Design and techno-economic analysis of high efficiency reversible solid oxide cell systems for distributed energy storage

Applied Energy 172 (2016) 118–131

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Design and techno-economic analysis of high efficiency reversible solid oxide cell systems for distributed energy storage Christopher H. Wendel, Robert J. Braun ⇑ Department of Mechanical Engineering, College of Engineering and Computational Sciences, Colorado School of Mines, 1610 Illinois Street, Golden, CO 80401, USA

h i g h l i g h t s
Reversible SOC systems for distributed electricity storage are conceptualized.
Computational modeling is used to assess system energetic and economic performance.
Impact of water management strategy via different configurations is assessed. 3


Roundtrip efficiency of nearly 74% and storage density of 90 kWh/m are achieved.
Capital cost is used to assess tradeoffs between efficiency and energy density.

a r t i c l e

i n f o

Article history: Received 10 September 2015 Received in revised form 6 March 2016 Accepted 16 March 2016

Keywords: Energy storage Solid oxide cell Reversible fuel cells Distributed generation Thermal management Techno-economic analysis

a b s t r a c t Reversible solid oxide cell (ReSOC) systems are conceptualized and analyzed to assess technical performance in distributed energy storage applications (100 kW/800 kWh). The ReSOC systems operate sequentially between fuel-producing electrolysis and power-producing fuel-cell modes with intermediate tanking of reactants and products. Maintaining the high conversion efficiencies seen in laboratoryscale cell tests at the system-level requires careful system design to integrate storage and electrochemical conversion functions. By leveraging C–O–H reaction chemistry and operating at intermediate temperature, the ReSOC is mildly exothermic in both operating modes, which simplifies balance-of-plant integration and thermal management. System configurations explored herein range from a simple system with minimal balance-of-plant components to more complex systems including turbine expansion for increased electrical efficiency, and separating water for higher energy density storage. The efficiency, energy density, and capital cost tradeoffs of these configurations are quantified through computational modeling. Results indicate that a roundtrip efficiency of nearly 74% is achieved with relatively low tanked energy density (20 kWh/m3) for systems configured to store water-vapor containing gases. Separately storing condensed water increases energy density of storage, but limits efficiency to 68% based on the energetic cost of evaporating reactant water during electrolysis operation. Further increases in energy density (to 90 kWh/m3) require higher storage pressures (e.g., 50-bar nominal) which lower roundtrip efficiency to about 65%. Cost of energy storage is strongly influenced by stack power and system energy densities because the storage tanks and stack comprise a majority of the system capital cost. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Electrolysis with solid oxide cells to generate fuel and other products from electricity is an attractive option for utilizing excess renewable energy generation [1–4]. This technology can also be used in a more traditional energy storage capacity by operating sequentially in both electrolysis and fuel cell modes to compete

⇑ Corresponding author. E-mail addresses: [email protected] (C.H. Wendel), rbraun@ mines.edu (R.J. Braun). http://dx.doi.org/10.1016/j.apenergy.2016.03.054 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

with advanced batteries, compressed air, and pumped hydro energy management methods [5–9]. Achieving competitive performance with reversible solid oxide cells (ReSOC) requires advancement in both materials and system design to enable efficient and inexpensive operation. The unique characteristics of solid oxide cells (i.e. high temperature, carbonaceous reactants) allow them to exceed the roundtrip energy storage efficiency of typical lowtemperature reversible fuel cells [10]. This study explores different system configurations and operating conditions in order to evaluate the potential of ReSOCs to compete with present and future energy storage technologies. It presents the first system

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configuration and economic trade study assessing hightemperature reversible solid oxide cells serving as a distributed energy storage system. The considered system operates in either fuel cell (SOFC) or electrolysis (SOEC) modes with intermediate tanked storage of reactants and products. Fig. 1 shows a simplified schematic of the envisioned process. The energy storage system charges by operating the ReSOC stack as an electrolyser, in which exhaust species – primarily H2O and CO2 – are discharged from a storage tank, heated, delivered to the stack, and co-electrolyzed with an input of electricity to produce a fuel mixture. The generated fuel is cooled and compressed to a separate storage tank for later use. The system discharges by operating in SOFC mode, in which the tanked fuel mixture is preheated, delivered to the stack and electrochemically oxidized, producing electricity and exhaust species to re-fill the exhaust tank. An oxidant flow is required in the SOFC mode to provide oxygen for the electrochemical reactions and regulate stack temperature. In SOEC mode, the airflow acts as a sweep gas to increase electrical efficiency by diluting generated oxygen in the oxygen channel and serves as a heat sink for exothermic operation. Some unique challenges arise in designing ReSOC systems, including: (i) overcoming the thermal disparity between fuel cell (typically exothermic) and electrolysis (typically endothermic or near thermoneutral) operation using a unitized cell-stack and common hardware, (ii) selecting configurations and operating conditions (T, p, utilization, composition) that promote high efficiency in both operating modes, and (iii) thermal integration between high temperature stack operation and lower temperature, pressurized storage. Furthermore, because reaction products are tanked for use in the opposite mode of operation, they must be processed to enable compression to storage pressure with minimal energetic cost. The systems under consideration simplify system thermal management by combining co-electrolysis with in-situ fuel synthesis (i.e., methanation) and electrochemical oxidation with internal fuel reforming such that the stack is slightly exothermic in both SOFC and SOEC modes. By using this strategy, the cell can operate exothermically at electrolysis voltages that would otherwise be endothermic, enabling increased electrical efficiency without utilizing an external heat source. This approach enables high efficiency and thermally self-sustaining operation, but requires operating the ReSOC stack under conditions that promote methane formation in electrolysis mode. Methanation is catalysed on nickel

