anode of a SOFC under open-circuit conditions

Transcription

1 Improvements to predictions of carbon deposition on the nickel anode of a SOFC under open-circuit conditions Won Yong Lee, a Jeff Hanna, a,z Ahmed F. Ghoniem a a Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA z Corresponding author; jfhanna@mit.edu 1

2 Abstract: Previous thermodynamic analyses of carbon formation in SOFCs assumed that graphite could be used to represent the properties of carbon formed in the anode. It is generally observed, however, that catalytically grown carbon nanofibers (CNF) are more likely to form in the SOFC anode with nickel catalysts. The energetic and entropic properties of CNF are different from those of graphite. We compare equilibrium results based on thermochemical properties for graphite, to new results based on a previously reported value of an empirically determined Gibbs free energy for carbon fibers grown on a nickel support (with fitted values of H CNF = kj/mol and S CNF = J/mol/K). There is little difference in predictions of carbon formation under open-circuit conditions between the two carbon types for methane mixtures, with graphite predicted to form at lower temperatures than CNF. There is a much bigger difference in predictions for methanol mixtures, especially at low steam-to-carbon (H 2 O/C) ratios. For dry mixtures, graphitic carbon forms at temperatures below 800 C, whereas CNF forms only in the range C. At H 2 O/C 1.0, CNF does not form out of methanol mixtures, but graphite forms below about 200 C. The differences for propane are even more pronounced, and the improved predictions assuming CNF are in closer agreement with past observations. If both carbons types are included, only the thermodynamically favored form (i.e., the type having the lowest formation energy) exists. Predicted Nernst potentials are more-or-less independent of the carbon type and in agreement with measured open-circuit voltages. Keywords: SOFC; nickel catalyst; hydrocarbon; syngas; multiphase thermodynamic equilibrium; carbon 2

3 1 Introduction Interest in solid-oxide fuel cells (SOFCs) operating on modern hydrocarbon fuels has steadily increased because high conversion efficiencies can be achieved with readily available real-world fuel sources. One of the biggest challenges to directly operating traditional solid-oxide fuel cells (SOFCs) on hydrocarbon (HC) fuels is performance degradation caused by solid carbon formation in the nickel-yttria-stabilized zirconia (Ni-YSZ) anode Carbon deposited in the anode can restrict and block the pores thereby inhibiting gas transport, prevent reforming reactions by covering or breaking the metal catalyst, or stop current generation by blocking the triple-phase boundary (TPB). At typical SOFC operating temperatures ( C) using hydrocarbon or syngas (H 2 - CO mixtures) fuels, the extent of carbon formation depends on factors such as the steam-carbon ratio and general operating conditions (e.g., temperature, pressure, current density), as well as the anode composition and structure. Although it is possible to minimize carbon deposition on traditional Ni-YSZ anodes by providing sufficient H 2 O in the fuel stream, the amounts required are generally excessive, diluting the fuel and reducing overall cell efficiency. In addition, this creates device- and system-scale complexity because of the need for water management solutions. Under typical SOFC operating conditions, there are two primary carbon formation mechanisms that can take place in the anode: 27 (1) homogeneously formed soot consisting of polycyclic aromatic hydrocarbons (PAHs) that can deposit anywhere in the anode, and (2) heterogeneously formed carbon fibers that grow on the catalyst surface. For each of these mechanisms, the formation characteristics and resulting impact on the anode (and therefore, the cell behavior) are summarized in Table I. These mechanisms have been studied extensively in applications such as reforming, 28,29 carbon nanofiber production, and combustion However, previous thermodynamic analyses of carbon formation in SOFCs 12 14,16,17,21 24,37,38 are almost all based on an assumption that the thermodynamic properties of graphite universally represent those of the carbon deposits, even though these properties are reported to be dependent on the mechanism and structure of deposited carbon and are different from those of graphite. 4,5,39 41 Predictions from past thermodynamic analyses mostly fail to agree with experimental observations of carbon deposition in the SOFC. 5,13 17,42 The one exception from those analyses is Cimenti and Hill, 37 who use graphite in their calculations, but discuss the impacts and differences between graphite and amorphous carbon. They note that 3

4 amorphous carbon is, in general, less likely to form because of its higher formation energy compared to graphite. The goal of the present study is to improve upon the ability to predict carbon deposition in SOFC Ni-YSZ anodes under equilibrium open-circuit conditions by adopting empirical-based representations of the carbon formation mechanism through the use of experimentally measured thermochemical properties for carbon fiber in place of those for graphite. We choose to focus on carbon-fiber growth and not soot formation for various reasons, namely because catalytically grown carbon fibers are the primary growth mechanism for SOFC operating conditions on a nickel catalyst, 30 33,43,44 and because soot formation from homogeneous gas-phase chemistry is likely insignificant in the small pore spaces of a typical Ni-YSZ cermet anode (i.e., heterogenous surface chemistry is dominant). Alternatively, the formation of soot and pyrolytic carbon are certainly of great importance in the fuel channels and in other system components that lack a metal catalyst. 1 To illustrate the improvements in our analysis, inconsistencies between previous analyses and experimental observations are discussed, and equilibrium predictions based on graphite (reproduced from Sasaki and Teraoka 21,22 ) are compared side-by-side with new results using carbon nanofiber (CNF). It is worthwhile to note at the outset that our work focuses on open-circuit or equilibrium conditions, when thermodynamics is the controlling factor for the formation of carbon. Thermodynamics is also expected to play a role (albeit a diminished one) at low current densities. Carbon deposition can be prevented at sufficiently high cell currents, even at low steam-to-carbon ratios. 45 However, under operation at finite currents, thermodynamics is not the sole factor in determining whether carbon will form. In fact, the kinetics are expected to play a major role at finite currents, at low temperatures, and any situation characterized by a departure from equilibrium. 20,27 2 Catalytically grown carbon nanofiber Carbon deposition from methane in the presence of a nickel catalyst has been extensively studied in the reforming industry. 29,30,46 48 This knowledge can be utilized directly in SOFC applications because the SOFC anode environment is similar to that of a methane reforming reactor in two ways: (1) the gas temperature ranges from about C, and (2) the microstructure of the reforming 4

