Exploring Conditions That Enhance Durability and Performance of a

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Exploring conditions that enhance durability and performance of a tubular solid oxide fuel cell fed with simulated biogas Courtney M. Jones, Joshua Persky, and Ravindra Datta Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02362 • Publication Date (Web): 07 Oct 2017 Downloaded from http://pubs.acs.org on October 9, 2017

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Submitted to Energy & Fuels

Exploring conditions that enhance durability and performance of a tubular solid oxide fuel cell fed with simulated biogas Courtney M. Jones,‡ Joshua Persky,# and Ravindra Datta‡*

Abstract Tubular solid-oxide fuel cells (t-SOFCs) fed directly with biogas, an equiproportioned mixture of CH4 and CO2 produced by fermentation of organic waste, are subject to nonuniform thermal stresses due to internal dry reforming in anode entrance region, coupled with structure exfoliation due to coking, resulting eventually in cell rupture. The integral tSOFC is of practical interest, although many laboratory studies are conducted in differential button cells. Guided by mechanistic understanding and a robust thermodynamic model, the operating temperature and biogas feed composition were explored experimentally in order to enhance durability and performance of the t-SOFC. Thus, a temperature of 900 °C, a feed CH4/CO2 ratio of 45/55, and a fuel utilization ≥ 25% were found to be optimal. The cell durability, performance, efficiency, and outlet gas composition at OCV as well as at different loads, were found to be in accord with a thermodynamic analysis and mechanistic understanding based on a set of four independent overall reactions (OR). It is shown that the OCV is independent of the chosen electrodic OR. In addition to single tube experiments, a 5tube SOFC pilot-unit was preliminarily tested as a step toward scaleup of this promising renewable energy technology. Keywords: Tubular SOFC, dry reforming, biogas, Ni/YSZ, coking, SOFC durability. ‡ Fuel Cell Center, Department of Chemical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA. # Protonex Technology Corp., 153 Northboro Road, Southborough, MA 01772, USA. * Email: [email protected]

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Graphical Abstract.

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1. Introduction Among the available renewable energy options, biogas is especially attractive because of its ubiquity, low cost, and a significant potential as a distributed energy resource.1 Biogas comprises mainly of an equiproportioned mixture of CH4 and CO2, both greenhouse gases, produced from anaerobic digestion of sewage sludge or organic residue in man-made biodigesters, or naturally in urban, industrial, or agricultural waste sites. When generated in situ in landfill or livestock sites, biogas is usually flared or vented, contributing significantly to greenhouse gas emissions, while squandering a significant renewable energy resource. In fact, 70% of methane emissions are anthropogenic, mainly from fossil fuel mining, landfills, and livestock sites, the rest being from natural sources.2 When harvested in a biodigester, on the other hand, which are not uncommon in rural communities of developing countries,3 biogas can be directly tapped for energy. However, it is a low-calorie fuel gas with a dilute and variable CH4 fraction, depending upon the raw biomass source and the digestion process. The typical biogas composition is: CH4 = 35-75%, CO2 = 25-65%, H2 = 1-5%, and N2 = 0.3-3%, along with traces of H2S, NH3, halides, and siloxane.1 Because of dilution by a large amount of CO2, it cannot be utilized effectively in traditional burners, or in IC, or heat engines.4 However, this is not an issue for solid-oxide fuel cells (SOFCs), which can efficiently utilize biogas directly with little pretreatment for electric power generation.2 This is because SOFCs can utilize both CH4 and CO2 via internal dry reforming, the latter as a source of oxygen, to produce a syngas mixture with a higher energy content, wherein both CO and H2 are electro-oxidized to produce current. Their high operating temperatures also impart SOFCs with tolerance to many biogas trace impurities, along with a high efficiency due to the low overpotentials and the high quality

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waste heat.5 Furthermore, internal dry reforming of biogas within the SOFC anode not only obviates any external reforming, but in situ thermal coupling of the endothermic dry CH4 reforming with the exothermic H2 and CO electro-oxidation reactions within the anode provides efficient heat integration. In short, if widespread utilization of biogas in SOFCs for distributed power generation were realized, it would provide multiple environmental benefits, by combining: 1) organic waste recycle, 2) carbon abatement, 3) clean and efficient electric power generation, and 4) rural electrification. The high operating temperature of the SOFC, in fact, offers both benefits and challenges. The former include absence of an external reformer, high electrical and thermal efficiency, and direct electro-oxidation of CO at the anode.6 The challenges include sealing, thermal mismatch, interconnect, and other material issues.7 On the other hand, lower temperature fuel cells require purified H2 produced via external reforming,8 along with the use of precious group metal electrocatalysts, the key techno-economic challenge in their commercial viability,9 while providing lower efficiency due to higher overpotentials. Clearly, there is a strong motivation to continue to work toward understanding and overcoming the current technological challenges of SOFCs. The tubular SOFC (t-SOFC) is typically more robust in terms of its ability to handle both thermal and mechanical stresses, while providing better sealing because of the low ratio of sealing area to active area as compared to a planar SOFC.10 On the other hand, planar cells provide easier current collection and can be treated as differential units, with relatively uniform gas composition and temperature, making laboratory data interpretation easier. On the other hand, tubular cells (like tubular reactors) are integral units with higher fuel

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utilization but with potentially significant axial variation of gas composition and temperature. There have been mainly four research groups so far that have investigated the direct use of biogas in SOFCs. Thus, Staniforth and Kendall11,12 at Keele University, UK, were the first to demonstrate the feasibility of a micro t-SOFC with a simulated biogas feed at 850 °C. Coking was found to be the key issue, addressed to some extent by humidifying the feed, and more effectively by feeding equimolar amounts of air mixed with the biogas to the anode. They also tested real biogas from a landfill, and found degradation of performance as a result of both sulfur poisoning of the Ni catalyst as well as coking. Yentekakis and coworkers at the Technical University at Crete, Greece, investigated two SOFC technologies: 1) an intermediate temperature (600-640 °C) SOFC based on gadolinia doped ceria (GDC) electrolyte,13 and 2) a higher temperature (875 °C) SOFC based on yttria stabilized zirconia (YSZ) electrolyte,14 in planar geometry and with simulated biogas feed. They found the equimolar feed of CH4/CO2 as optimal, providing a relatively stable performance of roughly 50-60 mW cm'( . Subsequently, they confirmed long-term (~600 h) stability of both these technologies.15 The research group at Kyushu University, Japan, used a button cell, first with synthetic biogas with equimolar CH4/CO2 and large amounts of added water,16 and subsequently with a real biogas with CH4/CO2 ratio of 1.8 without humidification but diluted with N2,17 and found that both provided a stable performance even with 1 ppm H2S, but at the high operating temperature of 1,000 °C. They also found that the highest CH4 consumption rate was for the equimolar feed at 900 °C.18 The open circuit voltage (OCV) was found to be in the order of increasing CH4/CO2 ratio. However, anodic overpotential also increased with increasing

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CH4/CO2 ratio. Subsequently, they used real biogas from a digester directly in a button cell at 800 °C after desulfurization.19 The CH4/CO2 ratio in the biogas fluctuated between 1.4 to 1.9 because of the variability of organic waste feed or digester operating conditions, causing a corresponding fluctuation in the cell voltage of around 50mV. To avoid coking, however, equal amounts of air were added to the biogas, resulting in relatively stable operation for a month. The most comprehensive experimental and theoretical investigation so far has been conducted by the research group at Politecnico di Torino, Italy, who used both planar20 and tubular (Acumentrics)21,22 cells at the moderate temperature of 800 °C. To avoid coking, however, they added a mol of CO2 for every mol of the 60/40 CH4/CO2 biogas feed. They also monitored anode exit gas compositions under OCV to check the extent of internal reforming at 800 °C. Finally, they analyzed,23 built, and tested a pilot plant24 in Turin under the SOFCOM project of EU, that directly coupled: 1) an anaerobic digester to produce biogas from waste, 2) a gas cleaning section, and 3) a 500 W 40 cell SOFC stack. The system was able to generate 16 A, and roughly 500 W, with a feed utilization 𝑈* = 55% and a fuel cell electrical efficiency 𝜀-,/0 ≈ 34%. The main reasons for cell degradation and failure are coke buildup25 and thermal stresses,26 in addition of course to sulfur.25 Takahashi et al.,27 experimentally investigated the temperature distributions in an operating SOFC via thermography, and found large spatial temperature gradients in the entrance region. Carbon deposition at the Ni/YSZ anode can further cause irreversible damage to the intricate anode structure through metal dusting,28 along with particle encapsulation and three-dimensional expansion via dissolution into the Ni/YSZ cermet. This not only increases the resistance of the electronically and ionically

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conductive pathways,29 but can also cause dusting in the anode and electrolyte layers leading to catastrophic cell rupture.30 In short, while biogas fed direct SOFC has been shown to be promising, it has been found necessary to add large amounts of oxygenated diluent (CO2, water, air) to the biogas anode feed to avoid coking. Further, operating conditions for optimized performance and durability under high fuel utilization have not yet been fully explored, which is the purpose of this paper, along with using biogas directly with little or no dilution with an oxygenate. The experimental investigations are coupled with a thorough thermodynamic analysis and mechanistic insights to explore conditions of temperature and feed composition that enhance durability and performance. While more detailed global kinetic,21 and even microkinetic,31 models of internal reforming are available, we show that significant insights can be obtained even with a simple but careful thermodynamic analysis. In fact, we find that even under load conditions, a quasi-equilibrium (QE) treatment of the major internal reforming reactions suffices due to the high operating temperature.

