Tortuosity of an SOFC anode estimated from saturation currents and a mass transport model in comparison with a real micro-structure
Introduction
Thanks to their high efficiency and the low level of pollutants they emit into the environment, solid oxide fuel cells (SOFCs) have the potential to become one of the most important energy conversion devices. A solid oxide fuel cell consists of two porous ceramic electrodes (the cathode and anode) separated by a solid ceramic electrolyte. The electrode microstructure is an important factor determining its electrochemical performance. A typical anode consists of a nickel phase (Ni), an yttria stabilized zirconia phase (YSZ) and a pore phase. A typical cathode is made from porous Lanthanum Strontium Cobalt Ferrite (LSCF). Each component plays a unique and important role in the transport processes inside an SOFC by providing a pathway for different spices; the YSZ phase for oxygen ions, the Ni and LSCF phases for electrons and the pore phase for gases. Therefore the electrochemical reaction can occur only in a place where all three phases meet each other so called Triple Phase Boundary (TPB). Numerical modeling can be a useful tool to design and optimize an anode microstructure [1], [2], [3]. However, to calculate transport phenomena inside a solid oxide fuel cell's anode, tortuosity plays a key role. The determination of the tortuosity value is a key issue for determining a pressure gradient, therefore it is necessary for any modeling of cell current–voltage characteristics [4]. Following Tsai and Schmidt [5], the tortuosity of an anode can be defined as a ratio of the real diffusion path length and electrode thickness. The concept of tortuosity was introduced to porous media study by Carman [6] who studied a flow through a bed of sand. He introduced tortuosity as a factor that takes into account the elongated diffusion path of fluid inside porous media. In his study he assumed that a porous bed of thickness Ls can be regarded as a bundle of sinuous capillary tubes with a uniform cross section and length Le. Carman's idea of tortuosity applied to general porous media is presented in Fig. 1(a). In this simplified system tortuosity is defined as the ratio of the length of the real diffusion patch, Le, to the patch in the straight channel case, Ls:
It is important to keep in mind the difference between tortuosity and the tortuosity factor. In the light of Carman's formulation, the tortuosity factor is defined as the square of the tortuosity and it is used as an enhancement factor in mass diffusion equation [7], [8], [9], [10], [11]:where ε is the porosity, Di is the diffusion coefficient of a gas spices i inside a gas mixture, and Di,eff is the effective diffusion coefficient taking into the account elongated diffusion path of the fluid inside the porous media.
The authors' literature survey unravels several problems related to tortuosity. First of all, depending on the context the term tortuosity might refer to τ, τ2, τ− 1 or τ− 2 [7], [8], [9], [10], [11], [12], [13], [14], [15]. Moreover, it is not clear to what extent Eq. (1) can be applied to the real porous structure and how to define Le from Eq. (2) in the SOFC anode where the fuel paths might be extremely complicated and gas communication paths can create many branches, separate and rejoin [11], [13], [14]. Such a complex structure makes it impossible to clearly define a diffusion path length and consequently the value of the tortuosity. Having said that, within this work, the authors decided to use (τ) to denote tortuosity and (τ2) to denote the tortuosity factor. However, it is important to keep in mind that only the tortuosity factor, symbolically presented as (τ2), and defined as in Eq. (2) can be quantitatively evaluated. The value of tortuosity (τ) is calculated afterwards with a simple assumption of the capillary model of the porous media. This approach is applied to avoid misunderstanding between tortuosity and the tortuosity factor. It also allows for easier comparison within already published data where the capillary model assumption was intentionally or unintentionally used.
The second problem is related to the value of the tortuosity itself. Even though modeling of the anode performance is very sensitive for the tortuosity factor there is a big disagreement in published data. Different tortuosities have been reported by various research groups working on the Ni/YSZ anode [7], [8], [9], [10], [11], [12], [16], [17], [18], [19], [20], [21], [22]. Some groups have reported a tortuosity between 2 and 10 [16], others have reported 3.0–4.5 [12], [17], [18], [19], [20], some reported smaller equal 1.16–2 [7], [8], [21]. Recent studies using X-ray computed tomography and focused ion beam scanning electron microscopy indicate that a typical tortuosity factor value for the SOFC anode oscillates between 1.5 and 4.0 [9], [10], [11], [22].