5 catalyst is almost identical to that of the SOFC anode in that the nickel catalyst is dispersed in a supporting material, Al 2 O 3 for reforming and YSZ in a SOFC. On catalysts such as Ni, Fe, and Co, it is known that carbon deposits and grows in a fiber-like shape, called carbon nanofiber (CNF) ,43,44,47,49 In the study of CNF growth mechanisms, the catalysts (Ni, Fe, and Co) are typically used as bulk particles (100 nm in size) or as supported particles (10 50 nm). All of these metals can dissolve carbon from a carbon-containing gaseous atmosphere to form a metal carbide. Typically, methane, carbon monoxide, syngas, ethyne, or ethane are employed to provide the carbon atoms. 30 The accepted formation mechanism for CNF 27,29,43,44 involves hydrocarbon adsorption on the catalyst surface, conversion of the adsorbed hydrocarbon to adsorbed surface carbon via surface reactions, subsequent segregation of surface carbon into layers near the surface, diffusion of carbon through the Ni (or Fe, or Co) catalyst, and precipitation on the rear side of the Ni particle. This sequence of steps is illustrated graphically in Figure 1. The properties of both adsorbed carbon on the front side of the catalyst and carbon fiber on the rear side are different from those of graphitic carbon. 50 The different chemical potentials of these carbon materials result in different solubility in the front and rear side of the Ni crystal, thus creating a driving force for the diffusion of carbon through Ni. 50,51 Carbon filaments do not immediately deactivate the catalyst as encapsulating pyrolytically formed soot does. Instead, the fiber separates the Ni from its original support but still allows active sites to be available. These fibers can be a serious problem, however, as they can completely fill the pore space and eventually lead to cracking of the electrode from mechanical stresses induced by many growing fibers Thermodynamic properties of carbon nanofiber Carbon formation from the decomposition of CO and CH 4 over a Ni catalyst has been studied for more than 75 years. 41 Further, many researchers report thermodynamic properties for deposited filamentous carbon that are different from those of graphite The thermodynamic properties for carbon fibers grown on Ni have been measured for the reaction describing methane cracking and the Boudouard reaction, given respectively as, CH 4 C f + 2H 2 (1) 5

6 2CO C f + CO 2 (2) where the subscript f refers to carbon nanofiber (CNF). By measuring the equilibrium concentrations of the gas species, the Gibbs free energy of the carbon fiber can be determined. Rostrup- Nielson 39 and de Bokx et al. 40 measured the difference between the Gibbs free energy of the CNF and that of graphite (i.e., the excess energy required to form CNF compared to graphite) based on the following equation ( ) Kf G = G f G gr = RT ln K gr (3) where K gr is the equilibrium constant computed using thermochemical data for graphite (i.e., assuming C gr appears in the reactions instead of C f ), and K f is the equilibrium constant calculated using the measured gas pressures in the experiments. The equation above describing the Gibbs free-energy difference can be applied to reaction 1 or 2, and the equilibrium constant K f,i for each reaction i is K f,1 = p2 H 2 p CH4 (4) K f,2 = p CO 2 p 2 CO (5) The left and right panels of Figure 2 show the equilibrium constant K f (for reactions 1 and 2, respectively) measured by Rostrup-Nielson 39 and de Bokx et al. 40 in comparison with the calculated equilibrium constant K gr. It is immediately evident that the measured equilibrium constants are very different from the values computed using graphite, which implies that carbon fiber has different thermodynamic properties than does graphite. Though CNF and graphite are both composed of carbon atoms, their different thermodynamic properties can be attributed to activation barriers relating to the carbon growth mechanism (e.g., the deposition and growth of hollow carbon tubes would have a different activation energy than a solid fiber, and even more so than a deposited carbon film). Rostrup-Nielsen 39 correlated the different free energies to nickel catalyst size, reporting whisker-like carbon structures having a diameter very close to that of the nickel crystallite attached to it. Likewise, Cullinan and Culpepper 32 offer a functional form (obtained from Ref. 52) for the change in Gibbs free energy G occurring when 6