2. Experimental A flow diagram of the test apparatus is shown in Figure 1, wherein the t-SOFC is enclosed within a tubular furnace and connected to various gas cylinders via mass flow controllers and to a load box and data acquisition system, along with a mass spectrometer (MS) for anode effluent gas analysis. The cells used in this study were fabricated in-house at Protonex, each cell with an active area of about 32 cm2, a length of 100 mm and a diameter of 10.2 mm. The anode-supported cells had a nickel-ytrria stabilized zirconia (Ni-YSZ) anode, with a thickness of about 1 mm, a YSZ electrolyte, about 15 µm thick, and a lanthanum strontium cobalt ferrite (LSCF) cathode, with a thickness of about 30-50 µm. For consistency, a new cell

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was used for each new experimental run. It was established beforehand that the manufacturing process was sufficiently consistent to ensure that each new cell provided reasonably uniform performance. High-purity gas bottles were obtained from Maine Oxy. The gas flow rates were controlled using Alicat Scientific mass flow controllers (model number: MC-2SLPM-D/5M). The total fuel gas flow rate was maintained constant at 0.2 SLPM for all experiments, but the ratio of CH4 flow to CO2 flow rate was varied to attain a desired feed ratio by mixing gases online. The air flowrate through the cathode was maintained at 2 SLPM for all experiments. The furnace was equipped with K-type Omega thermocouples (model number, CHAL-02024). Through interconnects, the SOFC was connected to an American Reliance, Inc. (AMREL) load bank (model number, FEL 60-1) used to collect polarization data with a data acquisition software developed at Protonex. Once the SOFC was placed in the furnace (Figure 1), the cell was heated to 900 °C with H2 flowing through it for 3 h to reduce the nickel (II) oxide into metallic nickel. Next, the cell was operated under a constant current density for 1 h with a H2 feed, and then polarization data were obtained for H2. Thereafter, the feed was switched from H2 to the simulated biogas, and a polarization plot was obtained. Finally, the cell was operated under a constant current density with the simulated biogas feed for 150 hours, to evaluate the degradation rate. The shut-down procedure involved cooling the cell while H2 flowed again through the cell. The overall experimental study was divided into the following objectives: 1) to establish the optimal operating temperature for reduced coking and degradation, 2) to fine-tune the feed composition around the reported equimolar CH4/CO2 optimal without significant addition of diluents or oxygenates as commonly done so far,

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3) to determine the effect of fuel utilization on performance, efficiency, and durability, 4) to determine if modest humidification of the feed mixture, as might be encountered in a gas issuing from a biodigester, might improve the performance and/or lifetime, 5) to evaluate the extents of internal reforming as well as H2 and CO electro-oxidation reactions via effluent analysis for comparison to thermodynamic predictions, and 6) to preliminarily evaluate the performance of a 5-cell t-SOFC assembly vis-à-vis that of a single cell. A key objective of this study, thus, was to investigate the effect of temperature and especially the composition of biogas on performance and lifetime of t-SOFC by focusing in the neighborhood of the optimal CH4/CO2 ratio of 50/50 reported in the literature.15,18 However, the reports so far have studied this effect only in broad jumps.15,18 For this study, thus, the synthetic biogas CH4/CO2 ratio was varied over a narrower range as follows among five different feeds: 40/60, 45/55, 50/50, 55/45, and 60/40. The fuel utilization is typically calculated as a ratio of the actual current I to the maximum current 𝐼567 that would result if all of the CH4 (denoted as the key species, A) were consumed, i.e., 𝑈* = 𝐼/𝐼567 , where 𝐼567 = 8𝐹𝑛A,= , i.e., 𝑈* ≡

𝐼 8𝐹𝑛A,=

(1)

where F is Faraday’s constant, 8 = 𝑛e@ is the number of electrons per CH4 molecule, and 𝑛A,= is the methane molar feed flow rate. This calculation of fuel utilization can, in fact, be slightly refined by using instead the equilibrium CH4 conversion, as discussed later on. To investigate the effect of modest humidification of the biogas mixture on the performance and/or lifetime of the cell, water vapor was added to the gas feed mixture by bubbling the

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CO2 stream through a 2-L flask filled about half way with water at room temperature, before being mixed with the CH4 feed stream. The flask was weighed before and after each run. The feed moisture level was thus estimated as roughly 3% water. Further, to investigate the extents of the internal reforming as well as the electro-oxidation reactions, for some of the experiments the fuel cell effluent gas was analyzed via the mks Spectra Products’s Cirrus™ MS. The partial pressure of each species was recorded via mks’s Process Eye Professional software. These values were corrected for a species’ ionization probability. In this manner, the mole fractions of all the species were calculated. To confirm the calibration of the MS data thus acquired, a series of CO/H2 blends of known concentrations were tested. Finally, preliminary experiments were performed with a 5-cell t-SOFC assembly in order to compare its performance to that anticipated based on a single cell performance. For the 5cell unit, the total fuel flow rate was thus set at 1 SLPM (0.2 SLPM x 5 cells) for the 45/55 CH4/CO2 feed ratio. The reduction/startup procedure for the 5-cell unit was similar to that for the single-cell test; however, the stack assembly was reduced at 700 °C instead of 900 °C to avoid any material issues while reducing the cells at OCV for 3 hours. Thus, a polarization plot was generated for the stack running under H2. After that, the temperature was brought up to 900 °C and the fuel switched over from H2 to the biogas feed mixture.

3. Thermodynamic Analysis Although very detailed transport and kinetic models exist,31 a robust thermodynamic analysis can provide powerful insights. It is undertaken here to shed light on the effect of temperature and feed composition on performance and durability observed experimentally.

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It is, in fact, shown later on that a quasi-equilibrium (QE) analysis for the internal reforming reactions is adequate in explaining results even under load conditions. 3.1 Multiple Reaction Equilibria There is ambiguity in the literature as to which overall reactions (ORs), reforming and electrochemical, are needed to describe appropriately the overall chemistry in a methane fed SOFC. Thus, many of the different ORs proposed in the literature are listed in Table 1.32,33 In addition to the numerous reforming ORs proposed in the literature,33 Table 1 includes the most common electrodic ORs, namely, the hydrogen oxidation reaction (HOR), OR4, and the carbon monoxide oxidation reaction (CMOR), OR5.34 Other plausible reactions are included, e.g., methane partial oxidation (MPOX), OR10,18 or even methane full oxidation (MFOX), OR11, although the direct electro-oxidation of CH4 may be kinetically limited.18,32 The standard reaction enthalpy changes at standard temperature ∆𝐻Co (𝑇CG* ) provided in Table 1 are based on thermodynamic data for the species obtained from NIST.35 In addition, Takahashi et al.,27 have provided reaction enthalpies of many of these ORs at 1100 K. Here, we have assumed C as graphite (i.e., with zero enthalpy of formation), although alternate forms of carbon can possess thermodynamic properties that are quite different.36 Under the methane dry reforming (MDR) conditions at 700-850 °C, thus, two forms of carbon are said to be produced:37 1) in the shape of tubular whiskers of diameter equivalent to the Ni metal crystal, and 2) as platelets or films that encapsulate the metal particles. However, both of these forms are graphitic. The first question that needs to be addressed is how many of the ORs listed in Table 1 are needed for a theoretical analysis. It turns out that, in fact, this may be accomplished by adopting any set of R = 4 “independent” reactions from this set of ORs. Thus, the number of

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independent ORs needed for a thermodynamic analysis of the system was arrived at by first counting the number of terminal species (i.e., those that appear in the overall process): CHK 𝑔 , CO( 𝑔 , CO 𝑔 , H( 𝑔 , H( O 𝑔 , O( 𝑔 , and C 𝑠 , i.e., n = 7. This list includes C formed at the anode, as well as the O( in the air that is fed to the cathode. These terminal species are further comprised of e = 3 elements ℓ (i.e., ℓ = C, H, O). Then, the number of independent ORs needed for a thermodynamic, or presumably for a kinetic, analysis,38 R = n – e = 4. Here, we have simply adopted the first four ORs listed in Table 1, namely, the three dryreforming reactions, OR1, OR2, and OR3, and one electrodic reaction, OR4: kJ ; ∆𝑆So = +256.63 mol kJ 𝑂𝑅( : CO( + H2 ⇄ CO + H2 O ; ∆𝐻(o = +41.16 ; ∆𝑆(o = +42.03 mol kJ 𝑂𝑅b : CH4 ⇄ C + 2H2 ; ∆𝐻bo = +74.9 ; ∆𝑆bo = +80.79 mol kJ 𝑂𝑅K : H2 + 1 2 O2 ⇄ H2 O ; ∆𝐻Ko = −241.8 ; ∆𝑆Ko = −44.35 mol 𝑂𝑅S : CH4 +CO2 ⇄2CO+2H2 ; ∆𝐻So = +247.33

J mol. K J mol. K (2) J mol. K J mol. K

However, this set of the 4 independent ORs chosen is not unique. In fact, any set of 4 ORs that contain among them all the terminal species would suffice. Clearly, however, these must include at least one electrodic reaction, as O2 participates only in these, while the other three can be internal reforming reactions. For instance, the CMOR may alternately be used to replace HOR in the chosen independent set. However, even though it has been shown to indeed occur within a SOFC,39 it is not needed for supplementing the chosen set of 4 independent ORs in Eq. (2). Thus, when CMOR (𝑂𝑅e ) is combined with the RWGS (𝑂𝑅( ), HOR (𝑂𝑅K ) results, i.e., 𝑂𝑅e + 𝑂𝑅( = 𝑂𝑅K ,39 and their thermodynamic state properties follow the same linear combination via Hess’s law. A choice of either HOR or CMOR, thus, suffices and, in fact, results in the same value for Nernst potential in a SOFC, as

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shown below. On the other hand, if it is desired to include both of these electrodic reactions (OR4, OR5), only two other reforming reactions are needed that account for the remaining terminal species, for instance OR1, and OR3. The Gibbs free energy change for the rth overall reaction (𝑂𝑅C ), ∆𝐺C ≡

i hjS 𝜈Ch

𝜇h , and using

in it the usual constitutive equation for the electrochemical potential 𝜇h , results in ∆𝐺C = −𝑅𝑇ln𝐾C + 𝑅𝑇ln𝑄C + 𝑛Ce@ 𝐹𝑉 ; (𝑟 = 1,2, … . , 𝑅)

(3)

Here, the reaction equilibrium constant 𝐾C , and the reaction quotient 𝑄C , respectively, are ∆𝐺Co 𝐾C ≡ exp − ; 𝑄C ≡ 𝑅𝑇

i u

𝑎h vw ; (𝑟 = 1,2, … . , 𝑅) hjS hxe@

(4)

where, ∆𝐺Co is the standard Gibbs free energy change of the rth OR (i.e., for pure species, as indicated by superscript o) that varies with temperature T, 𝜈Ch is the stoichiometric coefficient of the species i, 𝑎h its activity, R denotes the gas constant, but also the number of independent ORs (𝑟 = 1,2, … . , 𝑅), and V is the cell potential. At equilibrium, denoted by subscript “e,” when ∆𝐺C = 0, and when 𝑉 = 𝑉= , i.e., the Nernst potential, we write Eq. (3) for each of the four selected independent ORs chosen above. For the nonelectrodic reactions chosen, OR1, OR2, and OR3, with the number of electrons in the OR, 𝑛Ce@ = 0, along with ∆𝐺C = 0, it results in the Waage and Guldberg law of mass action i u

𝐾C = 𝑄C,G =

𝑎h,Gvw ; ( 𝑟 = 1,2,3) hjS hxe@

(5)

The standard Gibbs free energy used to determine the equilibrium constant is a function of temperature. For this, we write it as, ∆𝐺Co = ∆𝐻Co − 𝑇∆𝑆Co ,40 and further assume that the standard entropy change ∆𝑆Co and standard enthalpy change ∆𝐻Co of an OR to remain constant

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with temperature. Then, ∆𝐺Co varies linearly with temperature, and the equilibrium constant as a function of temperature then takes the van’t Hoff form ∆𝐻Co 1 1 𝐾C = 𝐾C,yvz{ exp − − 𝑅 𝑇 𝑇CG*

; ( 𝑟 = 1,2,3)

(6)

For an electrodic reaction, on the other hand, at equilibrium (with ∆𝐺C = 0, and 𝑉 = 𝑉= ), with the use of the relation ∆𝐺Co = ∆𝐻Co − 𝑇∆𝑆Co , Eq. (3) reduces for the Nernst potential 𝑉= to o 𝑉= = 𝑉C,=,y + vz{

