Novel electrical energy storage system based on reversible solid oxide cells: System design and operating conditions

Journal of Power Sources 276 (2015) 133e144

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Novel electrical energy storage system based on reversible solid oxide cells: System design and operating conditions C.H. Wendel, P. Kazempoor, R.J. Braun* Department of Mechanical Engineering, College of Engineering and Computational Sciences, Colorado School of Mines, 1610 Illinois Street, Golden, Colorado 80401, USA

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


An electrical energy storage system using reversible solid oxide cells is modeled.
Thermal management with carbonaceous reactant species increases system efficiency.
System modeling reveals tradeoffs between roundtrip efficiency and energy density.
Roundtrip efficiency >70% is achieved by operating the stack at 20 bar and 680  C.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 August 2014 Accepted 31 October 2014 Available online 14 November 2014

Electrical energy storage (EES) is an important component of the future electric grid. Given that no other widely available technology meets all the EES requirements, reversible (or regenerative) solid oxide cells (ReSOCs) working in both fuel cell (power producing) and electrolysis (fuel producing) modes are envisioned as a technology capable of providing highly efficient and cost-effective EES. However, there are still many challenges and questions from cell materials development to system level operation of ReSOCs that should be addressed before widespread application. This paper presents a novel system based on ReSOCs that employ a thermal management strategy of promoting exothermic methanation within the ReSOC cell-stack to provide thermal energy for the endothermic steam/CO2 electrolysis reactions during charging mode (fuel producing). This approach also serves to enhance the energy density of the stored gases. Modeling and parametric analysis of an energy storage concept is performed using a physically based ReSOC stack model coupled with thermodynamic system component models. Results indicate that roundtrip efficiencies greater than 70% can be achieved at intermediate stack temperature (680  C) and elevated stack pressure (20 bar). The optimal operating condition arises from a tradeoff between stack efficiency and auxiliary power requirements from balance of plant hardware. © 2014 Elsevier B.V. All rights reserved.

Keywords: Reversible solid oxide cell Solid oxide fuel cell Co-electrolysis Electrical energy storage System modeling

1. Introduction

* Corresponding author. E-mail addresses: [email protected] (C.H. Wendel), [email protected] (P. Kazempoor), [email protected] (R.J. Braun). http://dx.doi.org/10.1016/j.jpowsour.2014.10.205 0378-7753/© 2014 Elsevier B.V. All rights reserved.

Electrical energy storage (EES) allows for temporal decoupling of electric power generation and consumption and has been projected as a key component of the future electric grid to increase efficiency and allow large-scale penetration of intermittent renewable resources, such as wind and solar [1e4]. The U.S. DOE

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recently published long-term targets for grid energy storage of 80% roundtrip efficiency, 150 $/kWh capital cost and 10 ¢/kWh-cycle levelized cost to fulfill energy management applications like energy time-shifting, transmission and distribution upgrade deferral, and customer energy management services [1]. Many technology solutions are being considered to meet the above energy storage targets, although each faces unique implementation challenges. Pumped hydro storage presently accounts for 95% of worldwide electrical energy storage [1], but requires a geographically suitable site to be implemented effectively (i.e., adjacent reservoirs separated by a height difference). Other EES technologies including compressed air energy storage, conventional batteries (e.g., leadacid, nickelecadmium), advanced batteries (e.g., sodiumesulfur, lithium-ion, redox flow, etc.), and energy flywheels are at various stages of development and commercialization, though none are currently able to provide a comprehensive energy storage solution [5,6]. Furthermore, because of the variety of energy storage applications, a range of operating requirements are needed, including operating durations, dynamic requirements, and energy-to-power ratios, such that a portfolio of energy storage technologies is beneficial. Recent studies suggest that a reversible solid oxide cell (ReSOC) is a technology capable of working as a highly efficient (>70% roundtrip) and potentially cost-effective energy storage device at large-scales (<4 US¢/kWh/cycle) [7]. The ReSOC is a solid-state, electrochemical energy conversion device that operates at high temperature (600e1000  C). Physically, the ReSOC is constructed of a membrane electrode assembly (MEA) comprising a laminated fuel electrode, solid electrolyte, and oxygen electrode. State-of-theart ReSOCs typically leverage solid oxide fuel cell (SOFC) material sets made from nickeleimpregnated yttria-stabilized zirconia (NieYSZ) cermets for the fuel electrode, a dense YSZ electrolyte layer, and lanthanum strontium-doped manganite (LSM) for the oxygen electrode [8]. These state-of-the-art cells are mechanically supported by the fuel electrode (e.g., anode-supported) to allow thin solid electrolytes with low resistance and high catalyst surface area for heterogeneous fuel reforming on the nickel present in the fuel electrode. Intermediate temperature ReSOCs employing La0.9Sr0.1Ga0.8Mg0.2O3ed (LSGM) as the electrolyte are also promising candidates under development, particularly for operating temperatures <700  C [9,10]. Although fuel cells are currently the primary application, ReSOCs can operate either as a fuel cell to generate electrical power and consume fuel, or as an electrolyzer to produce fuel from reactant species such as H2O and CO2 with an input of electrical power [11]. A stand-alone energy storage system is realized from this technology by coupling the two modes of operation with intermediate storage of gaseous “fuel” and “exhaust” species. Thus, this system has the advantage of independently sizing power and energy capacity by the ReSOC stack and storage tank sizes, respectively. Fig. 1 shows a simplified schematic of an energy storage system concept based on ReSOC technology. The ReSOC stack is comprised of many single cells configured in electrical series. The energy storage device is charged by operating the stack as an electrolyzer or in solid oxide electrolysis cell (SOEC) mode. In this mode, reactant species are delivered to the stack from the “exhaust” storage tank where they are electrochemically reduced to form fuel species (i.e., H2, CO, CH4) with a supply of electricity from a renewable resource, for example. The produced fuel is compressed and stored in a “fuel” tank for later use. In SOFC mode, the device is discharged as fuel species are delivered to the stack from the “fuel” tank where they are electrochemically oxidized to generate electrical power. The exhaust species, which are primarily H2O and CO2 with some unspent fuel, are compressed and stored in the pressurized “exhaust” tank.

Fig. 1. Simplified schematic of a stand-alone energy storage system utilizing reversible solid oxide cells (ReSOCs).