7 a length dl of a carbon fiber is precipitated, 52 G = 2πσ(D t)dl + 1 ( ) D 12 πea2 ln dl π µ 0 [ D 2 (D 2t) 2] dl. (6) D 2t 4Ω This expression is the sum of the surface energy, the elastic energy, and the change in potential energy that is required to create the fiber; it includes the energy required to form graphite σ = 77 erg/cm 2 (at 970 C), the diameter D and wall thickness t of the hollow fiber, the chemical potential change µ 0 when a carbon atom precipitates from the dissolved phase, Ω = cm 3 /atom the volume of a carbon atom in graphite, a = nm the graphite interplanar spacing, and E = 1000 GPa Young s modulus. Values for σ, µ 0, Ω, a, and E are taken from Refs. 52 and 53. The catalyst size does not appear in this expression (though one could assume D is the catalyst diameter, but this assumption does not allow for growth of fibers smaller than the catalyst). In addition, the expression relates the change in free energy to the length of growing fiber. While this is useful in many contexts, our focus is centered on whether or not fibers will form, not with their detailed growth. The effect of growth will be explored in the future. Because the growth mechanism depends on operating conditions and catalyst type, the contribution of chemical kinetics, which has similar dependencies, is also likely important. In this paper, we limit our attention to equilibrium conditions only. 2.2 Carbon formation in Ni-based SOFC anodes at or near open-circuit conditions One of the major hurdles to mainstream adoption of SOFCs using traditional nickel-yttria-stabilized zirconia (Ni-YSZ) cermet anodes with carbon-containing fuels is the propensity for solid carbon formation within the anode, which can destroy the nickel catalyst and deactivate the cell altogether. Although other catalysts (e.g., Cu) do not promote catalyzed carbon-formation reactions, traditional Ni-YSZ anodes are favored for their relatively low cost and ease of manufacture Experimental studies Gorte and co-workers 3 5,7 10 have generally focused their efforts on the study of Cu-based anodes, which do not catalyze formation of carbon fiber. Given appropriate conditions for homogeneous 7

8 gas-phase reactions to play out in the anode, carbon deposition in Cu-based anodes is more likely to occur via the soot formation mechanism (see Table I). On the other hand, Barnett and co-workers have typically used conventional Ni-based anodes to study conversion of hydrocarbon sources. The role of methane pyrolysis was tested by flowing pure methane over Ni-YSZ anodes at open-circuit conditions, which resulted in increasing carbon deposition with increasing temperatures above 700 C. 11 Moreover, in another study using methane and natural gas as fuel, the same group found that cells having Ni-YSZ anodes were highly susceptible to carbon deposition at open-circuit conditions, so much so that at 800 C carbon deposition was severe enough to cause the cell to crack after approximately ten minutes. 12 This behavior is in agreement with observations by others as well, and is reportedly likely due to volume expansion associated with the formation of Ni carbides. 9,14 At temperatures lower than 700 C, it is generally found that cells can be kept at open-circuit conditions without any deleterious effects, while at higher temperatures, increasingly large currents are required to avoid coking and cell failure. 11,12,14,54 These results imply that the SOFC oxygen-ion current is, at the very least, somewhat responsible for preventing carbon formation. 14 To express these findings quantitatively, Lin et al. 14 defined a critical current density i crit, above which the SOFC (operating on humidified methane with a Ni-YSZ anode) was free from performance degradation. At temperatures of 650 C and 700 C, their cell exhibited excellent stability as long as the minimum cell current density exceeded i crit 0.1 A/cm 2. It was only at open circuit (i.e., i = 0) that the cell voltage decreased gradually over several hours, consistent with the formation of CNF as more and more nickel catalysts are lifted from the YSZ support and eventually broken (see Table I). At higher temperatures, the critical current densities were found to be in the ranges 0.8 < i crit < 1.2 A/cm 2 and 1.4 < i crit < 1.8 A/cm 2 for 750 C and 800 C, respectively. That is, at current densities below these values (especially near open circuit conditions), the cell voltage began dropping because of carbon growth, eventually causing it to stop working and even crack in multiple cases (reported to occur often at 650 C after long-term operation, and at 700 C and A/cm 2 after several hours). There are two exceptions that should be noted. The first is a study involving propane-oxygenargon mixtures (10.7% C 3 H % O % Ar) fed to a Ni-YSZ anode-supported cell in which no carbon was observed under any of the conditions tested. 13 While this was attributed to thermo- 8

9 dynamic and kinetic limitations, it may also be the result of oxidation of the solid carbon by the additional oxygen in the anode fuel stream. This explanation seems more likely, especially considering that at finite currents, when oxygen ions are transported across the electrolyte to the anode, carbon deposition is greatly suppressed even at very low oxygen partial pressures (10 20 atm). It is reasonable to assume the additional oxygen (even in small amounts) in the anode fuel stream helps to mitigate solid carbon formation even at open circuit. The second exception concerns additional catalysts (in all cases, Ru-CeO 2 ) added to the Ni-YSZ anode to specifically provide more stable output by reducing carbon deposition , Theoretical studies The two most used approaches to predicting carbon formation in a SOFC environment have been a thermodynamic equilibrium analysis (using the Boudouard and methane-cracking reactions only, 25,26 or using all possible reactions between assumed species 13,16,17,21 24,37,38 ) or a full kinetic analysis of homogeneous chemistry in non-catalytic regions 1,19,20,55 (e.g., the anode fuel channel). Based on a report that methane cracking (see reaction 1) and the Boudouard reaction (see reaction 2) are the two major pathways for solid carbon formation, 56 Klein et al. 26 defined two ratios to measure the departure of those reactions from equilibrium, or, in other words, to predict the driving force for carbon deposition. The ratios relate the measured reaction quotients to the reaction equilibrium constants according to α = p CO 2 /p 2 CO K 2 (7) β = p 2 H 2 /p CH 4 K 1 (8) where K 1 and K 2 are the equilibrium constants for reactions 1 and 2, respectively, and p k is the measured value of the local partial pressure for species k. For each reaction, if α or β < 1, the reaction is not yet at equilibrium and proceeds to the right (as written). Under these circumstances, formation of solid carbon is thermodynamically favored in that reaction. When either ratio is equal to unity, the corresponding reaction has reached equilibrium, but any solid carbon already formed will remain, though no further carbon formation should be observed. On the other hand, if α or 9