∆𝑆Co 𝑅𝑇 𝑇 − 𝑇CG* − ln𝑄C,G ; ( 𝑟 = 4) 𝑛e@ 𝐹 𝑛e@ 𝐹

(7)

o o where the standard Nernst potential at reference temperature, 𝑉C,=,y ≡ −∆𝐺C,y /𝑛e@ 𝐹. vz{ vz{

For the four relations represented by Eqs. (5) and (7) for the chosen independent ORs, the reaction quotient mass action relations are next written in terms of species equilibrium mole fractions 𝑥h 𝑄S,G

( 𝑥}~,G 𝑥•( € ,G 𝑥•( € ,G 𝑥}~,G 𝑥•€ ~,G 𝑥•€ O,G = ; 𝑄(,G = ; 𝑄b,G = ; 𝑄K,G = (8) 𝑥}•• ,G 𝑥}~€ ,G 𝑥}•• ,G 𝑥}~€ ,G 𝑥}•• ,G 𝑥•€ ,G 𝑥~€ ,G

where we have replaced species activities by their mole fractions, i.e., 𝑎h = 𝛾h 𝑥h ≈ 𝑥h , assuming ideal gas mixtures, i.e., the activity coefficients 𝛾h → 1, while the activity of solid carbon, as is common, is assumed as unity, 𝑎C = 1.41 The species equilibrium mole fractions in the reaction quotient terms 𝑄C,G for the above four ORs can further be written in terms of four dimensionless equilibrium reaction extents, 𝜀S,G , 𝜀(,G , 𝜀b,G , and 𝜀K,G , based on mass balance as described below. Then, the above four independent nonlinear algebraic relations (Eqs. 5 and 7, along with Eq. 8) can be solved via numerical root finding (e.g., using Mathematica®) for the four unknown equilibrium reaction extents, e.g., if the cell OCV were available, say in the presence of a small crossover current due to gas and electronic leakage, when 𝜀K is finite even when no external current is drawn.

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For true thermodynamic equilibrium, of course, the extent of the electrodic OR, 𝜀K,G = 0, and the OCV is then equal to the Nernst potential, 𝑉= . Then, the first 3 algebraic equations (Eq. 5) are independent of the 4th, and can be solved first to find the three equilibrium reaction extents 𝜀S,G , 𝜀(,G , and 𝜀b,G ,, followed by their use in the 4th algebraic relation (Eq. 7) to find the Nernst voltage 𝑉= . As mentioned above and further elaborated later on, the hence determined Nernst potential is independent of the electrodic OR chosen. In other words, cell voltage at equilibrium would be the same, had CMOR (𝑂𝑅e ) been chosen as the 4th independent reaction instead of HOR (𝑂𝑅K ), as shown theoretically by Li and Chyu,39 and experimentally by Eguchi et al.34 3.2 Species Mass Balance The gas mole fractions in Eq. (8) are related to the dimensionless reaction extents as follows. From species mass balance applied to the SOFC (Figure 1b), the molar flow rate 𝑛h of a species i at an axial location within a tubular flow SOFC is related to the R independent dimensionless reaction extents as follows42 …

𝑛h = 𝑛h,= + 𝑛A,=

(9)

𝜈Ch 𝜖C (𝑖 = 1, 2, … , 𝑛) CjS

where 𝑛A,= is the feed flow rate of the key reactant A (CH4), 𝑛h,= is that of a species i, and the dimensionless reaction extent, 𝜖C ≡ 𝜉C /𝑛A,= , where the reaction extent, 𝜉C ≡

‰

𝑟C 𝑑𝑉 , where

𝑟C is the rate of 𝑂𝑅C . For a single electrodic reaction (e.g., 𝑂𝑅K ), when a current I is drawn externally and 𝐼Š is any internal crossover or leakage current, due to any reactant crossover and/or a finite electronic conductivity of the electrolyte layer, the total current, 𝐼‹ = 𝐼 + 𝐼Š , and the corresponding extent of 𝑂𝑅K

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𝜖K =

𝐼 + 𝐼Š 2𝐹𝑛A,=

Page 16 of 67

(10)

which further shows that under the (steady-state) OCV conditions 𝜖K = 𝐼Š /2𝐹𝑛A,= , while for true equilibrium conditions, i.e., when there is no internal or external current, the equilibrium extent, 𝜖K,G = 0. Equation (10) may be written in the alternate form 𝜖K ≈ 4𝑈*

(11)

where fuel utilization defined by Eq. (1) is used, along with the assumption that 𝐼Š ≪ 𝐼. Summing the mass balance relations, Eq. (9), over all the n terminal species, the total molar gas flow rate 𝑛 at an axial location in the anode tube42 𝑛 = 𝑛A,=

1 + 𝑥A,=

…

Δ𝜈C 𝜖C

(12)

CjS

where 𝑥A,= is the feed mole fraction of the key reactant A, and the mole change for the rth OR, i

Δ𝜈C =

𝜈Ch (𝑟 = 1, 2, … , 𝑅)

(13)

hjS

For 𝑂𝑅S , e.g., the reaction mole change Δ𝜈S = +2, while for 𝑂𝑅( , Δ𝜈( = 0, i.e., there is no change in moles in the RWGSR. Further, Δ𝜈b = +2 in the gas phase for the MP, the C being in solid phase, and also Δ𝜈K = 0, since oxygen (as O(' ) enters the anode chamber via the solid electrolyte. Finally, the mole fraction of the gas phase species i is obtained from 𝑥h ≡ 𝑛h /𝑛, resulting in 𝑥h =

Θh + …CjS 𝜈Ch 𝜖C (𝑖 = 1, 2, … , 𝑛) 1/𝑥A,= + …CjS Δ𝜈C 𝜖C

(14)

where the molar feed ratio of species i to that of the key species, Θh ≡ 𝑛h,= /𝑛A,= . For equilibrium conditions, of course, 𝜖C = 𝜖C,G .

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Energy & Fuels

The species mole fractions for the five anode gas-phase terminal species participating in the four ORs are obtained from the above derived stoichiometric relation for species i 𝑥CH4 =

ΘCO2 − 𝜖S − 𝜖( 1 − 𝜖S − 𝜖b ; 𝑥CO2 = ; 1/𝑥CH4 ,= + 2𝜖S + 𝜖b 1/𝑥CH4 ,= + 2𝜖S + 𝜖b

𝑥H2 O =

ΘH 2 O + 𝜖( + 𝜖K ΘH + 2𝜖S − 𝜖( + 2𝜖b − 𝜖K ; 𝑥H2 = 2 ; 1/𝑥CH4 ,= + 2𝜖S + 𝜖b 1/𝑥CH4 ,= + 2𝜖S + 𝜖b

𝑥CO =

(15)

ΘCO + 2𝜖S + 𝜖( 1/𝑥CH4 ,= + 2𝜖S + 𝜖b

These relations may be substituted into the reaction quotient relations for the four reactions, i.e., in Eq. (8), which in turn, when used in Eq. (5) for the three internal reforming reactions, and in Eq. (7) for the electrodic reactions, can be solved simultaneously numerically to find 𝜖S,G , 𝜖(,G and 𝜖b,G , along with the Nernst potential 𝑉= based on the assumption that 𝜖K,G = 0 at true equilibrium. Actually, even for a non-equilibrium case, the first 3 ORs are usually deemed to be at equilibrium at the typical SOFC temperatures, while 𝜖K can be determined from the total current or fuel utilization (Eq. 10, or Eq. 11). These can then be used back in the above relations to find the gas composition at the exit, as illustrated later on. 3.3 Element Mass Balance Let us also employ element mass balance to obtain relations for the atom fractions 𝑥ℓ (element, ℓ = C, H, O), which of course, remain constant throughout the SOFC regardless of reactions, as elements are conserved in reactions. Assuming that the anode feed comprises only of CH4, CO2, and H2O, along with O2 at the cathode, the element balance provides

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𝑥C =

Page 18 of 67

1 + ΘCO2 4 + 2ΘH2 O ; 𝑥H = ; 5 + 3(ΘCO2 + ΘH2 O ) + 4𝑈* 5 + 3(ΘCO2 + ΘH2 O ) + 4𝑈*

2ΘCO2 + ΘH2 O + 4𝑈* 𝑥O = 5 + 3(ΘCO2 + ΘH2 O ) + 4𝑈*

(16)

where we have used Eq. (11) for 𝜖K . Determination of the element fractions 𝑥C , 𝑥H , and 𝑥O , hence locates the elemental makeup of the system on the ternary diagram, where the pure elements C, H, and O are located at the apexes of an equilateral triangle,43 so that a given feed composition and an operating current (utilization) can be represented as a point on the graph. Such plots are commonly used to indicate the propensity for coking of a system. 3.4 Energy Balance and Cell Efficiency We will obtain efficiency correlations based on the use of First law, or energy balance, applied to the two different SOFC sub-systems identified by the dotted boundaries shown in Figure 1 (b). At steady-state, this takes the form42 Δ𝐸‹ = 𝑄 + 𝑊- ≡

𝑊 𝜀-

(17)

where Δ𝐸‹ is the net (out – in) energy efflux from the system, and 𝑄 is the rate of entropic energy dissipation by the system to the surroundings. Thus, Δ𝐸‹ represents the maximum capacity of the system for useful work. Only some of this potential is realized in the SOFC as electric work produced (−𝑊- ), while the remaining is dissipated as heat (−𝑄). Consequently, the electrical efficiency of the system, 𝜀- ≡ 𝑊- /∆𝐸‹ . In terms of the electrical efficiency, the RHS of Eq. (17) can alternately be written as 𝑊- /𝜀- . (Note that as per the IUPAC convention, both rate of heat exchange and rate of work exchange are positive when added to the system from the surroundings.)