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present in the ReSOC fuel electrode and is promoted by low temperature and high pressure stack operation. Promoting in-situ methanation in ReSOCs has been considered previously for energy storage applications. Bierschenk et al. [6] showed thermodynamic analysis indicating that operating the stack at 600°C and/or 10 atm promotes sufficient methane formation for system thermal management. Wendel et al. [11] presented modeling analyses of large-scale (>10 MW) ReSOC systems showing roundtrip efficiency >70% at stack operating conditions of 680°C and 20 bar. Wendel et al. [12] also employed cell-stack models using parameters fitted from experimental button cell data to explore the effects of reactant composition, flow configuration, and current density on roundtrip efficiency and stack thermal behavior. Jensen et al. [5] considered large-scale ReSOC systems (250 MW) coupled with underground cavern storage of methane and carbon dioxide. The system achieved roundtrip efficiency of 70% and cost of 3 ¢/kWh performing load-levelling services with high penetration of wind energy. For comparison, low temperature reversible fuel cell systems typically achieve roundtrip efficiencies of 20–55% [13–15]. 1.1. Objectives The objective of this work is to determine favorable system configurations and operating conditions for stand-alone ReSOC systems by evaluating the technical and economic performance for distributed scale energy storage applications (100 kW/800 kWh). This objective is achieved by simulating roundtrip operation of a ReSOC system through steady-state computational modeling with a physically based ReSOC model and thermodynamic system component models. The ReSOC model was previously calibrated to high performance intermediate temperature magnesium- and strontium-doped lanthanum gallate (LSGM)-electrolyte cells operated at 600°C [12]. Various system configurations are evaluated based on roundtrip efficiency, tanked energy density, and capital cost. The conclusions from this study inform major design decisions that have not been considered in prior publications including storage conditions, system operating conditions, BOP configuration, and system hardware. These conclusions – along with the methods described herein – provide an important foundation for continued analysis and eventual deployment of ReSOC energy storage systems. First, the thermodynamics of ReSOC operation are considered by comparing steam–hydrogen, methane-CO2/H2O red-ox, and

Fig. 1. Simplified schematic of a reversible solid oxide cell system and cell schematic showing fuel channel, oxidant channel, and membrane electrode assembly.

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the syngas mixture used in the present study. Next, a model description that includes a brief discussion of the assumptions and calculation methodology with particular attention to simulating reversible systems, is given. In the results section, a series of system configurations are presented starting with the ‘‘stored-vapor” case, in which tanked reactants are stored at elevated temperature to maintain vapor phase of stored water. As will be shown, this system suffers from relatively low energy density, but achieves high efficiency, particularly with the inclusion of an expansion turbine to recuperate losses from compressing gas to tank pressure. Next, an alternate approach is considered in which water is condensed out of the gas streams and stored in a separate container prior to compression. This approach enables lower temperature and higher energy density storage for more economical tank sizing. The efficiency of this ‘‘water separation” configuration is limited by the energetic requirement to re-boil reactant water. Within each configuration, parametric studies reveal the impact of key operating conditions such as fuel utilization, current density, and tank pressure. The paper concludes by comparing the presented systems including a comparison of system capital cost and discussing the implications of transient tanked storage and projected improvements in ReSOC stack performance.

2. Thermodynamics and the case for intermediate temperature reversible solid oxide cells The advantages of using reversible solid oxide cells with carbonaceous reactant species over low temperature reversible fuel cells – or those operating on pure steam–hydrogen mixtures – are elucidated by considering the thermodynamics of the relevant electrochemical conversion processes. Similar thermodynamic analysis has been previously shown for steam electrolysis [16,17], co-electrolysis [18], and fuel-synthesis processes [19]. For roundtrip energy storage, the theoretical maximum roundtrip stack efficiency is DG/DH of the electrochemical conversion; or rather, the maximum electrical energy generated in fuel cell mode (Gibb’s Free Energy, DG) divided by the total energy required in electrolysis mode (Enthalpy, DH). Fig. 2(a) indicates these thermodynamic parameters for devices operating with steam–hydrogen. As temperature increases, the maximum roundtrip efficiency decreases because more waste heat (TDS) is generated during fuel cell operation. The electrical energy requirement for electrolysis is equivalent to the maximum electricity generation in fuel cell mode (DG), although the additional energy (TDS) must be provided as either heat or electricity (i.e., via increased overpotential). The theoretical maximum efficiency for the steam–hydrogen case falls below 80% at 625°C. Alternatively, the thermodynamic performance of the methane red-ox reaction is shown in Fig. 2(b). For this reaction, the TDS term is nearly zero, indicating almost complete reversibility, resulting in approximately 100% maximum efficiency independent of operating temperature. The thermodynamic results in Fig. 2 also include the maximum roundtrip efficiency when the H2O reactant is considered to be in the liquid phase by including the latent heat of vaporization in the reaction enthalpy. This calculation indicates the efficiency penalty associated with needing to boil water, which is around 10 percentage points, and motivates system designs where H2O is maintained in vapor phase during storage to achieve higher roundtrip efficiency. Because of several practical operating limitations, including the inability to directly electrochemically convert or produce CH4, the ideal case of methane red-ox cannot be executed. However, the operating conditions and catalytic activity of ReSOC material sets enable indirect methane red-ox reactions. Carbon deposition

Fig. 2. Thermodynamic performance of (a) steam–hydrogen and (b) methane redox reactions.