10 β > 1, that reaction proceeds to the left. Vakouftsi et al. 25 adopted the same criteria, and both applied it to a multi-dimensional CFD analysis to map the domain where carbon deposition is thermodynamically favored. However, the major shortcoming of this approach is the inability to account for the coupling between the two reactions. That is, if α < 1 and β > 1 (or vice versa), the approach fails to yield a decisive thermodynamic prediction because carbon is predicted to form in one reaction, while it is consumed in the other. Most equilibrium analyses of carbon deposition in SOFCs are performed on the basis of Gibbsfree-energy minimization of the system subject to an element balance of all the assumed species. 13,16,17,21 24,37,38 This is equivalent to considering all possible reactions between the allowed species, including reactions 1 and 2, as well as steam reforming and water-gas shift reactions. This approach can provide a thermodynamically accurate prediction when there are many possible reactions that can lead to carbon formation. Unfortunately, in all but one of those analyses, the properties of graphite were used to represent the carbon deposits even though CNF is the favored growth mechanism on nickel 30 33,43,44 and has different thermodynamic properties 4,5,39 41 (see Figure 2). The single exception is found in Cimenti and Hill, 37 who specifically note the enthalpy and entropy differences of amorphous carbon versus graphite, and comment that using the values for amorphous carbon results in a reduced amount of predicted solid carbon because of a higher formation energy. Moreover, the authors comment that if both carbon types are included in the calculation, the resulting compositions are identical to those obtained using graphite only. Unfortunately, the authors did not present any data from calculations using amorphous carbon. In this work, we use the measured Gibbs free energy for CNF 39,40 to predict carbon deposition under open-circuit conditions (when the propensity to form carbon deposits is highest) to build and improve upon limitations of past analysis methods. 3 Thermodynamic equilibrium calculations The equilibrium state of a mixture is calculated by minimizing the total Gibbs free energy subject to the constraint of element conservation. The element conservation constraints can be incorporated as a non-stoichiometric formulation or as a stoichiometric one, both being mathematically equivalent In the former, the element conservation equations are given as constraints and the 10

11 resulting equilibrium problem is a constrained optimization problem. An example is the Brinkley- NASA-RAND (BNR) algorithm. The stoichiometric formulation incorporates the element conservation equations by means of stoichiometric equations and the extent of reactions. The equilibrium problem becomes (essentially) an unconstrained optimization problem. The most advanced algorithm of this type is the Villars-Cruise-Smith (VCS) algorithm, which is known to be better for handling multiphase problems, especially those involving single-species phases, such as the solid phase that includes only carbon in the present analysis. We chose to develop and implement our own VCS equilibrium solver to give us the flexibility of controlling and defining the Gibbs free energy of the carbon nanofiber (CNF) through any functional form, including one that depends on the catalyst size (though, admittedly, there is currently a lack of good data to support defining the dependence of the Gibbs free energy of CNF as a function of catalyst type and size, the possibility does exist should this data become available). We validate the code by comparing two equilibrium calculations one gase-phase and one multiphase to the same calculations carried out using Cantera. 60 The results of these calculations are shown in Figure 3, and the equilibrium compositions overlay exactly. Because the equilibrium composition depends not only on the fuel mixtures, but also on temperature, the calculated results can be presented by fixing the fuel composition and varying the temperature (showing how the equilibrium mixture composition varies with temperature), or fixing the temperature and changing the composition (often displayed using a ternary diagram). The results in the sections to follow are presented as functions of temperature (i.e., the first option), but several useful ternary diagrams are included as well. It is also worth noting that compositions are presented as number of moles rather than partial pressures because the partial pressure of solid carbon cannot be defined. For the thermodynamic calculations, the following 34 species consisting of carbon, hydrogen, and oxygen are allowed: C(solid), CH, CH 2, CH 3, CH 3 O, CH 4, CH 3 OH, CO, CO 2, C 2 H, C 2 H 2, CH 2 CO, C 2 H 3, C 2 H 4, CH 3 CHO, C 2 H 5, C 2 H 6, C 2 H 5 OH, C 3 H 7, C 3 H 8, n-c 4 H 10, n-c 5 H 12, n-c 8 H 18, iso-c 8 H 18, H, HCO, HCCO, HO 2, H 2, H 2 O, H 2 O 2, O, OH, O 2. All thermodynamic properties are calculated using the NASA Glenn coefficients, 61 except for CNF, which is obtained from de Bokx et al. 40 Hereafter, we refer to this as de Bokx carbon in addition to graphite (properties from NASA Glenn), both of which are used to represent C(solid) depending on the assumption being 11