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Energy & Fuels

The system defined by the outer dashed boundary in Figure 1 (b) consists of the tubular SOFC fed via stream 𝑠= containing a biogas mixture of CH4 and CO2. The fuel cell effluent (stream 𝑠S ) passes through a furnace, or an oxidizer, OX, wherein any combustible components in it are burnt to produce heat. A part of this, 𝑄… , is recycled to the fuel cell to replenish the endothermic heat of MDR reactions within it, as well as to compensate for heat loss so as to maintain isothermal conditions, while the rest, −𝑄’Š , is rejected. On the other hand, the system enclosed by the inner dashed boundary shown in Figure 1 (b) comprises simply of the SOFC unit with convective transport of energy in and out of it via flowing gases, along with heat exchange at its surface, including −𝑄/0 , dissipated due to internal kinetic and transport resistances, while producing useful electric work −𝑊- . In addition to these two sub-systems (Figure 1b), however, it should be mentioned that there are other possible sub-systems of interest for such efficiency calculations, depending on the overall design of the SOFC power plant.44 For instance, the high-quality heat produced by the combustor (−𝑄’Š ) and by the fuel cell (−𝑄/0 ) may be utilized in a heat engine to produce additional electric power, along with recuperators to recover the waste heat, e.g., to pre-heat the biogas feed. Such systems for cogeneration and/or combined heat and power (CHP) are of great practical interest,44 and promise very high overall efficiency. However, for brevity, we will consider only the two systems defined in Figure 1 (b). Let us first apply energy balance to the system defined by the outer boundary in Figure 1 (b). Consequently, the rate of heat loss, −𝑄 = − 𝑄/0 + 𝑄’Š . Further, Δ𝐸‹ = 𝐸‹,( − 𝐸‹,= . Here, the total energy carried by a gas 𝐸‹,“ in a particular stream 𝑠“ is

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Page 20 of 67

i o 𝑛h,“ −∆𝐻0,h

𝐸‹,“ =

(18)

hjS o Here, the heat of combustion of a species, ∆𝐻0,h , is the same in any stream (Figure 1b) because

of the isothermality assumption. As shown in Figure 1 (b), assuming complete combustion within the combustor, the exiting gases from the system contains only the products of complete combustion, mainly, CO2 and H2O. Consequently, with 𝐸‹,( = 0, so that Δ𝐸‹ = −𝐸‹,= . Further, using −𝑊- = 𝐼𝑉 in terms of the total cell current I and the cell voltage V, and recognizing that methane (A) is the only combustible fuel in the feed (Eq. 18), the system electrical efficiency then 45,46 𝜀-,”•–‹G5 =

𝐼𝑉 o 𝑛A,= −∆𝐻0,A

(19)

In fact, here the cell voltage V is also a function of the cell current I via the polarization relation, which may be assumed to be Ohmic, or linear, due to the high operating temperature of SOFCs,47 as further discussed later on. Next, we apply Eq. (17) to just the fuel cell enclosed by the inner dashed boundary shown in Figure 1 (b). For this case, the effluent in stream 𝑠S contains combustible components such as CO and H2 due to incomplete fuel utilization, as shown in Figure 1 (b), so that energy content of the exiting gases from the fuel cell, 𝐸‹,S ≠ 0, but is given by Eq. (18). Further, the SOFC is supplied with 𝑄… to compensate for the endothermic internal reforming reactions. Thus, in Eq. (17), the net energy input, Δ𝐸‹ = 𝐸‹,S − 𝐸‹,= − 𝑄… , and energy dissipation term, −𝑄 = −𝑄/0 . Next, using Eq. (9) for the species exit molar flow rates from the SOFC in Eq. (18), switching the order of the two summations, and rearranging

20


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Energy & Fuels

…

∆𝐻Co 𝜖C

𝐸‹,S − 𝐸‹,= = 𝑛A,=

(20)

CjS

where the enthalpy change of the OR, ∆𝐻Co = temperature,42 ∆𝐻Co 𝑇 = ∆𝐻Co 𝑇CG* +

i o hjS 𝜈Ch ∆𝐻0,h , which, in general, a function of

y ∆𝐶™ 𝑑𝑇, where ∆𝐶™ is the reaction heat capacity yvz{

change, here neglected, so that ∆𝐻Co 𝑇 = ∆𝐻Co 𝑇CG* , as listed in Table 1. For instance, using Eq. (10) for the extent of OR4, and assuming the extent of coking reaction to be negligible, while assuming the remaining two internal reforming reactions to be at QE, the net energy input into the fuel cell ∆𝐸‹ = 𝑛A,=

∆𝐻So 𝜖S,G + ∆𝐻(o 𝜖(,G +

∆𝐻Ko (𝐼 + 𝐼šG6› ) − 𝑄… 2𝐹𝑛A,=

(21)

Let us next assume that the rate of heat recycle is simply equal to the MDR endothermicity, i.e., 𝑄… = 𝑛A,= ∆𝐻So 𝜖S,G + ∆𝐻(o 𝜖(,G . In such a case, from Eq. (21), ∆𝐸‹ = ∆𝐻Ko (𝐼 + 𝐼šG6› )/(2𝐹). Thus, from 𝜀- ≡ 𝑊- /∆𝐸‹ and using −𝑊- = 𝐼𝑉, the fuel cell efficiency46 𝜀-,/0 =

𝐼 𝐼 + 𝐼šG6›

𝑉 o 𝑉567

œ•,ž

œ•,Ÿ

(22)

where the first term on the RHS is the current, or Faradaic, efficiency, 𝜀-, , while the second o is the voltage efficiency, 𝜀-,‰ , and 𝑉567 ≡ −∆𝐻Ko /2𝐹 = 1.253 V.

Alternately, in the above efficiency correlations, Eqs. (19) and (22), Eq. (1) may be used to replace the current I in terms of the fuel utilization 𝑈* . Thus, efficiency may be plotted either as a function of current I or as a function of fuel utilization 𝑈* . Let us also obtain a more accurate estimate of fuel utilization than that provided by Eq. (1), as limited by thermodynamics. Let us assume that the H2 produced by OR1 and by the reverse of OR2 (WGS) is fully consumed within the SOFC via OR4, so that its exit concentration is zero.

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Page 22 of 67

Then, so would be that of CO due to the pseudo-equilibrium assumed for OR2. In other words, CO may be construed to be oxidized indirectly. Then, using Eq. (9) for 𝑛H€ = 0, and for 𝑛CO = 0, while assuming 𝜖b → 0 (negligible coking), and combining the two relations, provides 𝜖K = 4𝜖S,G . Finally, using this in Eq. (10) provides the maximum current that the cell produces under these conditions, namely, 𝐼567,G = 8𝐹𝑛A,= 𝜖S,G . Using this in its definition, the equilibrium-limited fuel utilization, 𝑈*,G = 𝐼/𝐼567,G 𝑈*,G =

𝐼 8𝐹𝑛A,= 𝜖S,G

(23)

which is a modified form of Eq. (1) that corrects it for thermodynamic limitations via the equilibrium extent of OR1. This relation provides 𝐼567,G = 50 A, under the experimental conditions of this study. In fact, there are transport and thermodynamic limitations that preclude 100% fuel utilization.45

4. Results and Discussion 4.1 Effect of Operating Temperature and Feed Composition on SOFC Durability The rate of cell degradation and the corresponding estimated lifetime was determined by drawing a constant current I, or operating at a constant 𝑈* , at a given temperature and feed composition for a period of up to 150 hours, unless the cell failure occurred sooner. Figure 2(a) shows, for example, the resulting power generated by the cell as a function of time in an experiment conducted at 700 °C for an equimolar feed ratio of CH4 /CO2 , i.e., Θ}~€ = 50/50. Thus, even though, the equimolar feed is normally deemed safe from the viewpoint of coking,15,18 clearly, such is not the case at the moderate operating temperature of 700 °C, as the cell failed quickly, in less than 1/2 h, evidently as a result of severe coking.

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Energy & Fuels

For thermodynamic guidance to narrow down the safe operating domains of temperature and feed composition, we start by plotting in Figure 3 the standard Gibbs free energy for the ORs of interest, namely, OR1 (MDR), OR2 (RWGS), OR3 (MP), plus OR8 (CDCG), as a function of temperature. We include CDCG here, as it can be construed as a part of the MDR. In other words, we can argue that MDR (𝑂𝑅S ) comprises of two processes: 1) MP, namely, CH4 decomposition on the catalyst to form C (𝑂𝑅b ), followed by 2) CDCG, i.e., gasification of C by CO2 (𝑂𝑅¡ ), the reverse of the Boudouard reaction. The straight lines in Figure 3 result from the use of the relation ∆𝐺Co = ∆𝐻Co − 𝑇∆𝑆Co , along with the assumption that the standard entropy change ∆𝑆Co as well as the standard enthalpy change ∆𝐻Co of a reaction are constant with temperature.37, 40 Figure 3 is, in fact, in the spirit of the Ellingham diagram commonly used in metallurgy.41 As a rough guide, thus, a reaction may be deemed favorable when its standard Gibbs free energy change, ∆𝐺Co < 0. Clearly, MP becomes exergonic (∆𝐺Co < 0) at a temperature lower than the other ORs. Further, between simultaneous reactions (e.g., OR1 and OR3), the more exergonic reaction is favored. Thus, at a temperature of around 700 °C or lower, coking via methane pyrolysis is favored thermodynamically over MDR, even though it is kinetically significant only above 500 °C.37 Finally, in sequential reactions (OR3 and OR8), the balance can shift with temperature. Thus, at a temperature above roughly 750 °C, the coke gasification reaction (OR8) becomes increasingly favored over the coking reaction (OR3), the difference in their standard Gibbs energy indicated by the shaded region in Figure 3. However, the Ellingham-type diagram (Figure 3) is only roughly indicative of regions of coking propensity, as the analysis is for “standard” conditions (∆𝐺Co ), or for unit species activities, and thus only a function of temperature. In fact, the driving force for a reaction is

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Page 24 of 67

its Gibbs free energy ∆𝐺C , which is a function of both temperature and composition (Eq. 3), not the “standard” Gibbs energy change, ∆𝐺Co . Such a thermodynamic analysis in the literature involving temperature as well as composition is typically in the form of the triangular ternary diagram in terms of C, H, O composition of the feed, an example of which is provided in Figure 4.43 The thermal boundaries separating coking from non-coking regions in it are determined numerically based on minimization of the system total Gibbs free energy, typically by assuming an equilibrium quantity of solid graphite as one-millionth of the C present in feed.43 In Figure 4, thus, the C-H-O composition domain above a curve for a given temperature indicates feed conditions conducive to coke deposition, while that below it is deemed largely coke free. Using Eq. (16), further, we have plotted in Figure 4, the composition trajectories for increasing fuel utilization, from 𝑈* = 0 to 𝑈* = 1 in increments of 0.1 for different feed compositions, ΘCO2 ≡ 𝑛CO€ ,= /𝑛CH• ,= . Increasing the fuel utilization, or load, leads to an increasingly higher O/C ratio, thus reducing coking. This is in accord with the early numerical thermodynamic investigation of Koh et al.,48 who found that beyond a threshold current at their temperature of interest of 750 ºC, there was no coke formation. Clearly, for the methane rich biogas feed, as indicated by ΘCO2 = 0.5 in Figure 4, even the highest operating temperatures are perilous, except when operating at a significant 𝑈* , or load. In fact, even for equimolar feed (ΘCO2 = 1.0), the OCV conditions (𝑈* = 0) indicate a significant penchant for coking. Figure 4 thus indicates that for the generally recommended equimolar CH4/CO2 biogas feed, the operating temperature must be ≥ 900 °C to avoid coking,18 although most biogas-fed SOFC studies have used a lower temperature, albeit with significant feed dilution with an

