Abstract
Growing concern over greenhouse gas emissions has driven research into clean coal power production alternatives. Novel coal power plant designs that lower CO2 emissions are imperative in the coming decades to mitigate global temperature rise. High-efficiency stationary power systems that integrate coal gasification with solid oxide fuel cells (SOFCs) have been championed by the Department of Energy for the past couple of decades. However, many fundamental questions about this system still need to be addressed by modeling the complex coupling between SOFC's and gasification. More specifically, work is needed to characterize SOFC performance with a range of syngas (H2+CO) mixtures produced by coal gasification. This thesis used a multi-scale modeling approach to analyze SOFC performance with coal syngas at both the systems level and at the surface reaction scale.
The first investigation in this thesis couples an equilibrium gasifier model to a detailed ID SOFC model to study the theoretical performance of the coupled system run on steam or carbon dioxide. The results of this study indicate that the system performs substantially better with steam gasification than with CO2 gasification as a result of the faster electro-oxidation kinetics of H2 relative to CO. The coupled system is then shown to reach higher current densities and efficiencies when the heat released by the fuel cell is sent to the gasifier instead of a bottoming cycle. 55-60% efficiency is then predicted for the system with heat transfer and steam gasification, making this technology competitive with other advanced system designs and almost twice as efficient as conventional coal-fired power plants.
The second study in this thesis investigates SOFC behavior with H2 and CO (syngas) mixtures that come from coal gasification. SOFC models typically neglect CO electrochemistry in the presence of H2 and H2O, assuming that the water-gas-shift reaction proceeds faster than CO electro-oxidation. The results of this study show, however, that CO electro-oxidation cannot be neglected in syngas mixtures, particularly at high current densities for high CO-content syigas. First the simulations demonstrate that incoming CO is not all shifted to form H2 by reforming reactions before reaching the electrochemical reaction sites. Furthermore, the results of this 'study confirm that direct electro-oxidation of CO contributes non-negligible current relative to H2 at high anode overpotentials. Together these results show that CO electro-oxidation plays an important role in SOFC performance not only via water-gas-shift reforming, but also via direct electro-oxidation when H2 is also present. This work suggests that accurate models for both surface reforming and direct electro-oxidation of CO in SOFC anodes must be included in order to capture performance when using coal syngas mixtures.
Finally, a multi-step mechanism for the simultaneous electro-oxidation of H2 and CO in SOFCs is implemented and studied. This mechanism combines a couple of reaction pathways: hydrogen (H) spillover to the electrolyte, and oxygen (O) spillover to hydrogen and CO on the anode. This mechanism is successfully verified in the model against a wide range of experimental data for mixtures of CO/CO2 , H2 /N2, H2/H2O, H2/CO, and H2/CO2 . The simulations show that H spillover is the dominant source of current at low anode activation overpotentials, but also demonstrate that the currents produced by O spillover are non-negligible at high overpotentials. Furthermore, it is shown that the current produced by O spillover to CO is not limited by the rate of CO adsorption on nickel, which leads CO to contribute more to cell performance at high currents. Together these three modeling studies demonstrate how coal can be efficiently converted to electricity via gasification and the simultaneous electro-oxidation of H2 and CO in a solid oxide fuel cell.
Chapter 1 Introduction
Novel coal power plant designs with lower CO2 emissions are imperative in the coming decades to mitigate global temperature rise. High-efficiency stationary power systems that integrate coal gasification with solid oxide fuel cells (SOFCs) have been championed by the Department of Energy for the past couple of decades [1]-[3]. However, many fundamental questions about this system still need to be addressed by modeling the complex coupling between SOFC's and gasification. A higher-level modeling analysis that scopes out the efficiency and power output for the combined gasifier and fuel cell system is needed. In addition, work is needed to characterize SOFC performance with a range of syngas (H2+CO) mixtures produced by coal gasification [4].
Understanding the parallel electro-oxidation pathways of H2 and CO in a SOFC is fundamental to predicting power system performance. This chapter first provides motivation for coupling &oal gasification with SOFCs, and then outlines how this thesis addresses the modeling challenges of this system.
1.1 Motivation
As world population grows and nations develop, the demand for energy accelerates. The current infrastructure is heavily reliant on fossil-based fuels, which contribute to pollution and global warming. Coal-fired power plants, in particular, are responsible for a large share of the carbon dioxide emitted, as shown in Figure 1.1. In fact, coal power plants are responsible for almost one third of U.S. CO2 emissions, which is greater than the CO2 emitted by the entire ground transportation sector [5]. New technologies and policies are therefore needed to mitigate CO2 emissions from coal-fired power plants in order to protect the environment.
Figure 1.1: Total U.S. carbon dioxide emissions by sector for 2008 [5].
Although there are many proponents who advise abandoning fossil fuels and replacing them with renewable sources like wind and solar, the technology and infrastructure are not prepared to make this transition rapidly. Fossil fuels are projected to play a major role in the global energy mix for the coming decades, particularly in industrializing nations like China and India where energy demand is booming. Even with new energy policies in place, the IEA projects a global rise in coal-fired generation over the next few decades, as shown in Figure 1.2. Therefore, innovations that allow coal to produce power with fewer CO2 emissions are imperative as the world transitions away from the current fossil fuel infrastructure over the next few decades.
Figure 1.2: Past and projected coal-fired electricity generation for 1990-2035 in China, India, and other countries in and outside the Organization for Economic Cooperation and Development [6].
Carbon dioxide emissions from coal power plants can be lowered by raising system efficiency in addition to sequestering excess CO2. Figure 1.3 compares the efficiencies of the state-of-the-art fossil power generation technologies as a function of power output. This plot demonstrates that fuel cell hybrid systems have the greatest potential for high efficiency stationary power production. The combination of a high-temperature solid oxide fuel cell (SOFC) with a gas turbine bottoming cycle can reach 60-70% efficiency, a remarkable value that is only achievable because fuel cells are direct energy converters. Fuel cell systems can also facilitate sequestration because the CO2 leaving the fuel cell is already separated from the oxidant stream, which is not the case for coal combustion.
Figure 1.3: Efficiencies of several energy conversion systems for electrical power generation [1].
Recent scoping studies on advanced coal power plants have also shown favorable efficiency and cost metrics for systems with fuel cells, as shown in Table 1.1. The results of four different studies are compared here for a traditional pulverized coal (PC) plant, an integrated gasification combined cycle (IGCC) plant, and an integrated gasifier + fuel cell (IGFC) plant run at both atmospheric and pressurized conditions. These studies consistently predict that IGFC plants will have substantially higher efficiencies and lower capital and operational costs than PC or IGCC plants. There is therefore a financial incentive to pursue fuel cell integration into coal-fired power generation in addition to the previously mentioned benefit of lowering CO2 emissions.
Table 1.1: Estimated cost and performance comparison for pulverized coal (PC), integrated gasification combined cycle (IGCC), and integrated gasifier fuel cell (IGFC) plants [3].
1.2 Thesis Overview
Integrating gasifiers and SOFC stacks into coal-fired power plants has the potential to substantially lower global CO2 emissions by raising plant efficiency. However, before this technology can be adopted, a better understanding of the fundamental characteristics of system coupling and performance is needed. This thesis addresses this requirement by building on an existing 1 D SOFC model that can handle both H2 and CO reforming and electro-oxidation [7]. Although this work is purely computational, results are repeatedly verified against a landmark experimental paper with extensive data for porous anode SOFCs [8].
The over-arching goal of this thesis is to model the performance of a SOFC with coal syngas. In order to accomplish this goal, this thesis takes a multi-scale modeling approach, as depicted in Figure 1.4. Chapters 2-3 analyze the system-level coupling of a gasifier and fuel cell, while Chapters 4-5 model the detailed transport and electro-chemistry within the fuel cell.
Figure 1.4: A schematic flow-chart illustrating the multi-scale structure of this thesis.
Chapter 2 gives a literature review of the modeling and experimental aspects of coupling a gasifier to a fuel cell. This chapter focuses on a closely coupled design, called the fluidized bed/SOFC, which integrates the gasifier directly into the fuel cell compartment. Chapter 3, in comparison, analyzes a less coupled variation of this system, called the indirect carbon fuel cell. In this chapter, an equilibrium gasifier model is coupled to the ID SOFC model to determine what efficiencies and power densities can be expected under different operating conditions. Chapter 4 then focuses on the SOFC model when different syngas mixtures are sent from the gasifier to the anode. This chapter uses detailed reforming and electro-oxidation models to determine how much power is coming from CO relative to hydrogen. Finally, Chapter 5 focuses on the interface of the SOFC anode and electrolyte, where most of the electrochemical reactions occur. Specifically, this chapter implements a detailed electrochemical mechanism and studies which reaction pathways produce current under different conditions. Together these four chapters characterize the performance of a SOFC coupled to a coal gasifier and provide insight into how coal is ultimately converted to power in this advanced system.
Chapter 2 Literature Review
Growing concern over greenhouse gas emissions has driven research into clean coal power production alternatives. Direct carbon fuel cell (DCFC) systems are a promising technology capable of highly efficient power production from coal, releasing a pure CO2 stream ready for capture and sequestration [1]. However, conventional DCFC systems either use highly corrosive molten materials, or achieve low power densities because of the sluggish carbon and CO oxidation kinetics. One promising DCFC design that has been explored for the last couple of decades is the fluidized bed/solid oxide fuel cell (FB/SOFC) system. This particular design forgoes molten materials and sluggish carbon oxidation kinetics by coupling gasification to a ceramic fuel cell run on gaseous fuels. First, this chapter introduces DCFCs and provides some background on the components and coupling in the FB/SOFC system. Next, the state-of-the-art in modeling and experiments for the FB/SOFC design is presented. Finally, a survey of both the operational and the modeling challenges associated with the FB/SOFC system is given.
2.1 Introduction to FB/SOFCs
2.1.1 Comparison of DCFC Types
A direct carbon fuel cell (DCFC) is a device that generates electricity through the direct electrochemical oxidation of solid carbon. A direct carbon fuel cell (DCFC) has a single process chamber for solid fuel conversion contacting the anode. The advantage of this design over indirect CFC's is that having a single chamber minimizes process steps and thermally couples the fuel'cell to the gasifier, increasing the maximum power output of the system [2]. From a thermodynamic standpoint, direct carbon conversion on the anode attains higher reversible efficiencies than is possible for fuel cells run on gaseous fuels, as shown in Figure 2.1. Therefore, there is a strong incentive to pursue DCFCs to raise the efficiency of fossil fuel power production systems.
Figure 2.1: Reversible efficiencies vs. temperature for the oxidation of H2, CO, and solid graphitic carbon : ๐ฎ rev = ๐ G/๐ H = -nโFE rev/๐Hยบ , reproduced from [3].
Table 2.1 depicts the different types of DCFCs under development, which can be classified into three categories based on electrolyte: molten hydroxide, molten carbonate and solid oxygen ion conducting ceramic. The solid ceramic category can be further sub-categorized based on fuel/anode design: fluidized bed, molten metal, and molten salt. The only DCFC design that does not use molten material in the electrolyte or anode is the solid oxygen ion ceramic electrolyte coupled to the fluidized bed anode.
Table 2.1: Main types of direct carbon fuel cells (DCFCs), reproduced from [4].
Molten hydroxide DCFCs consist of solid carbon immersed in a molten hydroxide electrolyte, as shown in Figure 2.2. In this configuration, the solid carbon acts as a consumable anode, and CO2 bubbles are released as a gas through the molten electrolyte. This type of cell was first implemented by William Jacques in 1896 [5], and later studied by Scientific Applications and Research Associates [6]. The fundamental challenge facing molten hydroxide electrolytes is corrosion via electrochemical formation of carbonates [7]. In addition, the power densities of current molten hydroxide DCFC prototypes are too low to be commercially viable. Molten carbonate DCFCs can either utilize a carbon rod [8] or dispersed carbon particles [9] as the anode in molten carbonate. Experiments have been done to enhance fuel surface groups to promote carbon conversion [6],[7], but a low power density of 100 mW cm-2 has been obtained in repeated tests [12]. Corrosion of the metal bipolar plates also limits cell life-time, and as a result, there is little commercial interest in further developing molten carbonate technology at this stage.
Figure 2.2: Molten carbonate direct carbon fuel cell schematic [13]. The electrochemical reaction sites (ers) occur at the interface of the molten electrolyte, solid carbon, and CO2 gas phases.
The third type of DCFC utilizes an oxygen ion conducting ceramic electrolyte, such as the YSZ conventionally used in a solid oxide fuel cell (SOFC). This DCFC design, shown in Figure 2.3, has an anode chamber filled with carbon particles dispersed in a gaseous medium, molten metal, or molten salt. The molten metal and salt designs are implemented to enhance the anode's electrical conductivity and contact area with the carbon fuel to promote faster conversion. However, the molten material corrodes the fuel cell electrolyte with time, and as a result, low power densities and efficiencies have been reported [14],[15]. In the fluidized bed design, fuel can either oxidize directly at the anode or indirectly react with a gaseous fuel that is then oxidized at the anode. The direct oxidation approach requires solid-to-solid contact between the fuel and electrolyte at the triple phase boundary (TPB). Direct oxidation has been reported by pressing a consumable carbon anode against the electrolyte [16],[17], and also by pyrolytic decomposition of a hydrocarbon fuel such as methane [18]-[20]. However, the consumable anode design only obtained a power density of 20 mW cm-2, and the pyrolytic decomposition method has the disadvantage of requiring intermittent charging.
Figure 2.3: Schematic of a DCFC with an oxygen ion conducting ceramic electrolyte [13].
Formation and oxidation of CO is likely the favored mechanism over direct oxidation of carbon in ceramic electrolyte DCFCs due to faster reaction kinetics and relative ease of travel for gas [21]. Therefore, the most commonly reported mode of oxidizing carbon in a ceramic electrolyte DCFC is to use a packed or fluidized bed a short distance from the anode [22], [23]. Thus, carbon is oxidized indirectly in the SOFC by converting the carbon to a synthesis gas (CO + H2) that is then electrochemically oxidized at the anode. Although the carbon fuel is oxidized indirectly, this design is still considered a direct CFC due to the close proximity of the gasifier and fuel cell, which leads to both thermal and gas phase coupling. This particular DCFC design that couples a fluidized bed (FB) gasifier to a high-temperature SOFC is called a FB/SOFC here for short. The FB/SOFC is selected here over the alternative DCFC designs due to reportedly higher power densities and less potential for corrosion.
2.1.2 SOFC Fundamentals
Solid oxide fuel cells (SOFCs) are typically selected over other fuel cell types to be used in conjunction with a fluidized bed in a DCFC configuration because they operate at high temperatures (700-1000°C). This allows the cell to run on CO in addition to H2 as a fuel, as shown in Figure 2.4, which makes it more compatible with hydrocarbon gasification. The temperature range is also similar to that of a fluidized bed gasifier, which makes thermal coupling of the two components more feasible. SOFCs typically consist of a thin ceramic yttria-stabilized zirconia (YSZ) electrolyte,. a nickel/YSZ anode, and a lanthanum-strontium manganate (LSM) cathode. Many numerical models have been developed to capture the reaction kinetics, heat transfer, flow fields and performance metrics of SOFCs [24]. However, the electrochemical oxidation mechanisms in a SOFC, particularly for fuels other than H2, are still poorly understood.
Figure 2.4: Solid oxide fuel cell (SOFC) schematic (www.fuelcelltoday.com).
The global reactions for CO and H2 oxidation are:
Jiang & Virkar provide the most comprehensive set of experimental data for porous Ni-YSZ anode-supported SOFCs with H2, CO and H2+CO oxidation [32]. They ran tests at 800°C for a wide range of compositions in order to characterize SOFC performance and compare H2 to CO oxidation. Their performance curves for H2/H2O, CO/CO2 , and H2/CO mixtures are shown in Figure 2.5. The SOFC performs significantly better with H2/H2O than it does with corresponding CO/CO2 mixtures, due to the relatively sluggish diffusion and reaction rates of CO. The SOFC, however, performs comparably well with H2-dominant H2/CO and H2/H2O mixtures, which the authors attribute to the water gas shift reaction, which converts most of the CO to H2 in the presence of H2O. This set of experiments provides a baseline set of data for fitting parameters in H2 and CO oxidation models. More experimental and modeling work is needed to determine the H2 , CO and H2+CO oxidation mechanisms on Ni-YSZ in order for SOFCs to be coupled effectively to coal or biomass gasification.
Figure 2.5: Performance of a SOFC button cell for different H2/H2O mixtures (upper left), CO/CO2 mixtures (upper right) and H2/CO mixtures (bottom) [32].
Hydrogen vs Methane properties
2.1.3 FB/SOFC Fundamentals
Because both H2 and CO can be oxidized at the anode of an SOFC, this allows some flexibility in the choice of gasification medium. CO2 or H2O are conventionally used to gasify carbon in the fluidized bed gasifier according to the Boudouard and steam-carbon reactions:
Figure 2.6 depicts the gas flows associated with the FB/SOFC system when CO2 and/or H2O are sent to the gasifier. The gasifier is fueled with coal, biomass or carbon particles that can range in diameter from to order of microns to millimeters. If only CO2 is sent through the gasifier, then CO is the primary fuel that exits the gasifier and is then oxidized on the porous Ni/YSZ anode. If, however, steam is sent to the gasifer, then syngas (H2 + CO) will be produced, and both fuels will be oxidized at the anode.
The physical proximity of the gasifier to the anode will impact both the thermal coupling and the rate of product (H2O + CO2 ) diffusion back to the gasifier. Placing the carbon particles closer to the anode also improves the cell's theoretical performance because the open-circuit voltage increases when carbon is directly oxidized on the anode [2]. For these reasons, there is a strong incentive to incorporate the fluidized bed gasifier and SOFC into the same chamber (DCFC) instead of placing the gasifier in a separate chamber further upstream (indirect CFC).
Figure 2.6: Schematic depiction of gas flows in a FB/SOFC system run on H2O and CO2 [23].
2.2 State-of-the-Art
The concept of a fluidized bed with a SOFC (FB/SOFC) was first patented by a group at Stanford in the early 1990s [22]. That research group and another group at Tsinghua University have since developed FB/SOFC models and run several experiments. Their modeling and experimental work is summarized here, and more detail can be found in a recent review paper published by the Stanford group [13].
2.2.1 FB/SOFC Models
The most fundamental modeling analysis of the FB/SOFC system was published by the group at Stanford in 2009 [2]. This analysis drew a control volume around the FB/SOFC and an air-side heat exchanger, as shown in Figure 2.7. Several simplifying assumptions were made about the fuel cell performance and operating conditions, then system efficiency was computed according to: ๐ฐ' = Wout,net / (Tfuel HHVfuel). The performance of the system was then analyzed for different fuels: pure carbon, a couple of grades of coal, and a few varieties of biomass. An efficiency of 58% was reported for pure carbon, while efficiency ranged from 40-55% for the alternative fuel candidates.
Figure 2.7: Schematic of a DCFC plant; gray partition represents SOFC stack [2].
The Stanford group also compared their DCFC system to a couple of alternative systems where the gasifier was separated from the fuel cell. System efficiency changed little in the second system because the fuel cell and gasifier were still thermally coupled. In the third system, however, performance dropped substantially because the gasifier relied on autothermal reforming, so all excess heat from the fuel cell was wasted. This study laid the foundation for understanding the thermodynamic advantage of a DCFC system. However, the SOFC model was overly simplified and the gasifier was modeled at equilibrium. More detailed analysis was still needed to understand the kinetic behavior of a FB/SOFC system and understand the complex interplay between the gasifier and fuel cell.
The same group at Stanford came out with a more detailed DCFC model a few years later [33]. This model was of a 2-D axisymmetric SOFC and packed fuel bed, developed in both Matlab and Comsol [33]. This model accounts for cell electrochemistry, heat transfer, gasification kinetics, and convection/diffusion of species as shown in Figure 2.8. For a fixed geometry and current density, the steady-state temperature, velocity, pressure, and concentration profiles can be resolved. This model answered some important questions about DCFC operation, such as the minimum gasifier bed height to provide a given current for different fuels.