12 made. Figure 4 compares the Gibbs free energy of graphite to that of catalytically grown carbon fiber as measured by de Bokx et al. 3.1 Equilibrium calculations for various fuel mixtures All calculations appearing in this section are based on one mole of carbon, the type of which is referred to as de Bokx carbon or CNF, or as graphite or C(gr). Performing the calculation for each carbon type facilitates side-by-side comparison of the two, as well as differentiation with experimental data when available Methane Among hydrocarbon fuels, methane is one of the most stable and it is the major component of natural gas. Figure 5 shows the equilibrium products of methane at temperatures between 100 C and 1000 C for steam-to-carbon (H 2 O/C) ratios of 0 (methane pyrolysis), 1.0, and 1.5 (methane reforming for both). In each panel, the results on the left are based on the measured Gibbs free energy of carbon formed on a nickel catalyst by de Bokx et al., 40 indicated as CNF for carbon nanofiber. The equilibrium compositions on the right are based on the assumption that the carbon formed in the anode is graphite. The top pair of equilibrium mixtures in Figure 5 involves no H 2 O, so the only possible reaction is methane cracking (i.e., reaction 1), which is endothermic at standard temperature and pressure (CH 4 C + 2H 2, r H 25 C = 74.6 kj/mol). At lower temperatures, there is not enough heat to support the endothermic reaction and CH 4 does not decompose. At higher temperatures (approximately 400 C for CNF, and 300 C for graphite), methane decomposition begins to take place yielding more and more solid carbon and hydrogen gas as the temperature continues to increase. Because CNF has a higher Gibbs free energy than graphite (until about 975 C as shown in Figure 4), it requires more energy to form, causing the onset of carbon deposition to occur at a higher temperature. Moreover, the predicted amount of CNF formed is less than that of graphite until saturation is reached around C. For a steam-to-carbon ratio H 2 O/C = 1.0, CH 4 is reformed to CO and H 2. Carbon monoxide can react in the water-gas shift reaction (CO+H 2 O CO 2 +H 2, r H25 C = 41.1 kj/mol), and the resulting CO 2 can participate in the Boudouard gasification reaction (reaction 2, C + CO 2 2CO, 12

13 r H25 C = kj/mol) to convert solid carbon from methane decomposition. In addition, any solid carbon formed can also participate in steam reforming (C + H 2 O CO + H 2, r H 25 C = kj/mol). The combination of these reactions and their energy requirements results in a small window ( C for CNF, and C for graphite) in which solid carbon is deposited. The difference in Gibbs free energies results in a shift of the carbon-formation region by about 200 C. At high temperatures, the energy input for each reaction is sufficient so that CO and H 2 are the only products, and any solid carbon formed via methane cracking is consumed in the Boudouard gasification reaction and steam reforming. No solid carbon is expected to exist at equilibrium for H 2 O/C = 1.5, as can be seen in the bottom panel of Figure 5. Here, there is no difference between the assumed carbon type because there is enough water to reform any solid carbon directly or indirectly (e.g., H 2 O is used in the water-gas shift to produce CO 2, which is then used to gasify solid carbon in the Boudouard reaction) Methanol Direct operation of SOFCs on methanol has been demonstrated in the literature, 38,42 and thermodynamic analyses (based on graphitic carbon) of a SOFC operating on methanol can also be found. 21,22,37,38 Figure 6 shows the equilibrium products of methanol mixtures at temperatures between 100 C and 1000 C for steam-to-carbon (H 2 O/C) ratios of 0, 1.0, and 1.5. As in the case for methane, the results on the left are based on the measured Gibbs free energy of carbon formed on a nickel catalyst by de Bokx et al., 40 indicated as CNF for carbon nanofiber. The equilibrium compositions on the right are based on the assumption that the carbon formed in the anode is graphite. Unlike methane pyrolysis, there are noticeable differences in the predictions between the de Bokx carbon and graphite at H 2 O/C = 0. For graphite, carbon deposition is predicted to occur at any temperature below 800 C, while CNF is only predicted to grow in the range C. When H 2 O/C is 1.0 or 1.5, the only difference between predictions using de Bokx carbon and graphite is that carbon is expected to form around 200 C for graphite, while CNF formation is not favored at any temperature. The complete suppression of carbon deposition for graphite at steam-to-carbon ratios greater than 1.0 (and temperatures above 327 C) are in agreement with past results. 38 Our quantitative results for CNF are supported qualitatively by Cimenti and Hill, who note that less 13

14 amorphous carbon is expected to form because of its higher free energy. 37 The amount of water in the equilibrium mixture in the case of methanol is much higher than that formed from methane. This is not surprising since alcohols can be regarded as hydrated hydrocarbons. 21 Therefore, less H 2 O is needed to suppress carbon deposition when using methanol compared to methane. Note that there is no methanol in the equilibrium products in all panels of Figure 6. The presence of methanol is thermodynamically unfavorable at any temperature; it decomposes to CH 4, H 2 O, and C at low temperatures. At high temperatures, carbon is removed by the Boudouard gasification reaction, and CH 4 is cracked to produce H Propane Zhan et al. 13 studied the performance of SOFCs operating on propane-air mixtures. They measured the anode exhaust gas composition as a function of temperature for a 10.7% C 3 H % O % Ar fuel mixture over a Ni-YSZ anode at open-circuit conditions. No carbon was detected on the anode side under any of the conditions tested at temperatures between 550 C and 800 C. However, their equilibrium calculation using graphite predicted that a large amount of carbon should be formed. This is consistent with our calculation as seen in the right panel of Figure 7. Zhan et al. attributed this to thermodynamic and kinetic limitations. However, when CNF is assumed for the equilibrium calculations, the resulting amount of predicted carbon is reduced dramatically, as shown in the left panel of Figure 7. While our improved prediction still does not match the observation made by Zhan et al. that no carbon was detected in the anode, this is likely the result of insufficient data to more accurately represent CNF formed in a Ni-YSZ anode. That is, the Gibbs free energy we use from de Bokx et al. 40 is for CNF formed on a supported nickel catalyst, where the mean catalyst particle size is 5.4 nm. The Gibbs free energy of formation for CNF is expected to be a function of the catalyst size. 32,33,43,44 In addition, Takeguchi et al. 23 showed that the diameter of carbon fiber formed in a Ni-YSZ anode is much larger than that formed on a supported nickel catalyst. This may be the major reason for discrepancies between our improved thermodynamic prediction and observation, either in and of itself, or in addition to the kinetic argument raised by Zhan et al. 14