24


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Energy & Fuels

oxidant. However, the large scale (0-100%) used for the atom fractions 𝑥ℓ in the conventional C-H-O plots compresses the domain of interest so that it is difficult to make subtle distinctions. To more carefully explore the choice of the operating temperature for an equimolar feed, thus, the equilibrium reaction extents 𝜖S,G , 𝜖(,G and 𝜖b,G , are plotted in Figure 5 as a function of temperature for an equimolar feed, i.e., for Θ}~€ = 1. This is done for the OCV case, i.e., when 𝜖K,G = 0, which, as indicated in Figure 4, represents the greatest proclivity for coking. The curves in Figure 5 are determined from the combination of Eqs. (5), (6), (8) and (15), for the case when Θ•€ ~ = Θ•€ = Θ}~ = 0, and 𝑥}•• ,= = 0.50. As indicated by its equilibrium extent, 𝜖b,G , it is seen that coking is the thermodynamically dominant reaction at temperatures < 700 °C, resulting, not surprisingly in very quick cell failure (Figure 2a). Of course, the actual extent would depend upon coking kinetics.49 At temperatures > 700 °C, MDR overtakes it significantly, but coking persists until around 880 °C, when finally 𝜖b,G → 0. It is further interesting that for temperatures higher than 880 °C, the reaction extent 𝜖b,G is < 0, i.e., beyond this temperature, OR3 tends to proceed in the reverse direction. In other words, coke gasification by H2 is indicated rather than CH4 pyrolysis. In addition, methanation (reverse of MDR, OR8) is favored (𝜖S,G < 0) below a temperature of 650 °C. Even at the higher and fairly common operating temperature of 800 °C, thus, the calculated equilibrium dimensionless extents for the case of equimolar feed are significant (Figure 5). In other words, the potential for coking remains very significant at this temperature. This is the reason for the addition of substantial amounts of CO2, water, or even air to biogas feeds in most studies reported in the literature.11,12,16,21,22 It is only at the substantially higher temperature of 880 °C, that the likelihood of coking becomes negligible. In short, an

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Page 26 of 67

operating temperature of around 900 °C is indicated to avoid coking for an equimolar CH4/ CO2 feed and with no other oxygenates mixed in. This is the reason for our choice of 900 °C as the operating temperature for a biogas-fed SOFC. Incidentally, once the reaction extents are numerically calculated as described above, the equilibrium gas phase composition following internal reforming of the feed can also be readily determined for a given feed with their use in Eq. (15). Thus, Figure 6 provides the cumulative equilibrium gas composition as a function of temperature for the same conditions as in Figure 5. In other words, the curves starting at the bottom for the equilibrium methane mole fraction, 𝑥CH4 ,G , provide sums of individual species mole fractions, while the difference between the curves are the individual species mole fractions. To confirm our choice of 900 °C as an appropriate operating temperature, arrived at via thermodynamic guidance, thus, Figure 2(b), shows the power generated at 900 °C by a single tubular cell as a function of time for a 150 h run, each under constant current conditions for feeds of different CH4/CO2 ratios in the vicinity of the equimolar feed. The fuel utilization 𝑈* was maintained at 25% for these experiments. It is seen that the electric power signal not only declines but gets more noisy with time for each feed composition. This is a direct indication of the progress of coking with time even at 900 °C, resulting in increased Ni and YSZ particle encapsulation or dislodging by carbon,29 thus leading to enhanced resistance for both electronic and ionic transport. In fact, it has been suggested that changes in cell resistance may hence be used to monitor in situ the extent of carbon formation as a function of time.29 This mechanism of coking and the resulting structural changes at the anode are schematically depicted in Figure 7,25 and discussed below.

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As evident from the noise in Figure 2(b), thus, the performance of the 50/50 (equimolar) and 55/45 CH4/CO2 (methane rich) feeds was poor after about the first 30 hours. On the other hand, the CH4/CO2 = 45/55, feed provided substantially more stable operation, even though the initial power was lower. The initial voltage produced actually increases with the CH4/CO2 ratio (Figure 2b). Somewhat inexplicably, however, the 40/60 CH4/CO2 feed also showed a fair degree of electrical signal noise after about the first 40 hours of operation. The degradation rates were estimated from the average slopes of the plots in Figure 2(b) for the different feed compositions. These slopes (in W h'S ) are: −0.015 for CH4/CO2 = 55/45; −0.0069 for CH4/CO2 = 50/50; −0.0012 for CH4/CO2 = 45/55; and −0.0061 for CH4/CO2 = 40/60. Thus, the CH4/CO2 = 45/55 ratio had the smallest degradation rate, and the longest calculated lifetime, roughly 5,000 h, for an assumed decline in power of 10%. Consequently, a feed ratio CH4/CO2 = 45/55 and the operating temperature of 900 °C were chosen for the remainder of this study. 4.2 The Effect of Feed Composition on SOFC Performance In addition to durability (Figure 2b), the SOFC performance at the hence chosen temperature of 900 °C was investigated as a function of feed composition. The goal was to allow a closer examination in the neighborhood of the optimal feed indicated above based on the durability consideration. In addition, fuel cell polarization for pure H2 and CO feeds was obtained. Figure 8(a) thus shows the polarization behavior of the t-SOFC for pure H2 and pure CO at 900 °C, while Figure 8(b) shows the polarization for all the five biogas feed ratios. Those for pure H2 and CO are also included in it for comparison, all at 900 °C. The total anode gas flow rate of 0.2 SLPM was maintained for both simulated biogas as well as for pure H2 and CO. It

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is noteworthy that polarization plots here plot cell voltage (V), or power (W), versus total cell current (A), rather than versus current density (A cm'( ), since these are integral cells. From Figure 8(a) it is evident that both CO and H2 can be directly electro-oxidized within the SOFC at this temperature. It has sometimes been conjectured50 that in the presence of both CO and H2, the main fuel electrochemically oxidized is H2, while CO is oxidized indirectly via the water-gas shift (WGS) reaction, i.e., CO + H( O ⇌ CO( + H( (reverse of OR2), followed by electro-oxidation of the hence formed H2 which, of course, also produces the water needed for the WGS reaction. However, since there is no H2O present in the experiments with a pure CO feed, it clearly shows that CO is directly electro-oxidized in the SOFC operating at 900 °C with a facility almost equal to that for H2 (Figure 8a). Thus, the overall cell resistance for CO from the average slope of the rather linear polarization curve, 𝑅¦Gšš,CO = 0.576 Ω cm( , while that for the pure H2, 𝑅¦Gšš,H€ = 0.515 Ω cm( . The essentially linear polarization curves may be explained because of the relatively small kinetic current densities in relation to the large exchange current densities at the high operating temperatures, when the BV kinetics can be linearized with the use of the approximation valid for small 𝑦, i.e., sinh'S 𝑦 ≈ 𝑦, where 𝑦 ≡ (𝑖/𝑖= )/2(1 − 𝑖/𝑖« ). Then, the polarization behavior may be described by51 𝑉 ≈ 𝑉= −

𝐿-« 𝑅𝑇 𝑖e@ ,Š − • 𝜎-«,e@ 𝐹𝜈®,e @ 𝑅𝑇 + • 𝐹𝜈0,e @

(𝑖 + 𝑖®,Š )/𝑖®,= 1 − (𝑖 + 𝑖®,Š )/𝑖®,«

(𝑖 + 𝑖0,Š )/𝑖0,= 𝐿-« − 𝑖 1 − (𝑖 + 𝑖®,Š )/𝑖0,« 𝜎-«

(24)

which predicts a linear polarization plot away from limiting current density, while closer to • @ it, the curve would bend more. Here, 𝜈®,e is the stoichiometric coefficient of electrons in the

rate-determining step (RDS) of the anode OR sequence of elementary steps, 𝑖®,= is the anode

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exchange current density, 𝑖®,Š is the crossover current density at the anode, and 𝑖®,« is the anode limiting current density, with corresponding quantities for cathode identified by the subscript C replacing A. The model accounts for potential: 1) leakage of H2 from anode to cathode accounting for anode crossover current density 𝑖®,Š ; 2) leakage of O2 accounting for cathode crossover current density 𝑖0,Š ; and 3) an electronic crossover current 𝑖e@ ,Š due to finite electronic conductivity 𝜎-«,e@ of the electrolyte layer. The species i (H2, CO) diffusion limiting current density for the anode is given by 𝑖h,« = 𝑛C,e@

𝐹 𝜀® 𝐷hG 𝑝𝑥h 𝑅𝑇 𝜏® 𝐿®

(25)

where the mole fraction of species i (H2, CO), 𝑥h , may be obtained as described above. There is a similar expression for O2 at the cathode. Modjtahedi et al.52 have recently, in accord with their theoretical estimates, found that at 850 ºC, the limiting current density in a SOFC with an equimolar CH4/CO2 feed was ~700 mA cm'( due the thick anodes typically utilized in anode supported SOFCs. Further, they found that CO electro-oxidation was the limiting factor rather than H2, because of its significantly smaller diffusion coefficient. This could also explain the bend in the polarization curve for pure CO at the higher current densities (Figure 8a) as a result of being affected by transport limitations. Further, as evident in Figure 8(b), further, the CH4/CO2 feed ratio has a significant effect on the cell voltage as well as on the entire polarization curve, although the slopes, or the cell resistances appear rather independent of feed composition and akin to that of pure H2. The latter observation appears to confirm that in the presence of both CO and H2, HOR is the preferred electro-oxidation route.

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In general, the higher the CH4/CO2 ratio, the higher the cell voltage at a given current density, as well as the OCV, the latter being qualitatively in accord with the literature,18 and with the Nernst equation written for the assumed overall reaction, CHK + 2O( ⇄ 2CO( + 2H( O. Further, as mentioned above, the Nernst potential is the same regardless of the selected electrodic reaction, i.e.,

𝑉= = 1.1847 −

44.354 2𝐹

𝑇 − 298 −

𝑥H€ O,G 𝑅𝑇 ln 2𝐹 𝑥H€ ,G 𝑥O€ ,G

= 1.3330 −

86.384 2𝐹

𝑇 − 298 −

𝑥CO€ ,G 𝑅𝑇 ln 2𝐹 𝑥CO,G 𝑥O€ ,G

= 1.0376 −

4.847 8𝐹

𝑇 − 298 −

(26)

𝑥CO€ ,G 𝑥H(€ O,G 𝑅𝑇 ln 8𝐹 𝑥CH• ,G 𝑥O(€ ,G

as the species compositions adjust at equilibrium to ensure this equality. In the above, the Nernst equations are written for H2, CO, and CH4 oxidation, respectively, from Eq. (7). For instance, for T = 1,173 K, Θ•€ ~ = Θ•€ = Θ}~ = 0, 𝑥}•• ,= = 0.45, along with 𝜖b,G = 0 (no coking), and 𝜖K,G = 0 (cell equilibrium), the remaining two reaction equilibria can be solved numerically to provide 𝜖S,G = 0.9638, and 𝜖(,G = 0.1703. When these are used in Eq. (15), the resulting equilibrium species mole fractions are: 𝑥}•• ,G = 0.0087; 𝑥}~€ ,G = 0.0212, 𝑥•€ ~,G = 0.0410, 𝑥•€ ,G = 0.4235, and 𝑥}~,G = 0.5055. Further, assuming that 𝑥~€ ,G = 0.21 at the airfed cathode, and using these mole fractions in all three relations Eq. (26), the calculated Nernst potential is precisely the same, i.e., 𝑉= = 1.06208 V, regardless of which of the three Nernst expressions is used. On the other hand, the experimental OCV for these conditions was found to be OCV = 1.004 V, which is lower than the Nernst potential by roughly 60 mV, possibly because of polarization losses due to internal leakage current, 𝐼Š . This may be a consequence of the