Figure 2.8: Flow-chart of packed carbon bed DCFC model [33].
However, there are a couple of limitations to the recent model developed by Stanford. One is that the convection/diffusion module is based on the assumption of a packed bed, and would require significant modification to account for fluidization of particles. Gas flow would no longer be governed by diffusion or laminar plug flow once the bed reaches minimum fluidization, so the results of this model are only applicable at low flow-rates when fuel particles are stationary.
Another drawback of this work is that it only focuses on a C/CO/CO2 system, so it cannot model H2O gasification or H2 oxidation. As explained later, there is a strong incentive to go with H2O over CO2 in a FB/DCFC to speed up reaction kinetics, so a model that can handle H2/H2O chemistry is necessary to scope out system performance.
A group at Tsinghua has also published a model for a gasification DCFC within the last couple of years [34]. Their model domain is ID and couples a packed fuel bed to a SOFC with a scandium-based electrolyte, as shown in Figure 2.9. Their model uses a multi-step carbon CO2 gasification mechanism for a packed bed, similar to gasification module implemented by Stanford. The model at Tsinghua is similarly limited to C/CO/CO2 systems and cannot account for H2O gasification or H2 oxidation. However, their model provides matches their experimental data well for both CO2 and inert gas flows, and it provides insight into the gas species profiles throughout the carbon bed. and anode. It also allowed the group to test the impact of adding a potassium-based catalyst to the gasifier bed [35].
Figure 2.9: Domain and dimensions for the lD-DCFC model at Tsinghua University [34].
2.2.2 FB/SOFC Experiments
The group at Tsinghua University currently has an experimental set-up for indirect CFC testing, as shown in Figure 2.10. The gasifier packed bed was made up of amorphous carbon black particles, and the SOFC button cells were composed of the material layers shown in Figure 2.9.
The packed carbon bed is placed in a separate chamber approximately 50 cm upstream from the SOFC. Therefore, separate furnaces are needed to heat the carbon bed and SOFC because they are not thermally coupled. Some experiments were performed on the gasifier and SOFC separately, but some data was also collected on both components simultaneously. Inert argon and CO2 were flowed separately to the carbon bed for temperatures ranging from 800-950⁰C. They used Gas Chromatography to determine the composition of the gasifier effluent in order to calculate the carbon conversion ratio in the packed bed. Platinum wires were also used to collect current and voltage data at the anode and cathode in order to plot the polarization curve for the SOFC.
Figure 2.10: Indirect carbon fuel cell experimental set-up at Tsinghua University [34].
The group at Tsinghua was able to calculate carbon conversion in the gasifier and power density in the SOFC for a range of temperatures and flow-rates. As expected, they found that increasing the temperature led to faster carbon conversion in the bed and higher performance in the cell. They also found that the cell performed best when CO2 was sent to the system and worst with an inert gas flow, as shown in Figure 2.11. The maximum power density obtained with CO2 flow was roughly 210 W cm- 2 whereas the maximum power density was only about 100 W cm-2 for Ar flow.
This result confirms that CO2 is producing CO in the gasifier via the Boudouard reaction, which is then oxidized at the fuel cell to produce power. The performance curve with 0 sccm also confirms that some CO is produced in the gasifier by CO2 that diffuses back from the fuel cell to the bed.
Figure 2.11: Experimental performance curves of Tsinghua's SOFC button cell at 800⁰C when Ar, CO2 and no flow are sent to the upstream gasifier [36].
The group at Stanford has also published experimental data for FB/SOFCs. Figure 2.12 portrays their initial experimental set-up, which is similar to the one used at Tsinghua. It contains a YSZ-based SOFC button cell downstream from a tray of carbon pellets, all enclosed in a quartz tube. The carbon and fuel cell are thermally decoupled, so the temperature of each compartment is be controlled independently by separate furnaces. The carbon gasifier section was operated between 524-955°C whereas the fuel cell section was always operated above 800°C. Gtir and Huggins from Stanford were granted a patent for this design along with concepts that involve thermal coupling and fluidized gasification [37]. Their initial experiments led to low power densities, on the order of mW cm-2 because there was no gasification medium and a large distance for CO2 to traverse from the fuel cell to the carbon pellets. However, their work proved the concept for the FB/SOFC.
Figure 2.12: a) schematic of the two-compartment DCFC apparatus at Stanford; b) performance curves of the given fuel cell at 932°C with the carbon bed held at 725°C and 955°C [22],[4].
Nakagawa and Ishida also performed button cell SOFC experiments with a charcoal bed adjacent to the anode [38]. They placed charcoal blocks in a crucible 5 mm away from the anode and flowed inert nitrogen gas over the charcoal at temperatures ranging from 802-1002°C. They analyzed the product gas in the anode chamber to confirm that CO was being produced by the Boudouard reaction. Their results confirmed that CO2 was diffusing back from the anode to react with carbon in the charcoal blocks to produce CO. The University of Akron has also been performing FB/SOFC experiments on button cells in order to study the impact of several anode and cathode catalysts [39]. They were able to obtain power densities ranging from 50-150 mW cm-2 for short-term experiments before ash built up on the anode [40]. They also reported that coal outperformed coal gas and methane in this configuration.
The group at Stanford later improved upon their initial experiment by fluidizing pulverized carbon particles directly on the anode, a better approximation of an actual FB/SOFC due to the fluidization and direct contact. In these experiments, they also explored different fuel types: carbon, almond shells and coal [41]. They used CO2 to fluidize and gasify the carbon in the particles, and obtained power densities up to 140 mW cm-2 for the synthesized carbon particles at 900°C. This corresponds to two orders of magnitude in improvement over Stanford's initial experiments.
The Stanford group obtained an even higher power density, 220 mW cm-2, in initial tests performed on tubular SOFCs instead of planar button cells [2]. A maximum power density of 450 mW/cm 2 was later achieved with Stanford's anode-supported tubular SOFC run on devolatilized coal at 0.64 V and 850°C, as shown in Figure 2.13. This power output stands as the highest performance value reported for this system in literature. However, it corresponds to an experimental set-up where the Boudouard gasifier is external to the SOFC chamber, making it easier to couple the two components. In general, performance of indirect gasifier + fuel cell systems is superior to direct designs, but the efficiency is lower. Thermal coupling and direct carbon oxidation have the potential to raise system efficiency when the gasifier is integrated directly with the fuel cell.
Figure 2.13: Cell voltage, efficiency and power density curves for a tubular SOFC run on gasified Alaskan coal char at 850°C [42].
Most FB/SOFC experiments have focused on CO2 and purge gases, but a recent study conducted by the China University of Mining & Technology used H2O in a direct CFC set up [43]. They tested a tubular SOFC with carbon black particles directly on the anode, with and without catalyst particles dispersed in the fuel bed. They obtained relatively poor performance in their uncatalyzed steam DCFC compared to a similar cell run on H2, as shown in Figure 2.14. However, this discrepancy may be a result of the nitrogen used to deliver steam to the gasifier, which lowers the theoretical potential of the cell. Their experiment was able to prove the viability of using H2O instead of CO2 as the gasifying agent in a FB/SOFC.
Figure 2.14: Performance curves at 850°C for a tubular SOFC gasifier (with no catalyst) vs. the same cell run directly coupled to a steam on H2 [43].
Table 2.2: Summary of studies published on FB/SOFCs.
2.3 Operational Considerations
2.3.1 Steam vs. Carbon Dioxide
All FB-DCFC models and experiments to date have used CO2 as the gasifying agent instead of H2O because it's easier to work with and model. From a thermodynamic standpoint, there's little incentive to use steam over CO2 because they lead to similar energy outputs per unit flow-rate of fuel [2]. However, from a power density standpoint, steam has an advantage over CO2 by a factor of 2-6 in a direct carbon fuel cell system due to faster gasification and oxidation kinetics. This translates into smaller, cheaper gasifiers and SOFC stacks to obtain the same power output, so steam is worth investigating as an alternative to CO2 in FB/SOFC systems.
Steam gasification is reported to proceed faster than CO2 gasification [45], and it also generates H2 along with CO, which the fuel cell favors electrochemically [46]. Steam is more commonly used than CO2 in gasifiers because steam gasification proceeds 2-6 times faster than CO2 gasification [47]-[50]. Steam gasification reaction kinetics have been extensively studied for decades [57-61]. Several heterogeneous reaction mechanisms have been proposed for steam gasification using empirical data and Langmuir-Hinshelwood kinetics [56], [57]. Hydrogen oxidation is known to proceed more rapidly than CO oxidation in SOFC's [27], [58]. The maximum power density obtained using pure CO is only 40-50% of that obtained using pure H2 [32], [59]. Therefore there is a great incentive to utilize steam gasification instead of CO2 gasification in order to produce H2 that will optimize cell performance.
Steam gasifiers have been placed upstream of SOFC stacks in configurations like fuel cell turbine hybrids [60], and IGCC plants [61], [62]. A steam gasifier is also included in the FutureGen prototype plant, which is the world's first coal-to-gas plant configured to optimize hydrogen production and carbon capture [63], [64]. However, steam gasification has yet to be integrated directly with a fuel cell in an experiment or model.
2.3.2 Anode Recycle
Figure 2.15 depicts a FB/SOFC system with CO2 gasification and recycle. Coal particles are fed into a bed fluidized by CO2 below a SOFC element. In this scenario, no external supply of CO2 is necessary to run the system at steady-state because CO2 is simply extracted from the anode exhaust and recycled back through the fluidized bed. Some of the CO2 produced at the anode may also diffuse back into the gasifier by the "CO shuttle mechanism" if the gas flow-rate is sufficiently slow [23]. These mechanisms make the FB/SOFC self-sustaining in an ideal scenario because only solid fuel must be provided externally to keep the reactions going. However, when H2O gasification is desired, recycling becomes more of a challenge because the steam must be condensed out of the flue before it can be sent back to the gasifier. This requires dropping the temperature of the flue gas significantly before recycling, and it also means that some H2O must still be provided externally to the gasifier to make up for the moisture that inevitably escapes the recycle loop in the flue after condensation.
Figure 2.15: Conceptual depiction of a FB/SOFC with CO2 recycle and capture [23].
2.3.3 Desulfurization
Most experiments and models of FB/SOFCs use either char or pure carbon in order to simplify computation and clean-up. In reality, pure carbon particles are not a cheap, readily available fuel source for stationary power generation. Therefore, biomass and coal are more likely candidates for integration in a large-scale FB/SOFC. Coal and biomass are composed of volatile materials in addition to carbon, so the syngas composition leaving the gasifier in a FB/SOFC will likely contain sulfur-based elements, like those listed in Table 2.3.
Table 2.3: Syngas compositions of typical entrained-flow coal gasifiers [65].
Dealing with coal or biomass adds to the modeling complexity of the gasifier portion of a FB/SOFC because there are side reactions with volatiles that must be accounted for. This realistic syngas composition is also problematic in an experimental set-up because the sulfurous gases can quickly degrade the fuel cell. H2S levels as low as 1-10ppm have been shown to be detrimental to nickel-YSZ anodes [66]. These trace levels cannot easily be obtained using limestone or calcium carbonate additives [67], [68]. Therefore, it is likely that the syngas will need to undergo an additional sulfur scrubbing step at a lower temperature before going to the anode. The alterative to this approach is to select a more sulfur-resistant anode material, such as GDC, which can handle a few hundred ppm of H2S without degrading [69]. However, this material change comes with a tradeoff of lower cell performance, so it's still an area for further investigation.
In addition to dealing with gas-phase contaminants, an actual FB/SOFC system would need to deal with ash clean-up. One simple configuration to mitigate the impact of ash on the fuel cell is to place the gasifier below the fuel cell, as shown conceptually in Figure 2.15. That way, solid particulates settle to the bottom of the gasifer rather than collecting on the anode, which can lead to a performance drop within hours [40]. This configuration, however, cannot prevent fly ash from colliding with the anode and potentially clogging the porous anode. Some sort of a porous grate must be placed above the gasifier bed in order to filter out fly ash and allow only gases to pass through to the anode. This approach has been implemented before, and has the potential to minimize fouling of the anode [33]. Additional modeling and experimental efforts are needed to determine how to sustainably operate a FB/SOFC with coal and biomass by accounting for both gaseous and solid contaminants from the gasifier.
2.4 Modeling Considerations
2.4.1 Fluidized Bed Modeling
Although fluidized beds have been implemented for decades, the concept of coupling a gas fluidized bed directly with a fuel cell is a relatively new concept [22]. The more common configuration involves a fluidized bed gasifier upstream of a fuel cell stack in an Integrated Gasification Combined Cycle (IGCC) power plant [62]. Several researchers have investigated molten fluidized bed electrodes in which fuel particles are suspended in a bubbling bed of molten carbonate or metal [70], [71]. A few groups have begun modeling and experimenting with FB gasification directly coupled to the fuel cell. However, the state-of-the art models for FB/SOFCs typically assume a packed carbon bed rather than developing a model for fluidization.
Fluidized bed technology was first commercialized for coal gasification in 1926, and has since been used in a diverse range of industrial applications. The advantages of using a fluidized bed are ease of continuous operation, enhanced heat and mass transfer, and protection against rapid temperature changes [72]. FB dynamics have been extensively studied and characterized based on particle properties, bubble size and gas flow regimes [73]-[79]. The basic flow regimes are shown conceptually in Figure 2.16 in order of increasing gas velocity.
Figure 2.16: Map of the different fluidized bed regimes based on increasing velocity [80].
In all likelihood, gasification in a DCFC configuration would fall under either the fixed bed or bubbling regime because flow within fuel cells is typically slow and laminar. For this reason, many researchers have assumed a packed bed in their FB/SOFC models and used packed carbon pellets in their experiments. However, a more comprehensive model that accounts for bubbling regime behavior should be developed in order to cover a wider range of potential operating conditions in a FB/SOFC and study the impact of flow rate on carbon conversion and gasifier characterization. The transition from fixed to bubbling regimes is dependent on minimum fluidization [81], which is a strong function of particle size [82], [83]. Therefore, it is conceivable that bubbling could occur in a FB/SOFC with finely ground fuel particles.
In order to create a fluidized bed model for a DCFC, established correlations for fluidization regimes based on particle classification would be needed to characterize the velocities of bubbles and particles in the bed. The simple two phase (STP) model [53], which subdivides fluidized beds into bubble and solid emulsion phases, could be used to estimate fluidized bed behavior. Bed hydrodynamics and heat and mass transfer coefficients in the bed could then be determined based on STP empirical correlations [84],[72]. Although the STP model is less accurate than using CFD, it would provide a better estimate for gasifier behavior than the packed bed model does for FB/SOFC models with flow-rates exceeding minimum fluidization.
2.4.2 SOFC Modeling with H2 and CO
A key advantage of solid oxide fuel cells (SOFCs) is their ability to electrochemically oxidize CO, which allows them to run on various abundant hydrocarbon fuels in addition to hydrogen [85]-[87]. SOFCs can potentially be coupled to a gasifier that converts coal, biomass or other solid carbonaceous fuels to syngas [44], [88], [89]. Because syngas is primarily composed of H2 and CO, which can both be directly oxidized on SOFCs [32], it is an ideal fuel stream once contaminants have been removed [90]. However, it has also been shown that H2 electro-oxidation proceeds 2-3 times faster than CO electro-oxidation on Ni/YSZ [46], [90]. Therefore, the importance of including a model for CO electro-oxidation in SOFC anodes is debatable when H2 is also present. Previous researchers have often used a hydrogen-spillover oxidation model but neglected CO electro-oxidation even when both species are present [28], [91]. Neglecting CO electrochemistry is often justified by the following arguments: (1) the rate of CO conversion via surface reforming exceeds the rate of CO electrochemical oxidation [32], [90], and (2) H2 dominates over CO in charge transfer chemistry [59]. However, these two assumptions may not hold for syngas mixtures with high CO content and low H2O content, like the output of a coal gasifier [65]. The water-gas-shift reforming reaction, in particular, can only convert CO to H2 when sufficient H2O is present [27]. Therefore, it is plausible that non-negligible quantities of CO could reach the triple-phase-boundary (TPB) to react electrochemically for certain syngas mixtures.
A couple of reaction mechanism types have been proposed to represent H2 electrochemical oxidation at the triple-phase boundary (TPB) of Ni-YSZ: (1) hydrogen spillover and (2) oxygen spillover. Hydrogen (H) spillover mechanisms involve a charge-transfer step where hydrogen spills over from nickel to YSZ to react with oxygen on the electrolyte. Oxygen (0) spillover mechanisms, on the other hand, involve a charge-transfer step where oxygen spills over from YSZ to nickel to react with hydrogen on nickel. Hydrogen electro-oxidation models typically select only one spillover pathway rather than implementing the H and O spillover pathways simultaneously. Although a few researchers have used O spillover mechanisms to describe H2 electro-oxidation [92], [93], the majority have proposed variations of the H spillover mechanism [25], [28], [94]-[99]. A few researchers have compared these spillover pathways and concluded that H spillover mechanisms are better than O spillover mechanisms at consistently predicting patterned-anode experimental data for H2/H2O mixtures [100]-[102]. One group has also developed an H spillover mechanism that accounts for rate-limiting H2 adsorption at high currents [95], but a similar study is needed for the O spillover mechanism.
Although CO electro-oxidation has been typically neglected in SOFC models with syngas, several researchers have proven its importance in CO+CO2 systems [103]. Experimental groups have tested nickel-pattern anodes and Ni-YSZ porous anodes with CO mixtures to study the power output from direct electrochemical oxidation [32], [59], [104], [105]. A few mechanisms for CO electro-oxidation on YSZ electrodes have also been proposed [106]-[108]. A comprehensive analysis of CO charge transfer and reaction kinetics on Ni-YSZ anodes appears in Yurkiv et al [109].Although these researchers agree that the rate of CO electro-oxidation is smaller than that of hydrogen, results indicate that their rates only differ by a factor of two or three [110]. Furthermore, some experimental studies of syngas electrochemical oxidation on Ni-YSZ conclude that CO electro-oxidation is non-negligible in comparison to H2 [27], [46], [105]. These results motivate the investigation of CO electro-oxidation in Ni-YSZ anodes when both fuel species are present.
Although the mechanisms for both H2 and CO electro-oxidation have been studied individually, few researchers have attempted to model the simultaneous electro-oxidation mechanism which is needed to characterize SOFC behavior with syngas mixtures [111]. It is a complicated task to simulate H2+ CO co-oxidation in SOFCs because it involves modeling parallel charge transfer pathways, water-gas shifting and interactions between gaseous and adsorbed species. Moyer et al. [30]recently performed a modeling study on H2 + CO co-oxidation that accounts for detailed heterogeneous thermochemistry as well as both spillover mechanisms. They fitted the kinetic parameters of each charge-transfer step in the hydrogen and oxygen spillover pathways to patterned-anode Tafel plots for mixtures containing H2 + H2O + CO + CO2 [92]. Moyer's model was best able to predict that data set when both the H and O spillover pathways were active instead of just one pathway. However, questions remain regarding the relative importance of these two spillover pathways and the roles of H2 and CO in these pathways. Charge-transfer steps were also always assumed rate-limiting in this study, so the possibility of fuel adsorption on nickel as rate-limiting processes in these mechanisms requires further investigation.
A recent study by Fu et al [112] has provided needed insight on the spillover pathways of H2 and CO electro-oxidation on Ni/YSZ from a micro-structural perspective using first principles simulations and the Monte Carlo method. This group found evidence to support previous claims that CO electro-oxidation can only proceed through the O spillover pathway. More importantly, Fu et al found that the O spillover pathway plays a vital role in H2 electro-oxidation in addition to H spillover. Their work therefore motivates the development of a MEA model that includes O spillover charge-transfer pathways to both CO and H2 on nickel in addition to H spillover to YSZ. Such a model is needed to accurately capture the reaction pathways of both fuels at the anode triple-phase-boundary (TPB) of SOFC's exposed to syngas fuels.