15 4 Comparison of predicted Nernst potentials with experimentally measured open-circuit voltages Liu and Barnett 12 report measurements of the open-circuit voltage (OCV) as a function of temperature for humidified H 2 and CH 4 (both in 3% H 2 O) for Ni-YSZ/YSZ/LSCF-GDC cells exposed to ambient air on the cathode side and operated at 1 atm. The left panel of Figure 8 compares the measurements of Liu and Barnett for humidified hydrogen and the computed equilibrium Nernst potentials. Because there is no carbon present, the difference between the measured OCV and Nernst potential can be attributed to leakage of oxygen from the cathode side into the anode, or current leakage through the electrolyte. 62,63 Because it represents a loss of polarization, this difference can be characterized by a leakage overpotential η leak = 0.02 to 0.03 V, which is more-or-less independent of fuel and increases by 10 mv over the 200 C temperature range (perhaps because of thermal expansion mismatch leading to increased oxygen leakage, or increased electronic conductivity of the electrolyte). Nevertheless, it is simply a way to characterize the baseline difference between measurements in a particular experimental setup, and ideal thermodynamic predictions. The right panel of Figure 8 compares OCV measurements by Liu and Barnett 12 for humidified methane on the same setup (meaning that the same leakage should exist) and the computed equilibrium Nernst potentials using one of three assumptions: (1) solid carbon is not considered in the equilibrium calculation, (2) solid carbon is assumed to be graphitic with corresponding thermodynamic properties, and (3) solid carbon is represented as CNF through properties from de Bokx et al. 40 The computed Nernst potential neglecting solid carbon is well outside the range of the leakage overpotential (i.e., V versus a leakage overpotential of V), which indicates that something is missing in the analysis. By including carbon in either form (graphite or CNF), the computed equilibrium potential is in agreement with the measurements and differs only by the same leakage overpotential seen in the hydrogen case. This is to be expected, and the calculations indicate that solid carbon will exist in the anode. The difference in computed Nernst potential for both assumed carbon types (so long as carbon is included) is not particularly significant. The different Gibbs free energies result in small changes in the mole numbers of the major species, as can be seen in Figure 9; at temperatures below 700 C, the amount of methane decomposition is slightly reduced for CNF (dashed lines), resulting 15

16 in higher CH 4 and lower H 2 and solid carbon, as compared to the same calculation with graphite (solid lines). Additionally, the equilibrium oxygen partial pressures in the anode span almost eight orders of magnitude (10 30 to 10 22, see Figure 10) and they do not depend significantly on the type of carbon. The open-circuit or reversible Nernst potential E OCV is related to the equilibrium oxygen partial pressures p O2,a and p O2,c on the anode and cathode side, respectively, by E OCV = RT 4F ln ( po2,c p O2,a ) (9) In this equation, p O2,c is determined by the cathode-side gas (e.g., if atmospheric air is used, p O2,c = 0.21 atm) and p O2,a is the predicted oxygen partial pressure on the anode side as given by the equilibrium composition of the fuel-gas mixture. Including carbon in the calculations shifts the resulting equilibrium composition, and hence changes p O2,a. 5 C-H-O Ternary diagrams The thermodynamic equilibrium chemical compositions for various fuel gases can be represented by the relative ratios among carbon, hydrogen, and oxygen atoms on a C-H-O ternary diagram. These diagrams are an extremely useful and powerful method for presenting data at specific operational temperatures Carbon deposits Figure 11 shows the constant-temperature contour lines corresponding to a carbon mole number of 10 6, which is defined arbitrarily as the carbon deposition demarcation line. (This value is used because choosing a different value between 10 3 and 10 9 had no appreciable change on the position of the line. Further, it is the same value used in Ref. 37.) The region below the demarcation line represents possible mixtures whose equilibrium composition at the specified temperature has less than 10 6 moles of carbon, and carbon formation is expected above (on the carbon-rich side) of the line. Several demarcation lines are presented in both diagrams, with each line corresponding to a different temperature between 200 C and 1000 C. The diagram on the left is produced under the assumption that CNF is formed, and the diagram on the right assumes graphite is the only 16