Airflow is delivered to the ReSOC stack in both modes of operation. In SOFC mode, air provides oxygen for the global electrochemical oxidation reactions; while in SOEC mode, air acts as a sweep gas to reduce the partial pressure of generated oxygen from the electrochemical reduction of steam/CO2, thereby increasing the efficiency of fuel production. ReSOCs themselves are capable of achieving highly efficient (>80%) roundtrip performance for energy storage applications [12,13]; however, the roundtrip system efficiency must also be assessed, including considerations for thermal integration and parasitic energy from system components, such as compressors. The EES system concept presented in Fig. 1 motivates lines of investigation towards determining desirable storage tank gas compositions and pressures, and establishing ReSOC stack temperature, pressure, and reactant utilizations to achieve roundtrip efficiencies that are competitive with other EES technologies. Here we present a viable system configuration based on the ReSOC concept suitable for intermediate- (~MWh) and large-scale (GWh) EES applications. Roundtrip system efficiency estimates are generated from computational modeling using performance on par with state-of-the-art H2/steam fueled ReSOCs in conjunction with a thermal management strategy during electrolysis mode that relies on exothermic methanation within the ReSOC. Parametric studies of important ReSOC operating conditions, including stack temperature, pressure, and fuel utilization are conducted with the objective of determining suitable operating points that retain the theoretically high energy conversion efficiency of the ReSOC stack itself.

1.1. System integration challenges One significant challenge of designing the proposed system is its thermal management. The hydrogen oxidation and steam reduction reactions are highly exothermic and endothermic, respectively, such that under typical operation the SOFC mode requires excess heat rejection while SOEC mode requires heat supply to maintain the desired ReSOC operating temperature. Another thermal management challenge is integrating ambient temperature gas storage and high temperature electrochemical energy conversion in the ReSOC stack. Because the system includes storage of vapors, specifically H2O, there is an added complication of storing and compressing both gaseous and liquid reactants and products. Among the above system design issues, overcoming the endothermic electrolysis process such that the system is thermally self-

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sustaining is a central challenge. Several strategies have been previously considered to address this challenge for systems employing steam and hydrogen as the lone reactant species. The most prevalent thermal management approach is to operate the ReSOC at a high current density during electrolysis such that excess thermal energy is generated from resistive heating (i.e., operating at cell voltages greater than the thermoneutral voltage) [13e15]. This strategy relies on operating the electrolyzer less efficiently to generate waste heat and the associated efficiency penalty may be unacceptable for many energy storage applications. Alternatively, studies have considered coupling a ReSOC with a thermal storage phase-change material (PCM) to store excess thermal energy generated in SOFC mode to be utilized in SOEC mode [16,17]. With a supply of heat from the PCM, the electrolyzer can operate at a lower current density (i.e., more efficiently). However the thermal energy put back into the system is necessarily lower than the storage temperature, restricting its utility. Another study considered utilizing a Mg-based metal hydride for hydrogen storage that operates at high temperature (~300  C) and produces an exotherm when absorbing hydrogen to offset some of the endothermic steamelectrolysis and evaporation load [18]. A different thermal management strategy is used in the present work that was initially proposed by Bierschenk et al. [12]. This strategy takes advantage of the operational flexibility of ReSOCs to utilize carbonaceous reactant species (e.g., CH4, CO, CO2) and involves carefully selecting the tank compositions and ReSOC stack temperature and pressure to promote the exothermic methanation reaction. The exothermic methanation reaction (see R2) helps to overcome the endothermic electrochemical reduction reactions such that the electrolysis process can operate more efficiently without the need to generate extensive resistive waste heat. Furthermore, the generation of methane in SOEC mode benefits operation in SOFC mode because the endothermic steam-methane reforming of the synthesized methane provides an in-situ sink for some of the thermal energy released from electrochemical oxidation. This thermal management strategy has the added benefit of storing a fuel mixture that is rich in methane, thereby increasing the storage energy density and alleviating some of the problems associated with hydrogen storage. Equilibrium calculations suggest that operating the ReSOC stack at an intermediate temperature of about 600  C or elevated pressure of about 10 bar promotes sufficient methane formation to allow efficient and thermally selfsustained SOEC mode operation [12].

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been studied both theoretically and experimentally with most studies focusing on pressures below 20 bar [8,25]. Finally, use of carbonaceous reactants is considered to be a major advantage of ReSOCs over lower temperature electrochemical cells that are irreversibly damaged from CO poisoning. The present work relies on providing the thermal energy required by the electrolysis reactions from exothermic synthesis of carbonaceous fuel (e.g., methanation) within the SOEC. The ability to simultaneously electrolyze steam and CO2 to produce syngas (i.e., co-electrolysis) allows efficient generation of feedstocks for synthetic natural gas and FischereTropsch fuel synthesis and has shown promising performance and durability [8,26e29]. Additionally, the balance of plant of fuel cell power systems is simplified when hydrocarbon fuels or reformate are used directly by the cell stack [30e32]. The following theory of operation section details the ReSOC reaction chemistry and reactant composition considerations to fully elucidate the proposed thermal management strategy and explain ReSOC operation in the context of the cell currentevoltage performance characteristic. The modeling approach is then presented including explanation of a practical implementation of the proposed system. Next, additional system considerations and modeling results are presented including parametric studies of the effect of ReSOC stack operating temperature, pressure, and fuel utilization on roundtrip efficiency.

2. Theory of operation 2.1. Reaction chemistry Global reaction chemistry within ReSOCs includes electrochemical fuel oxidation (or reduction), fuel reforming (or methanation), and wateregas shift (or reverse shift) processes. Equations (R1)e(R3) summarize these primary reactions that occur in a ReSOC where the Dh given is the molar heat of reaction at 800  C. As written, the forward reactions typically occur when the ReSOC is operated in fuel cell mode and the reverse reactions occur during electrolysis; although it is possible, for example to have both wateregas shift and reverse wateregas shift reactions occur at different locations within the ReSOC in a single operating mode

1.2. ReSOC operating requirements The ReSOC stack operating conditions suggested above including high pressure, intermediate temperature, and highly carbonaceous reactants are outside of the typical SOFC operating ranges; however, cell materials development and research has provided promising results, suggesting efficient and durable operation under these conditions in the near future [12,13,19]. Reducing the ReSOC temperature to an intermediate range (500e700  C) allows use of less expensive materials, simplifies the design of the balance of plant, decreases start-up time, and may increase durability. For these reasons, significant effort has been devoted to the research, design, and development of efficient, intermediate temperature ReSOCs [10,20,21]. Pressurized operation of solid-oxide cells is important to the present work because it promotes methane formation in SOEC mode. Pressurization has also been shown to increase cell electrical efficiency and improve system efficiency when coupled with other system processes (e.g., Brayton cycle power generation or synthetic hydrocarbon fuel production) [22e24]. Pressurized ReSOCs have

Fig. 2. Global reaction chemistry in the ReSOC for both SOFC mode and SOEC mode.

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depending on the reactant compositions and axial temperature profile.