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rather thin electrolyte layer (15 µm). In comparison, Shiratori et al.18 found an OCV = 1.03 V for an equimolar feed at 900 °C. The cell performance (Figure 8b) and lifetime (Figure 2b) are, thus, clearly competing factors, both of which are affected by the CH4/CO2 feed ratios. The fuel cell performance improves with the CH4/CO2 ratio (Figure 8b), i.e., for a methane rich biogas. On the other hand, cell lifetime declines at higher CH4/CO2 ratios (Figure 2b) due to increased propensity for coking. Thus, even though when the CH4/CO2 ratio is 50/50, i.e., stoichiometric (for OR1), and the conversion of both species via the dry reforming reaction is maximized, the somewhat lower 45/55 CH4/CO2 feed ratio is superior in ensuring a longer lifetime. Thus, dilution of a methane-rich biogas feed may be called for in such a power plant, which is readily accomplished, for instance, via a recycle of the anode effluent gas. A recycle stream would, in fact, further improve the fuel utilization and the cell efficiency. 4.3 The Effect of Feed Utilization on Durability and Efficiency While the hence selected operating conditions of 900 °C with a 45/55 CH4/CO2 feed ratio represent optimized conditions, these don’t guarantee coke-free operation, since in the entrance region there is a significant drop in temperature because of the endothermic methane reforming, making the anode inlet region more conducive to coking. Consequently, it is of interest to experimentally study the effect of fuel utilization (or cell current) and feed humidification (next section) on further improving the cell durability. Figure 9(a), thus, shows the power generated by the cell running at five different fuel utilizations, or cell currents, as a function of time. The indicated fuel utilizations of 𝑈* = 15%, 21%, 26%, 31% and 38%, were calculated based on the use of Eq. (23). Each cell was operated for 250 h, unless cell failure occurred earlier.

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The 𝑈* = 15% and 21% curves show noise beginning around 100 hours and 200 hours, respectively, a signature of significant coking. The 𝑈* = 26%, 31%, and 38% curves are much smoother, indicating a lower net rate of coking under higher fuel utilization conditions. Further, the slope of the curves, or the degradation rate, clearly reduces with increasing load, or increasing fuel utilization. This is consistent with the results in Figure 4, where a higher Uf, moves the system deeper into the no-coke territory as a result of the higher O content. In short, 𝑈* = 25% appears to be the minimum fuel utilization needed for reduced coking and degradation rate. Figure 9(b) further shows the polarization plot for the cell operated under 31% fuel utilization before and after the cell ran for 250 hours. Clearly, there is only a small difference between the two plots, indicating that there was not a significant degradation via coking in a cell running at 𝑈* = 31%, a 45/55 CH4/CO2 feed ratio, and a temperature of 900 ºC for 250 hours. The cell and system electrical efficiencies were determined experimentally via the use of Eqs. (22) and (19), respectively, and are plotted in Figure 10 versus cell current, I, or the fuel utilization, 𝑈* . These plots are in accord with the theoretical estimates provided by Zhu and Kee (their Figure 4).45 While the system electrical efficiency appears low, it may be recalled that in general the SOFC is coupled with cogen or CHP applications and so the overall energy efficiency of the SOFC system can be significantly higher.44 On the other hand, the cell efficiency in Figure 10 is high for two reasons: 1) the low overpotentials due to the high temperature of operation, and 2) the internal coupling of the endothermic reforming with exothermic electro-oxidation reactions.

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4.4 The Effect of Modest Feed Humidification on Durability To investigate the effect of modest feed humidification on the lifetime of the cell under otherwise optimized conditions, 4 different cells were operated for 250 hours each at 900 °C and a constant current density for a feed with CH4/CO2 ratio of 45/55 with and without 3% moisture. Thus, two of the cells were operated at 15.5 A (𝑈* = 31%), humidified and unhumidified, while the other two cells were operated at 10.33 A (𝑈* = 21%), humidified and unhumidified, above and below the threshold of roughly 25% fuel utilization indicated for stability. As seen in Figure 11, the water addition had no discernible effect on the degradation rate for the higher fuel utilization operation, but did reduce the degradation at the lower utilization. Overall, thus, a modest addition of moisture to the biogas feed appears to be a prudent strategy in decreasing the risk of carbon deposition. 4.5 Extent of Internal Reforming via Anode Effluent Gas Composition Analysis The anode effluent composition was analyzed via mass spectrometry for a t-SOFC running on 45/55 CH4/CO2 feed at OCV at 900 °C for 30 minutes in order to determine the extents of the internal reforming reactions. Then the current was increased incrementally, and the additional H2O and CO2 formed provided the extent of electrocatalytic reaction. The cell load was held constant for 5 minutes at each current value to ensure steady state. The results are shown in Figure 12. The experimental trends in the changes in mole fraction of each species are rather as expected. Thus, the mole fractions of CO and H2 decrease as they are converted via CMOR (𝑂𝑅e ), or via WGS (𝑂𝑅( ), and HOR (𝑂𝑅K ), respectively, while the mole fractions of CO2 and H2O, the products of these reactions, correspondingly increase with increasing current. However, the reason for the small increase observed in the mole fraction of methane with

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increasing load is somewhat puzzling, as both CO and H2 decline with increasing current, so that the reverse of the MDR, or methanation, is unlikely to be enhanced. Provided in Figure 12 also is a comparison with the predicted mole fractions at the anode exit both at the OCV and as a function of current, based on the quasi-equilibrium (QE) assumption for the reforming reactions. At the OCV, or under true equilibrium, when 𝐼 = 0 = 𝜖K,G , this is accomplished by computing the equilibrium extents of the remaining three reactions (𝑂𝑅S , 𝑂𝑅( , 𝑂𝑅b ), as described for Figure 6. Thus, at 900 °C and for 45/55 CH4/CO2 feed ratio, the calculated mole fractions are: 𝑥}•• ,G = 0.0087; 𝑥}~€ ,G = 0.0212, 𝑥•€ ~,G = 0.0410, 𝑥•€ ,G = 0.4235, and 𝑥}~,G = 0.5055. In comparison, the experimentally measured mole fractions are (Figure 12): 𝑥}•• ,G = 0.006, 𝑥}~€ ,G = 0.033, 𝑥•€ ~,G = 0.065, 𝑥•€ ,G = 0.389, and 𝑥}~,G = 0.503. These values are similar, although not identical to the predictions. In particular, there is a notable difference in the H2 mole fraction, which is lower, and the H2O mole fraction, which is higher than predicted. For the case when a current is drawn, 𝜖K is related to current via Eq. (10). However, the nonelectrodic reactions involved in the internal reforming may still be assumed to be at QE, as confirmed experimentally by Guerra et al.22 Thus, the same procedure as above was used to evaluate the species composition as a function of current and is also plotted in Figure 12. It is seen that while the comparison between theory and experiments for 𝑥•€ , 𝑥}~ , and 𝑥•€ ~ is reasonable, there is a discrepancy for the case of 𝑥}•• and especially for 𝑥}~€ . To investigate if this discrepancy was due to the constancy of the entropy and enthalpy change of the reaction as assumed in the van’t Hoff relation, Eq. (6), the enthalpy change of the ORs as a function of temperature was evaluated.40 For this, the specific heat of each species was modeled using, 𝐶™ /𝑅 = 𝐴 + 𝐵𝑇 + 𝐶𝑇 ( + 𝐷𝑇 '( , where the constants A, B, C, and

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D were obtained from Smith et al.35 Based on this, new values of equilibrium mole fractions at OCV were determined as: 𝑥}•• ,G = 0.0085, 𝑥}~€ ,G = 0.0206, 𝑥•€ ~,G = 0.0414, 𝑥•€ ,G = 0.4233, and 𝑥}~,G = 0.5061. When compared to the corresponding equilibrium composition calculated assuming constant reaction enthalpy, it is evident that the difference is negligible. Thus, the difference observed between the theoretical and experimental mole fractions cannot be attributed to approximations made in the thermodynamic analysis. The discrepancy at OCV might be explained if there were a finite, albeit small, internal (leakage) current, 𝐼Š , across the electrolyte layer,36 causing some of the H2 to get oxidized, resulting in less H2 and more H2O than predicted by thermodynamics. This could also conceivably account for a leakage current and an OCV less than the Nernst potential. However, this does not adequately explain the discrepancies at the higher currents. Of course, the difference between experiments and thermodynamic analysis could also simply be the result of experimental error, although the MS was calibrated for H2 and CO mole fractions. No comparison for such measurements is available in the literature. While Santarelli et al.53 measured exit gas composition, it was for a different set of conditions (a temperature of 800 °C and different feed composition). Finally, it is apparent that the QE model used here for the reforming reactions is adequate even under non-equilibrium, or load, conditions. Consequently, at least at the temperature of 900 ºC, a more detailed kinetic,21 or a microkinetic,31 model is not needed for predicting the anode composition. Further, in the absence of significant coking, e.g., when operating at 900 ºC, in fact, only two reforming ORs are adequate, in addition to one electrodic OR, unlike the usual assumption of 3 ORs.21,33 Finally, although the QE thermodynamic analysis is shown

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to be adequate for our operating temperature of 900 ºC, it is possible that at lower temperatures, a kinetic or a microkinetic model might be needed. 4.6 A Further Discussion of Coking and Anode Reaction Mechanism Our own experimental and theoretical observations described above, and the experimental54 and theoretical55, 56 mechanistic investigations reported in the literature, are consistent with a mechanism wherein CH4 first undergoes step-wise dehydrogenation on the Ni surface to form a carbonaceous species, which is subsequently oxidized by oxygenated intermediate species (O, OH) on the surface, stemming coming from the oxygenate terminal species in the anode feed (CO2, H2O), or from the cathode (O2) arriving at the anode via the electrolyte. Such a 16-step mechanism is summarized in Table 2, that also describes, via the stoichiometric numbers 𝜎¶“ listed on the right, the key pathways for all the four ORs listed at the bottom of the table. The mechanism is also schematically depicted in Figure 13. Thus, step-wise dehydrogenation to C∙S (where S is a surface site) occurs following methane adsorption on Ni (CH4 ∙S),51 with the first H abstraction step 𝑠( (CH4 ∙S + S ⇄ CH3 ∙S + H∙S) deemed the rate-determining step (RDS), as indicated by the low surface concentrations of the other CH7 ∙S fragments.54 The adsorbed CO2 (CO( ∙S) dissociates into O∙S and CO∙S in parallel.57 The hence resulting surface species C∙S, H∙S, O∙S, OH∙S, CH∙S, CO∙S, HCO∙S, then rapidly react among themselves to form the terminal products, H( , CO, and H( O. In addition, O( at the cathode forms oxygen anions O(' , which arrive at the anode via the YSZ electrolyte and supplements the supply of the surface oxygen, O∙S. This is also included in the mechanism (𝑠S¹ ), and in the schematic in Figure 13 to provide an overall picture of the molecular processes. However, the actual