2.5 Conclusions
Direct carbon fuel cells (DCFCs) have been proposed as an efficient technology for coal power production with CO2 capture. Although much research has been done on DCFCs with molten materials, more research is needed to examine the fluidized bed + solid oxide fuel cell (FB/SOFC) design, which is capable of higher efficiencies and a longer life-span. The few available FB/SOFC models are ID or 2D-axisymmetric with CO2 gasification in fixed beds. More modeling work is needed to study steam gasification, fluidization in the gasifier, and the 2D coupling of the gasifier and fuel cell. Preliminary bench scale experiments have also proven the FB/SOFC concept, but more experimental work is needed to test performance with steam gasification and in-situ desulfurization. Finally, understanding the complex coupling in the FB/SOFC system hinges on a proper understanding of SOFC behavior with synthesis gas fuels. Accurate models for parallel H2 and CO electro-oxidation in the SOFC anode are a precursor to modeling SOFC interactions with a fluidized bed gasifier.
Chapter 3 Carbon Fuel Cell System Optimization
An indirect carbon fuel cell (ICFC) system that couples coal gasification to a solid oxide fuel cell (SOFC) is a promising candidate for high efficiency stationary power. Although the ICFC system does integrate the gasifier into the same chamber as the fuel cell (like the FB/SOFC from Chapter 2), it is still capable of high efficiency due to heat transfer between the two components. This study couples an equilibrium gasifier model to a detailed ID MEA model to study the theoretical performance of an ICFC system run on steam or carbon dioxide. Results show that the fuel cell in the ICFC system is capable of power densities greater than 1.0 W cm-2 with H2O recycle, and power densities ranging from 0.2-0.4 W cm-2 with CO2 recycle. This result indicates that the ICFC system performs better with steam than with CO2 gasification as a result of the faster electro-oxidation kinetics of H2 relative to CO. The ICFC system is then shown to reach higher current densities and efficiencies than a thermally decoupled gasifier + fuel cell (G+FC) system because it does not include combustion losses associated with autothermal gasification. 55-60% efficiency is predicted for the ICFC system coupled to a bottoming cycle, making this technology competitive with other state-of-the-art stationary power candidates.
3.1 Introduction
Growing concern over greenhouse gas emissions has driven research into cleaner power production alternatives. However, even with progressive energy policies in place, the lEA projects a global rise in coal-fired power generation over the next few decades due to the industrialization of developing nations [1]. Clean coal technologies with higher system efficiency and CO2 capture are therefore necessary in the coming decades to mitigate harmful emissions. The carbon fuel cell (CFC) system is a promising candidate for highly-efficient coal power production that releases a diluent-free CO2 stream ready for capture and sequestration [2]. This paper focuses on a non-molten CFC system design that couples a ceramic solid oxide fuel cell (SOFC) to a gasifier [3].
Several bench-scale experiments and models have demonstrated the concept of this CFC system with CO2 as the gasification agent [4]-[6]. On the other hand, steam gasification has been largely neglected in previous work because it requires more pre-heating and it produces H2 S, which quickly degrades SOFC performance [7]. However, steam has a couple of significant advantages over CO2 in a CFC system: 1) H2O gasification proceeds 2-6 times faster than CO2 gasification [8], [9]; and 2) the H2 produced by steam gasification can be oxidized 2-3 times faster than CO is oxidized on the SOFC anode [10]. Therefore, there is a strong incentive to consider H2O as an alternative to CO2 in a CFC system to improve performance.
Two fundamental questions still need to be answered for this CFC system: 1) how much will system power density increase if steam is used instead of carbon dioxide as the gasifying agent?; and 2) how much will system efficiency increase when a gasifier is coupled to a SOFC? A preliminary CFC modeling study on this topic coupled an equilibrium gasifier to a SOFC with fixed voltage and current [11]. That study compared a few CFC systems with varying degrees of coupling between components, and used thermodynamic analyses to compare the performance of these systems with both CO2 and H2O. Although the paper gave a good overview of the different systems, it did not find an advantage of using H2O over CO2 because the model fixed cell voltage and did not include finite-rate kinetics for SOFC surface reforming and electrochemistry.
Similarly, that thermodynamic analysis did not accurately assess the efficiency gained by thermal coupling because a finite-rate kinetic model is needed to accurately determine fuel cell efficiency.
This paper addresses these fundamental questions about the CFC system using an equilibrium gasifier model coupled to a 1D-MEA model with finite-rate kinetics. The gasifier can be modeled in equilibrium because it is in a separate compartment upstream of the SOFC stack and can therefore be sized to ensure sufficient residence time. The SOFC model, on the other hand, includes finite-rate kinetics in order to accurately compare the H2 and CO electrochemical oxidation rates and assess the various losses in the cell. First the CFC system model is presented along with an explanation of the different CFC system classifications. Next the governing equations are presented for the gasifier and fuel cell components of the model. Finally, the two fundamental questions posed earlier are addressed sequentially with two modeling studies. The first study compares the impacts of H2O and CO2 gasification on system performance over a range of temperatures. The second study explores the impact of thermal coupling between the gasifier and fuel cell on system efficiency.
3.2 Model Description
The objective of this model is to determine CFC system power and efficiency over a range of current densities and operating conditions. The combined CFC system is presented first, followed by descriptions of the equilibrium gasifier model and fuel cell model. The fuel cell model has been previously validated against experimental data for many syngas mixtures at 800°C, and the governing equations of the model are described in detail elsewhere [12], [13].
3.2.1 CFC System Model
3.2.1.1 System Classifications
There is considerable debate over the proper terminology to describe CFC systems [14]. Table 3.1 breaks down the CFC system classification adopted here by the extent of coupling between the gasifier and SOFC. Systems listed higher are more coupled and theoretically capable of obtaining higher efficiencies, but at the expense of more complex integrated designs. The model in this paper focuses on the indirect CFC (ICFC) and gasifier + fuel cell (G+FC) systems, as described and justified below.
Table 3.1: Classification of Carbon Fuel Cell systems with different levels of coupling.
The most integrated design in Table 3.1, the direct oxidation CFC, is theoretically capable of high efficiencies across a wide range of operating temperatures based on the high Gibb's free energy of the direct carbon oxidation reaction, C + O2 ↔ CO2 [15]. However, bench-scale experiments have demonstrated that direct oxidation of solid carbon in SOFCs produces negligible current relative to gaseous fuels, which can diffuse to the electrochemical sites throughout the porous anode [16], [17]. Furthermore, all direct oxidation CFC proof-of-concept experiments have required a clamping mechanism to provide a high-pressure contact between a solid carbon pellet and the anode in order to produce current. Therefore, scaling up the direct oxidation CFC to an operational system with continuous solid fuel delivery poses a serious design challenge.
The direct-CFC (DCFC) design does not require physical contact between solid carbon particles and anode electrochemical sites, but still offers some efficiency gains by having carbon gasification occur in close proximity to the anode. This design promotes both chemical and thermal coupling between the gasification and electrochemical reactions, which happen in the same chamber. Several bench-scale experiments have successfully demonstrated that this DCFC concept is capable of competitive performance on a variety of solid fuels [18]-[20]. A couple of DCFC models have also been developed to complement these bench-scale experiments [6], [21]. The main drawback of the DCFC design is that solid fuels must be pre-processed into pure carbon because impurities like ash and H2S quickly degrade SOFC performance if they are produced in the same chamber as the anode [5], [7], [22]. Therefore, DCFC experiments typically involve activated carbon or char particles that have been chemically and thermally pre-treated to remove volatiles and enhance surface reactivity [14].
In comparison with the DCFC, carbon gasification reactions occur in a physically separate compartment upstream of the anode in the ICFC. Therefore, the ICFC system does not allow the gases produced by fuel cell oxidation to diffuse back to the solid carbon fuel and react with it further. However, the ICFC system does still allow the heat produced by fuel cell electrochemistry to transfer back to the endothermic gasification reactions. Practical implementation of the ICFC system therefore depends on a sophisticated heat exchanger composed of high temperature-rated materials. The least coupled system presented in Table 3.1 is simply a gasifier upstream of a fuel cell (G+FC). This combination of components has already appeared in several pilot plant designs [23], [24], but lacks the potential efficiency gains offered by the more integrated CFC configurations.
The direct-CFC (DCFC) system is promising, and will be pursued in future studies with a more coupled model. The focus of this paper, however, is on the last two CFC systems listed in Table 3.1: the indirect-CFC (ICFC) and the gasifier + fuel cell (G+FC). The key distinction between the ICFC and G+FC systems, shown in Figure 3.1, is the source of heat to the endothermic gasification reactions. The gasifier and fuel cell are thermally coupled in the ICFC, so heat is supplied to the gasifier from the exothermic fuel cell reactions. In contrast, the gasifier and fuel cell are not thermally coupled in the G+FC system, so the gasifier must operate auto-thermally by burning extra fuel. In both systems, 1iWis the electrical power generated by the fuel cell, QFC is the rate of heat release from the fuel cell, and OG is the heat rate input required by the gasifier, all measured per unit fuel cell area [W cm-2].
Figure 3.1: Model drawings of the ICFC (A) and G+FC (B) systems , as defined in Table 3.1. Molar flow-rates of species are denoted by ๐ฐj.
3.2.1.2 System Assumptions and Equations
The following assumptions apply to both the ICFC and G+FC systems from Figure 3.1 in order to simplify the analysis and isolate the impact of gasifier/fuel cell coupling on system performance:
1) Solid fuel is represented ideally here as pure carbon, which is supplied to the gasifier at the same rate that it's consumed by reactions. This carbon could be supplied in the form of coal char that has been heat pre-treated and ground into fine particles to enhance reactivity [14].
2) The residence time in the gasifier is long enough for gases to reach chemical equilibrium before entering the anode. This condition can be achieved by adjusting flow-rates and/or increasing gasifier size because the gasifier is a separate component from the fuel cell.
3) Steam or carbon dioxide can be supplied to the gasifier by extracting the needed species from the anode exhaust stream and recycling it back to the gasifier.
4) Any work or heat inputs required for separation before recycle are negligibly small and can be ignored in this analysis. Similarly, heat loads required to pre-heat incoming streams are neglected because the enthalpy of the streams exiting this system closely match those entering the system.
The following assumptions are only applicable to the ICFC system, as shown in subplot A of Figure 3.1:
5A) The fuel cell operates at or above the operating temperature of the gasifier to promote the flow of heat in the desired direction. A novel high-temperature heat exchanger transfers heat rejected from the fuel cell stack to the gasifier (e.g. using high-temperature heat pipes [25], [26]).
6A) The heat rejected by the fuel cell stack is sufficient to supply the heat demand of the gasifier (QFC QG). This assumption is checked and holds true for all results presented.
The energy and exergy efficiencies of the ICFC and G+FC systems are defined here as the ratio of fuel cell power output to the chemical potential of the fuel consumed:
is the total heating value of the anode exhaust after the recycle stream is extracted. Similarly, 
is the chemical exergy of carbon, and 
is the total chemical exergy of the anode exhaust after recycle extraction. Note that ๐ฐys and 
will differ for the two systems because the carbon flow-rate to the gasifier (๐ฐc) is larger in the G+FC system, which involves combustion to supply gasifier heat.
The previous definition of efficiency is based on the system boundaries shown in Figure 3.1, which can have a substantial net heat rejection. However, in a realistic system, high quality heat rejected by a system at 700-800°C would not go to waste. Therefore, a second set of system efficiencies are defined here in which the heat rejected by the ICFC or G+FC is sent to a bottoming cycle:
Efficiencies can also be defined for the gasifier and fuel cell components individually. Cold gas efficiency is used here to quantify gasifier performance, and an analogous expression is used to express gasifier exergy efficiency:
is the rate of exergy transferred by heat to gasifier (W cm- 2). These definitions of efficiency only account for the chemical energy and exergy of the species exiting the gasifier, but account for both the chemical and thermal energy and exergy of the species entering the gasifier. Enthalpy values for each species are calculated with the Shomate equation using NIST-JANAF coefficients [27], and standard chemical exergy values all come from Szargut et al [28]. The total exergy of a given material stream, ei, accounts for both chemical and physical exergy, as detailed in [29].
The energy and exergy efficiencies of the fuel cell are defined here as:
These definitions only account for the fuel that participates in cell electrochemistry because unspent fuel in the exhaust can still be used downstream.
These definitions only account for the fuel that participates in cell electrochemistry because unspent fuel in the exhaust can still be used downstream.
3.2.2 Gasifier Model
For both CFC systems, solid carbon fuel is sent to the gasifier along with a recycled stream of either pure H2O or pure CO2. Air is also sent to the gasifier for combustion in the G+FC system.
The following gasification reactions are modeled together in equilibrium:
Where P is the total pressure and ๐Gi is determined by taking the difference in Gibbs free energies between the products and reactants of the given reaction. The resulting equilibrium gas phase mixture is then determined by solving equations (3.9)-(3.12) for a fixed total pressure. The final constraint equations are derived from mass balances on reactions (G. 1)-(G.4).
The heat input required by the gasifier can be determined by a component energy balance:
3.2.3 Fuel Cell Model
The fuel cell model calculates the current density-voltage curve of a button SOFC for a given fixed temperature, pressure and fuel composition. This model applies to a porous anode-supported SOFC composed of the traditional material composites: a Ni/YSZ anode, YSZ electrolyte and LSM/YSZ cathode. Air is fed into the cathode, and the equilibrium output from the gasifier model is fed into the anode. The model domain is isothermal and ID with respect to distance from the triple-phase-boundary (TPB). The fuel cell model captures multiphysics processes of transport through porous electrodes, thermochemical surface reforming, and electrochemical oxidation mechanisms for both H2 and CO [12], [30]. The fuel cell model has already been validated against experimental data from a porous anode-supported SOFC button cell fueled by various mixtures of H2/H2O, CO/CO2 and H2/CO [13]. The H2 and CO oxidation mechanisms and governing equations are presented briefly here and in detail elsewhere [12], [31].
3.2.3.1 Conservation Equations
Gas and surface mass conservation equations are applied over a series of m discrete nodes in both electrodes, as shown in Figure 3.2. Gas-phase mass conservation is modeled using the dusty-gas-model (DGM), which accurately represents bulk and Knudsen diffusion in porous media [32].
Gas-phase reactions in the anode are neglected due to the relatively fast catalytic surface reactions on nickel at 700-8000 C [12]. Reforming reactions on nickel occur throughout the anode, and are modeled using a well-established 42-step heterogeneous mechanism [33], [34]. The electrochemical reactions occur only at the mth node, where the triple-phase boundary (TPB) is located [34], [35].
Figure 3.2: 1D MEA model discretization and species flows. Surface reforming reactions on nickel occur throughout the anode; electrochemical reactions occur at the mth nodes of the anode and cathode, where the TPB is located.
The molar fluxes of gas phase species at the anode TPB are:
where ๐พf is the input fuel utilization and
is the total production rate of H2 or CO
is the total production rate of H2 or CO
from surface reforming reactions in the anode. Equation (3.15) is defined in terms of CO for systems with CO2 recycle, and in terms of H2 for systems with H2O recycle. The flux of O2 at the cathode TPB is given by:
. The flow-rate of air into the cathode is then:
. The flow-rate of air into the cathode is then:
3.2.3.2 Electro-oxidation Mechanisms
This model implements multi-step mechanisms for both H2 and CO electro-oxidation, which are presented briefly here and described in detail elsewhere along with experimental validation [12], [30].
Hydrogen electro-oxidation is modeled by five elementary hydrogen spillover steps [36]:
The mechanism for CO oxidation involves three elementary steps [30]:
3.2.3.3 Cell Overpotentials
At finite current, the operating cell voltage can be expressed as the difference between the reversible cell potential and various overpotentials:
The anode activation overpotential, ๐ฐact,a, is a function of the currents produced by both the H2 and CO electro-oxidation mechanisms. Butler-Volmer expressions can be derived for each rate-limiting step in these mechanisms to relate current to anode activation overpotential. The following Butler-Volmer expressions are applied to the H2 mechanism:
The following Butler-Volmer expression applies to the CO mechanism [30]:
Values for the kinetic rate constants, kf and kb, were obtained previously by a least-squares fitting of the model to EIS patterned anode data at 700-775°C [10].
The electric potential difference across the anode-electrolyte double layer is given by: E = Eeq + ๐ฐact,a, where the equilibrium potential (Eeq) is determined by solving equation (3.22) for E with ๐ฐact,a = 0 and iCO = 0. A more detailed derivation and fitting of this CO mechanism with all of the governing equations is provided elsewhere [30].
Cathode activation overpotential is related to total current by the Butler-Volmer equation [37]:
Finally, the ohmic overpotential is given by [41]:
3.3 Simulation Procedure
In order to determine the performance of the CFC system over a range of current densities, the following sequence of steps are followed using a MATLAB' script. Steps 3)-5) are repeated for increasing anode activation overpotential until the fuel cell polarization curve is complete, as shown in Figure 3.3.
Figure 3.3: Simulation procedure flow-chart to generate a polarization curve and performance data for the carbon fuel cell system model.
1) Calculate gasifier output.
Equations (3.9)-(3.12) are solved along with constraint equations for fixed total pressure and mass using Matlab's non-linear "fsolve" function. When simulating autothermal gasification in the G+FC system, the air feed to the gasifier is incrementally increased until the net heat input to the gasifier approaches zero. Cantera's "equilibrate" function is then applied to the output mixture to determine the gas-phase equilibrium composition exiting the gasifier to the fuel cell anode.
2) Calculate reversible cell potential.
The equilibrium potential of the fuel cell is then determined by equation (3.19), where oxygen partial pressure in the anode channel comes from the equilibrium output of the previous step.
3) Resolve current densities and anode species profiles.
Initial guesses for concentrations and coverages are used to estimate the current densities from H2 and CO along with the initial fluxes of gas phase species at the anode TPB. These fluxes are boundary conditions to the gas species conservation and transport equations. Together these form a set of ordinary differential equations that can be solved simultaneously along with the surface reforming model for gas and surface species profiles until steady-state is reached using "ode 15s" in MATLAB*. The H2 and CO current densities are then updated based on the new concentration profiles, and this process repeats until the non-linear "fsolve" function converges on steady-state anode concentration profiles and current densities, as detailed in [12].
4) Resolve cathode species profiles and cell overpotentials.
A similar method is used to determine the species profiles in the cathode, but with no surface reforming and with pre-determined current densities and fluxes at the TPB. The cathode activation overpotential is then computed by applying the non-linear "fsolve" function to equation (3.26). The concentration overpotentials and ohmic overpotential are then determined by equations (3.27)-(3.29).
5) Calculate power, flow-rates, heat rates and efficiencies.
Cell power density is simply the product of total current density and operating voltage: W = i Ecell, where operating cell voltage comes from equation (3.18). The molar flow-rates of species into the anode and cathode are then given as functions of current density in equations (3.15)-(3.16).
The needed molar flow-rates of carbon and CO2 or H2O into the gasifier can then be determined based on mass balances applied to reactions (G. 1)-(G.4). The air flow-rate into the autothermal gasifier of the G+FC system can then be determined by setting QG = 0 in equation (3.13). For the ICFC system, air flow-rate to the gasifier is zero and heat input from the fuel cell to the gasifier is given by equation (3.13). The heat output of the fuel cell is then given by equation (3.17) for both systems, and efficiencies are given by equations (3.1)-(3.8).