17 condensed phase. The right panel is in agreement with Sasaki and Teraoka 22 who studied equilibria using graphite only, and therefore provides further validation (in addition to Figure 3) of our own thermodynamic calculations. At high temperatures (800 C and 1000 C, and likely above 700 C in general, though this temperature is not shown), the difference between the demarcation lines is minimal because the difference in Gibbs free energy between the two assumed carbon types is very small (see Figure 4) or because carbon formation is not favored at higher temperatures. At these high temperatures, the carbon-formation demarcation lines are more-or-less a linear connection between H 2 and CO, indicating that these are the dominant species and their relative amounts are determined by the lever rule. No carbon deposition is expected at these temperatures if the carbon-to-oxygen ratio is less than unity in the fuel mixture. Methanol (CH 3 OH) practically lies on the high-temperature demarcation lines, and it is clear that adding even a small amount of H 2 O or O 2 (or even CO 2 ) can help prevent carbon deposition with methanol. Methane (CH 4 ), on the other hand, lies above the demarcation line in the carbon-deposition region. One would need to add more water (compared to methanol) to suppress carbon deposition under operation with methane, consistent with our earlier statement in the discussion regarding methanol. The use of graphite instead of CNF to represent the properties of deposited carbon shows that as the temperature decreases the carbon-deposition region expands further into what was the carbon-free region. Additionally, the carbon demarcation lines transition from connections between H 2 and CO to the curves connecting CH 4 and CO 2. The first result indicates that a higher steam-to-carbon ratio or carbon-to-oxygen ratio is needed to prevent carbon deposition at lower temperatures. Whereas the addition of CO 2 reduces carbon deposition at high temperatures (due to gasification in the Boudouard reaction), the addition of CO 2 at low temperatures is not as effective. In general, the amount of H 2 O, O 2, or CO 2 needed to suppress carbon deposition increases at lower temperature. The transition of the demarcation line indicates that CH 4 and CO 2 are the stable species at lower temperatures, while H 2 and CO are the dominant species at higher temperatures because of the methane cracking and Boudouard reactions, as discussed in the section concerning methane. For CNF, the same transition to CH 4 and CO 2 is seen, but the penetration of the carbonformation region into the carbon-free region is much less. This is because of the larger Gibbs free 17

18 energy for CNF compared to graphite, meaning that formation of carbon requires more energy. 5.2 Equilibrium oxygen partial pressures and open-circuit voltages Figure 12 shows contours of the computed equilibrium oxygen partial pressure p O2,a in the anode using CNF at a temperature of 600 C. The contour lines are labeled with a value corresponding to log(p O2,a/1 bar) because the oxygen partial pressure spans several orders of magnitude for an open-circuit potential around 1 V. In the carbon deposition region, contour lines connect pure solid carbon at the top vertex to the carbon-deposition demarcation line, which is also shown. The same trend is reported by Sasaki and Teraoka 22 and Takeguchi et al. 23 because increasing the amount of carbon in the carbon-deposition region does not affect the gas partial pressures. Adding carbon to a mixture on the demarcation line moves the mixture composition along a contour. Thus, these lines also represent partial-pressure contours of any gaseous species in the equilibrium mixture noting that the contour value will depend on the species. Within the carbon deposition region, the oxygen partial pressure decreases as the hydrogen-tooxygen ratio increases. In the carbon-free region, the contours approach the complete oxidation line, defined by the straight line that connects H 2 O to CO 2, the products of full oxidation in a C-H-O system. Figure 13 shows the corresponding open-circuit or Nernst potential assuming that the cathode side is exposed to ambient air (p O2,c = 0.21 atm). The Nernst potential is evaluated from E OCV = (RT/4F ) ln(p O2,c/p O2,a), where p O2,a and p O2,c are the equilibrium oxygen partial pressures at the anode and cathode, respectively. When the composition drops below the complete oxidation line, the oxygen partial pressure increases rapidly, causing the ideal Nernst potential to drop significantly, from 1 V to 0.4 V. 6 Discussion In our equilibrium analyses, we compare the likelihood that solid carbon will be formed on the anode side of a SOFC using a Ni-YSZ cermet anode for various hydrocarbon gas mixtures. The calculations make use of the Gibbs free energy from de Bokx et al. 40 for carbon fiber grown on a nickel support, and we apply the same free energy to fibers grown on nickel catalyst particles, irrespective of particle 18

19 size. It is known, however, that the growth of carbon fiber on nickel is dependent on Ni particle size and the supporting material (in this case, YSZ). 32,33,43,44 We also note that the carbon fiber formed on Ni-YSZ has a larger diameter than that grown on a supported Ni catalyst. 23 There are inherent difficulties in correlating changes in Gibbs free energy to nickel particle size. Because a Ni-YSZ anode displays a range of nickel crystallite sizes, the equilibrium should, in principle, be established over the largest crystallites forming carbon with smaller energy. 39 However, the supersaturation required to start the reaction may initiate on small crystallites. 39 Moreover, though carbon fibers can form with diameters close to and not greater than that of the nickel crystallite, they may also have a diameter less than that of the crystallite. These effects all imply formation of carbon fibers with smaller diameter than the maximum nickel particle size, which, consequently, would increase the free energy of formation and reduce the likelihood that solid carbon is formed. 39 To our knowledge, measurement of the Gibbs free energy of carbon fiber in a Ni-YSZ anode has not been reported in the literature. In using carbon nanofiber (CNF) instead of graphite in our thermodynamic equilibrium calculations, we see different results for the equilibrium compositions, which seem to be qualitatively closer to experimental observations relating to whether or not carbon formation is anticipated for a given fuel and operating conditions. 5,13 17,42 There are still cases where prediction and observation disagree, which may be related to the kinetics of CNF growth, or simply can be improved with analytic expressions for the Gibbs free energy that depend on Ni particle size, for example. Such expressions do exist that relate the inner and outer radii of the carbon fiber, 32,39,41,44,52,53,65 which both depend on the size of the catalyst particle. 39,44 However, there is still uncertainty as to what controls the dimension of the inner and outer radii of the growing CNF. 32,52 If both forms of carbon are included in the equilibrium calculations, the resulting mixtures are composed only of the form that has the lower Gibbs free energy. Figure 4 shows a transition between the two types at approximately C, with graphite favored below this temperature, and CNF above it. With the exception of two cases, all of the mixtures presented in Figures 5, 6, and 7 remain unchanged if both forms of carbon are included in the calculations. The two exceptions are methane with H 2 O/C = 1.0 (Figure 5, middle row) and methanol pyrolysis (Figure 6, top row). Each of these compositions consist of regions where one form of carbon exists and the other does not. If both are included, one expects to see a transition at a temperature of C. To 19