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cathode mechanism, as well as the anode mechanism involving the oxygen anion species O(' , clearly involves other charge-transfer steps.58 Listed in the columns on the right in Table 2 are stoichiometric numbers 𝜎¶“ for an independent set of five reaction routes (RRg), or pathways, for the four independent ORs. These indicate the number of times a mechanistic step 𝑠“ is combined in the gth reaction route (RR¶ ), i.e., RR¶ :

» “jS 𝜎¶“ 𝑠“

= 0.59 The RRs in Table 2 were obtained simply via

inspection of this relatively simple mechanism, although more formal procedures are available.59 If a RR includes the OR, it is called a full route (FR); if only elementary reactions steps 𝑠“ are included, then the cycle represented by the RR is called an empty route (ER).59 Thus, FR1, indicated by the first column of stoichiometric numbers on the right in Table 2 is a pathway for the MDR, OR1, FR2 is a reaction route for the RWGSR, OR2, FR3 is a reaction route for the methane pyrolysis reaction, namely, OR3, while FR4 is a reaction route for the hydrogen oxidation reaction (HOR). Further, when the empty route ER1 is combined with a FR1, an alternate parallel pathway results for OR1. It is also clear from the set of steps comprising OR3, that it is a subset of those in OR1, i.e., (CH4 +CO2 ⇄ 2CO+2H2 ) = (CH4 ⇄ C + 2H2 ) + (C + CO2 ⇄ 2CO). In other words, we can envision that methane first decomposes to C on the surface which subsequently gets oxidized to CO and H2O, with the surface oxygen coming from CO2, or from the oxygen anion. This is consistent with the conclusions of the recent mechanistic study of Yin and Chuang60 based on their transient kinetic investigation. The corresponding pathways are shown in red and blue arrows, respectively, in the mechanism in Figure 13.

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Methane is pyrolyzed by Ni catalyst but only above 500 °C.37 Further, at lower temperatures the dissociative sorption of CO2 is not sufficiently activated to provide the surface oxygen needed for further reaction.56 The thermodynamics of the carbon gasification reaction via CO2 (OR8) are also not sufficiently favorable until a temperature of > 750 °C, as shown in Figure 3. Thus, 500 - 750 °C is the temperature range most susceptible to coking. The mechanism of anode coking and its effect on anode structure and metal dusting is shown schematically in Figure 7. It has now been known for some time that carbon deposition from CH4 pyrolysis on Ni occurs as whiskers via step-wise dehydrogenation of CH4 as described in Table 2 and shown schematically Figure 7, with the Ni nano-particles riding the tip of the growing nano-fibers,61 after being dislodged from the support. Further, in an in situ investigation of coking on Ni-YSZ cermet anodes, Kim et al.29 found that carbon initially forms on Ni, and then dissolves within the Ni-YSZ cermet, resulting in three-dimensional structure expansion (Figure 7), with a concomitant increase in electrical resistance. 4.7 Preliminary Testing of a 5-Cell SOFC Assembly The final objective of this study was to preliminarily test a 5-cell tubular SOFC assembly operating under the indicated optimal conditions of a 45/55 CH4 /CO2 biogas feed, 31% fuel utilization, and a temperature of 900 °C. Figure 14 shows a polarization curve for the 5-cell stack running under these conditions. The 5-cell stack, thus, achieved a power of about 52 watts. If there were no additional losses, this would simply be the product of the number of cells (5) and the power produced by each cell (12 W, Figure 8b), i.e., 60 watts. The somewhat lower power produced in the assembly indicates some additional resistive losses but, on the whole, substantiates that scaling up this SOFC system fed by biogas is feasible.

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The 5-cell assembly was next allowed to run under constant current to obtain an indication of its lifetime. However, failure of the unit occurred after 35 hours. Additional experimentation is, thus, needed to investigate the reasons for this earlier than expected failure, viz., mechanical stresses resulting from stack assembly, versus thermal or those from coking, and how these might be overcome to accomplish the much longer lifetime under optimal conditions promised by the single SOFC tube studies.

Conclusions From the experimental results with single-cell and a 5-cell t-SOFC assembly described herein, it is clear that the use of biogas in a SOFC unit to generate renewable electricity efficiently is entirely feasible. However, the operating conditions need to be carefully selected to avoid rapid cell degradation while realizing good performance. The optimal conditions were experimentally found to be an operating temperature of 900°C, a biogas feed composition of 45/55 CH4/CO2, and a fuel utilization ≥ 25%. Under these conditions, each tubular cell of 32 cm2 area produced 12 W (or, an average of 375 mW cm'( ), with a high fuel cell electrical efficiency (> 60%), while exhibiting a low degradation rate. It was also observed that modest humidification of the feed improved the lifetime of the SOFC operating at lower fuel utilizations. Composition analysis of the anode effluent gas largely confirmed the quasi-equilibrium thermodynamic analysis for the species’ concentrations at OCV as well as under load. It was also confirmed, via using pure feeds, that both H2 and CO are individually electro-oxidized at the anode with a similar facility, although under internal reforming conditions HOR appears to be the preferred electrochemical route, with CO indirectly oxidized via the quasi-equilibrated WGS reaction.

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A comprehensive thermodynamic analysis further helped to narrow down the window of operating temperature and feed composition. It was shown that this can be accomplished with a set of overall reactions that include any one electrodic reaction and any three internal reforming reactions. Furthermore, it was rigorously shown that the Nernst potential is independent of the choice of the electrodic reaction, e.g., H2 or CO electro-oxidation. Finally, the 5-cell unit operating with a 45/55 CH4/CO2 feed at 900 °C achieved a power only somewhat less than that indicated by single cells, although additional work is needed to attain the promised lifetime.

Acknowledgement We are grateful to the Protonex Technology Corp. for their consent to publish this work.

Nomenclature 𝑎h

activity of species i, 𝑎h = 𝛾h 𝑥h

𝐷hG

effective gas-phase diffusivity of species i

𝐸‹,“

total energy carried by a gas in the stream 𝑠“

e

number of elements

F

Faraday’s constant, 96,485 C/eq

I

total current drawn externally from fuel cell

𝐼567

theoretical maximum current from complete methane conversion

𝐼Š

internal crossover or leakage current

i

fuel cell current density, A cm-2 of MEA area

𝑖®,=

anode exchange current density

𝑖®,«

anode limiting current density

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Energy & Fuels

𝑖®,Š

current density at the anode area due to oxidant crossover across the electrolyte layer

𝑖0,=

cathode exchange current density

𝑖0,«

cathode limiting current density

𝑖0,Š

current density at the cathode based on MEA area due to fuel crossover across the electrolyte layer

𝑖e@ ,Š

current density due to finite electronic conductivity of the electrolyte layer

𝐾C

thermodynamic equilibrium constant for rth overall reaction

𝐿®

anode layer thickness

𝐿-«

electrolyte layer thickness

𝑛h

molar flow rate of a species i at an axial location within a tubular flow SOFC

𝑛A,=

methane molar feed flow rate

𝑛h,=

molar feed rate of a species i,

𝑛Ce@

number of electrons in electrodic overall reaction r

ORr

rth overall reaction

p

pressure

𝑄

rate of heat transferred from the surroundings to the system

𝑄/0

rate of heat transferred from the surroundings to the fuel cell

𝑄’Š

rate of heat exchange between the surroundings and the combustor

𝑄…

rate of heat recycled to the fuel cell to replenish endothermic reactions in it

𝑄C

reaction quotient of rth overall reaction

R

gas constant

R

number of independent overall reactions

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Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

𝑅¦Gšš

overall cell resistance

𝑟

rth overall reaction

𝑟C

rate of the rth overall reaction.

T

temperature

𝑇CG*

reference temperature, 298 K

𝑈*

fuel utilization

𝑈*,G

equilibrium conversion-limited fuel utilization

V

cell voltage

𝑉=

thermodynamic (Nernst) cell voltage

o 𝑉567

maximum theoretical cell voltage determined from ∆𝐻Co

𝑊-

rate of electric work exchange between the surroundings and the fuel cell

𝑥i

mole fraction of species i

𝑥i,=

feed mole fraction of species i

Greek Symbols 𝛾h

activity coefficient for species i

∆𝐶™

heat capacity change for rth overall reaction

Δ𝐸‹

net (out – in) efflux of energy from a system

∆𝐺C

Gibbs free energy change for rth overall reaction

∆𝐺Co

standard Gibbs free energy change for the rth overall reaction

o ∆𝐻0,h

heat of combustion of a species i

∆𝐻Co

standard enthalpy change for the rth overall reaction

∆𝑆Co

standard entropy change for the rth overall reaction

Δ𝜈C

mole change for the rth overall reaction

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Energy & Fuels

𝜀-,/0

fuel cell electrical efficiency

𝜀-,

Faradaic efficiency

𝜀-,‰

voltage efficiency

𝜖C

dimensionless extent of the rth overall reaction

𝜀®

anode porosity

Θh

molar feed ratio of species i to that of hey species (methane)

𝜇h

electrochemical potential of species i

𝜈Ch

stoichiometric coefficient of the species i

• @ 𝜈®,e

stoichiometric coefficient of electrons in the RDS of the anode OR sequence

• @ 𝜈0,e

stoichiometric coefficient of electrons in the RDS of the cathode OR sequence

𝜉C

extent of the rth overall reaction

𝜎-«

effective electrolyte ionic conductivity

𝜎-«,e@

electrolyte layer electronic conductivity

𝜏®

anode tortuosity

Subscripts/superscripts •

rate-determining step

A

methane

A

anode layer

C

cathode layer

e

equilibrium

e'

electron

i

species

L

limiting

S

unoccupied surface site

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

o

standard conditions (pure species)

ref

reference

X

crossover

Abbreviations CDCG

carbon dioxide carbon gasification (the reverse of Boudouard reaction)