3.4 Results and Discussion
The operating conditions and SOFC structural parameters used in these simulations are listed in Table 3.2. Temperature is only varied from 700-800°C to coincide with the temperature range of the experimental data that the rate constants were fitted to in the H2 and CO mechanisms [10], [42].The only recycle stream compositions considered in this study are pure H2O and pure CO2 in order to compare the performance of CFC systems with these two gasification mediums. Unity fuel and oxygen utilizations are used here in order to determine the maximum theoretical performance of the system. Although conventional SOFC stacks have oxygen utilizations substantially lower than one, a near-perfect value is theoretically possible in a CFC system because the distributed heat removal from the stack to the gasifier eliminates the need to send excess air to the cathode for cooling purposes [25]. The anode is divided into ten nodes, which is the optimal resolution for minimizing run-time without sacrificing accuracy in the surface and gas species profiles. The majority of the structural parameters for the SOFC come from another group's work that fitted a similar detailed model to porous anode experimental data [37]. The TPB length was derived by fitting the model to experimental data for CO/CO2 mixtures [31], [42].
Table 3.2: Constant operational and structural parameters for the SOFC.
Figure 3.4 displays gasifier output as a function of temperature for the ICFC system (subplots A-B)and the G+FC system (subplots C-D). Subplots A and C correspond to systems with CO2 sent to the gasifier, while subplots B and D correspond to systems with H2O sent to the gasifier. Figure 3.4 demonstrates that the equilibrium output is strongly temperature-dependent for both H2O and CO2 feeds. Higher temperatures facilitate the formation of H2 and CO, leading to a more fuel-rich output, which is beneficial to the SOFC. Subplot A shows that CO is the dominant species in the gasifier output when CO2 is the gasification agent, particularly at higher temperatures. Subplot B shows that H2 is the dominant fuel species in the gasifier output when H2O is the gasifying medium, but a large portion of the stream is also composed of CO, which can later shift to form more H2 on the fuel cell anode or be directly oxidized at the TPB to produce power.
Subplots C-D of Figure 3.4 correspond to the G+FC system, which operates autothermally because no heat is supplied externally from the fuel cell stack. In both of these cases, the gasifier output is significantly diluted by N2 as a result of the combustion reaction with air. This in turn dilutes the fuel content of the gasifier output, which then lowers the potential of the SOFC. These results imply that one disadvantage of the G+FC system is the reduced fuel content of the gasifier output as a result of autothermal gasification. This loss could potentially be combatted by sending pure oxygen rather than air to the gasifier, but that would require an air separation unit, which would add a parasitic loss to the system. The gasifier outputs from Figure 3.4 are the same mixtures sent to the anode of the fuel cell in the results presented later for these CFC systems.
Figure 3.4: Gasifier equilibrium output vs. temperature for H2O recycle (B,D) and CO2 recycle (A,C) from the anode to the gasifier. The gasifier's heat is supplied from an external heat source in the ICFC system (A,B), while the gasifier operates autothermally with an air input for combustion in the G+FC system (C,D).
The following sub-sections seek to address the two questions posed in the introduction of this paper: 1) how much will power density improve when H2O is used as the gasification medium instead of CO2 ?; and 2) how much will system efficiency improve when the gasifier and SOFC are thermally coupled? In order to address these questions, the first sub-section focuses on the ICFC system and compares fuel cell performance when H2O and CO2 are sent to the gasifier over a range of temperatures. The second sub-section compares the efficiencies of the ICFC and G+FC systems to measure the benefit of transferring rejected heat from the fuel cell to the gasifier before using it in a bottoming cycle.
3.4.1 Steam vs. Dry Gasification
Previous experimental work has demonstrated that H2 electro-oxidation proceeds 2-3 times faster than CO electro-oxidation on Ni-YSZ [43], resulting in a lower anode activation overpotential. It is therefore expected that the fuel cell will attain higher power densities when coupled to H2O gasification than CO2 gasification. Therefore, the goal of this section is to quantify this advantage of H2O over CO2 gasification in a CFC system. In order to isolate the impact of the gasification medium, results here focus on the ICFC system from subplot A of Figure 3.1, which does not require any air input to the gasifier. These results focus specifically on fuel cell performance, with corresponding input streams from the gasifier as shown in subplots A-B of Figure 3.4. Several fuel cell metrics are compared over a range of operating temperatures to gain insight on the relative advantage of steam over dry gasification when coupled to a fuel cell.
Figure 3.5 displays the current-voltage-power curves for CO2 and H2O recycle in an ICFC system over a range of operating temperatures. As expected, voltage and power curves shift up as temperature increases for both H2O and CO2 recycle systems. This trend is partly due to the more fuel-rich mixtures exiting the gasifier at higher temperatures, and also due to faster reaction kinetics in the fuel cell. The results for CO2 recycle are shown in subplot A, and the results for H2O recycle are shown in subplot B. A quick visual comparison between these two subplots confirms that the fuel cell attains significantly higher current and power densities when coupled to H2O rather than CO2 gasification.
Subplot C of Figure 3.5 also compares the maximum power densities for the H2O and CO2 system curves in subplots A-B as a function of temperature. The maximum power densities for CO2 recycle range from about 0.2 to 0.4 W cm-2, which are consistent with reported values from CFC bench-scale experiments with CO2 gasification [11], [44]. The maximum power densities for H2O recycle, on the other hand, reach values upward of 1.0 W cm-2, which makes this system competitive with SOFCs run on H2-rich synthesis gas [42]. From subplot C, it is clear that the ICFC system with H2O recycle outperforms the same system with CO2 recycle in terms of maximum power output by a factor of 3-5. These findings are consistent with previous experimental work demonstrating that a porous anode-supported SOFC attained significantly higher power densities with H2+CO mixtures compared to CO+CO2 mixtures [42].
Figure 3.5: Fuel cell operating voltage and power density curves vs. temperature for the ICFC system with CO2 recycle (A) and H2O recycle (B). Maximum power densities for H2O and CO2 recycle are also compared vs. temperature (C).
In order to gain a clearer understanding of why the ICFC performs substantially better with H2O recycle, it's helpful to compare the different loss modes in the fuel cell. A breakdown of the fuel cell overpotentials as a function of current density is presented in Figure 3.6 for H2O and CO2 recycle at both 7000C and 8000C. As expected, most of the overpotentials are lower at the higher temperature (subplots C-D). This trend with respect to temperature is especially noticeable when comparing subplots A and C, which correspond to the system with CO2 recycle. Raising the temperature by 1000 C causes anode activation overpotential to drop dramatically in the CO2 system, resulting in a limiting current density that's approximately twice as large at 800°C. This result indicates that the CO oxidation mechanism is strongly dependent on temperature and has especially sluggish kinetics at lower operating temperatures.
However, at both temperatures, anode activation overpotential dominates over the other loss modes for CO2 recycle (subplots A,C), contributing to a voltage drop of more than 0.4V in the limiting current regime. In contrast, anode activation overpotential remains below 0.1V for H2O recycle (subplots B,D) until H2 adsorption becomes rate-limiting at the end of the curve. These results show that the sluggish kinetics of CO oxidation relative to H2 oxidation are the main factor contributing to worse cell performance with CO2 recycle. Anode concentration overpotentials are also relatively higher for the CO2 recycle system because CO diffuses more slowly through the anode than H2 [30]. However, the anode concentration overpotentials are substantially lower than the anode activation overpotentials in the fuel cell with CO2 recycle, so the sluggish CO diffusion is only a secondary factor in the lower performance curves observed in systems with CO2 recycle.
Figure 3.6: Fuel cell overpotentials as a function of current density for the ICFC system with CO2 recycle (A,C) and H2O recycle (B,D). Subplots A-B are at 700°C; subplots C-D are at 800°C.
The previous two figures demonstrated that a fuel cell is capable of substantially higher performance when H2O is sent to the gasifier instead of CO2 because the electrochemical kinetics are much faster for H2 than for CO. One might argue that the H2O recycle system could outperform the CO2 recycle system by an even greater factor if a higher steam-to-carbon ratio was implemented in the gasifier, which typically produces a more H2-rich yield that could benefit the fuel cell. However, it was found in this study that raising the steam-to-carbon ratio did not significantly boost the hydrogen yield of the gasifier because lower temperatures are needed to promote the water-gas-shift reaction. Therefore, steam-to-carbon is fixed at one for the results presented here to optimize performance.
However, maximum power densities are still 3-5 times larger when H2O is used instead of CO2 in the ICFC system, even with a low steam-to-carbon ratio. This result provides a clear incentive to select H2O over CO2 as the gasifying medium for the ICFC system. However, implementing steam in this system presents a couple of practical design challenges: 1) poisonous H2S will be produced by untreated solid fuels in the gasifier, and 2) steam must be condensed out of the anode exhaust for recycle. This would likely result in a more complex system with additional components like a desulfurizer and a condenser. This would also lead to parasitic losses because these components operate at lower temperatures than the rest of the system, and additional steam would need to be supplied to the gasifier to compensate for water vapor escaping in the anode exhaust after the condenser. However, the staggering advantage of steam over CO2 from a power density perspective would likely outweigh these challenges.
3.4.2 Impact of Thermal Coupling
The previous results all focused on the ICFC system from subplot A of Figure 3.1, which assumes that the heat demand of the gasifier can be supplied by the fuel cell's rejected heat. Such a system would require a sophisticated high-temperature heat exchanger between the two components and a finite temperature gap to promote the flow of heat. Therefore, the ICFC system poses more design challenges than the decoupled gasifier + fuel cell (G+FC) system in subplot B of Figure 3.1. However, the ICFC has a theoretically higher efficiency than the G+FC because fuel doesn't need to be burned to supply the gasifier with heat. This section seeks to quantify the efficiency advantage of the ICFC over the G+FC for both H2O and CO2 recycle at the optimal temperature of 800°C.
Figure 3.7 compares the component and system efficiencies of the G+FC (subplots A,C) to the ICFC (subplots B,D), as defined in equations (3.1), (3.3) and (3.4). Subplots A-B show results for these systems with CO2 recycle, while subplots C-D show results for the system with H2O recycle. The gasifier efficiency remains relatively constant with respect to current density in all four cases because flow-rates of gas species into and out of the equilibrium gasifier simply scale with current. The gasifier efficiency is also high due to the idealized pure carbon feed, which bypasses gasifier losses to devolatilization and other side reactions.
The other efficiencies shown in Figure 3.7 closely follow the cell operating voltage curves, which drop off with current density as overpotentials increase. This negative trend highlights the intrinsic trade-off between power and efficiency in the CFC system: theoretically high efficiencies can be obtained when very little current is drawn, but efficiencies diminish when cell power output is maximized. It is clear from Figure 3.7 that the CFC system efficiency is strongly dependent on the operating point of the fuel cell along the polarization curve. Because system efficiency closely tracks with the fuel cell polarization curve, the systems with H2O recycle attain higher efficiencies and reach higher current densities than the systems with CO2 recycle. This result is consistent with the key finding of the previous section that system performance is substantially higher with H2O recycle due to the faster kinetics of H2 oxidation in the fuel cell.
A comparison between the G+FC (subplots A,C) and ICFC (subplots B,D) systems of Figure 3.7 demonstrates that the coupled ICFC system is capable of attaining significantly higher system efficiencies and current densities. This difference is mostly due to the fact that about 30% of the incoming carbon fuel is sacrificed to combustion in the G+FC system. This results in a lower system efficiency because more fuel is sent to the system for a given fuel cell power output.
A secondary cause for this system performance gap can be observed by comparing the fuel cell efficiencies, which extend to higher current densities in the ICFC system than in the G+FC system. This is due to the fact that the autothermal gasifier output in the G+FC system is diluted by N2, as shown in subplots C-D. This in turn lowers the fuel content of the mixture sent to the anode of the G+FC, resulting in both a lower open-circuit potential and a higher anode activation overpotential.
Therefore, performance of the G+FC system is hurt by both the combustion of fuel in the gasifier and also by the diluted gasifier output from the air feed.
Figure 3.7: Operating voltage and efficiency curves of the gasifier, fuel cell and combined system for the G+FC (A,C) and ICFC (B,D) systems. Results are shown for CO2 recycle (A-B) and H2O recycle (C-D) all at T = 800°C.
Although the results in Figure 3.7 show a large performance gap between the ICFC and G+FC systems, it is important to address a couple of idealized assumptions that were made in order to reach those results. First of all, it was assumed that the gasifier and fuel cell could operate at the same temperature in the ICFC system despite the fact that heat must be transferred between them.
In a real system, however, a temperature drop of roughly AT = 10-15°C would be needed between the components for a conventional heat exchanger to transfer heat. A more conservative estimate of AT =50°C is used here to account for the fact that this system would require a novel high-temperature heat exchanger, such as liquid sodium heat pipes [29].
The other idealized assumption taken earlier comes from the definition of system efficiency in equation (1), which does not account for useful work that could be extracted from rejected heat. This particularly hurts the efficiency of the G+FC system, which rejects all fuel cell heat to the environment according to this assumption. A more realistic comparison of the two systems uses efficiency as defined in equation (2), which allows the heat rejected by the system to power a bottoming cycle. By accounting for a bottoming cycle and a temperature drop between ICFC components, a more fair comparison between the ICFC and G+FC systems is possible.
Figure 3.8 compares the efficiencies of the ICFC and G+FC systems before and after these two real-world adjustments have been made. Consistent with previous findings, all efficiency curves are higher and reach larger current densities for the systems with H2O recycle than for the systems with CO2 recycle. The G+FC system plots (subplots A,C) indicate that the inclusion of a bottoming cycle significantly boosts efficiency. This result is expected because all heat rejected by the fuel cell stack goes to waste according to the original definition of system efficiency for the G+FC. Adding a bottoming cycle also boosts system efficiency in the ICFC results (subplots B,D) because there's still a net heat output after heat is sent to the gasifier. However, the extent of the efficiency gain is noticeably smaller with the addition of a bottoming cycle in the ICFC system compared to the G+FC system because the net heat output is smaller. Despite the fact that the G+FC system efficiency increases more with the addition of a bottoming cycle, the ICFC system still attains superior performance even with the inclusion of a bottoming cycle.
A more fair comparison between the systems in Figure 3.8, however, is between the G+FC with the bottoming cycle and the ICFC with the bottoming cycle and the lower gasifier temperature.
Operating the gasifier 50°C cooler causes the ICFC system efficiency to drop because a lower gasifier temperature translates to less fuel exiting the gasifier and entering the anode. This in turn lowers the efficiencies of both the gasifier and the fuel cell and therefore the overall system. However, even when a conservatively large temperature drop is assumed, the ICFC system still performs more efficiently than the G+FC system and reaches higher currents. Thus, the ICFC system has a performance advantage over the G+FC system even when a couple of practical operating considerations are factored into the comparison. The efficiency of the adjusted ICFC system is still highly dependent on the operating point along the polarization curve. However, even at the high-current point of maximum power output, the ICFC system with a bottoming cycle reaches 59% and 55% efficiencies with CO2 and H2O, respectively. These values are within a few percentage points of the predictions made in a previous analysis of a similar ICFC system operating at 0.7V with CO2 and H2O [11]. These predicted efficiencies upward of 55% also make this CFC system competitive with other state-of-the-art stationary power candidates, such as gas turbine combined cycles and SOFC/gas turbine hybrid systems [24], [45].
Figure 3.8: G+FC system (A,C) and ICFC system (B,D) efficiency curves for CO2 recycle (A-B)and H2O recycle (C-D) with TFC= 800°C . Solid lines take the system efficiency as defined in equation (1); dashed lines take the system efficiency as defined in equation (2). Vertical lines denote the current densities that correspond to maximum power output.
Finally, the exergy efficiencies of the G+FC and ICFC systems with CO2 and H2O recycle are compared in Figure 3.9. Efficiencies versus current density are shown for the gasifier, fuel cell and combined system with a bottoming cycle, as defined in equations (3.6), (3.8) and (3.4). The heat exchanger temperature drop of AT =50"C is implemented again here for the ICFC system (subplots B,D), which requires a heat transfer from the fuel cell to the gasifier across a finite temperature drop. The exergy efficiency curves in Figure 3.9 closely resemble the energy efficiency curves of the gasifier, fuel cell and system from Figure 3.7. Gasifier exergy efficiencies are constant with respect to current density because all terms in that expression scale with flow-rate and therefore current. Fuel cell exergy efficiencies, on the other hand, drop with respect to current as a result of increasing overpotentials in the cell. The system exergy efficiencies follow a similar trend with respect to current as a result of increasing fuel cell losses.
The gasifier efficiencies in Figure 3.9 are also consistently higher than 0.8 as a result of using pure carbon fuel, whereas the fuel cell efficiencies drop off to values below 0.3 as a result of increasing cell voltage losses in the limiting current regime. These results indicate that the fuel cell is the component where most of the system's exergy destruction occurs, not the gasifier. Therefore, CFC system performance is likely limited by the fuel cell, particularly at higher current densities, which correspond to maximum power operation. The system efficiency curves in Figure 3.9 also confirm that the coupled ICFC system (subplots B,D) outperforms the de-coupled G+FC system (subplots A,C). Similarly, a comparison of the system efficiencies indicates that recycling H2O (subplots C-D) rather than CO2 (subplots A-B) boosts performance in terms of both efficiency and power density. These trends are all consistent with the results of the energy efficiency analysis from Figure 3.8, which also highlighted the benefits of a thermally-coupled ICFC system run on steam.
Figure 3.9: Exergy efficiency curves for the gasifier, fuel cell and combined system with a bottoming cycle, as defined in equations (3.6), (3.8) and (3.4). Efficiency curves are compared for the G+FC system (A,C) and ICFC system (B,D) for CO2 recycle (A-B) and H2O recycle (C-D). Fuel cell operates at 800°C for all systems, while gasifier operates at 800°C for the G+FC systems (A,C) and at 750°C for the ICFC systems (B,D).
A detailed 1 D MEA model is coupled to an equilibrium gasifier to model a carbon fuel cell (CFC) system. The purpose of this study is twofold: 1) to quantify the advantage of recycling H2O rather than CO2 from the anode to the gasifier, and 2) to quantify the advantage of direct thermal coupling between the gasifier and fuel cell in a CFC system. The results of the first study show that the fuel cell consistently performs better when H2O is recycled from the anode to the gasifier instead of CO2. A dominant anode activation overpotential loss in the fuel cell run on CO2 recycle indicates that the sluggish kinetics of CO electrochemical oxidation are responsible for this discrepancy in performance. Fuel cell performance curves from 700-800°C show that the fuel cell performs 3-5 times better with H2O instead of CO2 recycle, with maximum power density values exceeding 1.0 W cm-2 in the H2O recycle system.
The results of the second study show that the ICFC system reaches significantly larger current densities and efficiencies than the G+FC system. This advantage arises because the autothermal gasifier in the G+FC system sacrifices carbon fuel and dilutes the gasifier output with nitrogen. Finally, it is shown that the ICFC system still outperforms the G+FC system when a bottoming cycle is included and a finite temperature drop is applied between the ICFC components. Overall system efficiencies of 55-60% are predicted for the final ICFC system when operating at maximum power. An exergy analysis of the different components and systems indicates that the fuel cell is the largest source of lost work potential, especially at high currents. These preliminary findings indicate that the CFC system will perform best when steam is sent to the gasifier and when fuel cell heat is transferred to the gasifier. Such a system is capable of state-of-the-art efficiencies that could significantly reduce CO2 emissions from coal conversion in the stationary power generation sector. However, further work must go into the design of a high-temperature heat exchanger between the gasifier and fuel cell stack in order to implement this concept. Furthermore, a 2D model for a direct CFC (DCFC) should be developed to study the added benefits of allowing gasification and electrochemical oxidation to occur simultaneously in the same chamber.
Chapter 4 Study of Syngas Behavior in SOFCs
One of the distinct advantages of solid oxide fuel cells (SOFCs) is their ability to directly oxidize CO in addition to H2, which allows them to be run on syngas mixtures. However, membrane-electrode-assembly (MEA) models typically neglect CO electrochemistry in the presence of H2 and H2O, assuming that the water-gas-shift reaction proceeds faster than sluggish CO electro-oxidation. In this paper, however, we demonstrate with a comprehensive ID-MEA model that CO electro-oxidation cannot be neglected in syngas mixtures, particularly at high current densities for high CO-content syngas. We first demonstrate that incoming CO is not all shifted to form H2 before reaching the triple-phase boundary, as previously assumed, due to the equilibrium limitation of the water-gas-shift reaction at 800°C. Furthermore, we confirm that direct oxidation of CO contributes non-negligible current relative to H2 at high anode overpotentials in syngas mixtures.