20 illustrate this point, see Figure 14, in which the top panel corresponds to the aforementioned case for methane and the bottom for methanol. Because they are both carbon, and only have different formation energy barriers, the type with the lowest formation energy is always favored and the two cannot coexist. This is the same conclusion reported in Cimenti and Hill Conclusions The ability to predict carbon formation in nickel-based SOFC anodes is absolutely necessary for stable, long-term operation. Under sufficiently high cell currents, carbon deposition can be mitigated, even at low steam-to-carbon ratios. 45 However, under operation at finite currents, thermodynamics is not the sole factor in determining whether carbon will form. In fact, the kinetics are expected to play a major role at finite currents, at low temperatures, and any situation characterized by a departure from equilibrium. 20,27 This work focuses primarily on open-circuit or equilibrium conditions, when thermodynamics is the controlling factor for the formation of carbon. Thermodynamics is also expected to play a role (albeit a diminished one) at low current densities. Past thermodynamic analyses that attempt to predict carbon formation for a set of operating conditions assume graphite (and its thermochemical properties) to be representative of the carbon formed in the anode, even though catalytically grown CNFs are actually observed. The energetic and entropic properties of CNFs are different from those of graphite, so past analyses have found inconsistencies between thermodynamic predictions and observed behavior (i.e., thermodynamics predicts carbon formation though it is not observed experimentally, and vice versa). In this paper, we adopt a Gibbs free energy for CNF from de Bokx et al. 40 and use that value in a multiphase thermodynamic equilibrium calculation to study carbon formation for various hydrocarbon fuels over a range of temperatures at open-circuit conditions. The new approach improves the prediction of the likelihood of carbon deposition, particularly in cases where previous analyses have failed. Very little difference was found between the two carbon types for methane mixtures, though there is about a 100 C to 200 C shift for the onset of carbon formation (with graphite predicted to form at lower temperatures than CNF). There is a much bigger difference in predictions for methanol mixtures, especially at low steam-to-carbon (H 2 O/C) ratios. For graphite, carbon formation is predicted at temperatures below 800 C when no steam is provided in the initial mixture, whereas 20

21 CNF is predicted to form only in the range C. At H 2 O/C 1.0, CNF is not predicted to form out of methanol mixtures, whereas graphite is still predicted below about 200 C. The differences for propane are even more pronounced, with large amounts of graphite predicted to form and much less CNF for the single mixture investigated here. Experiments using the same mixture did not result in carbon formation under any of the conditions tested, which differs greatly from the thermodynamic prediction using graphite and only slightly from predictions using the assumed properties for CNF. Further, we find that predicted reversible Nernst potentials are moreor-less independent of carbon type, but highly dependent on whether or not solid carbon is included in the calculation. Including either of the two forms yields Nernst potentials that are in agreement with measured open-circuit voltages. Lastly, allowing for both forms of carbon in our calculations results in equilibrium mixtures in which only the thermodynamically favored form will be present. That is, both forms cannot coexist. Because graphite and CNF are both carbon, and only have different formation energy barriers (from a thermodynamic standpoint), the type with the lowest formation energy is always favored. 21

22 Table I. Different pathways for carbon deposition (adapted from Ref. 29) Formation pathway Fibrous carbon Encapsulating polymers Pyrolytic carbon Heterogeneous chemistry on a metal (e.g., Ni) catalyst Diffusion of C through the Ni crystal Nucleation and whisker growth from below the Ni particle, eventually separating the particle from the electrolyte (see Figure 1) Heterogeneous chemistry on a metal (e.g., Ni) catalyst Slow polymerization of C n H m radicals on the Ni surface, eventually forming an encapsulating film Homogeneous gas-phase chemistry Thermal cracking of hydrocarbon Deposition of C precursors on catalyst Effects No deactivation of Ni surface Breakdown of catalyst and increasing pressure drop Progressive deactivation Encapsulation of catalyst particle Deactivation and increasing pressure drop Temperature > 450 C ( 720 K) < 500 C ( 770 K) > 600 C ( 870 K) Critical parameters Intermediate temperature Low H 2 O/C n H m ratio Low activity Aromatic feed No enhanced H 2 O adsorption Low temperature Low H 2 O/C n H m ratio Low H 2 /C n H m ratio Aromatic feed High temperature High void fraction Low H 2 O/C n H m ratio High pressure Activity of catalyst 22

23 Figure 1 Adsorption of C n Hm Surface reactions produce chemisorbed C Ni particle Dissolution of carbon layers at front of Ni; Diffusion through Ni particle; Precipitation at rear of Ni Growth of carbon fiber Support 23

24 Figure 2 T (K) CH 4 C + 2H2 600 T (K) CO C + CO ln(k f ) or ln(k gr ) Ni-MgO [Rostrup-Nielsen, J. Catal., 27(3): , 1972.] Graphite [NASA] ln(k f ) or ln(k gr ) Graphite [NASA] Ni-MgO [Rostrup-Nielsen, J. Catal., 27(3): , 1972.] -6 Ni-SiO2 [de Bokx et al., J. Catal., 96(2): , 1985.] /T 10 3 (K -1 ) 1 Ni-SiO2 [de Bokx et al., J. Catal., 96(2): , 1985.] /T 10 3 (K -1 ) 24