Validation of pore network simulations of ex-situ water distributions in a gas diffusion layer of proton exchange membrane fuel cells with X-ray tomographic images
Graphical abstract
Introduction
Water management is a crucial aspect of Polymer Electrolyte Membrane Fuel Cells (PEMFC) operation. Water produced in excess by the oxygen reduction reaction needs to be removed from the cell to prevent flooding while the polymer membrane must stay well hydrated to conduct protons. Gas diffusion layers (GDL) are one of the electrodes porous layers [1] and a key component with respect to the water management. During fuel cell operation, liquid water can also appear in GDLs as a result of condensation [2]. Its effect is to impede the gas flux towards the catalyst layer where the electro-chemical reactions take place, decreasing the fuel cell performance. The biphasic, electrical, thermal and mechanical behaviors of GDLs must be therefore understood and well characterized in order to optimize fuel cell performance. In this respect, it is desirable to develop efficient and accurate numerical tools to simulate two-phase flows in GDLs.
Biphasic simulations in PEMFCs porous media have been widely investigated [3], [4]. The simulation methods can be divided into direct methods such as Lattice-Boltzmann and (mesoscale) geometry based methods like the full morphology [5] and pore networks models [6], [7], [8]. Mesoscale methods are preferred here in order to keep the computational cost low to allow for using images large enough to be representative of the GDL structure. It should be noted that the pore network models (PNM) have been frequently used to investigate two-phase flows in GDL, e.g. Refs. [2], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. Therefore, it is particularly important to confirm that PNM are well adapted to describe two-phase flows in fibrous materials, especially for the case of the capillarity driven regime that is expected to prevail in GDLs [9]. This is not obvious a priori because the microstructure of fibrous materials is quite different from the structure of granular materials or porous rocks mostly considered in previous applications of PNM, e.g. Refs. [23], [24].
It is usual to distinguish the structured pore networks from the unstructured ones. A structured pore network is constructed on a given lattice, typically a cubic lattice for 3D simulations. The pores are located on the nodes of the lattice and connected by narrower channels, also referred to as links, corresponding to the constrictions of the pore space. In a simple cubic network the channels are aligned with the three main directions of a Cartesian coordinate system. By, contrast, the unstructured networks offer the possibility to respect much more closely the local geometry of a given microstructure. Starting from a digital image of the “real” microstructure, the network is directly constructed from the image using appropriate numerical techniques. It is the approach taken in the present paper.
In this context, the main objective of the present paper is to investigate the capabilities of image based unstructured pore network and full morphology models to predict water distributions in fibrous materials such as the ones used in GDL. These simulation methods have already been successfully used to predict capillary pressure curves and saturation levels, e.g. Ref. [10] where a simple structured cubic network is used. The novelty in the present effort is to develop an image based unstructured pore network and to look at the three dimensional water distributions and not only to slice averaged saturation levels.
Extracting an unstructured pore network from a 3D digital image of a microstructure is described in a number of publications [25], [26], [27], [28], [29]. Most methods are based on medial axis analysis or the consideration of maximal balls. Several articles reviewed and discussed these methods [30], [31], [32], [33]. As far as we are concerned, we develop a method based on watershed segmentation. Watershed segmentation [34], [35] or similar methods [36], [37] are used in several articles as an image analysis tool to segment pores without doing pore network extraction [38], [39], [40]. Recently a few approaches use watershed segmentation or similar methods as part of a pore network extraction procedure [26], [28], [29], [41], [42]. The principle of watershed segmentation is to find constrictions, defined in a robust way as watershed lines. It has several advantages: it is a well-known tool in image analysis, it is robust and off-the-shell open source codes are available. It also offers an explicit degree of freedom regarding the pore merging, thanks to pore markers defined by the user.
In order to validate our pore network extraction procedure and to study the impact of the pore merging degree of freedom, we compare pore network simulations with experimental data and full morphology simulations. Full morphology simulations are in fact suggested as a useful benchmark to test pore network extraction procedures.