CFSM

carbon full steam methanation

CHP

combined heat and power

CMOR

carbon monoxide oxidation reaction

COX

carbon oxidation

CSM

carbon steam methanation

HOR

hydrogen oxidation reaction

LSCF

lanthanum strontium cobalt ferrite

MDR

methane dry reforming

MFDR

methane full dry reforming

MFOX

methane full oxidation

MFSR

methane full steam reforming

MP

methane pyrolysis

MS

mass spectrometer

MPOX

methane partial oxidation

MSR

methane steam reforming

OCV

open circuit voltage

ORR

oxygen reduction reaction

QE

quasi-equilibrium

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Energy & Fuels

RDS

rate-determining step

RWGS

reverse water-gas shift

SCG

steam carbon gasification

SFCG

steam full carbon gasification

SLPM

standard liters per minute

SOFC

solid-oxide fuel cell

t-SOFC

tubular solid-oxide fuel cell

YSZ

yttria-stabilized zirconia

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Page 52 of 67

Table 1. List of plausible internal reforming and electrochemical overall reactions (ORs)32,33 in a biogas fed SOFC and their standard enthalpies ∆𝐻Co .‡ kJ MDR mol kJ 𝑂𝑅( : CO( + H2 ⇄ CO + H2 O ; ∆𝐻(o = +41.2 RWGS mol kJ 𝑂𝑅b : CH4 ⇄ C + 2H2 ; ∆𝐻bo = +74.9 MP mol kJ 𝑂𝑅K : H2 + 1 2 O2 ⇄ H2 O ; ∆𝐻Ko = −241.8 HOR mol kJ 𝑂𝑅e : CO + 1 2 O2 ⇄ CO2 ; ∆𝐻eo = −283.0 CMOR mol kJ 𝑂𝑅¹ : CH4 + H2 O ⇄ CO+3H2 ; ∆𝐻¹o = +206.2 MSR mol kJ 𝑂𝑅À : CH4 + 2H2 O ⇄ CO2 +2H2 ; ∆𝐻Ào = +165.0 MFSR mol kJ 𝑂𝑅¡ : C + CO2 ⇄ 2CO ; ∆𝐻¡o = +172.5 CDCG mol kJ 𝑂𝑅Â : C + H2 O ⇄ CO+H2 ; ∆𝐻Âo = +131.3 SCG mol kJ o 𝑂𝑅S= : CH4 + 1 2 O2 ⇄ CO+2H2 ; ∆𝐻S= = −35.7 MPOX mol kJ o 𝑂𝑅SS : CH4 + 2O2 ⇄ CO2 +2H2 O ; ∆𝐻SS = −802.3 MFOX mol kJ o 𝑂𝑅S( : C + 1 2 O2 ⇄ CO ; ∆𝐻S( = −110.5 COX mol kJ o 𝑂𝑅Sb : CH4 +3CO2 ⇄2H2 O+4CO ; ∆𝐻Sb = +329.7 MFDR mol kJ o 𝑂𝑅SK : C + 2H2 O ⇄ CO2 +2H2 ; ∆𝐻SK = +90.1 SFCG mol kJ o 𝑂𝑅Se : 2C + 2H2 O ⇄ CO2 +CH4 ; ∆𝐻Se = +15.3 CFSM mol kJ o 𝑂𝑅S¹ : 3C + H2 O ⇄ 2CO+CH4 ; ∆𝐻S¹ = −54.1 CSM mol

𝑂𝑅S : CH4 +CO2 ⇄ 2CO+2H2 ; ∆𝐻So = +247.3

‡ Reaction abbreviations: MDR = methane dry reforming, RWGS = reverse water-gas shift, MP

= methane pyrolysis, HOR = hydrogen oxidation reaction, CMOR = carbon monoxide oxidation reaction, MSR = methane steam reforming, MFSR = methane full steam reforming, CDCG = carbon dioxide carbon gasification (the reverse of Boudouard reaction), SCG = steam carbon gasification, MPOX = methane partial oxidation, MFOX = methane full oxidation, and COX = carbon oxidation, MFDR = methane full dry reforming, SFCG = steam full carbon gasification, CFSM = carbon full steam methanation, CSM = carbon steam methanation.

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Energy & Fuels

Table 2. Plausible mechanism and reaction routes for the methane dry reforming (𝑂𝑅S ), reverse water-gas shift (𝑂𝑅b ), methane pyrolysis (𝑂𝑅b ), and hydrogen oxidation (𝑂𝑅K ) reactions at the anode. 𝑠“ :

Reaction

𝑠S : CH4 + S ⇄ CH4 ∙S 𝑠( : CH4 ∙S + S ⇄ CH3 ∙S + H∙S 𝑠b : CH3 ∙S + S ⇄ CH2 ∙S + H∙S 𝑠K : CH2 ∙S + S ⇄ CH∙S + H∙S 𝑠e CH∙S ⇄ C∙S + H∙S 𝑠¹ : CO( + S ⇄ CO( ∙S 𝑠À : CO( ∙S + S ⇄ CO∙S + O∙S 𝑠¡ : O∙S + CH∙S ⇄ HCO∙S + S 𝑠Â : HCO∙S + S ⇄ CO∙S + H∙S 𝑠S= : O∙S + C∙S ⇄ CO∙S + S 𝑠SS : CO∙S ⇄ CO + S 𝑠S( : H∙S + H∙S ⇄ H( + 2S 𝑠Sb : H∙S + O∙S ⇄ OH∙S + S 𝑠SK : H∙S + OH∙S ⇄ H( O∙S + S 𝑠Se : H( O∙S ⇄ H( O + S 1 O + S ⇄ O∙S 𝑠S¹ : 2 2 _____ ____________________________ 𝑂𝑅S : CH4 + CO( ⇄ 2CO + 2H( 𝑂𝑅( : CO( + H( ⇄ H2 O + CO 𝑂𝑅b : CH4 + S ⇄ C∙S + 2H( 𝑂𝑅K : H2 + 1 2 O2 ⇄ H2 O

FRS

FR (

FR b

FR K

ERS

+1 +1 +1 +1 +1 +1 +1 0 0 +1 +1 +2 0 0 0 0 ____ −1 0 0 0

0 0 0 0 0 +1 +1 0 0 0 +1 −1 +1 +1 +1 0 ____ 0 −1 0 0

+1 +1 +1 +1 +1 0 0 0 0 0 0 +2 0 0 0 0 ____ 0 0 −1 0

0 0 0 0 0 0 0 0 0 0 0 −1 +1 +1 +1 +1 ____ 0 0 0 −1

0 0 0 0 +1 0 0 −1 −1 +1 0 0 0 0 0 0 ____ 0 0 0 0

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(a)

(b)

Figure 1 (a). Process flow diagram for the biogas-fed SOFC experimental setup. (b) The SOFC fed with a biogas mixture at the anode and an exhaust with products of MDR and electro-oxidation, a part of which is oxidized and used to supply MDR endothermic heat, along with O2 flowing through the cathode and exchange of heat and electric work.

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(a)

10 9

(b)

8 7

Power (W)

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Energy & Fuels

6 5 4 3

40:60 CH :CO 4

2

45:55 CH :CO

2

4

2

50:50 CH :CO 4

1 0 0

2

55:45 CH :CO 4

50

Time (h)

100

2

150

Figure 2. (a) Lifetime plots of power produced for 50/50 CH4/CO2 feed at 700°C in a t-SOFC at 0.7 V, and (b) power generated from four different CH4/CO2 feed ratios at 900°C.

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Figure 3. Ellingham Diagram for Gibbs free energy change as a function of temperature for the methane dry reforming, MDR (𝑂𝑅S ), reverse water-gas shift, RWGS (𝑂𝑅( ), methane pyrolysis, MP (𝑂𝑅b ), and carbon dioxide coke gasification, CDCG (𝑂𝑅¡ ), i.e., the reverse Boudouard, reactions.

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Energy & Fuels

Figure 4. Atom fractions 𝑥C , 𝑥H , and 𝑥O for different values of feed ratios, ΘCO€ , and different fuel utilizations, 𝑈* , showing that methane-rich feed (ΘCO€ ≤ 1) are in the carbon deposition region even at high operating temperatures and OCV, whereas for ΘCO€ > 1, operating temperatures of around 900 °C are safe, especially under load (𝑈* > 0). Each dot (red for ΘCO€ = 0.5, blue for ΘCO€ = 1.0, and green for ΘCO€ = 1.5) represents 𝑈* from 0 to 1.0 in increments of 0.1.

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Energy & Fuels

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Figure 5. Equilibrium dimensionless reaction extents, 𝜖C,G , for 𝑂𝑅S , 𝑂𝑅( and 𝑂𝑅b , for equimolar feed CH4/CO2 = 50/50 at OCV, i.e., when 𝜖K,G = 0. Above 880 °C, 𝜖b,G < 0, i.e., coke removal occurs via hydrogenation above this temperature, while for temperatures < 650 °C, 𝜖S,G < 0, i.e., methanation is favored.

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Energy & Fuels

Figure 6. Cumulative equilibrium gas composition at OCV as a function of temperature for an equimolar feed CH4/CO2 = 50/50. The vertical distance between two curves represents the indicated species mole fraction.

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Energy & Fuels

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Figure 7. (a) A schematic of anode cermet structure and (b) its destruction via coking that encapsulates YSZ particles and lifts Ni nanoparticles atop growing whiskers.25

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15

1.05

Voltage (V)

10

H2 Hydrogen CO CO

0.85

5

Power (W)

(a)

0.95

0.75 0.65

0 0

1.05

5

10 Current (A)

15

20

(b)

0.95

H2 CO 40:60 CH4 :CO2 45:55 CH4 :CO2 50:50 CH4 :CO2 55:45 CH4 :CO2 60:40 CH4 :CO2

0.85

10

5

0.75

0.65

Power (W)

15 Voltage (V)

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Energy & Fuels

0 0

5

10 15 Current (A)

20

25

Figure 8. Integral polarization curves at 900°C in a t-SOFC with active area of 32 cm2 for (a) H2 and CO, and (b) for 5 different CH4/CO2 feed ratios as well as for pure H2 and CO.

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Energy & Fuels

20

1.1 1.05

(b) 15

1

0.9

Before 250 Hours After 250 Hours

Power (W)

0.95

Voltage (V)

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10

0.85 5

0.8 0.75 0.7 0

5

10

Current (A)

15

20

0 25

Figure 9. (a) Power produced and degradation rates for 5 different fuel utilizations and (b) polarization before and after 250 h run at 𝑈* = 31% for CH4/CO2=45/55 feed at 900 °C.

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Energy & Fuels

Figure 10. The experimental fuel cell and system (Figure 1b) electrical efficiencies evaluated via Eqs. (22) and (19), respectively, versus cell current, I, or fuel utilization, 𝑈* .

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Energy & Fuels

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Figure 11. Power produced at constant current versus time for cells running with and without modest humidification (~3% water) of a CH4/CO2 = 45/55 feed gas feed at two different fuel utilizations at 900°C.

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Energy & Fuels

Figure 12. Changes in the anode effluent mole fractions of species for a CH4/CO2= 45/55 feed at 900 °C for incremental current values, starting at OCV, in a t-SOFC with active area of 32 cm2. Curves represent predictions based on assuming quasi-equilibrium for internal reforming reactions.

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Energy & Fuels

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Figure 13. A reaction schematic of the mechanism listed in Table 2. Circular nodes represent terminal (green are anode reactants, ocher are products, and blue is cathode reactant) species, while rectangular nodes are intermediate species, with S representing a surface site. Red arrows represent CH4 pyrolysis reaction pathway steps, while blue represent oxidation pathways. More CO than H2 results from RWGS reaction that uses a molecule of H2 and CO2 coproducing a molecule of H2O. The first step in CH4 dehydrogenation sequence is the rate-determining step (RDS).

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Energy & Fuels

Figure 14. Polarization for a 5-cell t-SOFC assembly fed by synthetic biogas with CH4/CO2= 45/55 at 900 °C, each t-SOFC cell with an active area of 32 cm2.

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