and reactant utilization limitations also require that the ReSOC reactants and products are not pure or in stoichiometric ratios as indicated by the reaction equation in Fig. 2(b). In fact, the tanked gases will be some mixture of syngas and exhaust species falling somewhere in between the pure hydrogen and methane cases. The thermodynamics of the practical operating case can be assessed by assuming equilibrium of the reactants and products. Fig. 3(a) shows the theoretical efficiency and voltage for electrochemical conversion of a syngas mixture with hydrogen-tocarbon ratio of 9.9, fuel oxygen content of 5% and exhaust oxygen content of 29%. This C–O–H composition is selected to prevent graphitic carbon deposition at equilibrium [12,20,21]. The optimal theoretical efficiency of 97% is achieved around 570°C and decreases at higher or lower temperatures. The maximum efficiency decreases to 85% when including the energy associated with the latent heat of vaporization. The equilibrium gas compositions are shown in Fig. 3(b), where the fuel composition (i.e. that stored in the fuel tank in Fig. 1) is indicated at an oxygen content of 5%. During fuel cell operation, the fuel species are oxidized to a mixture oxygen content of 29% – this extent of conversion correlates with 60% fuel utilization. However, the roundtrip efficiency is not penalized by the utilization <100% as in a typical fuel cell system because the reaction products are tanked forming a closed system between the fuel tank, exhaust tank, and stack fuel channel. The fuel mixture is composed of primarily hydrogen with 20% methane, while the exhaust composition includes similar amounts of steam and hydrogen with 15% CO2. The thermodynamic analysis in Fig. 3 demonstrates the benefit of using intermediate temperature ReSOCs optimized to operate at <650°C. This temperature range precludes present day anodesupported yttria stabilized zirconia (YSZ)-electrolytes, which have relatively high resistance at temperatures below 700°C for conventional electrolyte thicknesses of 10–15 lm [22,23]. Moreover, the

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Fig. 3. Thermodynamic performance of a carbonaceous mixture red-ox process showing (a) efficiency and thermodynamic properties vs. temperature and (b) equilibrium species mole fractions for varying oxygen content at expected ReSOC system operating conditions.

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LSGM electrolyte cells offer high ionic conductivity and remain electrically resistive even at low oxygen partial pressure [22,33,34]. Cells constructed with LSGM-electrolyte have achieved high power density >2 W/cm2 at 650°C, and can be fabricated with conventional tape-casting methods. Currently, the cost of LSGM is substantially higher compared to ceria [22], and the high performance is achieved with a nickel-catalyst infiltration process [35] which will need to be adapted for high production volume manufacturing. Stability issues, including gallium depletion and insulating secondary phases, have been reported for some LSGM materials [22,36]. The results in Fig. 3 along with continued development of ITReSOCs suggest that high roundtrip cell efficiency can be achieved at thermodynamically favorable conditions. Here LSGM-electrolyte cell performance is captured in a calibrated model to determine stack performance, however cell performance improvement is still needed to achieve competitive efficiency at 600°C while maintaining reasonable current density. In this work, a lower operating current density (0.20 A/cm2) is chosen to maintain high efficiency with present technology and the implications of expected cell performance improvements are discussed in Section 5.2. While LSGMelectrolyte cell performance has been used here, it should be noted that different intermediate temperature cells may also be employed in such reversible systems so long as they meet the resistance, durability, cyclability, and dual-mode operating requirements which include reforming capability. Overpotential losses associated with operating at non-zero current density and auxiliary power loads from balance of plant (BOP) will necessarily reduce the roundtrip efficiency below the theoretical limit. The following modeling results predict these losses to estimate the system roundtrip efficiency. 3. Modeling approach

kinetic losses increase exponentially with decreasing temperature, necessitating a shift from micro- to nano-scale microstructure to increase active site density [24]. Development of intermediate temperature (IT) solid oxide cells has achieved high performance within the desired temperature range in laboratory tests using, for example, reduced thickness YSZ (e.g., ultra-thin or thin-film), LSGM, or doped ceria (e.g., by gadolinium or samarium) electrolytes, and nano-scale catalysts in the porous electrodes. Reviews of IT solid oxide cells have been carried out by Brett et al. [22], Laguna-Bercero [25], and Gao et al. [26]. Intermediate temperature cells still face development challenges, but continual advances show promise for these next generation ReSOCs. Thin-film YSZ electrolyte cells with electrolyte thickness <1 lm overcome the higher resistance of the YSZ material at intermediate temperature and have achieved power density >2 W/cm2 at 650°C [27]. Recently different research groups have manufactured thin-film YSZ-electrolyte cells with gasimpermeable electrolyte layers on conventional large planform porous anode substrates [27–29], indicating compatibility with established stack and system technologies. Challenges remain to consistently produce such thin membranes with manufacturing methods amenable to production scale-up. Ceria-based electrolytes have high ionic conductivity, but stability issues arise at low oxygen partial pressure and high temperature [30]. These issues are compounded during electrolysis mode operation, indicating that a stand-alone doped-ceria electrolyte cannot be used for electrolysis [31]. Bi-layer ceria/zirconia electrolytes have been used to overcome the limitations of ceria, but manufacturing of the bi-layer electrolytes requires further investigation to prevent formation of a low conductivity interfacial layer [32].