H2 þ 1 2 O2 4H2 O

Dh ¼ 248 kJ mol1

=

CH4 þ H2 O43H2 þ CO H2 O þ CO4H2 þ CO2

Dh ¼ 226 kJ mol1 Dh ¼ 34 kJ mol1

(R1) (R2) (R3)

Fig. 2 illustrates the chemistry and transport occurring within the cell layers in each mode of operation, that is, charging during electrolytic operation and discharging during fuel cell operation. In SOFC mode, hydrogen is consumed and water vapor is produced at the fuel side electrodeeelectrolyte interface as a result of the fuel cell electrochemical oxidation reaction (R1). If carbon-containing species (CO, CO2, CH4) are present in the anode feed gas, steammethane reforming (R2) and wateregas shift (R3) reactions may also take place in the fuel electrode compartment depending on the operating conditions and material sets employed. Endothermic steam-methane reforming (R2) is promoted as a result of H2 depletion and H2O production (from R1), and under low pressure and high temperature cell conditions. This reaction helps to mitigate the excess oxidant cooling typically required during power producing SOFC mode. However, the steam-reforming reaction rate over NieYSZ electrodes is rapid and can create large temperature gradients within the cell. The reverse of reactions (R1)e(R3) occurs when the cell is operated in SOEC mode as shown in Fig. 2. The electrolytic reduction reaction (reverse of R1) proceeds when a cell voltage greater than the open-circuit voltage is applied across the electrodes thereby reversing the flux of oxygen through the solid electrolyte. The methanation reaction (reverse R2) is promoted by production of H2, consumption of H2O, and lower temperature and higher pressure operating conditions. The exothermic methanation reaction helps to offset the thermal energy consumed by the endothermic electrolysis reaction (reverse R1), which is important in maintaining the high temperature required for the ReSOC to operate. Direct oxidation and reduction of CO and CO2, respectively, are known to occur in ReSOCs [26], although the wateregas shift and reverse shift reactions are typically assumed to be the dominant reaction pathways for these species. 2.2. Reactant gas composition considerations The simplified system concept depicted in Fig. 1 includes two gas compositions associated with the “fuel” and “exhaust” storage tanks, however it is not immediately clear which compositions are most suitable for efficient operation. Furthermore, because this is a closed system, the reactant compositions are not determined by a feedstock input, such as natural gas in an SOFC power system or some ratio of steam and CO2 in a co-electrolysis process. Rather, the gas occupying the “exhaust” tank is produced during SOFC mode where its composition is established from the SOFC stack operating conditions including temperature, pressure, and fuel utilization. Similarly, the composition of the gas in the “fuel” tank is established from the fuel channel product stream when the system is operated in SOEC mode at its respective operating conditions. The two compositions are conveniently depicted on the CeHeO ternary diagram as shown in Fig. 3. They have equivalent hydrogento-carbon ratios, but the oxygen content changes with the addition of oxygen during SOFC mode and removal of oxygen during SOEC mode. The possible compositions are bounded by the fully oxidized region and carbon deposition region. Solid carbon deposition causes irreversible damage in ReSOCs (i.e., catalyst poisoning,

Fig. 3. CeHeO ternary diagram depicting fully oxidized (blue) and carbon deposition (gray) regions and possible “fuel” and “exhaust” reactant compositions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

increased mass transport resistance in the gas diffusion electrode, etc.) and its formation depends on many factors including temperature, pressure, and mixture composition. The thermodynamic carbon deposition boundary is determined by equilibrium calculations assuming solid carbon forms graphite on the ReSOC [33]. It is a function of temperature and pressure alone and can be used to estimate deleterious operating conditions. Selection of viable gas compositions must mitigate carbon deposition, ensure sufficient methane for thermal management, and allow high fuel energy density for increased energy storage capacity. Thus, it is desirable to operate with a highly carbonaceous composition (i.e., low hydrogen-to-carbon ratio) that does not exceed the carbon deposition boundary. A utilization parameter (i.e., fuel utilization or reactant utilization) quantifies the fraction of reactant delivered to the stack which is electrochemically converted. For a reversible system, it is also useful to consider the utilization in terms of oxygen transport across the electrolyte. Thus, the utilization parameters are used to mathematically relate the “fuel” and “exhaust” compositions. In the case of fuel cell mode, the fuel utilization is defined as the ratio of the molar rate of electrochemical hydrogen consumption to the equivalent molar flow of hydrogen supplied to the fuel channel of the SOFC mode stack:

N_ H2 ;consumed  UF ¼
N_ H2 þ N_ CO þ 4N_ CH4

(1) SOFC inlet

where Ṅi is the molar flow of species i and N_ H2 ;consumed is the molar rate of hydrogen consumption at the fuel electrode. Alternatively, reactant utilization for electrolysis operation can be defined as the ratio of oxygen generated at the oxygen electrode to the total oxygen available in the reactant species entering the fuel channel:

N_ O2 ;produced  UR ¼
2 N_ H2 O þ 2N_ CO2 þ N_ CO

(2) SOEC inlet

The above definition suggests that complete electrochemical reduction of the reactant species (i.e., UR ¼ 1) includes reducing CO.

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In practice, the presence of heterogeneous side-reactions at the fuel electrode offers other chemical formation pathways, such as CH4 formation via methanation, making this definition especially useful for lower temperature, pressurized systems. Despite Eqs. (1) and (2) being defined for SOFC and SOEC operation, respectively, each parameter also influences the opposite operating mode for a reversible system. For example, the fuel utilization affects SOEC mode operating parameters. Specifically, in a closed energy storage system, oxygen is either transferred to or removed from the fuel electrode and the utilization term is a measure of this. In turn, the magnitude of the utilization affects the tank composition for the subsequent mode switching operation. Because the ReSOC EES system must ensure continuous reversible operation, the storage tanks must eventually return to their original state of charge (i.e., respective composition or oxygen content). In other words, the mass flows and conversion rates associated with a prescribed SOFC mode fuel utilization define the operating conditions (i.e., reactant utilization) required in SOEC mode such that the system is recharged to the original state exhibited by the storage tanks. To recharge the system in this way, the value of reactant utilization (UR) is not necessarily equivalent to the value of the fuel utilization (UF) because the reactant utilization measures the extent of reduction of a gas mixture, while the fuel utilization measures the extent of oxidation of a different gas mixture. Additionally, a given fuel utilization does not indicate a specific reactant utilization which will return the system to its original state because the two parameters are not explicitly related.