Together these results show that CO electro-oxidation plays an important role in SOFC performance not only via water-gas-shift reforming, but also via direct oxidation even when H2 is present. This work suggests that accurate models for both surface reforming and direct electro-oxidation of CO in SOFC anodes must be included in order to capture performance when using syngas mixtures.
4.1 Introduction
A key advantage of solid oxide fuel cells (SOFCs) is their ability to electrochemically oxidize CO, which allows them to run on various abundant hydrocarbon fuels in addition to hydrogen [1]-[3]. SOFCs can potentially be coupled to a gasifier that converts coal, biomass or other solid carbonaceous fuels to syngas [4]-[6]. Because syngas is primarily composed of H2 and CO, which can both be directly oxidized on SOFCs [7], it is an ideal fuel stream once contaminants have been removed [8]. However, it has also been shown that H2 electro-oxidation proceeds 2-3 times faster than CO electro-oxidation on Ni/YSZ [8], [9]. Therefore, the importance of including a model for CO electro-oxidation in SOFC anodes is debatable when H2 is also present.
Previous researchers have often used a hydrogen-spillover oxidation model but neglected CO electro-oxidation even when both species are present [10], [11]. Neglecting CO electrochemistry is often justified by the following arguments: (1) the rate of CO conversion via surface reforming exceeds the rate of CO electrochemical oxidation [7], [8], and (2) H2 dominates over CO in charge transfer chemistry [12]. However, these two assumptions may not hold for syngas mixtures with high CO content and low H2O content, like the output of a coal gasifier [13]. The water-gas-shift reforming reaction, in particular, can only convert CO to H2 when sufficient H2O is present [14].
Therefore, it is plausible that non-negligible quantities of CO could reach the triple-phase-boundary (TPB) to react electrochemically for certain syngas mixtures.
Although CO electro-oxidation has been typically neglected in SOFC models with syngas, several researchers have proven its importance in CO+CO2 systems [15]. Experimental groups have tested nickel-pattern anodes and Ni-YSZ porous anodes with CO mixtures to study the power output from direct electrochemical oxidation [7], [12], [16], [17]. A few mechanisms for CO electro-oxidation on YSZ electrodes have also been proposed [18]-[20]. A comprehensive analysis of CO charge transfer and reaction kinetics on Ni-YSZ anodes appears in Yurkiv et al [21]. Although these researchers agree that the rate of CO electro-oxidation is smaller than that of hydrogen, results indicate that their rates only differ by a factor of two or three [22]. Furthermore, some experimental studies of syngas electrochemical oxidation on Ni-YSZ conclude that CO electro-oxidation is non-negligible in comparison to H2 [9], [14], [17]. These results motivate the investigation of CO electro-oxidation in Ni-YSZ anodes when both fuel species are present.
The goal of this work is to quantify the extent to which CO impacts SOFC performance via surface reforming and direct electro-oxidation for a range of syngas mixtures. More specifically, this study breaks down the impact of CO into two parallel pathways: 1) reforming throughout the anode to produce H2, and 2) direct electro-oxidation at the TPB. This paper implements a 1D MEA model with detailed surface reforming and electrochemical mechanisms for both CO and H2 electro-oxidation. Anode structural parameters in the model are first fitted to H2/H2O and CO/CO2 experimental data sets. Model polarization curves are then compared to H2/CO experimental data in order to determine carbon monoxide's impact on cell performance via reforming and direct oxidation in syngas mixtures.
4.2 Model Description
The objective of the MEA model is to calculate the polarization voltage-current density curve for a given temperature, pressure and syngas fuel composition. The model is isothermal and the domain is 1D with respect to distance from the TPB. The model captures multiphysics processes of transport through porous electrodes, thermochemical reactions, and electrochemical mechanisms for both H2 and CO [23]-[25]. The governing equations for conservation, transport and thermochemistry are introduced first, followed by a breakdown of how each cell overpotential is modeled. The focus of this study is to isolate the role of CO in the anode by comparing the model to experimental polarization data by Jiang and Virkar [7]. Therefore, anode concentration and activation overpotentials are modeled in detail to capture the complex coupling of H2 and CO via reforming and oxidation. However, open-circuit potential, ohmic losses and cathode overpotentials are taken directly from the experiment in order to minimize uncertainty and isolate the role of CO in the anode.
4.2.1 Conservation Equations
The gas phase mass conservation equation in the porous electrodes is:
currents:
The surface species mass conservation equation in the porous anode is:
These gas and surface mass conservation equations are applied over a series of m discrete nodes in both electrodes. Surface reforming occurs along all nodes of the anode because nickel is dispersed throughout the anode. The electrochemical reactions, however, occur only at the mth node of each electrode, where the TPB is located. Although YSZ is dispersed throughout the anode thickness, the diffusion of O²⁻ ions through YSZ in the anode is slow relative to the rate of electrochemical oxidation. Therefore, although the TPB is theoretically distributed throughout the entire anode, it's reasonable to assume that electrochemical reactions occur at the last node of the anode model, since the TPB is localized to a small region (~10 ๐ตm thick) adjacent to the electrolyte [11], [26]. Moreover, we note that this localized electrochemistry assumption applies to the experiment considered here because the cell is anode-supported (~1 mm thick). Because the model is 1D with respect to distance from the TPB, it physically represents a button cell configuration, like the set-up of the experiment of interest.
4.2.2 Transport in Porous Media
The gas phase fluxes Jโ from equation (4.1) are computed using the dusty gas model (DGM), an extension of the Stefan-Maxwell diffusion equations [27]. The DGM is a convenient approach to modeling combined bulk and Knudsen diffusion, and can explain physical phenomena in porous media that cannot be captured by Fick's model [28]. The DGM can be written as an implicit relationship among molar concentrations, molar fluxes and concentration gradients:
where 
is the total molar concentration [mol m-3],
is the effective binary diffusion coefficient in the porous medium [m² s⁻¹], 
is the mixture viscosity [kg m s⁻¹], B₀ is the permeability [m²], and 
is the effective Knudsen diffusion coefficient [m² s⁻¹].
is the total molar concentration [mol m-3], is the effective binary diffusion coefficient in the porous medium [m² s⁻¹], is the mixture viscosity [kg m s⁻¹], B₀ is the permeability [m²], and is the effective Knudsen diffusion coefficient [m² s⁻¹].
The effective Knudsen diffusion coefficient for component i is governed by [27]:
4.2.3 Thermochemistry
Because of the high temperatures (700-800°C) and catalytic surfaces in the anode, various thermochemical reactions occur throughout the anode. This model implements a detailed surface mechanism on nickel that was first developed by Hecht et al [3], and then extended to a wider temperature range by Janardhanan and Deutschmann [11]. This mechanism consists of 42 reactions involving six gaseous species and twelve surface species. The net production rate of gas or surface species k due to heterogeneous reactions is given by:
4.2.4 Cell Overpotentials
In order to determine the polarization curve, an accurate model for cell operating voltage as a function of current density is needed. First, the equilibrium potential of the cell at open-circuit conditions is given by [15]:
The cathode oxygen partial pressure is simply Po2,c = .21P for air sent to the cathode. Here, reversible potential must be defined in terms of oxygen concentration because there are two parallel charge-transfer pathways.
At non-zero current, the operating cell voltage is lower than the OCV due to several loss modes quantified as overpotentials. Operating voltage can thus be expressed as the difference between the reversible cell potential and these various voltage losses:
Detailed physical models for the anode activation and concentration overpotentials are implemented here to accurately capture all the major reforming and charge-transfer reactions involving CO and H2. The values for ohmic and cathodic overpotentials, however, are taken directly from experimental measurements previously published by Virkar's group [29]. Similarly, OCV values are matched to the same experimental data set by adjusting the anode mixture for air leakage. This approach is taken to isolate the impact of CO on anode overpotentials while comparing the model predictions to experimental data for operating voltage.
4.2.4.1 Experimental Overpotentials
In order to focus on how CO impacts cell performance, physical models are replaced with experimental data for portions of the model outside the anode. First, the model and experimental OCVs are matched by introducing air leakage into the anode channel until the reversible potential from equation (7) matches the experimental OCV for that anode mixture. This is necessary to account for the offset between theoretical and experimental OCV's, which is a common problem encountered in SOFC modeling, and is often attributed to electronic or gas leakages [7], [10], [30]. Some previous groups have accounted for this offset by introducing an electronic leakage overpotential term that gets subtracted off from the reversible potential [10], [23]. It is assumed here, however, that the OCV difference is caused by air leakage into the anode chamber rather than electronic leakage, consistent with claims made by the experimental group of interest here [7].This model accounts for air leakage by adjusting the reported fuel stream mixture at the anode channel until theoretical and experimental OCV's match, as described in the simulation procedure. This novel approach of physically accounting for air leakage into the anode channel is explored and compared against the electronic leakage model in more detail elsewhere [31].
The total cathode and ohmic overpotentials are fitted to experimental values versus current provided by the same research group that the polarization curves in this study come from [29]. A simple polynomial curve fit to their total cathode overpotential data yields:
The total ohmic overpotential of this same button cell is:
4.2.4.2 Anode Overpotentials
Unlike the other loss modes that are taken directly from the experimental data, the anode overpotentials are represented by detailed physical models in order to study the impact of CO on cell performance. Anode concentration overpotential accounts for losses associated with the diffusion of gas species through the thick porous anode to reach the TPB at the last node. Anode concentration overpotential is modeled as the difference between reversible cell potential at the anode channel and at the anode TPB:
The anode activation overpotential is a function of currents from both H2 and CO. Detailed multistep mechanisms for both species are implemented in this model, resulting in Butler-Volmer expressions that relate current to anode activation overpotential. Although alternative models have been suggested [32], Butler-Volmer expressions are still considered the standard model for capturing non-linear behavior at low current densities [33]. Certain steps must be assumed rate-limiting in each mechanism due to a lack of available kinetic data to implement the full mechanisms. These rate-limiting steps were selected based on previous researchers' work, and both the H2 and CO mechanisms have been previously published [23], [24].
4.2.4.2.1 Hydrogen Electro-oxidation Mechanism
The mechanism for H2 oxidation consists of five elementary reactions [10], [34]:
are determined by fitting the model to experimental H2 /H2O data later.
4.2.4.2.2 Carbon Monoxide Electro-oxidation Mechanism
The global electro-oxidation reaction for CO can be written in Kroger-Vink notation as:
is an oxygen ion on a YSZ oxygen surface site, and Vo**(YSZ) is a vacant YSZ oxygen surface site. A mechanism that includes three elementary reactions on a Ni-YSZ patterned anode is used here [24]:
The adsorption step (CO.1) is always modeled in equilibrium because CO charge-transfer kinetics are relatively sluggish and CO has a strong affinity to nickel (๐ฌco = .5 [10]). Current from CO is simply given by the sum of the currents produced by the two charge-transfer steps, since oxygen only spills over to CO in this model:
The forward and backward rate constants come from previous work that fitted this mechanism to patterned-anode Tafel plot data [24]. Arrhenius expressions were derived for each rate constant to fit the model to data at temperatures of 700-775°C. A minor extrapolation is made here to 800°C, the operating temperature for the experimental data presented later. Evaluating the rate constants at 800°C yields the following values:
As an example, the coverages of CO (Ni) and H (Ni) at the TPB are listed in Table 4.1 for several syngas mixtures at open-circuit conditions. These cases show that CO occupies a disproportionately large fraction of the available nickel surface sites at the TPB, which further motivates this investigation of the importance of CO electro-oxidation.
Table 4.1: Coverages of hydrogen and carbon monoxide on nickel at the TPB at open-circuit conditions for several syngas mixtures.
E in equations (4.17)-(4.18) is defined as the electric potential difference across the anode electrolyte double layer, which can be expressed as the sum of the equilibrium potential difference and the anode activation overpotential: E = Eeq + ๐ฐ act,a. Equilibrium potential is defined as the anode-electrolyte double layer potential difference at open-circuit conditions, and Eeq is determined by solving equations (4.17)-(4.18) with ๐ฐ act,a = 0, i(CO.2) = 0, and i(CO.3) = 0. At steady-state, equations (4.17)-(4.18) can be solved for ๐ฑO- because i(CO.2) = i(CO.3) at steady-state in order to maintain a constant surface coverage of ๐ฑ O- [24]. Total current from CO can then be calculated from equation (4.16), which reduces to ico = 2i(CO.2 ) at steady-state.
4.3 Simulation Procedure
Temperature, pressure and experimental OCV are inputs to the model, which generates a current density-voltage curve by iterating through anode activation overpotential. Steps 2)-3) are repeated for increasing anode activation overpotential until a full polarization curve is generated. The following steps are implemented in a MATLAB@ script for each cell performance curve, as shown in Figure 4.1.
Figure 4.1: Simulation procedure to generate a polarization curve for a given anode mixture.
1) Calculate the equilibrium mixture at the anode channel.
As mentioned earlier, the reversible cell potential from equation (4.7) is typically larger than the experimental OCV for a reported anode mixture as a result of air leakage into the anode. Therefore, the anode channel composition in the model is adjusted by incrementally adding air to the experimentally reported anode mixture until the theoretical and experimental OCV values match, as detailed in Appendix A. The final equilibrated gas mixture is also assumed to be the actual mixture present in the anode channel because oxygen leaking into the anode reacts very quickly with H2 and CO. Gas-phase equilibrium is also a good assumption for this particular experimental set-up because the gases have a long residence time in the fuel delivery system before reaching the cell [7]. The anode channel mixture determined in this step is also used in the following steps for finite current to accurately represent the physical impact of air leakage on cell performance.
2) Resolve current densities and anode species profiles.
The final equilibrium anode channel mixture from step 1) is the mixture used in the anode channel for the model. Because anode activation overpotential is an input, current densities from H2 and CO can be estimated along with an initial guess for TPB concentrations using equations (4.14) and (4.16). The initial fluxes of gas-phase species at the TPB are then given by equation (4.2), and these fluxes are boundary conditions to equation (4.4), which is cast in matrix form as:
The left-hand-side of equation (4.21) is calculated using present values for concentrations and boundary conditions, estimating ▽ci using a forward difference approximation. The matrix [H] is also calculated using present concentrations. The molar fluxes are then given by the system:
and fluxes Jk can then be substituted into gas species conservation equations (4.1) and (4.3). These conservation equations become a set of ordinary differential equations when equation (4.23) is cast into a finite-volume form using the flux boundary conditions at the interface.
The surface generation rates in the conservation equations are calculated using the heterogeneous reforming model based on the present gas surface species concentrations. The gas and surface species are solved simultaneously using the "ode 15s" function in MATLAB® until steady-state is reached [23]. The H2 and CO current densities are then updated based on the new concentration profiles, and this process is repeated until the non-linear "fsolve" function converges on anode concentration profiles and current densities.
3) Calculate cell overpotentials and operating voltage.
Once the anode profiles and currents are resolved, all of the cell overpotentials can be computed. The anode concentration overpotential is given by equation (4.11), where the equilibrium partial pressure of oxygen at the anode TPB is given by running the Cantera "equilibrate" function on the actual gas mixture at the last node where the TPB is located. Total cathode ohmic overpotentials are determined as functions of total current densities using equations (4.9) and (4.10). Finally, the operating voltage is given by subtracting all overpotentials from the reversible cell potential,
according to equation (4.8).
4.4 Simulation Results
Table 4.2 lists all the constant operating conditions and anode structural parameters, which are mostly taken directly from Virkar's experimental group [7]. This approach is taken to minimize uncertainty and to match this model to their particular experiment, which provides the most comprehensive published data set for anode-supported Ni/YSZ SOFCs with CO/CO2, H2/H2O and H2/CO mixtures.
Table 4.2: Constant operational and structural parameters for the SOFC model.
Results are presented here in two sections: 1) parameter fitting and 2) syngas studies. The first section fits unknown physical parameters in the model to H2/H2O and CO/CO2 experimental data sets [7]. The combined model is then validated against H2/CO data from the same group to ensure that the fitted values accurately represent the cell used in all their experiments. The impact of CO is then investigated by comparing experimental H2/CO data to the model with and without reforming and CO electro-oxidation enabled.
4.4.1 Fitting the Model
Unknown parameters in the anode are determined by fitting the model to H2/H2O and CO/CO2 data sets [7]. These parameters are intentionally fit to data sets from the same experimental group providing the H2/CO data used later in order to accurately represent the physical anode structure of the cells used throughout these experiments. The four fitting parameters are listed in Table 4.3 along with their corresponding equations.
Table 4.3: Parameters obtained by fitting the model to porous anode experimental data. i*(H.4) and ๐ชTPB come from fitting to H2/H2O mixtures; lTPB and ๐ฝ come from fitting to CO/CO2 mixtures. The equations these parameters show up in are given in the last column.
The two parameters fitted to H2/H2O data, i*(H.4) and ๐ชTPB, are unknown constants that appear in equations (4.12) and (4.13), the Butler-Volmer expressions for the two rate-limiting steps in the H2 mechanism. i*(H.4) is an exchange current density pre-factor that includes rate constants from other steps in the mechanism [10], and aTPB is a dimensionless ratio of TPB area to cell footprint area. i*(H.4), fits the model to operating voltage data at lower currents while ๐ชTPB fits the model to operating voltage data at higher current densities where hydrogen adsorption is rate-limiting. The values of these two fitting parameters are the same order of magnitude as previously reported values (i*(H.4) = 8.5, ๐ชTPB = .0086) that correspond to a different set of structural parameters than those given in Table 4.2 [23].
The resulting performance curves for this fitted model are plotted against experimental data [7], for four H2/H2O mixtures in Figure 4.2. These results demonstrate that the H2 electro-oxidation model is capable of accurately predicting cell performance away from the limiting current regime over a wide range of H2/H2O mixtures. The switch-over to rate-limiting H2 adsorption can be readily observed in these plots as the points where operating voltage begins to rapidly drop off. This switch-over causes the model to under-predict experimental limiting current for lean H2/H2O mixtures. However, the model would significantly over-predict experimental limiting current densities if this switch-over to rate-limiting adsorption were not accounted for [10], [23]. Overall, the fit of this model to H2/H2O data is an improvement over previously published efforts to fit the same data set [10].
mixtures in a SOFC at 800°C [i*(H.4) = 10 A cm-2 atm^-3/4, ๐ชTPB = .013]
The two parameters that are fitted to the CO/CO2 data, 1TPB and T, are unknown anode structural constants that appear in equations (4.17)-(4.18) and (4.5), respectively. TPB length, 1TPB, is a physical parameter that shows up in the two Butler-Volmer expressions for the CO mechanism.
Note that this parameter does not appear explicitly in the H2 mechanism equations because it is embedded along with other constants in the pre-factor terms, which were derived by assuming a rate-limiting step. Tortuosity is another unknown physical parameter that is needed to determine the effective diffusivities in the porous transport DGM equation (4.4), which models the transport of all gas species including H2 and H2O.
The performance curves for the fitted CO model are plotted against experimental data [7] for three different CO/CO2 mixtures in Figure 4.3. The model predicts limiting current density well for the two moderate CO/CO2 mixtures. In addition, the model provides a reasonable fit to experimental data for 100% CO. Although the model provides a rough estimate of the experimental CO/CO2 data, it is the first published model to fit this data set. Because the fitted model reasonably predicts a wide range of H2/H2O and CO/CO2 mixtures, it can also be applied to a wide range of syngas mixtures to predict cell performance.
Figure 4.3. Polarization curves for the fitted model compared to experimental data for CO/CO2 mixtures in a SOFC at 8000 C [;TPB= 300 m cm-2, ๐ฝ= 2.0].