The modeling approach detailed in this section includes the assumptions used in modeling the ReSOC stack and system components, the methodology to simulate roundtrip ReSOC systems at steady state, system costing procedure, and performance metric definitions. 3.1. ReSOC stack model The one-dimensional, steady-state ReSOC model used herein has been published elsewhere [12]. The model includes mass and energy conservation in an adiabatic channel assumed to be in the middle cell of a ReSOC cell-stack. Single channel performance is extrapolated to represent cell and stack performance. The electrochemical characteristic is calibrated to cells constructed using an La0.8Sr0.2Ga0.8Mg0.2O3d-electrolyte with nickel infiltrated LSGM fuel electrode, nickel infiltrated lanthanum strontium titanate (Ni-SLT) fuel electrode support, and La0.6Sr0.4Fe0.8Co0.2O3-d–Gd0.1Ce0.9O1.95 (LSCF–GDC) oxygen electrode. The electrochemical model captures the effects of ohmic overpotential with ohm’s law, activation overpotential with the Butler–Volmer equation, and concentration overpotential with Fickian diffusion. The performance used here is indicative of the cell performance and does not include a penalty associated with cell-stacking. This characteristic represents the performance achievable with a current material set that can be manufactured with common methods and has shown promising durability. As the technology matures and benefits from larger scale manufacturing, losses associated with cell-stacking will decrease. The cell V–j characteristic is shown in Fig. 4(a) at a nominal operating temperature of 600°C. Note that the discontinuity in the performance curve at zero current density arises from the dif-

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characteristics (such as, efficiency or pinch point temperature difference). Component performance parameters are given in Table 1. A minimum pinch temperature of 25°C is imposed for heat transfer processes [39]. Thermal integration of heat exchangers, evaporator, and condensers involves matching heat sources (e.g., hot stack exhaust gas) and sinks (e.g., steam generation) within the system. However, condenser loads have excess heat rejection requirements not satisfied by system process streams. The condensers are air cooled with a parasitic power penalty of 0.04 kWe per kWth of rejected heat and minimum condenser outlet temperature of 50°C. The parasitic load is determined from a simple calculation assuming fan efficiency of 75%, air temperature rise from 30 to 80°C, and pressure change across the fan of 1.5 kPa. 3.3. Calculation procedure

Fig. 4. (a.) Current–voltage characteristic for an intermediate temperature LSGMelectrolyte ReSOC model at 600°C, 1 atm, and fixed reactant flowrate, (b). C–O–H ternary diagram for operation.

ferent reactant compositions employed in each operating mode. The compositions are representative of the storage system simulation results and are taken from the ‘‘fuel” and ‘‘exhaust” compositions given previously in Fig. 3(b). This cell characteristic at 600°C has an elevated area-specific resistance (ASR) of about 0.40 Ocm2 compared to higher temperature LSGM [35] or YSZ [37] cells achieving ASR < 0.25 Ocm2 at 650 and 850°C, respectively. Operating reactant gas compositions are carefully selected to avoid thermodynamically favorable regions for carbon deposition. Carbon deposition is influenced by several factors including temperature, pressure, and composition. Local variation of these factors along the fuel channel and into the electrode structure make predicting operating limits at which coking occurs difficult [38]. Typically SOFC systems operate with elevated steam to carbon ratio (e.g., S/C = 1.5–3) to prevent deleterious coking, but the different operating conditions of the system considered here (lower temperature, near equilibrium reactants) may allow more carbonaceous and more reduced compositions without suffering deposition. Fig. 4(b) shows a ternary diagram indicating the C–O–H compositions at which graphitic carbon forms at equilibrium (shaded regions). The dashed blue line provides an indication of the C–O–H operating region for the system studies herein (H/ C = 9.9) and for the V–j characteristic given in Fig. 4(a). Note that system operation is such that the reactant gases are never fully oxidized or reduced. Carbon deposition is predicted with the selected ‘‘fuel” composition at 800°C operation, but not for the lower temperature regimes here. 3.2. System component models The system components used in the present modeling study include compressor, expander, heat exchanger, condenser, boiler, and ejector. These components are all modeled thermodynamically with lumped mass and energy balances and constant performance

To accurately simulate reversible systems, the charge and discharge operating conditions must be selected so that the system is eventually returned to the original state of charge, thereby allowing continuous operation. The state of charge – defined as the total amount of charge that can be delivered by the system at its current conditions – is directly proportional to the hydrogen equivalence of the gas mixture stored in the ‘‘fuel” tank. It depends on both the quantity and composition of the stored gas mixtures. The system must be operated so that the tanks are not depleted of mass or diluted of their respective ‘‘fuel” or ‘‘exhaust” compositions. These constraints manifest by selecting appropriate combinations of current density, reactant gas flow, operating duration, and utilization parameters. This study considers steady state simulations, so the operating parameter constraints are defined on a rate basis (e.g., current, mass flow, etc.) as opposed to the cumulative property change (e.g., energy, total mass). To ensure complete system recharge, the total mass entering and leaving each tank must be equal over some operating duration. For example, the flow discharged from the ‘‘fuel” tank during SOFC operation must equal the mass flow entering the ‘‘fuel” tank in SOEC mode to recharge the system. The mass flow constraints are represented by the following equations:

_ \fuel";SOEC;in t SOEC _ \fuel";SOFC;out t SOFC ¼ m m

ð1Þ

_ \exhaust";SOEC;out t SOEC _ \exhaust";SOFC;in t SOFC ¼ m m

ð2Þ

Table 1 Nominal system operating conditions. Parameter Average stack temperature Gross stack power Min. HX pinch temp. Compressor/expander isentropic efficiency HX pressure drop Fuel composition Stack nominal pressure Average current density Cell voltage Cell efficiency* Fuel utilization Fuel channel inlet temperature Air channel temperature increase

Stored vapor (Fig. 5)

Water separation (Fig. 9) 600 100 25 80

50 H/C = 9.9, O = 5% 1 0.20 0.27 936 (SOFC) 917 (SOFC) 1119 (SOEC) 1148 (SOEC) 86 (SOFC) 86 (SOFC) 97 (SOEC) 93 (SOEC) 65 55 550 (SOFC) 550 (SOFC) 528 (SOEC) 531 (SOEC) 150 (SOFC) 150 (SOFC) 50 (SOEC) 151 (SOEC)

Unit °C kW °C % mbar – atm A/cm2 mV % % °C °C

* Based on thermoneutral voltages of 1.087 V and 1.062 V for Figs. 5 and 9, respectively.