2.3. Currentevoltage relationship The relationship between current and voltage in a ReSOC is a determining characteristic of the cell efficiency. The open circuit voltage (OCV) is estimated by the Nernst potential, calculated as:

xH2 x0:5 RT O2 ln EN ¼ E þ nF x H2 O 0

! þ

  RT P ln 2nF P0

(3)

where EN is Nernst potential, E0 is standard equilibrium potential, and the species mole fractions, temperature, pressure, Faraday constant and universal gas constant are represented by xi, T, P, F and R, respectively. The number of electrons transferred per reaction is n ¼ 2 for reaction (R1). The cell voltage in each mode of operation is calculated as a deviation from OCV by a current-dependent overpotential. A representative voltageecurrent plot for a ReSOC at both atmospheric and elevated pressure (20 bar) is shown in Fig. 4 where the current is positive in SOFC mode and negative in SOEC mode. An intermediate fidelity cell model [34,35] was employed to generate Figs. 4 and 5. For high temperature (800e1000  C) ReSOCs, activation overpotential is relatively small compared to low temperature electrochemical cells, particularly in the electrolysis mode of operation. However, under intermediate temperature conditions (550e800  C), the activation overpotential is more significant, particularly at low current density [34]. Ohmic overpotential increases linearly with current density and is attributed to the resistance to electron and ion transport in the MEA. The majority of ohmic resistance is attributed to ion transport in the electrolyte and interfacial contact resistances between cell components and layers. Concentration overpotential due to reactant depletion at the electrodeeelectrolyte interface arising from diffusion limitations in the porous electrodes occurs at both the fuel and oxygen electrodes. Inefficiency (i.e., overpotential) increases with increased current density; however, it is essential to operate at reasonably high current density in order to achieve an economically high stack power

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Fig. 4. Voltage (left) and power density (right) vs. current density for a ReSOC under atmospheric (black) and pressurized (red) conditions. Interconnects are isothermal at 800  C to simulate laboratory conditions, inlet fuel composition is 15% H2, 35% CO, 15% H2O, and 35% CO2, 99.99% oxygen is supplied to the oxygen channel, and fuel and airflowrates are constant at 25 NL/h and 20 NL/h, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

density. Interestingly, a unitized stack for reversible operation requires balancing design considerations for both modes of operation. For example, heat generation associated with cell-stack inefficiency helps to offset the endothermic reduction reaction (reverse R1) in electrolysis mode, but can cause excessive heat generation in fuel cell mode. The currentevoltage relationship is influenced by the cell operating conditions (e.g., T, p, xi) and these effects must be considered when determining suitable operating conditions for energy storage. The results in Fig. 4 show that pressurized operation has advantages for enhancing ReSOC performance, particularly in SOFC mode where the ratio of power produced to power consumed in SOEC mode at a given current density is higher. Increasing the pressure also changes the cell thermal behavior, for example by promoting the exothermic methanation reaction. The cell temperature at a given current density is relatively higher if the methanation reaction occurs inside the fuel channels. Therefore, pressurized operation allows more efficient (i.e., lower overpotential) operation for a practical system when methanation occurs in the fuel channel. Pressurized operation has two distinct effects on the cell electrochemical performance: (1) increased Nernst potential and (2) reduced losses associated with the activation and concentration polarizations. The third term in the right side of the Eq. (3) represents the pressure dependence of the Nernst potential. As the cell pressure increases, this term rises from 0 (at 1 bar) to larger values, resulting in increased Nernst potential at each current density. With an increase in EN, the SOFC power production and efficiency also increases. Although, pressurized operation has the opposite effect in electrolysis mode at low magnitude current densities (i.e., it increases the cell power consumption because the applied voltage must be higher for a given current density). At high current density (i.e., past the “intersection point” in Fig. 4) the pressurized SOEC has better performance compared to atmospheric because the increased Nernst potential is offset by reduced activation and concentration losses. Indeed, pressurized operation significantly reduces the concentration losses and enhances the chargeetransfer reaction kinetics in both modes of operation [34]. Despite increased SOEC mode power consumption at elevated pressure in the low current density regime, increased power production in fuel cell mode results in a net benefit for roundtrip

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follow a Vej characteristic more closely represented by constant fuel utilization than constant fuel flow. In both operating modes, the cell performance is lower for the constant utilization case compared to constant fuel flow at current density magnitudes <1 A/cm2 because of higher reactant consumption and associated changes in OCV. Beyond 1 A/cm2, the constant fuel flow case exhibits higher fuel utilization (>70%), resulting in lower cell performance compared to the constant utilization case. The constant utilization curves are not shown near OCV because portions of the cell become inactive at low current density when high fuel utilization is maintained. 2.4. Energy storage efficiency

Fig. 5. Voltage vs. current density for a ReSOC operating with different reactant compositions in each mode. SOFC composition (molar): 35.3% H2, 1.0% CO, 51.1% CH4, 12.0% H2O, 0.7% CO2; SOEC composition (molar): 17.4% H2, 3.2% CO, 4.6% CH4, 54.2% H2O, 20.6% CO2). The constant fuel flow case has an inlet fuel flowrate of 4.3 NL/h and 8.0 NL/h in SOFC and SOEC mode, respectively. The constant utilization case has a constant fuel utilization of 70%. Stack pressure is 20 bar, interconnects are isothermal at 650  C to simulate laboratory conditions, and 99.99% oxygen is supplied to the oxygen channel at 20 NL/h.

storage efficiency (see the roundtrip efficiency definitions below). The combined effects of the phenomena described above indicate that pressurization increases the overall performance of the cell in both operating modes. Thus, the present work focuses on pressurized ReSOC systems. It should be noted that the results shown in Fig. 4 are produced with the same feedstock gas composition in both fuel cell and electrolysis modes, resulting in a continuous curve as the cell moves through polarity switching at zero current. This result is representative of constant fuel flow, cell-level laboratory testing practices. However, for the proposed energy storage application, the reactant gas compositions in each mode will not be the same and it is therefore necessary to explore the implications of different compositions on the cell characteristic. Fig. 5 shows predicted voltageecurrent curves considering unique reactant compositions in SOFC and SOEC modes for both constant fuel flow and constant fuel utilization. As can be seen from the constant fuel flow case, the curves associated with each composition have distinctly different OCV values. Comparing the constant fuel flow results presented in Figs. 4 and 5 shows that the ReSOC performance increases when the feedstock gas compositions are not the same. For example, with more hydrogen (reactant) and less water (product) in the feedstock gas composition in SOFC mode, the Nernst potential, and consequently power output, increases. Alternatively, since water is the main reactant in the SOEC mode, high amounts of water in the SOEC mode feedstock gas composition decrease the Nernst potential and consequently reduce the cell power consumption for a given current density. To consider the implications of the voltageecurrent characteristic in the context of system level operation it is re-emphasized that for a practical system, the inlet composition in one mode of operation is determined based on the exhaust gas conditions established from operation in the opposite mode. For the constant fuel flow Vej curve in Fig. 5, the feedstock composition in SOEC mode is produced from the stack in SOFC mode only at a specific current density which corresponds to 70% fuel utilization (i.e., at 1 A/cm2 where the constant fuel flow and constant utilization curves cross). Because of the interdependence of the two feedstock compositions, roundtrip operation in the proposed system will