For the combined model with both H2 and CO electrochemical oxidation, all fitting parameters are
the same as those presented in Table 4.3. This full version of the model includes the effects of both surface reforming and direct electro-oxidation of both species. Although the fundamental oxidation mechanisms for H2 and CO are not altered when both species are oxidized simultaneously, the two species interact via surface reforming and also compete for active sites on nickel. Therefore, the current contributions of H2 and CO are inter-dependent because partial pressures and surface coverages of both species at the TPB are accounted for in both mechanisms. The predictions of this combined model agree well with experimental data over a wide range of H2/CO mixture, as shown in Figure 4.4. This indicates that the H2 and CO mechanisms fitted individually to H2/H2O and CO/CO2 data can successfully be implemented together to model cell performance with syngas mixtures.
4.4.2 Study of CO in SOFCs
In order to study the impact of CO on cell performance via reforming and direct electro-oxidation, three different versions of the model are compared here to experimental data: 1) no reforming or CO oxidation, 2) reforming but no CO oxidation, and 3) reforming and CO oxidation. This breakdown gives clear insight on how the addition of CO impacts cell performance via surface reforming reactions and direct electro-oxidation. Figure 4.5 compares the model to experimental data for four H2/CO mixtures [7]. Each subplot in Figure 4.5 compares the experimental data set to these three versions of the model in order to isolate the impacts of CO on performance via reforming and direct oxidation. The model without reforming or CO oxidation reasonably predicts the data in subplot A, which has more H2 than CO in the gas phase. This result implies that CO only makes a minor contribution to cell performance (via reforming and oxidation) when SOFCs are fed a hydrogen-rich syngas mixture.
However, the model without reforming or CO oxidation under-predicts the limiting current in the three cases where CO is the dominant species in the mixture (subplots B-D of Figure 4.5). The model with reforming but no CO oxidation shows a sizeable improvement over the model without reforming in those three cases, which indicates that CO contributes to cell performance via water-gas-shift reforming to produce H2 in those cases. However, including reforming in the model without adding direct CO oxidation is still insufficient to predict high current data, particularly in CO-rich mixtures (subplots C-D). A sharp drop-off can still be observed in the second version of the model (as a result of the switch-over to rate-limiting H2 adsorption, not concentration losses).
This switch to rate-limiting hydrogen adsorption explains why the model under-predicts high current data when CO electro-oxidation is neglected. The third version of the model, however, is able to accurately predict experimental data at high currents. This result indicates that CO electro-oxidation contributes to cell performance in the limiting current regime.
Figure 4.5: Cell polarization curves for four syngas mixtures at 800°C. Model results with and without reforming and CO electro-oxidation are compared to experimental data [7].
First, in order to determine how much carbon monoxide contributes to performance via reforming, we show the extent to which reforming impacts the gas species profiles in the anode. It is often assumed that the majority of CO entering the anode reacts with steam via the water-gas-shift reaction to form hydrogen before reaching the TPB. However, there may be insufficient steam present in CO-rich mixtures to shift all of the incoming carbon monoxide. Furthermore, the extent to which CO shifts to form H2 may be limited by the equilibrium constraint of the water-gas-shift reaction at high operating temperatures. Therefore, the importance of surface reforming in SOFCs fueled by syngas requires thorough investigation.
Figure 4.6 compares the H2 and CO gas-phase profiles with and without surface reforming for the same four syngas mixtures presented in Figure 4.5. The left side of each subplot corresponds to the anode channel while the right side corresponds to the anode TPB where electrochemical oxidation of H2 occurs (CO oxidation is disabled here to isolate CO's impact via reforming). For each case, profiles were taken at the current density where switch-over occurred to rate-limiting hydrogen adsorption in the absence of reforming. This particular point along the curve was selected to ensure a sufficient rate of H2 oxidation at the TPB without confounding the results by diffusion limitations that occur at higher currents. It is worth noting that the impact of surface reforming scales with current density because gas fluxes at the TPB scale with current.
In all four Figure 4.6 subplots, H2 content is boosted and CO content is diminished at the TPB when reforming is enabled. These results confirm that the water-gas-shift reaction (H2O + CO ↔ H2 + CO2) cannot be ignored in electrochemically active SOFC anodes run on syngas. However, these results also indicate that not all CO is shifted to form H2 before reaching the TPB. This is the case for all four syngas mixtures, and is partly due to the fact that chemical equilibrium of the water-gas-shift reaction at 800°C predicts a roughly equal mixture of products and reactants. This trend is most pronounced in the CO-rich syngas cases (subplots C-D) because relatively less H2O is produced at the TPB to shift incoming CO. These results indicate that CO in syngas mixtures will not all shift to form H2 in SOFC anodes before reaching the TPB.
Figure 4.6: Gas-phase profiles of H2 and CO throughout the anode for four syngas mixtures, with and without reforming . The anode-electrolyte interface (right boundary of all plots) is located 1100 micrometers from the anode-channel interface (left boundary of all plots). These profiles are taken at the current density where switch-over occurs in the absence of reforming (~3.0 A cm-2 in A, 2.5 A cm-2 in B, 1.5 A cm-2 in C, 0.93 A cm-2 in D). T = 800°C and direct CO oxidation is disabled in all cases shown.
It is clear from the previous figures that CO contributes indirectly to SOFC performance via water-gas-shift reforming for a range of syngas mixtures. However, the importance of direct CO electro-oxidation for different H2:CO ratios still requires further investigation. In order to compare the relative contributions of CO and H2 electro-oxidation, Figure 4.7 breaks down the current density contributions versus anode activation overpotential for the same four syngas mixtures presented before. Increasing the anode activation overpotential is equivalent to increasing the cell current density in Figure 4.5, and the switch-over point to rate-limiting H2 adsorption can readily be observed as the sharp bend in H2 current in all four subplots. The slope of CO current vs. activation overpotential also increases at these switch-over points to compensate for the declining rate of H2 electro-oxidation when H2 adsorption to nickel becomes rate-limiting.
The first key conclusion from Figure 4.7 is that current from H2 dominates over current from CO, particularly at lower currents before the switch-over point. This comparison holds true even for the CO-rich syngas cases, and is consistent with the fact that H2 oxidizes and diffuses faster than CO in the anode. It appears that the contribution of CO via direct electro-oxidation is negligible along the first part of the polarization curve for a range of syngas mixtures. However, the current produced by direct electro-oxidation of CO picks up after the switch-over to rate-limiting H2 adsorption occurs, so its contribution to cell performance cannot be ignored at higher currents. This holds particularly true for the CO-rich mixtures, and the current produced by CO exceeds the current from H2 at the end of the curve for 80% CO + 20% H2 in subplot D. These figures indicate that CO plays a non-negligible role in electro-oxidation once H2 current saturates due to rate-limiting H2 adsorption. This finding is consistent with the polarization curves from Figure 4.5, which predict a sharp voltage drop-off in the absence of CO oxidation but a more gradual descent when direct electro-oxidation of CO is accounted for.
Figure 4.7: Current densities from electro-oxidation of H2 and CO versus anode activation overpotential for four syngas mixtures at 800°C . Surface reforming is enabled in all cases.
The previous results indicate that CO contributes to cell performance via both reforming and direct electro-oxidation, particularly for higher CO-content mixtures towards the end of the polarization curve. However, in order to compare the relative contributions of CO via these two pathways, it's helpful to know what fraction of incoming CO is consumed by each route. Figure 4.8 provides a break-down of how incoming CO is used for the same four syngas mixtures at the points of maximum power operation. These pie charts display the percentages of CO in the anode channel that get directly oxidized and consumed via reforming along with the percentage still present in the anode exhaust after electrochemistry. Over 50% of the incoming CO is exhausted in all cases shown, which occurs because the model represents a button cell. In a realistic planar or tubular SOFC system, this CO in the exhaust would get consumed downstream in the anode flow channel via reforming and direct oxidation.
In order to compare the relative usage of CO via reforming and direct electro-oxidation, it's more instructive to focus on the relative sizes of the "R" and "0"portions of the pie charts in Figure 4.8.
It's clear that both portions are non-negligible for the four cases shown. Direct oxidation of CO appears to be important relative to CO reforming even in the syngas mixtures that contain roughly equal parts of H2 and CO (subplots A-B). As the CO content of the syngas mixture increases, the relative amount of CO consumed by direct oxidation increases, and outweighs reforming by a factor of more than 2.5 in the most CO-rich case (subplot D).
Figure 4.8: Percentage breakdown of the usage of incoming CO to the anode between direct oxidation (0), surface reforming (R) and anode exhaust (E) for four syngas mixtures at 800°C These results are taken at the operating points of maximum power output for each polarization curve, which occur at the following current densities: 3.3 A cm-2 in A, 3.0 A cm-2 in B, 2.3 A cm-2 in C, and 1.8 A cm-2 in D.
4.5 Conclusions
Because SOFCs are capable of running on syngas, it is critical to determine the extent to which CO contributes to cell performance for syngas mixtures. In order to study carbon monoxide's impact on cell performance via reforming and direct oxidation when H2 is also present, an MEA model with surface reforming and electrochemical mechanisms for both H2 and CO oxidation is needed. The MEA model presented here possesses these features, and directly implements experimentally measured values for OCV and overpotentials outside the anode in order to isolate the role of CO in the anode. A comparison of three versions of the model to experimental syngas data indicates that CO contributions via both reforming and direct oxidation are non-negligible.
A close study of the anode gas species profiles shows that only a portion of incoming CO shifts to form H2 before reaching the TPB as a result of the chemical equilibrium limit of the water-gas-shift reaction at 800°C. This result challenges the traditional assumption that water-gas-shift reforming is the dominant pathway for CO to contribute to cell current when syngas is sent to SOFCs. Furthermore, a comparison of the current contributions from direct electro-oxidation shows that current from CO is non-negligible relative to H2 current towards the end of the polarization curve where H2 current is limited by slow adsorption to nickel. Finally, it is shown that the relative importance of direct electro-oxidation versus reforming of CO increases as the CO-content of the syngas mixture is raised. These findings suggest that CO contributions via both reforming and direct electro-oxidation are critical in predicting SOFC performance with syngas mixtures, particularly at high currents.
Chapter 5 Mechanism for Syngas Electro-oxidation in a SOFC
An accurate, comprehensive model for the individual and simultaneous electro-oxidation of H2 and CO on Ni-YSZ is necessary to predict SOFC performance for a range of gaseous fuels. A mechanism that combines hydrogen (H) spillover to YSZ with oxygen (0) spillover to hydrogen and CO on nickel is proposed. This combined spillover model is implemented in a previously-validated 1D-MEA model with detailed gas-phase transport and surface reforming kinetics in the anode. This model is then verified against a range of experimental porous anode polarization data for mixtures of CO/CO2, H2/N2, H2 /H2O, H2/CO and H2/CO2. The results of that fitting confirm that the proposed mechanism is capable of representing the individual and simultaneous electro-oxidation of H2 and CO on Ni/YSZ. The current spillover pathways are then studied for two anode fuel mixtures: 20% H2 + 80% N2 and 20% H2 + 80% CO. Although these studies confirm that H spillover is the dominant source of current at low anode activation overpotentials, they also show that the currents produced by O spillover are non-negligible at high overpotentials. Furthermore, it is shown that the current produced by O spillover to CO(Ni) is not limited by the rate of CO adsorption on nickel, whereas the currents produced by both H spillover and O spillover to H(Ni) are limited by the rate of H2 adsorption at high anode overpotentials.
5.1 Introduction
The thermochemical and electrochemical reaction mechanisms within a SOFC anode are complex, particularly when hydrocarbon species are involved [1]-[3]. Elementary reaction steps are needed to accurately depict gas-phase chemistry, heterogeneous surface reforming, and heterogeneous charge-transfer reactions. Understanding the governing mechanisms for internal reforming and electrochemistry is paramount to optimize anode structure and operating conditions. More specifically, it is critical to identify the correct rate-limiting steps in these elementary mechanisms because those steps control the rate at which the cell can produce current. The elementary electrochemical oxidation reaction mechanisms for H2 and CO require special attention because these constitute the primary SOFC fuel candidates present in practical gaseous fuels such as hydrocarbons, natural gas, coal syngas and biogas [4].
A couple of reaction mechanism types have been proposed to represent H2 electrochemical oxidation at the triple-phase boundary (TPB) of Ni-YSZ: (1) hydrogen spillover and (2) oxygen spillover. Hydrogen (H) spillover mechanisms involve a charge-transfer step where hydrogen spills over from nickel to YSZ to react with oxygen on the electrolyte. Oxygen (O) spillover mechanisms, on the other hand, involve a charge-transfer step where oxygen spills over from YSZ to nickel to react with hydrogen on nickel. Hydrogen electro-oxidation models typically select only one spillover pathway rather than implementing the H and O spillover pathways simultaneously. Although a few researchers have used O spillover mechanisms to describe H2 electro-oxidation [5], [6], the majority have proposed variations of the H spillover mechanism [7]-[14].A few researchers have compared these spillover pathways and concluded that H spillover mechanisms are better than O spillover mechanisms at consistently predicting patterned-anode experimental data for H2/H2O mixtures [15]-[17]. One group has also developed an H spillover mechanism that accounts for rate-limiting H2 adsorption at high currents [10], but a similar study is needed for the O spillover mechanism.
Although both CO and H2 are both electrochemically active species on SOFCs, research on the subject of CO electro-oxidation is much less expansive, partly because the reaction rate of CO is lower than that of H2 [18]-[2 1]. However, understanding the mechanism for CO electro-oxidation is still critical to accurately represent syngas mixtures because CO and H2 electro-oxidation rates have the same order of magnitude [20], [22]. Researchers have typically found that CO electro-oxidation is governed by O spillover to nickel as opposed to CO spillover to YSZ, which is an unlikely pathway due to the strong affinity of CO to nickel [23]-[25]. However, most MEA models represent CO electro-oxidation as a global reaction rather than implementing the O spillover pathway due to a lack of reaction kinetic data. Charge-transfer is also typically assumed rate-limiting in CO electro-oxidation mechanisms, so a study on CO adsorption as a potentially rate-limiting step at high currents is needed.
Although the mechanisms for both H2 and CO electro-oxidation have been studied individually, few researchers have attempted to model the simultaneous electro-oxidation mechanism which is needed to characterize SOFC behavior with syngas mixtures [26]. It is a complicated task to simulate H2+ CO co-oxidation in SOFCs because it involves modeling parallel charge transfer pathways, water-gas shifting and interactions between gaseous and adsorbed species. Moyer et al. [27]recently performed a modeling study on H2 + CO co-oxidation that accounts for detailed heterogeneous thermochemistry as well as both spillover mechanisms. They fitted the kinetic parameters of each charge-transfer step in the hydrogen and oxygen spillover pathways to patterned-anode Tafel plots for mixtures containing H2 + H2O + CO + CO2 [5]. Moyer's model was best able to predict that data set when both the H and O spillover pathways were active instead of just one pathway. However, questions remain regarding the relative importance of these two spillover pathways and the roles of H2 and CO in these pathways. Charge-transfer steps were also always assumed rate-limiting in this study, so the possibility of fuel adsorption on nickel as rate-limiting processes in these mechanisms requires further investigation.
A recent study by Fu et al [28] has provided needed insight on the spillover pathways of H2 and CO electro-oxidation on Ni/YSZ from a micro-structural perspective using first principles simulations and the Monte Carlo method. This group found evidence to support previous claims that CO electro-oxidation can only proceed through the O spillover pathway. More importantly, Fu et al found that the O spillover pathway plays a vital role in H2 electro-oxidation in addition to
H spillover. An independent first principles study also found that adsorbed oxygen on nickel lowers the energy barrier for the oxidation of hydrogen via O spillover [29]. These recent findings motivates the development of a MEA model that includes O spillover charge-transfer pathways to both CO and H2 on nickel in addition to H spillover to YSZ. Such a model is needed to accurately capture the reaction pathways of both fuels at the anode triple-phase-boundary (TPB) of SOFC's exposed to syngas fuels.
The first part of this paper describes the integration of this newly-proposed combination of spillover pathways into a detailed ID-MEA model [26]. Furthermore, the H and O spillover mechanisms described in this model account for rate-limiting H2 and CO adsorption onto nickel at high currents. The validity of this detailed model is then tested by comparing model predictions to experimental polarization data for a wide range of anode fuel mixtures [21]. Finally, the study focuses on just two fuel mixtures in order to investigate the relative importance of the different spillover pathways and rate-limiting processes along the polarization curve.
5.2 Model Description
The objective of the MEA model is to calculate the voltage-current density curve for a given temperature, pressure and fuel composition. The model is isothermal and the domain is ID with respect to distance from the triple-phase boundary (TPB). This representation is consistent with the geometry of a button cell, where the entire anode is exposed to the same anode fuel mixture. The previously-published [26] models for conservation, transport, thermochemistry and overpotentials will be briefly introduced, followed by a detailed description of the proposed hydrogen and oxygen spillover mechanism.
5.2.1 Conservation Equations
The gas phase mass conservation equation in the porous electrodes is:
The surface species mass conservation equation in the porous anode is:
5.2.2 Transport in Porous Media
The gas phase fluxes Uk) from equation (1) are computed using the dusty gas model (DGM), an extension of the Stefan-Maxwell diffusion equations that captures both Knudsen and binary diffusion [32]. The DGM can be written as an implicit relationship among the molar concentrations, molar fluxes, concentration gradients, and the pressure gradient:
5.2.3 Thermochemistry
Surface reforming in the anode is usually modeled with simplifying assumptions, such as local equilibrium or global reaction kinetics [31], [33]. However, a detailed kinetic model is used here that was first developed by Hecht et al [3], and then extended to a wider temperature range by Janardhanan and Deutschmann [30]. This mechanism consists of 42 reactions, and involves six gaseous species and twelve surface species. The net production rate of gas or surface species k due to heterogeneous reactions is given by:
5.2.4 Cell Overpotentials
Operating voltage can be expressed as the difference between the reversible cell potential and various overpotentials:
First, the model and experimental OCVs are matched by introducing air leakage into the anode channel until the reversible potential matches the experimental OCV for that anode mixture:
This approach of accounting for error in the open-circuit potential by physically adjusting the anode mixture with air is addressed in more detail elsewhere [26], [34].
Overpotentials in the electrolyte and cathode are also taken directly from the experimental group in order to minimize uncertainly in the model and focus on the impact of the anode mechanism. Ohmic and total cathodic overpotential are thus given by simple curve fits to their data sets:
Unlike the other loss modes that are taken directly from Virkar et al's experimental data, the anode overpotentials are represented physically in order to study the impact of the proposed electro-oxidation mechanisms on cell performance. Anode concentration overpotential is modeled as the difference in reversible cell potential at the anode channel and the anode TPB:
5.2.5 Electro-oxidation Mechanisms
The hydrogen spillover mechanism consists of five steps, and the oxygen spillover mechanism consists of ten steps, as depicted in Figure 5.1. Both mechanisms have two charge-transfer steps that come from previously proposed mechanisms [17]. All of the reactions that occur on nickel come from the 42-step surface reforming mechanism presented previously [30]. The novel aspects of this proposed mechanism are: 1) that it accounts for both spillover pathways for H2 electro-oxidation simultaneously, and 2) that it distinguishes oxygen spillover to H(Ni) from oxygen spillover to CO(Ni). This novel combination of three spillover pathways makes it possible to investigate how current is produced for a range of anode overpotentials and fuel mixtures later.
Figure 5.1: Depiction of the reaction steps at the TPB for the hydrogen spillover mechanism (A) and oxygen spillover mechanism (B) . Both mechanisms involve two charge-transfer steps across the Ni-YSZ TPB. The oxygen spillover mechanism (B) involves surface reactions with both H and CO on nickel.