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_ i is the flowrate into or out of the ‘‘fuel” or ‘‘exhaust” tank where m in either SOFC or SOEC mode, and ti is the operating duration in either SOFC or SOEC mode. In the present study, the charging and discharging durations are assumed equal. A charge balance constraint ensures that the tanks are not diluted because each transfer of charge in the ReSOC requires an associated oxygen ion transfer. This condition requires that charge transfer in each mode is equal such that the atomic oxygen content of each tank is eventually returned to its original state (i.e., low oxygen content in the ‘‘fuel” tank and oxidized gas mixture in the ‘‘exhaust” tank). This constraint is imposed through the current density as:

jSOFC tSOFC ¼ jSOEC tSOEC

ð3Þ

where ji is the operating current density. The above constraints for mass flow and current density are also connected to the fuel utiliza_ and UF) are assigned for a simtion. As such, two out of three (j, m, ulation, which determines the third. The fuel utilization is defined as follows:

N_ H2 ;consumed  UF ¼
_NH þ N_ CO þ 4N_ CH 2 4

ð4Þ SOFC inlet

where N_ H2 ;consumed is the electrochemical hydrogen consumption in SOFC mode and N_ i is the molar flowrate of species i entering the stack in SOFC mode. The fuel utilization is defined explicitly only in SOFC mode, but it is also used to influence the operating conditions of the opposite mode. For example, prescribing a given fuel utilization in SOFC mode implies that the SOEC mode operating conditions (i.e., reactant flowrate, current density, reactant utilization) must be set to return the system to its original state of charge. Further details on the process for simulating roundtrip operation of ReSOC stacks, which include consideration of carbon deposition, can be found in our previous work [12]. Parameter selection for system simulation includes selecting the stack average temperature, pressure, current density, fuel utilization, air channel temperature increase, and fuel channel inlet temperature. Values for these parameters are given in Table 1. Current density selection is balanced by consideration of achieving high roundtrip stack efficiency at low current density with improved system thermal management through increased waste heat availability at high current density. Even though the stack may operate exothermically, system heating processes typically require additional waste heat to meet heat exchange pinch temperature specifications. The simulations are run at steady-state and constant tank pressure. In practice, to mitigate over-sizing tanks, the storage pressure of rigid tanks can vary considerably during operation. The dynamics of tank operation are complicated due to tank temperature and pressure variation during filling and evacuation. The consequences of tanked storage are discussed further in Section 5.3. In the basecase system results, both fuel and exhaust tank are assumed to be fixed at 20 bar, suggesting that the system is at a 50% state of charge, where both tanks are approximately half-full. This approach implies that tanks will vary between 2 and 40 bar over the full range of operation. 3.4. System costing procedure A preliminary economic analysis is performed to distinguish between the technical performance tradeoffs (i.e., efficiency vs. energy density) of the various system configurations. Considerable uncertainty remains for the cost of solid oxide cells, particularly for novel intermediate temperature cells. Thus, the results are most useful when comparing the relative cost of the different ReSOC sys-

tems by individually assessing the capital and annualized costs of the various system components. James et al. [40] presented a detailed costing of SOFC stacks and systems for 1–100 kWe systems over a range of annual production scales. The LSGM-electrolyte cells chosen for this study require mostly conventional manufacturing methods suitable for commercial production (i.e., tape-casting, screen-printing). The increased cost of LSGM compared to YSZ is a small problem because the electrolyte material cost is only considered to comprise about 1% of the total assembled ReSOC stack cost [40]. Ultimately the stack cost is estimated at 874 $/m2 for 100 kW stacks based on a production volume of 10,000 systems per annum, and a 30% contingency to account for uncertainty in material cost and manufacturing. The stack area (m2) is calculated for each system by dividing the SOFC mode stack power of 100 kW by the SOFC mode power density (W/m2). The stack is assumed to be replaced every 5 years, while the other system components have an assumed life of 20 years. Storage tank cost is assessed based on 170 l steel compressed natural gas tanks with a pressure capacity of 200 bar and unit cost of $310 [41]. The tank volumes for the ReSOC systems presented here are such that between 50 and 200 tanks are required per system. An import tariff cost of 25% and shipping, plumbing, insulation, and packaging cost of 30% is assumed for a final cost of $2960/m3 of tank volume. System component capital cost including heat exchanger equipment, turbomachinery, and power electronics are determined from several sources [40,42–45] and scaled based on the component size (e.g., heat exchanger area, compressor load, etc.). Scaling equations for all system components are given in Table 2. Miscellaneous costs including valves and piping are taken from Ref. [46] with a value of 74.1 $/kWstack. All costs have been converted to 2012 prices using the Chemical Engineering Plant Cost Index. System costs reported here reflect the cost of the energy storage device neglecting the power conversion system (PCS) required to convert between ac power from the grid and dc power used by the ReSOC stack [47]. PCS costs can vary by energy storage technology and application [48]. Furthermore, the cost is known to be sensitive to power rating, battery voltage, and production scale [49]. Cost of PCS systems is estimated to be as high as $600-790/kW for the 100 kW systems considered here, but drop as low as $40/kW for GW scale systems [47,49]. 3.5. Performance metrics The roundtrip system efficiency is defined as the net energy produced in SOFC mode divided by the total energy consumed to recharge the system in SOEC mode:

gRT;sys ¼

ðW stk  W BOP ÞSOFC ðW stk þ W BOP ÞSOEC

ð5Þ

where Wstk is the cell-stack electricity consumption in SOEC mode or production in SOFC mode, and WBOP is the net BOP energy Table 2 Component capital cost scaling functions. Component

Cost function ($)

Ref.