The experimental data are 3D microscopic liquid water distributions from water injection experiments obtained by X-ray tomographic microscopy [11]. X-ray tomography has been used in several works to visualize liquid water in GDLs [23], [24], [43], [44], [45], [46], [47], [48], [49]. Liquid water distributions in GDL obtained by X-ray tomography have also been used in some previous works in conjunction with numerical simulations, e.g. Ref. [9]. However, the present work is the first one, to the best of our knowledge, to propose a detailed comparison between PNM simulations and X-ray tomography images of the liquid water distribution in a GDL.
The aim of this article is thus to assess the predictability of pore network and full morphology models to simulate capillarity dominated biphasic flows in GDLs and to study a pore network extraction procedure based on watershed segmentation.
Regarding two-phase flows in GDL, one can distinguish in situ two-phase flows from ex-situ two phase flows. In situ refers to GDL in an operating fuel cell whereas ex situ refers to GDL typically used in characterization experiments involving the sole GDL (as opposed to the GDLs in the membrane electrode assembly (MEA) for the in-situ case). A typical objective of ex-situ experiments is to characterize the capillary pressure curve, an important parameter of the porous media classical two-phase flow model. In situ two-phase flows are a priori more complex than the ones observed in typical ex-situ experiments because of the coupling with heat transfer and the significance of phase change phenomena. Also, obtaining images of in situ liquid distribution from X-ray microscopy is more challenging. For these reasons, it is natural to first develop comparisons between simulations and experiments for the simpler ex-situ conditions. In this paper, an ex-situ configuration is considered.
Section snippets
Material
Gas diffusion layer material of the type SGL™ 24BA (SGL Carbon, D) is chosen for this study. SGL™ gas diffusion layer materials are composed from carbon fibers and a micro-porous carbonaceous binder. The pore size of the binder is typically less than 1 μm. SGL™ 24 has an uncompressed thickness of 190 μm and an uncompressed porosity of 84%. The suffix “BA” means that the material is hydrophobized with 5% (w/w) of PTFE and that there is no microporous layer (MPL).
X-ray tomographic microscopy
Experimental water distributions
Benchmarking network extraction parameters against full morphology results
As mentioned before pore network extraction from an image is a complex procedure which involves making a choice regarding the definition of pores. We discuss in this section the consequences of the choice of the pore merging parameter. We also suggest that comparing pore network two-phase simulations with full morphology simulations can help verify that the extracted pore network is valid.
The extracted pore network is not unique because the markers choice gives a degree of freedom on pore
Discussion
The agreement between the experiments and the simulations is considered as good but is not perfect. Possible model improvements are briefly discussed in this section.
Uncertainties regarding the inlet conditions are considered as a major cause of discrepancies between the simulations and the experiment. In this work we imposed inlet boundary conditions considering the hydrophilic membrane as a water reservoir. Accordingly, water enters the GDL where the fibers in contact with the membrane
Conclusion
Pore network and full morphology simulations of quasi-static two-phase flow in a gas diffusion layer were performed. A pore network extraction method based on watershed segmentation was developed. The geometry of the tomographic image was analyzed to identify pores and constrictions. A comparison between full morphology and pore network two-phase simulations was performed. This validated the extraction procedure. The extraction computations are fast (40min for a 700 million voxels image) and
Acknowledgements
The authors gratefully acknowledge the funding from the EU project IMPALA (“IMprove Pemfc with Advanced water management and gas diffusion Layers for Automotive application”, project number: 303446) within the Fuel Cells and Hydrogen Joint Undertaking (FCHJU), and SGL Carbon for the supply with gas diffusion layer materials.
References (59)
- et al.
Gas diffusion layer for proton exchange membrane fuel cells—A review
J. Power Sources
(2009) - et al.
Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow
Adv. Water Resour.
(2002) Flow in porous media—pore-network models and multiphase flow
Curr. Opin. Colloid Interface Sci.
(2001)- et al.
Two-phase flow and evaporation in model fibrous media
J. Power Sources
(2008) - et al.
Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells
J. Power Sources
(2007) - et al.
Determination of transport parameters for multiphase flow in porous gas diffusion electrodes using a capillary network model
J. Power Sources
(2007) - et al.
Modeling liquid water transport in gas diffusion layers by topologically equivalent pore network
Electrochim. Acta
(2010) - et al.
Scale effect and two-phase flow in a thin hydrophobic porous layer. Application to water transport in gas diffusion layers of proton exchange membrane fuel cells
J. Power Sources
(2009) - et al.