The efficiency of a ReSOC system for energy storage depends on both the efficiency of the ReSOC and the auxiliary power required by the balance of plant components (BOP). The roundtrip system efficiency, hRT, is defined as the quotient of the net energy generated in SOFC mode to the total energy supplied in SOEC mode:

hRT ¼

VSOFC qSOFC  WBOP;SOFC VSOEC qSOEC þ WBOP;SOEC

(4)

where VSOFC and VSOEC are the operating nominal cell voltages, qSOFC and qSOEC are the total charge transferred across the electrolyte, and WBOP, SOFC and WBOP, SOEC are the total BOP energy required during SOFC mode and SOEC mode, respectively. The BOP energy includes parasitic power loads from components, such as compressors, power produced from turbines, and energy entering the system in the form of fuel or process streams. As the definition implies, for achieving high roundtrip efficiency, it is desirable to operate at high cell voltage in SOFC mode and low applied voltage in SOEC mode (i.e., operate at low overpotential), as well as to have low BOP energy consumption in both modes of operation. It is convenient to define the efficiency in terms of energy (rather than power) to allow different operating durations in SOFC and SOEC modes. However, for repeatable and self-sustaining operation, the system must be returned to the initial state of charge (i.e., “charged” state) by operating in SOEC mode. Depending on the energy storage application and operating strategy, the “charged” state may be achieved, for example, daily, weekly, or seasonally. The state of charge is defined as the hydrogen equivalence of the gas stored in the SOFC tank, which is proportional to the charge transfer required to completely oxidize the stored fuel. Thus, to ensure repeatable operation, the total charge transferred during SOEC mode must be equal to the charge transferred while discharging the system in SOFC mode: qSOFC ¼ qSOEC. The roundtrip stack efficiency, hRT,stack is calculated by neglecting the BOP energy required in both modes such that Eq. (4) is simplified to:

hRT;stack ¼ VSOFC =VSOEC

(5)

The roundtrip stack efficiency is useful for understanding system performance by quantifying the efficiency impact of the ReSOC stack and the BOP independently. 3. Modeling approach System level modeling is employed to determine suitable system configurations and operating conditions that enable high roundtrip efficiency. The cell models that have been developed can accurately predict ReSOC performance and are reported on elsewhere [34,35]. Because an EES system based on ReSOCs must carefully incorporate thermal management strategies, the model

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needs to accurately predict both the system electrical and thermal energy characteristics. To estimate the roundtrip efficiency, steadystate performance is determined for each operating mode assuming that the system is fully recharged after one discharge/ charge cycle. This assumption simplifies the modeling effort, although certainly other operating strategies could easily be explored depending on the requirements of a specific energy storage application. Fig. 6 illustrates the system concept considered in this study which includes several salient elements related to thermal and water management that are not featured in the simplified schematic given in Fig. 1. In each mode of operation the reactant species, either from the “fuel” (mostly CH4 and H2) or “exhaust” (mostly CO2) tank, are expanded, preheated, and mixed with steam evaporated from a separate water storage tank before entering the stack at statepoint (3). The reactants are converted to products in the ReSOC stack with either consumption or generation of dc electric power. Finally, the product species from the stack are cooled to condense out any H2O (statepoint 5) before compression and additional cooling for tank storage (6). Liquid water is stored separately such that evaporation, condensation, and additional pumping hardware are required. This configuration suggests that much of the BOP hardware is utilized in both modes of operation, but system simulation is ultimately required to determine the feasibility of this approach. Additional BOP components are needed to pre-heat and compress air to the required stack inlet conditions (statepoint 9) and then to recuperate thermal and mechanical energy from the exhausted air (10) after it is utilized in the stack. Furthermore, an ejector is employed to recycle some of the airflow (11) exiting the stack to reduce the cost and power load of the BOP components with only a slight penalty to stack efficiency. The gaseous storage function for this system may assume a variety of configurations depending on the scale of application. For example, lower capacity distributed applications may economically employ pressurized tanks for storage of gaseous species while large capacity (e.g., GWh) grid-scale applications may more economically utilize underground caverns such as has been done with natural gas and compressed air [7]. A study on compressed air energy storage systems noted that above ground tanks are economically favorable compared to underground caverns up to sizes of around 40,000 m3, above which the capital investment in developing an underground

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storage cavern is justified [36]. Furthermore, the use of fixed vs. variable volume storage components will have considerable impact on dynamic operation [37,39]. Specific storage configurations will not be considered in this study because under steady-state conditions the storage vessels are simply considered as sources and sinks. Many BOP components must be thermally integrated in this system including pre-heat and recuperative heat exchangers, condenser, and evaporator. For the purposes of this study, specific configurations of these thermal components are not declared. Rather, duty requirements are used to ensure the energetic feasibility of operation with a pinch temperature of >15  C and no violations of the 2nd Law occur. The ReSOC stack performance is estimated from a steady-state, one-dimensional, cell-level model adapted from the literature [34,35] with a simplification applied to the electrochemical model. Specifically, the ReSOC currentevoltage characteristic is represented by a constant area specific resistance (ASR) such that the cell voltage is determined by:

Vcell ¼ EN  j ASR

(6)

where j is the current density. Although the cell currentevoltage performance is known to depend on temperature, pressure, and composition, modeling the system with fixed ASR is useful in isolating the changes in system-level performance irrespective of changes in ReSOC resistance. Because of this decision, the system results can be useful in selecting ReSOC material sets which are typically optimized to operate within a relatively small temperature range. Or said differently, the system-level study can establish the temperature, pressure, and utilization for a specified ASR to achieve a given system performance, which then serves as an MEA design requirement for materials development. Compressors and turbines are modeled with isentropic efficiencies listed in Table 1. The ejector performance is described by the following equation which is used to determine the driving flow pressure required by the compressor to entrain the desired flowrate of recycled oxidant [38,40].

hejector ¼

V_ 2 p2 lnðp3 =p2 Þ V_ ðp  p Þ 1

1

(7)

3

Fig. 6. Energy storage system schematic with component electric power loads in both SOFC (ẆSOFC) and SOEC (ẆSOEC) modes for the base case system (see Tables 1 and 2 for operating conditions and statepoint data, respectively).