ReSOC stack Balance of stack Storage tank

C 1 ¼ 874ðAstack ½m2 Þ C 2 ¼ 55:0ðAstack ½m2 Þ C 3 ¼ 2960ðV tnk;fuel þ V tnk;exst ½m3 Þ

[40] [40] [41]

Heat exchanger or boiler

C 4 ¼ 2290ðAHX ½m2 Þ

Gas compressor

_ ½kW=1000Þ C 5 ¼ 8:64E5ðW

[59]

Air blower

C 6 ¼ 3:07E5ðV_ ½m3 =s=30Þ

[43]

Expander

_ ½kW=10Þ C 7 ¼ 1:6E4ðW

Air cooled condenser

C 8 ¼ 1:34E5ðAHX ½m =280Þ

[42]

0:6 0:9

3

0:61

0:61

[59] 0:8

[43]

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consumption. For the steady state modeling approach used here where charge/discharge duration are equal, the efficiency metric is accurately described in terms of either power or energy. Stack efficiency is determined by neglecting BOP energy and is useful in interpreting system results. Applying the current density constraints in the previous section, the stack efficiency is simplified to the ratio of operating voltages:

gRT;stk ¼

W stk;SOFC V SOFC ¼ W stk;SOEC V SOEC

ð6Þ

The stored tank energy density, st is measured in kWh/m3, or rather the net energy produced in SOFC mode divided by the combined fuel and exhaust tank volume. PSOFC,net is the net power produced by the system in SOFC mode. The tank volumes are calculated assuming rigid tanks based on stored gas composition, temperature, minimum pressure, maximum pressure, and the total mass required to sustain operation for a prescribed duration, tSOFC (assumed to be 8 h).

st ¼

PSOFC;net t SOFC V tank;fuel þ V tank;exhaust

ð7Þ

The preliminary energy storage cost with typical units of ¢/ kWh-cycle is calculated as in Yang et al. [50] based on the system capital cost, energy capacity, roundtrip efficiency, and number of cycles.

P

Energy storage cost ¼

Cj PSOFC;net tSOFC gRT;sys ðCycle LifeÞ

ð8Þ

This cost metric neglects O&M and installation costs which must be included in future analysis. The cycle life is determined from assumed daily energy shift at 75% capacity, indicating 5475 cycles over 20 years, or <1500 cycles per stack assuming stack replacement every 5 years. The annualized cost for component j is calculated from Eq. (9) assuming a fixed annuity loan with 5% interest, i and accounts for differences in stack and system component life, n.

C j;annualized ¼ C j

i n ð1  ð1 þ iÞ Þ

ð9Þ

4. Results The results include system schematics, statepoint data, and performance metrics for various ReSOC system configurations. To explain the performance and operating limitations, particular focus is given to the thermal loads required to preheat reactants and the electrical loads required by the compressors and blowers. It should also be noted that while these systems are intended for dual mode operation, process flowsheet details such as heat exchanger bypass flows are not depicted here for sake of simplicity. The reactant gas flow configuration within the ReSOC stack is preferentially switched between co- and counter-flow arrangements (as shown in Fig. 1) based on prior analysis [12]. The stack is operated in co-flow in SOFC mode and in counter-flow for SOEC operation, which benefits system thermal performance. 4.1. Stored vapor system results The stored vapor system schematic and statepoint data for SOFC and SOEC modes are shown in Fig. 5. This system includes heat exchangers to preheat reactants and cool stack products, and compressors to pump stack products back to the storage tanks. The reactant species are preheated from the storage tank temperature (fixed to 50°C above saturation) to the stack inlet temperature, which requires a thermal load of 7–9 kW depending on the operat-

ing mode. The gas streams are heated and electrochemically converted in the stack which operates at sufficiently high overpotentials to be net exothermic. Thus, the hot fuel and air channel tail-gases can be used to recuperatively preheat the incoming reactant streams. Additional preheating is provided from hot gases downstream of the fuel compressors. The stack inlet reactant gas temperatures are 50°C and 72°C below nominal stack temperature in SOFC and SOEC modes, respectively. The lower stack inlet temperature in SOEC mode ensures that the pinch temperature is met in the fuel preheater due to the higher heat capacitance rate of the cold-side gas. A different preheating strategy of using an electric heater is discussed in Section 4.1.2, but ultimately is not considered feasible under the present operating conditions. The fuel heat exchanger serves two functions: to preheat reactant gases and to cool product gases for compression. Because of the imbalance in flow rates and heat of compression, the fuel preheat does not lower the stack tail-gas enough to achieve a sufficiently low compressor inlet temperature. Thus, pre-compressor cooling and inter-stage cooling using system airflow as a heat sink lowers compression temperature to a minimum compressor inlet temperature of 50°C above saturation. The air preheater and intercooling processes increase the ambient air temperature from 25°C to an inlet ReSOC oxygen channel temperature of 460°C (SOFC) or 544°C (SOEC) as shown in Fig. 5. The air flowrate and stack-inlet temperature are selected such that a nominal stack temperature (e.g., 600°C) is achieved with a specified air temperature rise of 150°C (SOFC) and 50°C (SOEC) across the air electrode side of the stack. Despite the internal chemical reactions balancing the thermal load between operating modes, the stack is more exothermic in SOFC mode. Thus, the air temperature rise in SOFC mode is higher compared to SOEC mode resulting in more similar air flowrates and exhaust temperatures (350– 365°C). The stack and system efficiencies for the stored vapor system are 83.6% and 65.4%, respectively, indicating that a significant efficiency penalty is incurred from compression parasitics. In each operating mode, the fuel compressor load is 7–12 times larger than the air blower load due to the much higher pressure ratio. However, the preheat load is higher on the air-side due to the higher flowrate of air compared to fuel and exhaust. The thermal or electric loads on the BOP are similar enough between SOFC and SOEC modes that the system may be dual-mode operated using the same components, favourably reducing system capital cost; although system simulation with specified hardware is required to validate this design approach. The volumetric energy density is 18.9 kWh/m3 for the stored vapor system. For an 8 h operating duration at 100 kW stack discharge power, the fuel and exhaust tank volumes are 14.3 and 21.6 m3, respectively. The temperature of the compressed fuel and exhaust streams enter their respective storage tanks above the tank temperature. The elevated gas inlet temperature allows for heat loss to the environment through the tank insulation, but additional heat may need to be removed from the stream prior to tanking to account for compression heat within the rigid tank. In any case, higher fidelity analysis to explore the transient effects of storage with specified tank geometry and materials is necessary to complete this element of the system design. Improving system efficiency requires reducing the auxiliary power loads. The performance impacts of operating conditions, including fuel utilization and current density, and the addition of a fuel expander are considered for the stored vapor system in the following subsections. 4.1.1. Fuel utilization parameter study A consequence of the relatively low fuel utilization (65%) given in the Fig. 5 results is that a significant fraction of the reactants and

