Saturation levels for this model varied from 0-0.5 based on contact angle. The saturation levels seen here are lower than the previous model because water takes the preferential routes through the hydrophilic regions of the GDM.

wettability of the GDM during manufacturing should occur since there is no current method to precisely control the hydrophobic distribution in the GDM and if this method could be produced then custom mixed-wet GDMs could be engineered.

Figure 7: Hydrophilic distributions in Mixed-Wet GDM Analysis [46]

Figure 6: Stable-Front Water Transport in mixed-wet GDM [45] Sinha and Wang [46] found that two-phase Darcy’s law is still applicable for use in mixed-wet GDMs which is in opposition to results found by the authors in their previous pore network model stated above. They find that the mixed-wet conditions better describe the actual conditions of GDM materials since the contact angle for carbon varies and the PTFE distributions are not constant. Sinha and Wang [46] also analyze for a non-uniform distribution of hydrophilic areas. It is found that high distributions of hydrophilic properties towards the center of the GDM thickness (Fig. 7) results in higher liquid water saturation in the center of the GDM. This results in higher levels of mass transport losses due to the fact that the gas diffusion paths for the reactants are much more tortuous. The authors describe the need to optimize the wettability distribution to limit the effects of mass transport losses. Need for Future Work: The current models by Sinha and Wang are assumed isothermal and therefore does not account for phase change of water. This needs to be addressed due to the temperature gradients across the GDM in non-isothermal analyses. Temperature gradients and phase change could significantly affect the liquid water distributions found in this analysis. The actual morphology of the GDM should be taken into account to better represent the actual structure of the GDM. This could affect liquid water distributions due to the pore size distributions within the GDM. As suggested by the authors, there is a need to experimentally analyze the actual properties of GDM pore walls since this will give true insight into the distribution of hydrophilic properties. Research into controlled

2.3 PASAOGULLARI ET AL. [32] TWO PHASE MODEL Model Description: Pasaogullari et al. [32] developed a two-phase flow model to analyze the effects of anisotropic properties of the GDM on water transport. The authors constructed a 2-D, two-phase flow, non-isothermal model developed for the cross-section of the GDM. The main focus of the model was to investigate how modeling the GDM with anisotropic properties due to its inherent structure would affect current density, temperature distribution, reactant fluid velocities, and liquid water content. Due to the stacking of carbon fibers, GDM has higher thermal conductivity in the in-plane direction along the fibers whereas the thermal conductivity is lower through-plane because of crossing through fibers. The model developed by the authors is based on the multiphase mixture model (M2). This computational method is capable of explicitly tracking the interface between single- and two-phase regions. The Brinkman extension to Darcy’s Law is used to govern conservation of momentum. Due to the low solubility of oxygen and nitrogen in water, water is assumed to be the only liquid in the mixture. To account for the anisotropic structure of the GDM, effective diffusivity is calculated for both the in-plane and through-plane directions. The calculated diffusivities show that the in-plane diffusion is favored since it is much higher than the through-plane direction. Permeability and capillary pressure are also calculated for both the x and y directions to account for anisotropy. Assumptions made include analyzing water content in the membrane and anode based on a function of water content and

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temperature within the GDM given that the anode side is fully saturated, negligible anode overpotential, and the catalyst layer is a thin layer between the GDM and membrane. The first assumption was made to simplify the model and to reduce the model to just the cathode GDM as it was assumed that there would be a net zero water transport coefficient. Model Results: To highlight the effects of anisotropic properties, the authors ran two identical simulations where one simulation had anisotropic properties while the second had isotropic properties. These tests were calibrated to Toray TGPH carbon paper. It was found that temperature effects can vary significantly between anisotropic and isotropic properties as seen in Fig. 8. Because of the higher thermal conductivity in the in-plane direction the temperature profile is significantly more linear when moving from the catalyst layer to the bi-polar plate. This change in temperature distribution greatly affects the water transport and saturation levels as seen in Figure 9. Liquid water concentration increases in the areas above the lands due to the lower temperatures seen there in the anisotropic trials when compared to the isotropic trials. Overall lower temperatures are predicted for the anisotropic conditions which result in higher liquid water content in the GDM. It was also found that the capillary transport of liquid water and diffusion of water vapor aid each other in the through-plane direction but oppose each other in the in-plane direction since water is condensing near the channel land areas which cause a shift between phases. The authors call for the strong need for coupled, anisotropic twophase heat and water transport modeling to further explore this phenomenon and its effect on fuel cell performance.

Figure 9: Liquid Water Saturation Distribution Comparison at 0.6V [32] Need for Future Work: The model should be applied to a cell wide model so that the actual water content within the membrane and anode can be calculated. This will eliminate the assumption of water content and link the effects of anisotropic properties to the overall cell performance. Extension into compression effects should be considered since compression could make the properties more isotropic since the resistance in the through-plane direction would be reduced due to the contact pressure. Also, a move to 3D should be performed for this model to test for the existence of 3D anisotropy and its affect on cell performance.