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Table 1 Model parameters for the base case and parametric studies. Operating parameter

Base value (range)

Stack pressure Average stack temperature Fuel utilization Hydrogen-to-carbon ratio Average current density Area specific resistance (ASR) Charge/discharge duration ratio Storage tank temperature Storage tank pressure SOFC mode oxidant recycle ratio SOEC mode oxidant recycle ratio Minimum SOFC excess air ratio Oxidant channel temp. increase Fuel channel inlet temp. Compressor isentropic efficiency Turbine isentropic efficiency Ejector efficiency

20 bar (5e150) 650  C (500e800) 90% (55e90%) 6.19 (5e10) 0.695 A/cm2 (0.55e1.15) 0.20 U cm2 1.0 25  C 160 bar 60e65% 50e70% 1.5 stoichs 150  C 100  C less stack temp. 88% 90% 20%

where V_ 1 and V_ 2 are the volumetric flowrates of the primary driving flow and the recycled oxidant flow, respectively, and p1, p2, and p3 are the static pressures of the driving flow (statepoint 8), recycle oxidant (11), and ejector discharge stream (9), respectively. The pressure drop across the ReSOC stack air channel significantly impacts ejector performance and is assumed to be 30 mbar. 4. System operating considerations The selected current density and fuel composition are important model parameters that depend on the stack temperature and pressure. As noted previously, it is desirable to operate with high concentrations of carbonaceous species (i.e., low hydrogen-tocarbon ratio) for stack and system thermal management, for example, using methane. However, at these operating temperatures (>550  C), carbon containing reactant gases can deposit coke on electrode surfaces, reducing performance. For this study, the thermodynamic carbon deposition limit is used to select reactant compositions that are expected to avoid coke formation. The current density is selected to ensure that enough waste heat is generated by the stack to meet the process gas heating requirements including reactant preheat and steam evaporation. The waste heat generated within the cell stack due to resistive losses is a nonlinear function of the operating current density and is a direct result of stack inefficiency. Operating the stack efficiently enough to maintain high roundtrip efficiency while also generating enough waste heat for gas processing can be a challenge. In many stationary energy storage applications, high system efficiency is valued over high power density (i.e., high current density). Ultimately establishing the most judicious balance between these performance parameters is best accomplished through techno-economic assessment [e.g., 41]. Practically, the minimum current density is determined based on the thermal requirements in SOEC mode because a large quantity of steam must be generated and the electrochemical reduction reactions are endothermic. These endothermic processes are offset by heat generated in the stack from both methanation of generated fuel species (reverse R2) and resistive heating associated with stack polarizations. If, for example, less heat is generated from the methanation reaction because of the selected fuel constituents or stack conditions (T, p), then a greater operating current density is required to provide the needed thermal energy. The ‘discharging’ (SOFC) mode is exothermic for all but very low current densities. Selecting the current density in each mode of operation also requires considering the operating durations. For example, if the

charge duration is twice as long as the discharge duration, then the discharge current density must be twice as large as the charging current density to return the system to its original state of charge. For this study, the charge and discharge duration are assumed to be equal, such that the current density is equal in both modes and is set to the minimum value that allows exothermic ‘charging’ (SOEC) mode. In the following modeling results, the fuel utilization parameter (UF) is used to describe the extent of electrochemical conversion in both operating modes. This implies that the SOFC mode operating conditions (e.g., fuel flow) satisfy Eq. (1), and the SOEC mode conditions are such that the fuel flowrate generates a fuel mixture suitable for sustaining repeated charge/discharge cycles. That is, the charging mode parameters are set to return the system to its original state of charge following system discharge at the prescribed fuel utilization. The reactant utilization could alternatively be used in place of the fuel utilization parameter, but was not considered in the present study. 5. System modeling results & discussion 5.1. Base case results The base case system operating parameters include a nominal stack temperature of 650  C, stack pressure of 20 bar, and fuel utilization of 90%. Other relevant operating parameters for the base case are listed in Table 1 along with the ranges explored in the following parametric studies. The electric power from the ReSOC stack and system components in both modes of operation are shown in Fig. 6 for a 1 MW stack discharge power rating. Nevertheless, the efficiency results presented in this paper are considered to be scale-independent because the stack performance is estimated by extrapolating from a channel-level cell model and the BOP performance is set by isentropic efficiency specifications. The statepoint data and gas mixture compositions for the base case system are listed in Table 2. The base case system stores electricity with dc roundtrip stack and system efficiencies of 72.8% and 72.6%, respectively. It is notable that the system efficiency is nearly as large as the stack efficiency, indicating that most of the power consumed during compression is recuperated in the expansion processes. This configuration is similar to an SOFCegas turbine hybrid system, but differs because stack tail-gases are not combusted such that a smaller fraction of the compressor power is recuperated from expansion. The ensuing parametric studies show that some net power is generated from the BOP under certain operating conditions. In the base case system, for example, the air expansion process in SOFC mode produces 205 kW while air compression consumes only 189 kW. Net power is generated by the air turbomachinery in SOFC mode but not in SOEC mode. The reason for this difference can be explained by the thermal interactions of the BOP components. For example, in SOEC mode the main reactant is H2O which leads to a high evaporation heat load and the air exhausted from the stack is the primary heat source for this evaporation process. Therefore, relatively less power is generated from the SOEC mode air expansion compared to SOFC mode because the expansion temperatures are lower after heat is provided to the evaporator. The power loads on the air turbomachinery are an order of magnitude larger than the fuel expansion/compression processes because of high airflowrates. Thus, system performance is more drastically impacted by the air BOP components than fuel BOP components, which is a useful conclusion in understanding the parametric study results. Also, the power requirement of the air expansion/compression in SOFC mode is about 2.5e3.5 times larger

C.H. Wendel et al. / Journal of Power Sources 276 (2015) 133e144 Table 2 System statepoint data for the base case. State point

Flow [kg s1]

SOFC mode (discharge) 1 25.8 2 32.3 3 32.3 4 128.5 5 63.5 6 63.5 7 523.9 8 523.9 9 1284.3 10 1188.0 11 760.4 12 427.6 13 427.6 SOEC mode (charge) 1 63.2 2 128.5 3 128.5 4 32.3 5 26.0 6 26.0 7 227.6 8 227.6 9 802.7 10 898.9 11 575.0 12 323.8 13 323.8

T [ C]

p [bar]

25 145 550 615 50 139 25 288 517 667 667 667 100

160.0 20.0 20.0 20.0 20.0 160.0 1.0 20.38 20.0 19.97 19.97 19.97 1.1

Fuel (stored) Fuel þ steam Fuel þ steam Exhaust þ steam Exhaust (stored) Exhaust (stored) 21% O2/79% N2 21% O2/79% N2 12% O2/88% N2 5% O2/95% N2 5% O2/95% N2 5% O2/93% N2 5% O2/95% N2