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Fig. 5. Stored vapor system schematic and statepoint data.

products transported through the system are not used in the electrochemical conversion. On the other hand, heat evolution in the ReSOC stack is strongly influenced by fuel utilization, resulting in either more exothermic SOFC operation or more endothermic SOEC operation with increasing fuel utilization [51]. Stack and system efficiency are plotted as a function of fuel utilization in Fig. 6(a) at a fixed current density of 0.20 A/cm2, meaning that fuel utilization is increased by reducing the reactant flow. Roundtrip system efficiency increases with increased fuel utilization because the fuel compressor loads are lower relative to stack power. Stack efficiency is relatively constant with fuel utilization, but experiences a slightly negative effect from increasing reactant depletion in the fuel and oxygen channels. A limiting condition occurs near 72% fuel utilization where the SOEC mode stack shifts from exothermic to thermoneutral operation. Fig. 6(b) shows the electricity consumption by the fuel and air pumps. The SOEC mode air blower load drops to zero at 72% utilization, indicating that no cooling airflow is required (i.e., thermoneutral point reached). The opposite trend is seen in SOFC mode where the low air blower parasitic power at low utilization results from the stack being more endothermic (efficient) and thus requiring less cooling airflow. The fuel compressor load decreases significantly with fuel utilization in SOFC mode. In SOEC mode, the compressor load decreases slightly because of competing effects between lower gas flows and higher inlet compressor temperatures due to the lower available airstream heat capacitance rate which provides

intercooling. Lack of intercooling leads to a rapid increase in SOEC compressor power and an associated decrease in system efficiency as thermoneutral operation is approached. Using an alternate intercooling heat sink (e.g., ambient air or process water) can mitigate the decreased roundtrip efficiency at 72% fuel utilization, but the energy deficit in SOEC mode prevents further efficiency improvement within the present system design. Increasing utilization to around 70% maximizes roundtrip efficiency, but also imbalances the air-side BOP load between SOFC and SOEC modes, potentially making it difficult to use the same set of BOP components in both modes. Energy density increases with increased fuel utilization as shown in Fig. 6(a) because a lesser volume of fuel and exhaust must be stored for equivalent energy capacity. The storage conditions (T, p, xi) do not vary significantly with fuel utilization, so the energy density is solely attributed to a smaller amount of gas stored. 4.1.2. Current density parameter study The system efficiency is improved by operating the stack more efficiently (i.e., at lower current density), but the ultimate merit of this design condition is best informed through an economic analysis that judiciously weights low power density stack operation, capital cost associated with system thermal management, and operating costs (electrical energy, O&M). At lower current density, the stack generates less waste heat and therefore preheating process streams with reasonable pinch temperatures is problematic.

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with current density if the stack is at or below the thermoneutral voltage. However, a roundtrip efficiency benefit may be realized due to a higher operating voltage in SOFC mode, which is required to satisfy the charge balance constraint with equal charge/discharge durations. Ultimately, this strategy is not considered in the present work because exothermic operation can be achieved in SOEC mode at low overpotential (<60 mV) due to the opencircuit and thermoneutral voltages of 1.028 V and 1.087 V, respectively, under the present operating conditions (see Fig. 3). Therefore, operating at even lower overpotential, and consequently lower power density, values is not considered economically feasible. The electric heater approach may be more realistically considered in steam–hydrogen systems where reaching the thermoneutral voltage requires high overpotential.