2.4 PHAROAH ET AL. [36] TWO PHASE MODEL

Figure 8: Temperature Distributions in GDM at 0.6V Comparing Anisotropic and Isotropic Properties [32]

Model Description: Pharoah et al. [36] performed an extensive review into the methods of accounting for anisotropic properties and then developed a 2D cathode model to analyze the effects of anisotropic properties. The review that was performed concluded that most current models assume that volumetric averages are appropriate and use isotropic properties. The authors ran their model with both isotropic and anisotropic properties to compare the results between the two. The model developed is a 2D electrochemical model that tracks the multi-component diffusion of species within the GDM, electron transport across the GDM, and the electrochemical reactions taking place at the catalyst layer. Diffusion through the GDM is governed by the Maxwell-Stefan equation. The electrochemical reaction is governed by the Butler-Volmer equation modified to account for catalyst microstructure and the charge transfer is governed by Ohm’s Law. Model Results: The authors compare data for isotropic effective diffusivity found using the Bruggeman relation, isotropic effective

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diffusivity found using percolation theory, and anisotropic effective diffusivity found using percolation theory. It was found that anisotropic properties have considerable effect on current density distribution when compared to isotropic properties as can be seen in Fig. 10. The difference between anisotropic and isotropic properties increases as porosity decreases. The reason for this is the oxygen transport is higher with greater porosity which increases the overall reaction. It is also shown that the Bruggeman relation typically overestimates the current density by 5-6%. As shown in Fig. 11, there is minimal influence on the calculated polarization curve for different material models. What is important to note is that the current density distribution is affected.

More work should be performed to understand the differences that arise when modeling with isotropic or anisotropic properties. This is important since it is often assumed that properties are isotropic in many current models while the actual structure of the GDM lends itself to anisotropic properties. Also, the model should be adapted to two-phase flow so that saturation levels could be obtained with reference to the diffusivities through the GDM. 2.5 NIU ET AL. [29] TWO PHASE MODEL Model Description: The authors constructed a 3D, 2-phase flow model using the multiphase, multiple-relaxation-time lattice Boltzmann model. The model is based on the mean-field diffuse interface theory. This model is capable of tracking the Liquid-Gas Phase Interface through the GDM and varies liquid saturation levels from 0-0.6. GDM structure was represented by a 3D reconstruction using the Dissipative Particle Dynamics (DPD) method as seen below in Fig. 12.

Figure 10: Comparison of Effective Diffusivity on Current Density [36]

Figure 12: Dissipative Particle Dynamics Reconstruction of GDM. [29] The MRT lattice Boltzmann method solves the NavierStokes and Cahn-Hilliard equations for N discrete velocities. The benefit of the lattice Boltzmann method over other solution methods is that it can solve the Navier-Stokes equations over complex geometries like that of a GDM. The forces in the interface of the liquid and gas are also analyzed in this method.

Figure 11: Comparison of Polarization Curves [36]

Model Results: The MRT lattice Boltzmann method is found to give better simulation results when compared to the Bhatnagar-GrossKrook (BGK) method which is typically used for this type of analysis. The calculated liquid interface can be seen in Figure 13 where the GDM image has been removed for better visibility. The authors used the MRT lattice Boltzmann method to calculate absolute and relative permeabilities. The calculated

Need for Future Work:

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results compare well with current numerical methods including other two-phase flow methods and pore network methods. Need for Future Work: Integration of water vapor in gas phase and the effects of temperature gradients could turn this modeling method into a powerful tool. Currently, the model only analyzes air as the gas phase when water vapor could become important under certain operational ranges. Further work should be performed to verify this modeling method since it is new to fuel cell analysis.

typically the method of capillary flow of water through the GDM in most current models and was shown to transition to stable-front flow by Sinha and Wang [46]. This transition to stable-front flow allows for the justification of the use of Darcy Law transport modeling. Anisotropic property effects were analyzed by Pasaogullari et al. [32] and Pharoah et al. [36]. These effects were shown to significantly affect liquid water and current density distributions. This is significant because many current models volume-average properties and assume isotropic properties. Niu et al. [29] presented a new modeling method for water transport models with the use of the multiphase MRT lattice Boltzmann method. The use of this new method allows for the tracking of the actual liquid-gas interface in a complex 3D reconstructed model of the GDM. 4 CONCLUSION This paper has given a detailed review of several modeling methods currently employed to investigate water management within a PEM fuel cell. It has been shown through each of the models how temperature gradients within the GDM can affect the water phase and saturation level. Therefore, it is critical to couple heat transfer with water transport to properly model phase change and saturation levels of water in the GDM. As models account for phase change of water with greater detail, a better understanding of the actual operational conditions in the fuel cell will be obtained. Several recommendations for improvement to the current models addressed within this paper have been made. All models discussed in this paper lack a combination of two-phase flow, phase change of water, and an actual representation of the GDM. The three of these combined could result in an improved model of the GDM. The phase change of water needs to be implemented in models since it can effect the actual liquid water saturation in the GDM possibly resulting in underor over-estimation of saturation levels when not accounted for. Actual GDM structure needs to be implemented with phase change since the actual structure of the GDM could significantly influence condensation and evaporation with the random pore sizes that exist. These recommendations could improve the current knowledge of PEM operation and result in an overall improvement in fuel cell performance. The current models combined with futures models based off of the recommendations made in this paper will lead to better water management techniques that will improve overall performance of the fuel cell. This increased performance will ensure that the PEM fuel cell will be capable of performing in its role of internal combustion engine replacement. ACKNOWLEDGMENTS This work was supported by the US Department of Energy under contract No. DE-FG36-07G017018.

Figure 13: Graphical Representation of Liquid-Gas Interface. [29] 2.6 MODEL SUMMARY The models reviewed within this paper all present innovative and/or critical items for water transport modeling. Gostick et al. [11] discovered the possible overestimation of gas phase transport in most current models and discussed the need to address this in future modeling. Fractal fingering is

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