25 207 550 618 50 162 25 112 506 656 656 656 87

160.0 20.0 20.0 20.0 20.0 160.0 1.0 20.93 20.0 19.97 19.97 19.97 1.1

Exhaust (stored) Exhaust þ steam Exhaust þ steam Fuel þ steam Fuel (stored) Fuel (stored) 21% O2/79% N2 21% O2/79% N2 36% O2/64% N2 43% O2/57% N2 43% O2/57% N2 43% O2/57% N2 43% O2/57% N2

Composition

Gas composition mole fractions (%)

Exhaust (stored) Exhaust þ steam Fuel (stored) Fuel þ steam

H2

CO

CH4

H2O

CO2

23.6 8.2 38.2 33.1

3.4 1.2 0.5 0.4

2.0 0.7 60.9 52.8

<0.1 65.4 <0.1 13.3

71.0 24.6 0.5 0.4

than that for SOEC mode. This is because the SOFC mode stack operates more exothermically and thus requires more cooling airflow. The following parametric studies consider the effect of ReSOC stack temperature, pressure, and fuel utilization on system efficiency. These parameters are significant because they impact stack thermal management, including the kinetic and thermodynamic effect on methane formation and steam-methane reforming. System operation is also affected by these parameters, for example, by

Fig. 7. Minimum current density required for exothermic SOEC mode operation (left) and minimum hydrogen-to-carbon ratio as dictated by the carbon deposition boundary (right) vs. stack pressure.

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the influences on heat exchanger preheating and recuperation duties, and compressor and turbine power consumption and generation. 5.2. Stack pressure parametric results The operating pressure of the ReSOC stack has a significant impact on the system efficiency. Importantly, stack pressure also affects the minimum current density required to satisfy gas processing thermal loads, and the reactant composition which is expected to mitigate carbon deposition. Fig. 7 shows the fuel composition in terms of the minimum molar hydrogen-to-carbon ratio (HTCR) allowed and average stack current density as a function of ReSOC operating pressure at a fixed average stack temperature of 650  C, fuel utilization of 90%, and storage pressure of 160 bar. A plot of the minimum HTCR needed to avoid carbon deposition (see Fig. 7) shows that increasing stack operating pressure enables higher concentrations of carbonaceous species in the “fuel” and “exhaust” compositions. A certain amount of stack waste heat is essential to meet the process gas heating load in the stack periphery. As the ReSOC stack pressure increases, more heat is generated from the methanation reaction in ‘charging’ (SOEC) mode; therefore less heat is required from stack inefficiency (i.e., resistive heating) and a lower current density can be used. Fig. 7 shows the current density as a function of stack pressure, where the current density is relatively low at high pressure and increases sharply at lower pressure to overcome the heating deficit caused by lower conversion of the exothermic methanation reaction. There are two primary reasons for higher conversion of the methanation reaction at higher pressure: (1) the HTCR of the fuel composition decreases, approaching closer to the stoichiometric ratio for methane (i.e., H/C ¼ 4), and (2) improved reaction kinetics of methanation. The optimum roundtrip system efficiency is achieved based on a trade-off between stack efficiency and auxiliary power. As shown in Fig. 8, the roundtrip stack efficiency increases with increased stack pressure because the current density required for exothermic SOEC mode operation decreases (See also Fig. 7). However, the increased stack efficiency is counterbalanced by increased auxiliary power consumption at high stack pressure. The right-axis in Fig. 8 shows the net auxiliary power generated in each mode as a fraction of the stack electric power where

Fig. 8. Roundtrip stack and system efficiency (left), net BOP power produced (ẆBOP) relative to stack power (Ẇstack) (right), and stored methane mole fraction (top) vs. stack pressure.

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negative values imply that more power is required by compression processes than is generated by the turbines. At lower stack pressure, the SOFC mode auxiliary components produce net power because the turbine expansion of air exhausted from the stack produces more power than is required to compress air to the stack operating pressure. Yet, the benefit of net energy generation from the auxiliary components is overcome by a rapid decline in stack efficiency at low stack pressure. The competing trends of stack efficiency and auxiliary power result in an optimal system efficiency of 72.5% at a stack pressure of about 20 bar. The reason the SOFC mode auxiliary power generation increases with decreased stack pressure is that the air does not need to be compressed to as great a pressure and the exhausted air from the stack can be expanded at higher temperatures while still performing the required heating processes. Another consideration when determining the most suitable stack pressure is the affect it has on the composition of the stored gases. The top horizontal axis of Fig 8 shows the mole fraction of stored methane in the “fuel” tank where the remaining stored gas is primarily hydrogen. As stack pressure increases, the amount of stored methane increases due to increased methanation in SOEC mode. Higher purities of produced methane can be achieved at high stack pressure with limited efficiency loss which allows for increased energy storage density and the possibility of coupling such an energy storage system with existing natural gas infrastructure. It is an important result that the system efficiency is significantly influenced by the system BOP when turbomachinery is employed because the desirable operating conditions expected from only analysis of the ReSOC stack differ from the operating conditions that achieve optimal system efficiency. Furthermore, the optimal system configuration must, in addition to efficiency, also consider cost, dynamic operation, and control.

5.3. Stack temperature parametric results The average stack temperature impacts roundtrip efficiency; however, as shown in the previous parametric study, much of this impact can be understood by considering the effect of stack operating temperature on the hydrogen-to-carbon ratio of the reactant gas mixture and average operating current density. Fig. 9 illustrates how the current density and HTCR of the reactant mixtures vary with changes in average stack temperature. The HTCR is set based on the thermodynamic carbon deposition limit and increases with

Fig. 9. Minimum current density required for exothermic SOEC mode operation (left) and minimum hydrogen-to-carbon ratio as dictated by the carbon deposition boundary (right) vs. stack temperature.