The most precise value of tortuosity can be derived from real structural analysis. A method such as Focused Ion Beam–Scanning Electron Microscope (FIB–SEM) can provide very detailed information about the structure and allows us to estimate tortuosity properly. However, the cost of the FIB–SEM equipment is an obstacle for many laboratories, therefore a simple method, based on current–voltage measurements would be the most welcome. Such method was proposed in the past before FIB–SEM reconstruction was introduced into the field of SOFC [12] and more recently by Schmidt including molecular scale modeling [8]. According to the authors' literature survey, no studies have been conducted to verify the value of tortuosity obtained from the limiting current and mass transport model. With this research work, the authors aim to fill the void present in the literature and evaluate how precise the value of tortuosity can be derived from saturation currents and a mass transport model. From two models described in the literature the authors chose the one proposed by Jiang and Virkar [12] for its simplicity. The objective is met by comparing the results of the estimation with the real structure of the sample obtained by the FIB–SEM analysis. The effect of the adsorption of the reactant and the surface diffusion was also discussed.
Section snippets
The button-type solid oxide fuel cell
The anode-supported button type solid oxide fuel cell sample used in the presented study is a commercial product manufactured by H.C. Starck [23]. The geometry of the sample is presented in Fig. 2(a), and the detailed properties of the sample are summarized in the last section of this paper.
The experimental set-up
The schematic view of the experimental set-up is presented in Fig. 2(b). The Ni/YSZ–YSZ–LSCF sample was located between two ceramic tubes in the electric furnace as it is presented in Fig. 2(b). The ceramic
Mass transfer for gas flow in the SOFC's anode
The main fluxes contributing to mass transport in a porous anode electrode are a diffusive flux and a viscous flux. Because the total pressure gradient in the SOFC anode is small the viscous flow can be neglected [12]. The diffusion of chemical components through porous anode includes a free molecular and a continuum flow. The diffusion process for a multicomponent gas in the SOFC anode can be described by the Stefan–Maxwell equation:where Ni and Nj are molar
Sample preparation
After the power generation experiment, the sample was impregnated using epoxy resin (Marumoto Struers KK) under vacuum conditions. Filling the pores with resin is important for the recognition of the pore region during SEM observation. The impregnated sample was cut and polished using sand paper and diamond paste to prepare the sample for the FIB–SEM observation.
FIB–SEM observation
A three dimensional structure of the anode was observed using the FIB–SEM system installed at Kyoto University, Japan. The
Results and discussion
Fig. 9 presents the results of tortuosity calculated for different concentrations of hydrogen in the fuel. As can be seen in Fig. 9, the discrepancy between the measured and estimated tortuosities increases together with the concentration of hydrogen. Estimation of the tortuosity from the limiting current can be done only when concentration overpotential is clearly observed in experiments. The observed overestimation could be expected because, at a high concentration of hydrogen, clear
Conclusions
In the present study the current–voltage characteristics of the anode-supported solid oxide fuel cell have been measured. The limiting currents obtained in the experiment were employed in the mass transport model to obtain the tortuosity of the sample. The system to be analyzed was a ternary system where hydrogen (H2) was humidified with 3% addition of steam and diluted with nitrogen (N2). Measurements were conducted at 700 and 800 [°C]. After the power generation experiment, the
Acknowledgments
The first author was supported by JSPS Postdoctoral Fellowship for Foreign Researchers. Additionally, the present work was partially supported by the PAN-JSPS Joint Research Project “Thermal Interaction between Stack and Reformer in Small Scale SOFC” and partially by the New Energy and Industrial Technology Development Organization (NEDO).
References (33)
- et al.
Solid State Ionics
(2012) - et al.
Solid State Ionics
(2013) - et al.
J. Power Sources
(2011) - et al.
Solid State Ionics
(1995) - et al.
J. Power Sources
(2008) - et al.
J. Power Sources
(2010) - et al.
J. Power Sources
(2011) - et al.
J. Electrochem. Soc.
(1999) - et al.
J. Power Sources
(2000) Electrochim. Acta
(2009)
Int. J. Therm. Sci.
J. Power Sources
J. Power Sources
Surf. Sci.
J. Power Sources
Solid State Ionics
Cited by (45)
Boosting solid oxide electrolyzer performance by fine tuning the microstructure of electrodes – Preliminary study
2023, International Journal of Hydrogen EnergyNanosecond pulsed laser surface modification of yttria doped zirconia for Solid Oxide Fuel Cell applications: Damage and microstructural changes
2023, Journal of the European Ceramic SocietyAsymmetric behavior of solid oxide cells between fuel cell and electrolyzer operations
2023, International Journal of Hydrogen EnergyCitation Excerpt :Moreover, the surface diffusion of the reactants from the adsorption site to the reaction site in the hydrogen electrode is not considered in the current numerical model. It was reported that the surface diffusion influences the concentration overpotential at high current density and low hydrogen concentration [33–35]. Hence, to reproduce the experimental results more accurately, particularly in the high-current range, the tortuosity factor of the hydrogen electrode was used as a fitting parameter to adjust the simulation results to the experimental data.