The step of oxygen transfer from bulk to surface YSZ sites is common to both mechanisms: (H.2) in H-spillover and (0.3) in O-spillover. This oxygen transfer step occurs rapidly at SOFC operating temperatures, and is thus modeled in equilibrium for both mechanisms according to the expression [17]:
The surface vacancy fraction is given by accounting for all potential species occupying surface YSZ sites:
5.2.5.1 Rate-limiting Charge-transfer
The charge-transfer processes, (H.3)-(H.4) and (0.4)-(0.5), are typically assumed to be the rate-limiting steps in both spillover pathways. When this is the case, the current densities associated with each charge-transfer step are given by the following expressions:
The TPB species coverages on nickel (๐ฑi,Ni) in equations (5.13)-(5.16) are resolved simultaneously with the anode concentration profiles and currents, according to the algorithm described in the simulation procedure section. These coverages are governed by the anode transport and mass conservation equations along with the detailed surface reforming mechanism, which accounts for twelve surface species [30]. The vacancy fraction of nickel at the TPB is then given by:
where the summation occurs over all twelve possible surface species on nickel at the TPB: H, OH, H2O, CH4, CH3, CH2, CH, CO, CO2,C, and HCO.
The electric potential difference in equations (5.13)-(5.16) can be expressed as the sum of the equilibrium potential and the anode activation overpotential: E = Eeq + ๐ฐ act,a The anode activation overpotential is a known input quantity in the simulation procedure, and the equilibrium potential is determined by solving for Eeq in equations (5.13)-(5.14) or (5.15)-(5.16) with ๐ฐ act,a = 0 and i(k) = 0, as detailed in Appendix B. 1:
Once the equilibrium potential (Eeq) and YSZ coverages are known, the current densities of each charge-transfer step can be determined by equations (5.13)-(5.16) for a given anode activation overpotential and steady-state TPB nickel coverages. The total current densities associated with the H and O spillover pathways are then given by:
Finally, the distribution of current between the two fuels, H2 and CO, is determined directly from their rates of reaction at the TPB. Specifically, the current density produced by CO electro-oxidation is given by evaluating step (0.8) at steady-state:
Current density associated with H2 electro-oxidation is then the difference between total current density and CO current density:
5.2.5.2 Rate-limiting Fuel Adsorption
Although the charge-transfer processes are typically rate-limiting, it is possible that hydrogen adsorption or CO adsorption can become rate-limiting steps in the two pathways at higher current densities. This phenomenon is described in previous work as the "switch-over" mechanism, which provided a better fit to experimental H2 + H2O data in the limiting current regime for a H spillover model[10], [26]. If hydrogen adsorption onto nickel is rate-limiting, then the current for that pathway is given by the following Butler-Volmer relationship [10]:
Although CO molecules adsorb more readily to nickel than H2 [28], it is still conceivable that CO adsorption could be a rate-limiting step under some conditions. Therefore, an analogous Butler-Volmer expression is developed to represent the current associated with CO electro-oxidation when CO adsorption to nickel is the rate-limiting step:
The point at which fuel adsorption becomes the rate-limiting step in a given pathway is determined by comparing the currents predicted by the expressions for charge-transfer and adsorption. More specifically, H2 adsorption becomes rate-limiting in the H spillover mechanism when iH-ads < iH-spill and in the O spillover mechanism when iH-ads < iO-spill. Similarly, CO adsorption becomes rate-limiting in the O spillover mechanism when ico-ads < io-spill. Thus, there are theoretically three distinct points along the polarization curve where fuel adsorption becomes rate-limiting for the three fuel electro-oxidation pathways.
5.3 Simulation Procedure
Temperature, pressure and anode composition are inputs to the model, which generates a current density-voltage curve by iterating through anode activation overpotential, as shown in Figure 2.
Steps 1)-2) are carried out once for a given anode mixture, then steps 3)-4) are repeated for increasing anode overpotential until an entire polarization curve is generated.
Figure 5.2: Simulation procedure to generate a polarization curve for a given fuel mixture.
The following steps are implemented in a MATLAB@ script to generate each cell polarization curve:
4) Calculate the equilibrium mixture at the anode channel.
The reported anode mixture is adjusted in the model by incrementally adding air until the theoretical and experimental OCV values match, as detailed in Appendix A. Cantera's "equilibrate" function is applied to each adjusted anode mixture at fixed temperature and pressure to determine the equilibrium partial pressure of oxygen, po2,a. This value is then used in equation (5.7) to calculate the reversible cell potential, which is compared to the experimental OCV value for that mixture. This process is repeated for increasing air content until the calculated and experimental OCV values match. The final equilibrated fuel + air mixture is also assumed to be the actual mixture present at the anode channel to account for experimental air leakage and the quick reaction of oxygen with anode fuels.
5) Calculate the equilibrium potential drop across the anode/electrolyte double-layer.
The equilibrium potential difference across the anode/electrolyte double-layer (Eeq) is needed to determine the currents produced by the various charge-transfer steps, which are exponential functions of E = Eeq + ๐ฐact,a. E = Eeq at open-circuit because ๐ฐ act,a = 0, so the equilibrium potential difference can be determined by setting the individual currents in equations (5.13)-(5.14) or (5.15)-(5.16) to zero. For mixtures without H2, O spillover is the only active pathway, so i(O.4) and i(O.5) are both set to zero, and equations (5.15)-(5.16) are solved along with equations (5.1 1)-(5.12) for Eeq and the open-circuit coverages on YSZ. For mixtures containing H2, the H spillover pathway is dominant at low currents, so i(H.3) and i(H.4) are set to zero, and equations (5.11)-(5.14) are solved for Eeq and open-circuit YSZ coverages, as detailed in Appendix B.
6) Resolve current densities and anode species profiles.
The final equilibrium mixture adjusted for air leakage from step 1) is the mixture sent to the channel in the anode model. Because anode activation overpotential is an input to the model, current densities from both spillover pathways can be determined by solving equations (5.13)-(5.16) simultaneously with the transport equations throughout the anode. The initial fluxes of surface species at the TPB, given by equation (5.3), are boundary conditions to the DGM transport equation (5.4), which is cast in matrix form. An ordinary differential equation solver, the "ode 15s" function in MATLAB*, resolves the steady-state gas and surface species profiles throughout the anode. The steady-state current densities and YSZ surface coverages are updated with the new concentrations at the TPB, and then the fluxes of surface species at the TPB are updated based on the new current densities. These new fluxes are fed back into the DGM solver as boundary conditions, and this process repeats until the non-linear "fsolve" function converges on steady-state current densities, YSZ coverages, and anode species profiles. More details on the mechanics of this complex algorithm from an earlier version of this model are given elsewhere [10].
7) Calculate cell overpotentials and operating voltage.
Once the anode profiles and currents are resolved, all of the cell overpotentials can be readily computed. The anode activation overpotential is an input to step 3), so its value is known. The anode concentration overpotential is given by equation (5.10), where the partial pressure of oxygen at the anode TPB is determined by the Cantera "equilibrate" function applied to the anode gas mixture at the last node. Total cathode overpotential and ohmic overpotential are then given as functions of total current in equations (5.8) and (5.9). Finally, the operating voltage is determined by subtracting all overpotentials from the reversible cell potential, according to equation (5.6).
5.4 Simulation Results
The results are presented here in two sections: model verification and mechanism investigation. The first section presents the model against experimental porous anode polarization data for a wide range of mixtures with H2 and/or CO. This comparison is conducted in order to confirm a reasonable fit for the combined hydrogen and oxygen spillover model against a wide range of anode fuel stream conditions. The second section investigates how current is divided between the different spillover pathways for fuel mixtures with and without CO. This second study also investigates how the rate-limiting assumptions in the mechanism impact the current pathways and the accuracy of performance predictions.
The operating conditions and anode structural parameters that are held constant in all these simulations are listed in Table 5.2. All of the other parameters in the table are obtained directly from Jiang & Virkar's experiment [21] unless otherwise indicated. This approach minimizes uncertainty and matches this model to their experimental button cell. Structural parameters are only listed for the anode in Table 5.2 because the electrolyte and cathode overpotentials are taken directly from Virkar's experimental measurements [35], as described earlier. The triple-phase-boundary length selected here is the same one reported by Moyer et al [27] to fit the same hydrogen and oxygen spillover models to patterned-anode Tafel plots. This TPB length is also the same order of magnitude as the one calculated by Wilson et al [38] in their 3D reconstruction of a porous Ni-YSZ anode. The two highlighted rows, tortuosity and area-specific TPB, are the only two constants in the model that were treated as fitting parameters to match experimental data.
Table 5.2: Constant operational and structural parameters for the SOFC model [21].
5.4.1 Model Verification
Before the different current pathways and rate-limiting processes of the proposed mechanism can be investigated, the model must be verified as a reasonable predictor of cell performance for mixtures with hydrogen, CO or both fuel species. Therefore, the model is presented here alongside a comprehensive set of porous anode SOFC experimental data for CO/CO2, H2/H2O, H2/N2, H2/CO, and H2/CO2 mixtures [21]. This particular experimental paper is cited by many modelers, but very few have presented a convincing fit to multiple data sets from this paper [39]. Therefore, fitting the model here to data for a wide range of mixtures will provide some evidence for the validity of the proposed mechanism.
Tortuosity and area-specific TPB length are the only parameters that were adjusted to match the model to this wide range of data, and their fitted values (listed in Table 5.2) are consistent with previously reported values in literature [9], [10], [21], [38]. The fact that this model implements believable values for all known and unknown fitted parameters provides supporting evidence for the proposed mechanism. Whereas previous modeling efforts have studied a similar mechanism with only syngas data [27], this work applies the mechanism to a variety of mixtures with and without H2 and CO. This approach facilitates the independent verification of the mechanisms for O spillover and H spillover by comparing the model to mixtures with different charge-transfer pathways. Similar to the approach taken in the previous analysis [27], this study compares the model to data in Tafel form (i.e. logarithm of current density as a function of anode activation overpotential). This comparison also purposely neglects the limiting current regime where concentration effects confound the impact of the electro-oxidation mechanism on operating voltage.
Figure 5.3 plots the model polarization curves along with experimental data for a couple of CO/CO2 mixtures. This particular data set is unique in that no hydrogen compounds are present, which means that oxygen spillover to CO is the only electrochemically active pathway. Therefore, studying the fit of the model to this particular data set provides some insight on the oxygen spillover pathway. The model predicts the experimental data reasonably well at low currents, but some divergence occurs from the data set at higher currents. However, some level of error is anticipated for these CO/CO2 mixtures because the kinetic parameters in the O spillover mechanism were fitted to mixtures of H2/H2O rather than mixtures of CO/CO2 [17]. The reasonable fit of model to experimental CO/CO2 data at low currents in Figure 5.3, however, does provide some verification that the O spillover pathway is a plausible model for CO electro-oxidation.
Figure 5.4 compares the simulated and experimental polarization curves for mixtures containing H2 rather than CO, which provides insight on the application of the combined spillover mechanism to hydrogen electro-oxidation. The model is compared to data for mixtures of H2 with N2 (subplot A)and H2 with H2O (subplot B) in order to verify that the combined spillover mechanism is applicable to a wide range of H2:H2O ratios. The model is able to consistently reproduce experimental data in Figure 5.4 for a wide range of mixtures at moderate currents. Some deviation occurs from experimental values at very low currents, which is partly due to the fact that the open-circuit potential can only be fixed for one of the two spillover pathways, as described in Appendix B. 1. The overall match between the simulated and experimental polarization curves in Figure 5.4 is a significant improvement over previous efforts to fit this full data set [9], [10]. This good fit over a wide range of H2:H2O ratios indicates that the combined hydrogen and oxygen spillover model can be applied to mixtures where hydrogen is the only electro-active species.
Figure 5.4: Comparison of polarization characteristics between model and data for mixtures of H2+N2 (A) and H2+H2O (B) at 800°C and 1 atm. Both the hydrogen spillover and oxygen spillover charge-transfer pathways are active.
Figure 5.5 compares simulated and experimental polarization curves for mixtures where both H2 and CO are present in gas-phase equilibrium. For these syngas mixtures, current is produced simultaneously by H spillover and by O spillover to both H2 and CO. Therefore, these results provide verification that the combined spillover mechanism can accurately represent the simultaneous oxidation of H2 and CO. The model is presented against experimental data for mixtures of H2 and CO2 (subplot A) and for mixtures of H2 and CO (subplot B). Because the fuel stream is modeled in gas-phase equilibrium at the anode, these data sets cover a range of H2:H2O and CO:CO2 ratios. The model fits the experimental data well at moderate currents but somewhat over-predicts voltage at lower currents. This discrepancy near open-circuit conditions can again be attributed to that fact that equilibrium potential across the anode-electrolyte double-layer can only be set for one spillover pathway. The combined spillover mechanism, however, provides reasonable prediction of cell operating voltage for a wide range of syngas mixtures and current densities in Figure 5.5. These fitting results in Figures 5.3-5 provide verification that the proposed mechanism can represent the electro-oxidation of H2 and CO on Ni-YSZ when either or both species are present.
Figure 5.5: Comparison of polarization characteristics between model and data for mixtures of H2 +CO2 (A) and H2+CO (B) at 800°C and 1 atm. Both the hydrogen spillover and oxygen spillover charge-transfer pathways are active, and oxygen spills over to both hydrogen and CO on nickel.
Figures 5.3-5 demonstrate that the model is able to predict cell performance over a wide range of anode mixtures. Only two model parameters, tortuosity and area-specific TPB length, were varied to fit the model to data for all of these mixtures. Figure 5.6 shows how sensitive the model predictions are to changes in these two tuning parameters for the case of 43% H2+57% N2. All model parameters are held constant except for tortuosity in subplot A, and all parameters except for area-specific TPB length are held constant in subplot B. Both tuning parameters are adjusted from 50% to 150% of their fitted values (๐ฝ = 2, ๐ชTPB = .0065) in these figures. The entire polarization curve is affected by changes in tortuosity, as demonstrated in subplot A, because this parameter always affects diffusion of gases to the TPB. Lowering the tortuosity raises current for a given voltage because the path for gases to reach the TPB is more direct.
In comparison, adjusting aTPB in subplot B of Figure 5.6 only impacts model predictions at high currents because this term only appears in equations (5.25)-(5.26) where H2 adsorption is rate-limiting. Lowering aTPB causes the limiting current density to decrease because this parameter is proportional to the TPB length where electro-chemical reactions occur. Both subplots in Figure 5.6 demonstrate that the model is responsive to changes in the two tuning parameters. However, the flexibility of the model to fit a single data set by adjusting these two parameters does not compromise the verification in Figures 5.3-5 because varying these values affects the model's fit to all data sets. Therefore, the model sensitivity to T and aTPB seems reasonable, given that the model is able to predict data for a wide range of fuel mixtures using fixed values for these two parameters.
5.4.2 Mechanism Investigation
The results from the previous section demonstrated the model's ability to reasonably predict cell performance for H2, CO and simultaneous H2+CO oxidation over a wide range of fuel mixtures. This section now focuses on the different spillover pathways in this electro-oxidation mechanism as a function of current density for mixtures with and without CO. This investigation will provide insight on the relative importance of the H and O spillover pathways under different conditions. This section will also explore the impact of rate-limiting assumptions in the spillover mechanisms at higher currents. More specifically, the model will be compared to experimental polarization curves for cases where charge-transfer is always assumed rate-limiting (Case 1) and cases where hydrogen adsorption becomes the rate-limiting step at higher currents (Case 2). Two hydrogen-lean mixtures, with and without CO, are selected for this study because experimental polarization data that extended into the limiting current regime was available for these mixtures. The spillover current pathways, polarization curves and TPB coverages are presented first for a mixture with only H2 electro-oxidation (20% H2 + 80% N2), and then for a mixture with both H2 and CO electro-oxidation (20% H2 + 80% CO).
5.4.2.1 Only Hydrogen Present
The current produced by the H and O spillover pathways are compared in Figure 5.7 for an anode fuel mixture of 20% H2 and 80% N2. For this mixture, H2 is the only electro-active species, but it can produce current by both the H spillover and O spillover pathways. If charge-transfer steps are always modeled as rate-limiting in both pathways (Case 1, Fig. 5.7A), then the majority of current is initially produced by the H spillover pathway, as predicted by previous literature. However, the current produced by H spillover reaches a peak and declines at higher anode activation overpotentials while O spillover current escalates and surpasses H spillover current at high overpotentials. If hydrogen adsorption to nickel is modeled as rate-limiting for higher currents (Case 2, Fig. 5.7B), then the shapes of the curves change at higher anode activation overpotentials. H spillover is still the dominant source of current at low overpotentials in Case 2, but it reaches a lower peak value at a smaller overpotential when hydrogen adsorption becomes rate-limiting (denoted by "switch #1"). Once the H spillover pathway becomes limited by H2 adsorption, the current produced by O spillover ramps up until that pathway also becomes limited by the rate of H2 adsorption to nickel (denoted by "switch #2"). Beyond that point, the currents produced by both spillover pathways are equal because they are both governed by the rate of hydrogen adsorption to nickel. For both cases presented in Figure 5.7, it is evident that the H spillover pathway is the dominant source of current for H2 electro-oxidation at low overpotentials.
However, it is also clear that the O spillover pathway is a non-negligible source of current for H2 electro-oxidation at moderate to high anode overpotentials.
Figure 5.7: Current densities of the H spillover and O spillover pathways as a function of activation anode overpotential for an anode fuel mixture of 20% H2 and 80% N2. The charge-transfer steps are always rate-limiting for both pathways in Case 1 (A); hydrogen adsorption is rate-limiting at high currents for both pathways in Case 2 (B). Arrows denote the points where the rate-limiting step switches from charge-transfer to hydrogen adsorption in each spillover pathway in Case 2.
The model polarization curves for Cases 1 and 2 are compared to experimental data in Figure 5.8 for an anode fuel mixture of 20% H2 and 80% N2. The modeled current densities in this plot account for the total current produced by both of the spillover pathways shown in Figure 5.7. More specifically, the dashed line in Figure 5.8 corresponds to Case 1 in Figure 5.7A, and the solid line and arrows in Figure 5.8 correspond to Case 2 in Figure 5.7B. The model for Case 1 in Figure 5.8 over-predicts current density towards the end of the polarization curve because it does not account for the limitation of hydrogen adsorption rates at high anode overpotentials. The Case 2 curve, on the other hand, is able to predict the experimental voltage drop-off because it accounts for H2 adsorption as the rate-limiting step at high overpotentials. These findings are consistent with the results of a previous modeling study based only on the H spillover mechanism [10].
The two cases of the model diverge at the second switch point in Figure 5.8, which is where H2 adsorption becomes the rate-limiting step in the O spillover mechanism. Up to that point, the polarization curves for the two cases of the model match, despite the fact that H2 adsorption is rate-limiting in the H spillover mechanism for Case 2 after the first switch point. This result indicates that the total current density for both cases is the same, which implies that more current is routed through the O spillover pathway in Case 2 once the H spillover pathway becomes limited by the rate of hydrogen adsorption. The fact that Case 2 of the model is able to better predict experimental polarization behavior provides reason to believe that the current pathway division in Figure 5.7B is more likely than the current breakdown in Figure 5.7A. Thus, it appears that the mechanism for H2 electro-oxidation on Ni-YSZ is governed first by the rate of H spillover charge-transfer, then by the rate of O spillover charge-transfer, and finally by the rate of H2 adsorption to nickel for both spillover pathways.
Figure 5.8: Modeled polarization curves alongside experimental data for an anode fuel mixture of 20% H2 and 80% N2. The charge-transfer steps are always rate-limiting for both pathways in model Case 1; hydrogen adsorption is rate-limiting at high currents for both pathways in model Case 2. Arrows denote the points along the polarization curve where the rate-limiting step switches from charge-transfer to hydrogen adsorption in each spillover pathway.