Pore-network simulations of two-phase flow in a thin porous layer of mixed wettability: application to water transport in gas diffusion layers of proton exchange membrane fuel cells
J. Power Sources
(2011) - et al.
Impacts of the mixed wettability on liquid water and reactant gas transport through the gas diffusion layer of proton exchange membrane fuel cells
Int. J. Heat. Mass Transf.
(2012)
Liquid water transport in a mixed-wet gas diffusion layer of a polymer electrolyte fuel cell
Chem. Eng. Sci.
Liquid water distribution in hydrophobic gas-diffusion layers with interconnect rib geometry: an invasion-percolation pore network analysis
Int. J. Hydrogen Energy
Steady saturation distribution in hydrophobic gas-diffusion layers of polymer electrolyte membrane fuel cells: a pore-network study
J. Power Sources
Pore-network analysis of two-phase water transport in gas diffusion layers of polymer electrolyte membrane fuel cells
Electrochim. Acta
Pore-network modeling of liquid water transport in gas diffusion layer of a polymer electrolyte fuel cell
Electrochim. Acta
Evaporation, two phase flow, and thermal transport in porous media with application to low-temperature fuel cells
Int. J. Heat. Mass Transf.
Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: effect of through-plane saturation distribution
Int. J. Heat. Mass Transf.
Electrochemistry Communications Probing water distribution in compressed fuel-cell gas-diffusion layers using X-ray computed tomography
Electrochem. Commun.
An automated simple algorithm for realistic pore network extraction from micro-tomography images
J. Pet. Sci. Eng.
X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems
Adv. Water Resour.
Quantitative computer reconstruction of particulate materials from microtomography images
Powder Technol.
Analysis of pore interconnectivity in bioactive glass foams using X-ray microtomography
Scr. Mater
Liquid water visualization in PEM fuel cells: a review
Int. J. Hydrogen Energy
Investigation of liquid water in gas diffusion layers of polymer electrolyte fuel cells using X-ray tomographic microscopy
Electrochim. Acta
Investigation of 3D water transport paths in gas diffusion layers by combined in-situ synchrotron X-ray radiography and tomography
Electrochem. Commun.
Performance loss of proton exchange membrane fuel cell due to hydrophobicity loss in gas diffusion layer: analysis by multiscale approach combining pore network and performance modelling
Int. J. Hydrogen Energy
Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: effect of local saturation and application to macroscopic continuum models
J. Power Sources
The geometry of primary drainage
J. Colloid Interface Sci.
Water transport in gas diffusion layer of a polymer electrolyte fuel cell in the presence of a temperature gradient. Phase change effect
Int. J. Hydrogen Energy
Cited by (49)
Progresses on two-phase modeling of proton exchange membrane water electrolyzer
2024, Energy ReviewsImage-based pore-scale modelling of the effect of wettability on breakthrough capillary pressure in gas diffusion layers
2023, Journal of Power SourcesPore network modeling of advection-diffusion-reaction in porous media: The effects of channels
2023, Chemical Engineering ScienceWater cluster characteristics of fuel cell gas diffusion layers with artificial microporous layer crack dilation
2023, Journal of Power SourcesExperimental and simulation analysis of liquid capillary fingering process in the gas diffusion layer
2023, Journal of Power SourcesCitation Excerpt :The experimental method is useful for revealing the phenomenon of liquid water capillary fingering within the GDL [21], but the simulation method for simulating liquid water movement in the GDL is useful for solving the microscopic characteristics of two-phase transport, which is a useful tool for control and study of geometric and other parameters provide the opportunity to address fundamental causal relationships that are not explained by experimental studies [22]. The volume of fluid (VOF) [23–40], pore-network modeling (PNM) [41–61], and lattice Boltzmann method (LBM) [62–93] are the main simulation methods for simulating liquid phase movement in the GDL, and the specific study contents are listed in Table 1. The main factors impacting the internal liquid water movement for GDL are GDL thickness [53,54,72], fiber structure [30,57,79,92], pore distribution [26,28,45,46,69,83], compression deformation [26,27,32,34,49,59,66,67,70,88], PTFE content and distribution (wettability) [26,31,36,39,40,43,44,55,56,60,64,65,67,68,73,76,86,87,89–93].