increased temperature. The required average current density to meet process thermal loads decreases with increasing stack temperature in the low temperature range primarily because the exhaust airflow used to supply heat to the evaporator in ‘charging’ (SOEC) mode exits the stack at a lower temperature, therefore necessitating more heat generation in the stack to satisfy pinchpoint temperatures. A minimum current density is reached at an average stack temperature of about 680  C. At higher temperatures the required current density increases because more waste heat is required from the stack at higher temperatures where the exothermic methanation reaction has lower equilibrium conversion. Fig. 10 shows the stack and system roundtrip efficiencies as a function of average stack temperature. System efficiency is maximized at an intermediate operating temperature of about 680  C and is primarily influenced by the stack efficiency and discharge mode auxiliary power. The stack efficiency increases slightly with increased stack temperature at lower temperatures and then drops off sharply at temperatures above 700  C in accordance with the increased current density (see also Fig. 9). Recall that cell ASR has been fixed (i.e., the temperature dependence removed) so that the plots shown here are a direct result of the influence of changes in reaction energies and BOP power, and are decoupled from changes in cell resistance. Nevertheless, previous work has shown cell performance for operating temperatures below 650  C to be on par with the total cell resistance of 0.20 U cm2 assumed in the present study [9,10]. The SOFC (discharge) mode BOP power shifts from consuming net power at lower temperatures to producing net power at higher temperatures. The net auxiliary power generation in SOFC mode increases with increased average stack temperature primarily because the excess air exhausted from the stack is at a higher temperature such that more power is generated from expanding it to ambient pressure. One conclusion from these results indicates that low temperature cell operation (<650  C) is not necessarily a materials requirement for ReSOC energy storage systems configured in this way, so long as the stack pressure is sufficiently high. Additionally, the optimum associated with roundtrip efficiency is relatively shallow, changing by only 5% across a large temperature range. The methane content in the stored gas mixture is a strong function of stack temperature as shown by the top axis of Fig. 10.

Fig. 10. Roundtrip stack and system efficiency (left), net BOP power produced (ẆBOP) relative to stack power (Ẇstack) (right), and stored methane mole fraction (top) vs. stack temperature.

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Greater than 80% methane content is achieved at stack temperature below 550  C, although that value drops to 55% at optimal efficiency at 680  C. This trend exemplifies a distinct tradeoff between efficiency and stored energy density and such tradeoffs must ultimately be informed by economic analysis.

5.4. Fuel utilization parametric results In the present study, lowering the fuel utilization implies oxidizing the stored “fuel” species to a lesser extent. In other words, the HeCeO composition of the “fuel” tank remains fixed as dictated by the carbon deposition boundary and at higher fuel utilization the “exhaust” tank contains a more oxidized gas mixture. The “stored fuel” and “fuel þ steam” compositions are only slightly impacted by changing the fuel utilization and are similar to compositions from the base case system (see Table 2). The stack efficiency is affected by the fuel utilization parameter through the open-circuit voltage which is a function of the bulk composition; however, this affect is minor, particularly compared with changes in stack efficiency from current density variation. Finally, it should be noted that unlike typical SOFC systems, lowering the fuel utilization in the present system does not directly correspond to reduced system efficiency. This is because the proposed system is “closed” and the denominator of the efficiency definitions is the power input to the system, rather than rate of energy input from fuel. Lower fuel utilization, however, requires storing a larger proportion of unused fuel species, negatively impacting energy density. The fuel utilization changes the thermal operating characteristic of the ReSOC such that for higher fuel utilization, more waste heat must be generated from the ReSOC stack for exothermic operation in SOEC mode. This necessitates an increased current density with increased fuel utilization (not shown). The causal relationship between fuel utilization and stack thermal behavior is complicated and can be better understood through the thermoneutral voltage parameter, which is beyond the scope of this study. Fig. 11 shows the stack and system efficiencies as a function of fuel utilization. Stack efficiency increases with decreased fuel utilization because the stack can operate more efficiently (i.e., lower current density) while still satisfy system thermal loads. The roundtrip system efficiency is affected by the fuel utilization both because of the effect on stack efficiency and the impact on the BOP performance due to transporting a different proportion of unreacted species throughout the system and different cooling

Fig. 11. Roundtrip stack and system efficiency (left) and net BOP power produced (ẆBOP) relative to stack power (Ẇstack) (right) vs. fuel utilization.

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airflow requirements. The stack efficiency increases with decreased fuel utilization (see Fig. 11). However, the parasitic losses from the BOP increase with decreased utilization such that the roundtrip system efficiency is maximized to nearly 74% at about 70% fuel utilization. It is clear from these results that the roundtrip system efficiency is only mildly affected by changes in fuel utilization. Fig. 11 also shows the ratio of net BOP power generated to stack electric power in each mode as a function of fuel utilization. The SOEC mode net BOP power is relatively constant with fuel utilization. The cooling airflow in SOEC mode is mostly independent of fuel utilization because any reduction in heat generation from the internal chemical reactions is subsidized with increased current density to satisfy the required system heating loads. Thus, with similar airflows, and stack temperature and pressure, the air turbomachinery loads are nearly independent of fuel utilization. Alternatively, based on the changed thermal characteristic of the ReSOC stack with fuel utilization in SOFC mode, the BOP net power increases with increased utilization. This is because less heat is generated in the SOFC mode stack when it is operated more efficiently such that the excess oxidant exhausted from the stack is expanded at a lower temperature after fulfilling the required system heating processes. As a result, less power is recuperated from the air turbine. The fuel utilization also affects the reactant and product turbomachinery, but the flowrate of the air is significantly higher, such that the air turbomachinery dominate the BOP performance. The stack pressure and fuel utilization studies show a common trend in that increased stack efficiency correlates with increased parasitic BOP power in SOFC mode due to the decreased excess heat generation from the stack. In short, these studies illustrate the competing trends between stack efficiency and BOP power consumption that lead to optimal system efficiency operating points. 6. Conclusions This paper has analyzed a novel EES system based on ReSOCs to estimate achievable roundtrip efficiencies and to examine the influence of stack temperature, pressure, and fuel utilization on system efficiency. By implementing a thermal management strategy using carbonaceous reaction chemistry it was shown that >70% roundtrip storage efficiencies can be achieved. Steady-state system modeling results indicate that system efficiency is maximized at intermediate ReSOC stack operating conditions of about 680  C, 20 bar, and 70% fuel utilization based on the trade-off between stack efficiency and balance of plant power consumption. The auxiliary power generation has a significant effect on system efficiency, and it is important to note that the nature of this impact could change for alternately configured ReSOC EES systems, potentially shifting or eliminating the optimal efficiency points. It is promising, however, that the initial results suggest optimal behavior at intermediate operating conditions such that extreme operation (i.e., low temperature, high pressure) are not necessarily required for efficient energy storage. Several system challenges have been revealed, which motivate further study of this promising EES system. One challenge is that the roundtrip efficiency is strongly influenced by system thermal integration. Specifically, the stack efficiency is constrained by the system heating requirements such that the stack efficiency cannot be arbitrarily increased by lower current density operation within the present system configuration. Another challenge is the difference in gas flowrates (i.e., air, fuel, and exhaust streams) processed by the BOP in each mode of operation. Assessing the feasibility of utilizing the same BOP components in both operating modes requires system simulation and may ultimately require system configuration modifications. Finally, the parametric studies

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