Figure 5.9 provides the surface coverages on nickel (Fig. 5.9A) and YSZ (Fig. 5.9B) at the TPB as a function of current for the same mixture of 20% H2 + 80% N2. These coverage profiles correspond to Case 2 in Figures 5.7 and 5.8, where rate-limiting hydrogen adsorption is enabled at high currents. This rate-limiting assumption can be observed in Figure 5.9B, where ionic species coverages spike at high currents. The increasing coverages of intermediate ionic species in Fig. 5.9B, O⁻(YSZ) and OH⁻(YSZ), are a reflection of the increasing currents of both the O spillover and H spillover pathways, respectively. Similarly, the increasing coverages of product species O(Ni), OH(Ni), and H2O(Ni) in Fig. 5.9A reflect the increasing current of both spillover pathways. In comparison, coverages of H(Ni) and O²⁻(YSZ) in Figure 5.9 decline with current because they are both reactants in each of the two spillover pathways. Whereas the majority of YSZ sites are occupied by O²⁻ ions, the majority of the nickel sites are vacant at the TPB. The orders of magnitude of the coverages presented in Figure 5.9 are consistent with predictions from previous models [17], [27], providing some verification for the implementation of the mechanism in this model.
Figure 5.9: Modeled TPB coverages for an anode fuel mixture of 20% H2 and 80% N2. Surface coverages on nickel are shown in (A); surface coverages on YSZ are shown in (B). Hydrogen adsorption becomes rate-limiting in both spillover pathways at high currents (Case 2).
5.4.2.2 Hydrogen and CO Present
Figures 5.6-9 focused on a mixture where hydrogen was the only electrochemically active species so that the relative importance of the hydrogen adsorption, H spillover charge-transfer and O spillover charge-transfer steps could be studied. Figures 5.10-12 build on the previous analysis by investigating an anode syngas mixture where both fuel species are present: 20% H2 + 80% CO. For this syngas mixture, current can be produced by O spillover to CO(Ni) in addition to O spillover to H(Ni) and H spillover to YSZ. When CO is present, there is also the possibility that CO adsorption on nickel becomes a rate-limiting step in the O spillover mechanism at high anode activation overpotentials. Therefore, a detailed study of the current pathways and polarization curves for this syngas mixture should provide insight into the rate-limiting processes that govern cell performance when CO is present in the fuel stream.
Figure 5.10 shows the current densities associated with each spillover pathway as a function of anode activation overpotential for an anode syngas mixture of 20% H2 and 80% CO. Current is produced here by three pathways: H spillover to YSZ, O spillover to H(Ni) and O spillover to CO(Ni). Figure 5.10A corresponds to Case 1, where charge-transfer steps are assumed rate-limiting for all spillover pathways across all anode overpotentials; Figure 5.10B corresponds to Case 2, where fuel adsorption steps can become rate-limiting at high currents. The relative magnitudes and shapes of the H spillover and O spillover to H curves in Figure 5.10 resemble those in Figure 5.7, indicating that the rate-limiting processes in the H2 electro-oxidation mechanism are largely unaffected by the introduction of CO.
A more interesting comparison in Figure 5.10 is between the curves for oxygen spillover to H and oxygen spillover to CO. Although CO produces some current from oxygen spillover, substantially more current is produced via oxygen spillover to H2. This finding is perhaps surprising given the high concentration of CO in the gas phase, but it is consistent with the fact that H(Ni) reacts faster than CO(Ni) does with O(Ni) [30]. This result challenges previous assertions that most oxygen spills over to CO in mixtures of H2 + CO [27], and provides justification for modeling O spillover to H(Ni) in addition to H spillover. Although the current produced by CO electro-oxidation is small, it appears to be non-negligible at high anode activation overpotentials for both cases in Figure 5.10. Therefore, accurate prediction of cell performance at high currents with CO-rich syngas may still require a model for CO electro-oxidation.
Figure 5.10B also provides some qualitative insight on the relative likelihoods of H2 and CO adsorption to nickel becoming rate-limiting at high overpotentials. Similar to the results in Figure 5.7B, both H spillover and O spillover to H switch over to rate-limiting H2 adsorption at high overpotentials (denoted by the "Switch #1" and "Switch #2" arrows, respectively). However, a similar switch to rate-limiting CO adsorption on nickel does not occur in Figure 5.10B. In fact, CO current density would have to exceed 10 A cm-2 at these anode overpotentials in order for CO adsorption to become the rate-limiting step. This order-of-magnitude difference between H2 and CO adsorption rates is consistent with the difference in these fuels' sticking coefficients to nickel: ๐ฌH2 = .01 and ๐ฌCO = 0.5 [30]. Because CO molecules have such a strong affinity to nickel, the CO electro-oxidation mechanism is always limited by O spillover charge-transfer kinetics. The current produced by O spillover to CO(Ni) can thus exceed the current produced by O spillover to at high anode activation overpotentials, where the hydrogen pathway is limited by the rate of H2 adsorption to nickel.
Figure 5.10: Current densities of the H spillover and O spillover pathways as a function of activation anode overpotential for an anode fuel mixture of 20% H2 and 80% CO. The charge-transfer steps are always rate-limiting for both pathways in Case 1 (A); hydrogen adsorption is rate-limiting at high currents for both pathways in Case 2 (B). Arrows denote the points where the rate-limiting step switches from charge-transfer to hydrogen adsorption in each of the hydrogen fuel electro-oxidation pathways.
The model polarization curves for Cases 1 and 2 are compared to experimental data for the anode mixture of 20% H2 and 80% CO in Figure 5.11. The modeled current densities in this plot account for the total current produced by all three of the spillover pathways shown in Figure 5.10. As was the case in Figure 5.8, the model for Case 1 in Figure 5.11 over-predicts current density towards the end of the polarization curve because it does not account for the limitation of hydrogen adsorption rates at high anode overpotentials. The Case 2 curve, on the other hand, is able to better predict the experimental voltage curve at high currents because it accounts for H2 adsorption as the rate-limiting step. The two cases of the model again diverge at the second switch point in Figure 5.11, which is where H2 adsorption becomes the rate-limiting step in the O spillover mechanism. The fact that Case 2 of the model is able to better predict experimental polarization behavior provides reason to believe that the current pathway division in Figure 5.10B is more likely than the current breakdown in Figure 5.10A. Thus, it appears that the mechanism for H2 CO electro-oxidation on Ni-YSZ is governed first by the rate of H spillover charge-transfer, then by the rate of O spillover to H (Ni), and finally by the rate of O spillover to CO(Ni) at high anode overpotentials.
Figure 5.11: Modeled polarization curves alongside experimental data for an anode fuel mixture of 20% H2 and 80% CO. The charge-transfer steps are always rate-limiting for both pathways in model Case 1; hydrogen adsorption is rate-limiting at high currents for both pathways in model Case 2. Arrows denote the points along the polarization curve where the rate-limiting step switches from charge-transfer to hydrogen adsorption in each of the hydrogen fuel electro-oxidation pathways.
Figure 5.12 provides the TPB surface coverages on nickel and YSZ for Case 2 from Figures 5.10-11.The second switch point to rate-limiting hydrogen adsorption can be observed in Fig. 5.12B by the spike in intermediate ionic species coverages. The increase in both intermediate ionic species in Fig. 5. 1sB, O⁻(YSZ) and OH⁻(YSZ), is a reflection of the increasing currents produced by the O spillover and H spillover pathways, respectively. Similarly, the increasing coverages of product species O(Ni), CO2 (Ni), and H2O(Ni) in Fig. 5.12A reflects the increasing current of both spillover pathways. In comparison, coverages of H (Ni), CO(Ni), and O²⁻(YSZ) in Figure 5.12 decline with current because they are reactants in the spillover pathways. In comparison with Fig. 5.9A, there are fewer nickel vacancies in Fig. 5.12A because CO occupies a large number of nickel sites. This is a result of carbon monoxide's strong affinity to nickel, which causes it to bind easily and prevents it from spilling over to YSZ. The orders of magnitude of the coverages presented in Figure 5.12 are also consistent with predictions from previous models [17], [27], providing further verification for this model. Overall, the results in Figures 5.10-5.12 provide some indication of the relative importance and rate-limiting steps of the H and O spillover pathways as a function of current for syngas mixtures.
Figure 5.12: Modeled TPB coverages for an anode fuel mixture of 20% H2 and 80% CO. Surface coverages on nickel are shown in (A); surface coverages on YSZ are shown in (B). Hydrogen adsorption becomes rate-limiting in both spillover pathways at high currents (Case 2).
5.5 Conclusions
It is critical to understand the individual and simultaneous electro-oxidation mechanisms for H2 and CO in SOFCs in order to optimize cell performance with practical gaseous fuel mixtures.
Recent microstructural studies on Ni/YSZ anodes have demonstrated that H2 electro-oxidation proceeds by means of both H and O spillover, while CO electro-oxidation can only proceed through the O spillover pathway [28]. This combined spillover pathway model is integrated into a ID-MEA model here that also accounts for gas-phase transport and heterogeneous reforming on nickel in the anode. The steps of these H and O spillover pathways are outlined along with the governing equations and rate-limiting assumptions in the anode model.
This model is then compared to experimental porous anode polarization data for a wide range of anode fuel stream mixtures containing H2 and/or CO. The model is able to predict these data sets well with only two unknown fitting parameters adjusted. These results imply that this combined spillover pathway model is capable of representing H2 and CO electro-oxidation not only individually, but also in parallel. A break-down of current pathways versus anode activation overpotential is then given for two mixtures: 20% H2 + 80% N2 and 20% H2 + 80% CO. These plots confirm that H spillover is the dominant source of current at low anode overpotentials, but also indicate that O spillover to H and CO contribute to cell performance at high anode overpotentials. These results challenge previous modeling assumptions that O spillover to H and CO are negligible sources of current compared to the H spillover pathway.
Finally, the model is compared to experimental polarization data for two cases: charge-transfer steps are always rate-limiting (Case 1) and fuel adsorption can become rate-limiting at high anode overpotentials (Case 2). It is found that CO adsorption to nickel is never a rate-limiting step, whereas H2 adsorption to nickel becomes rate-limiting in both the H spillover and O spillover to H(Ni) pathways. Thus, the O spillover pathway becomes an increasingly important source of current at high anode activation overpotentials, where H2 adsorption to nickel is rate-limiting.
Experimental measurements at the anode TPB could provide further evidence for the various current pathways and rate-limiting processes proposed in this study.
Chapter 6 Conclusions
Systems that integrate coal gasification with solid oxide fuel cells (SOFCs) are a promising candidate for high-efficiency stationary power production with lower CO2 emissions. This thesis used a multi-scale modeling approach to analyze SOFC performance with coal syngas from the systems level down to the surface reaction scale. This work builds on a detailed ID SOFC model [1], and repeatedly validates results against experimental data from another group [2] to scope out system and reaction interface behavior. This chapter first outlines the key contributions of this thesis, and then provides suggestions for future work on this topic.
6.1 Key Contributions
This thesis has contributed to understanding SOFC performance with coal syngas from both a systems and a surface reaction perspective. The key contributions of this thesis are summarized succinctly in Figure 1.4, and are enumerated in more detail by chapter below.
Chapter 2 provided a literature review of a highly-coupled fluidized bed gasifier + fuel cell system, known as the FB/SOFC. This chapter provided a summary of the state-of-the-art modeling and experimental work done on this system, and also described the key operational and modeling challenges associated with FB/SOFCs.
Chapter 3 used an equilibrium gasifier model coupled to a ID SOFC model to determine that the coupled system is capable of 55-60% efficiency at maximum power operation. This chapter also compared system performance with steam and CO2 as the recycled gas, and found that 2-3 times the power density could be achieved when steam was selected due to faster H2 electro-oxidation. Finally, this system modeling study determined that higher efficiencies and power outputs could be obtained when the heat output of the fuel cell stack was sent to the gasifier.
Figure 6.1: A schematic diagram summarizing the contributions of this thesis by chapter.
Chapter 4 used the ID SOFC model to study how much current is produced by H2 and CO for different coal syngas mixtures. This investigation found that a significant portion of CO does not react with steam in the anode before reaching the electro-chemical reaction sites. This study also found that a model for CO electro-oxidation is needed to accurately predict SOFC performance at high currents.
Chapter 5 implemented a detailed elementary mechanism for the simultaneous electro-oxidation of H2 and CO. This study found that current is produced from H2 by two different reaction pathways. This study also found that oxygen spills over to H(Ni) at lower currents and then to CO(Ni) at higher currents. Finally, this study confirmed that fuel adsorption onto nickel can be a rate-limiting step for H2 electro-oxidation but not for CO electro-oxidation.
Together these chapters provided insight into the coupling of coal gasification with SOFCs to better predict and optimize system performance for efficient stationary power generation.
6.2 Future Work
The results from Chapter 3 indicate that state-of-the-art efficiencies near 60% are possible when the gasifier and SOFC stack are coupled by heat transfer. However, even higher efficiencies are theoretically possible with the FB/SOFC design from Chapter 2, which integrates the gasifier into the SOFC compartment. This highly-coupled system boosts efficiency by promoting heat and gas exchange between the gasifier and fuel cell. In order to accurately predict the performance of this FB/SOFC system, a 2D model should be developed to capture gas transport and heat transfer between the gasification and anode reactions occurring in parallel. Detailed kinetic models for both steam and CO2 coal gasification must be implemented and coupled with the detailed SOFC model from this work to capture the relative reaction rates and by-products.
Experimental work is also needed in this space to better understand the complex coupling of coal gasification with a SOFC stack under normal operating conditions. In particular, a bench scale experimental set-up with steam gasification of coal particles upstream from a SOFC button cell could be used to study the impact of sulfur contamination and clean-up strategies. This bench set-up could also be used to scope out SOFC performance for a range of coal types and temperatures. Finally, a pilot scale hardware-in-the-loop-simulation of a real coal gasifier coupled to a simulated SOFC stack is critical to investigate the complex coupling of these two components before implementing these technologies in a full-scale power plant. A similar pilot scale demonstration has been developed for a SOFC coupled to a gas turbine at the DOE National Energy Technology Laboratory [3], and has provided invaluable insight on transient system performance. This pilot scale system could also be used to test novel high-temperature heat exchangers between the fuel cell stack and gasifier. Future modeling and experimental studies on the coupling of coal gasification with SOFCs will pave the way for large-scale fossil fuel power production with substantially lower CO2 emissions.
Appendices
Appendix A: Method for Obtaining Anode Mixture with OCV
The goal of this section is to provide further description of the method implemented in Chapters 4-5 to determine the actual anode fuel mixture based on the reported mixture and open-circuit voltage (OCV) given by the experimental paper [1]. The motivation for this approach is that multiple experimentalists cite air leakage as the culprit for their low open-circuit voltage measurements. In order to get the modeled OCV to match the experimentally reported OCV for a reported anode fuel mixture, the following procedure was used (also shown in Figure A. 1):
- The gas-phase chemical equilibrium mixture was calculated by running Cantera's "equilibrate" function on the reported anode mixture at fixed temperature and pressure.
- The OCV was then calculated using the following equation: OCV = RT/4F ln (pO2,c/pO2,a), where pO2,a is the oxygen partial pressure in the equilibrated mixture from the previous step and pO2,c is simply the partial pressure of oxygen in the cathode air stream (pO2,c = .21P).
- If the calculated OCV from the previous step is greater than the experimentally reported OCV (OCV > OCVexp), then a small amount of air was added to the equilibrated anode mixture.
Steps 2)-3) were then repeated until OCV ⥶ OCVexp, at which point the adjusted anode mixture with air leakage and gas-phase chemical equilibrium was taken as the actual mixture seen by the anode in the model. Chemical equilibrium was assumed for the following reasons: 1) the gas delivered to the anode had a long upstream residence time, and 2) oxygen from the air leak would likely react quickly with fuels in the mixture.
Figure A.1: Flow-chart of the process for adjusting anode fuel mixture for air leakage to match experimental OCV values.
In order to illustrate how this method works, consider the mixture of 20% H2 + 80% H2O from Jiang and Virkar's experimental paper. They provide an experimental polarization curve for that mixture that includes an open-circuit data point at 0.84 V. However, the calculated OCV for that equilibrate mixture is 0.04 V higher: OCV = RT / 4F ln [(. 21 * 101325) / (7.23 * 10⁻¹³)] = 0.88 V. A small increment of air (.1% of the overall mixture) is then added, resulting in the following anode mixture: 19.98% H2 + 79.92% H2O + .021% O2 + .079% N2. The calculated OCV for that equilibrated mixture is still almost 0.04 V higher than the experimental value, so another .1% of air is added. This process is repeated until OCV ⥶ 0.84 V, which occurs for unequilibrated anode mixture of: 16.2% H2 + 64.8% H2O + 3.99% O2 + 15.01% N2 . This mixture corresponds to 19% air by volume, as listed in the first row of Table A. 1.
Table A. 1: Calculated vs. experimental OCV values along with the percentage of air in the adjusted anode mixtures for each of the reported anode fuel mixtures from Jiang and Virkar [1].
The percentages of air in all of the final anode mixtures used in this thesis are listed in the last column of Table A. 1. The mean value of this column is 28%, which indicates that roughly one mole of air is leaking into the anode gas supply for every three moles of fuel mixture supplied. Although this seems like a high value, it's not necessarily unreasonable given the following justifications:
- Virkar's experimental group cites air leakage as the most likely cause of open-circuit voltage dips in their paper [1].
- This experimental group also reports higher air-side flow-rates than fuel-side flow-rates to their button cell (550 mL/min vs. 140 mL/min). Therefore, a small leak could still result in a relatively large air flow-rate across the membrane.
- The air leakage percentages don't vary much for different fuel mixtures, particularly those within the same data set (e.g. H2 + N2 mixtures only vary from 21-27% air leakage). This provides some indication of a constant air leak into the anode while experiments were performed.
Even in light of this evidence, it is still likely that air leakage is only one of the sources of loss in cell potential in this experiment. Other possible contributors are electronic leakage through the cell and morphological changes to the cell (i.e. carbon deposition) that degrade performance. However, the air leakage model described here was implemented because it consistently provided a better fit to the experimental data than the alternative electronic leakage model. Further research should be done to compare the competing theories for cell performance loss using detailed modeling and experimental data from multiple independent sources.
Appendix B: Detailed Solutions for Spillover Mechanism
The goal of this section is to provide some of the detailed steps in solving for equilibrium potential (Eeq) and YSZ coverages
when the charge-transfer processes in the spillover mechanisms are rate-limiting. This explanation supplements the model description provided in Chapter 5, and is specific to the case when both the H spillover and O spillover pathways are active. A similar procedure can be applied to cases where only one spillover pathway is active to solve for equilibrium potential and the relevant YSZ coverages.
when the charge-transfer processes in the spillover mechanisms are rate-limiting. This explanation supplements the model description provided in Chapter 5, and is specific to the case when both the H spillover and O spillover pathways are active. A similar procedure can be applied to cases where only one spillover pathway is active to solve for equilibrium potential and the relevant YSZ coverages.
B.1 Equilibrium Potential
The equilibrium potential difference across the anode-electrolyte double-layer (Eeq) is needed to determine the currents for each charge-transfer step since E = Eeq + ๐ฐact,a in equations (5.13)-(5.16). The equilibrium potential Eeq is simply the potential difference at open-circuit conditions, where ๐ฐact,a = 0 and all currents are zero. Therefore, Eeq can theoretically be determined by setting E = Eeq and ik = 0 in charge-transfer equations (5.13)-(5.16). In practice, however, this leads to an over-constrained system of equations with no solution. Thus, Eeq can only be determined by setting setting E = Eeq and ik = 0 for either equations (5.13)-(5.14) or equations (5.15)-(5.16). The errors resulting from this simplification are minor when equations (5.13)-(5.14) are selected, since the H spillover mechanism is the dominant source of current near open-circuit.
Setting E = Eeq and ik = 0 for equations (5.13)-(5.14) yields the following set of equations:
B.2 YSZ Coverages
Once Eeq is calculated using equation (B.9), the double-layer potential difference at finite current (E = Eeq + ๐ฐact,a) is also a known quantity, since 7lact,a is a model input. The current densities associated with each charge-transfer step from equations (5.13)-(5.16) can then be written in terms of known nickel coverages and the four unknown YSZ coverages at the TPB:
Source: Katherine M. Ong - Georgia Institute of Technology
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