Fig. 7 shows the roundtrip efficiency for varied current density for the stored vapor system. Improvement to 66.8% system efficiency is achieved at 0.15 A/cm2. However, at lower current density the system efficiency degrades because much less cooling airflow is available for compressor intercooling in SOEC mode as the SOEC approaches the thermoneutral point at about 0.10 A/cm2. An alternate operating strategy might consider operating at voltages below the thermoneutral voltage and supplying the deficit thermal energy in the SOEC stack with, for example, an electric heater integrated with the stack to preheat reactant gases or otherwise maintain stack temperature. The electric heater allows the SOEC stack to operate under endothermic conditions, but the power supplied to the heater must be included in the efficiency definition as auxiliary power. The SOEC stack efficiency is constant

4.1.3. Expansion turbine system configuration Another method for system performance improvement is integrating a fuel expansion turbine to recover energy as reactant streams are discharged from pressurized tanks. For the conditions in Fig. 5, including an 80% isentropic efficiency turbine in place of the tank discharge valve in both operating modes increases system efficiency to 73.7% – an 8.5-percentage point increase. Small-scale (1–10 kW) scroll expanders developed for PEM fuel cell systems and experimental organic Rankine cycles suggest that high efficiency expansion is viable at the proposed scale [52]. The system efficiency and tank energy density are shown as a function of tank pressure in Fig. 8 (recall that this nominal tank pressure is approximately half of the maximum tank pressure). Using a turbine expander increases the system efficiency, particularly at high tank pressure. Furthermore, the energy density increases significantly with increased storage pressure and the turbine configuration enables higher storage pressure while maintaining >70% roundtrip efficiency. The energy density trend shown in Fig. 8 is explained because less volume is required to store the required quantity of gas at high pressure. In fact, the stored compositions do not deviate from those shown in Fig. 5 as storage pressure increases. The compositions in the tanks are not chemically altered between the stack fuel-channel outlet and storage tank, meaning that they are not in chemical equilibrium at the storage conditions. The composition is expected to remain stable over the time-scales of roundtrip storage (e.g., days to weeks) when uncatalyzed. The energy density improves slightly when a turbine is included in the system because the system roundtrip efficiency is higher and therefore less gas must be stored for equivalent energy discharge capacity. That is, because the net power generation in SOFC mode is higher due to the added turbine, more energy can be extracted from a fixed amount of stored fuel.

Fig. 7. Efficiency vs. current density for the stored vapor system at nominal stack temperature of 600°C, fuel utilization of 65%, and tank pressure of 20 bar.

Fig. 8. Efficiency and tank volume vs. tank pressure for the stored vapor system with and without a recuperative expander.

Fig. 6. (a) Efficiency, energy density, and (b) auxiliary power load for varying fuel utilization in the stored vapor system at nominal stack temperature of 600°C, current density of 0.20 A/cm2, and tank pressure of 20 bar.

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4.2. Water separation system results Separating water from the fuel and exhaust gas streams prior to storage benefits system efficiency by reducing the compressor flowrate and temperature; and it also benefits energy density by reducing the mass and temperature of the stored reactants. These benefits come at the expense of needing to supply thermal energy to re-boil reactant water, which particularly impacts the process thermal management in electrolysis mode where steam is a major reactant. The statepoint data and system configuration for the water separation case are shown in Fig. 9. The reactant heating load increases from the stored vapor case to 15.3 and 33.9 kW in SOFC and SOEC mode, respectively, because of the lower storage temperature and additional boiler load. Operating conditions are selected to satisfy the increased thermal load while maintaining high stack efficiency. For example, an ejector is included to recycle air sweepgas exhausted from the stack in SOEC mode. Mixing the recycled gas with fresh air achieves the stack inlet temperature setpoint such that 16.3 kW can be extracted from the high temperature air exhaust for boiling and water superheat. The remaining boiler load is satisfied by hot gas exhausted from the stack fuel channel. Most of the fuel preheat is provided by the hot compressor exhaust gas (5.1 kW) at 343°C so that the higher quality fuel exhaust can be utilized for water superheat at 461°C.

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Despite these operating modifications, the stack must operate less efficiently compared to the stored vapor system to overcome the increased preheating requirements. Stack efficiency of nearly 80% is achieved with an operating current density of 0.27 A/cm2. However, the auxiliary power load is also lower relative to the stored vapor case as a consequence of lower flowrate and lower temperature at the compressor inlet. The system efficiency is 65.1%, which is slightly lower than the stored vapor basecase shown in Fig. 5. Because the stack efficiency is limited by the need to generate enough waste heat for the preheating load, the stack cannot be operated more efficiently, for example as shown in the stored vapor case results of Fig. 7. The system concept employing water separation achieves a tank energy density of 36.8 kWh/m3 (95% higher than storing vapor). Both fuel and exhaust tanks are set to ambient temperature for storage, which allows higher energy density and mitigates the need to maintain high tank temperature during operation (as in the stored vapor case). Tank inlet gases are at an elevated temperature of 121–135°C, which may increase storage temperature if heat loss through the tank walls is not sufficient. The saturation temperature is higher at the elevated storage pressure compared to the ambient pressure condenser. Thus, additional water condensation will occur as tanked gases cool to ambient temperature. This water may condense in the storage tank or be removed with a condenser prior to tanking. For the results presented in Fig. 6, the

Fig. 9. System schematic and statepoint data for the water separation system.

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water is assumed to condense in the storage tanks, meaning that more water must be re-boiled than was condensed in the opposite operating mode. This approach also requires intermittent blowdown of the liquid accumulated in the tanks. The difference in preheating loads between operating modes results in a significant imbalance of the thermal load on some components. Specifically, the boiler load differs by a factor of 7, while the condenser and air preheater are each only used in one operating mode. This imbalance in thermal loads may require bypass lines when selecting specific BOP hardware. Including an expansion turbine in the water separation system improves roundtrip efficiency to 68.3%; although the turbine is only used in SOFC operating mode. Because efficiency is limited by SOEC mode heat generation, extracting enthalpy from the preheat gas streams with a turbine requires operating the stack at lower efficiency (e.g., by increasing current density) such that the system efficiency is ultimately lowered. 5. Discussion 5.1. System configuration comparison Performance of the stored vapor and water separation system configurations are summarized in Table 3. The highest roundtrip efficiency of 73.7% is obtained using the stored vapor configuration with a fuel expander. This high roundtrip efficiency is achieved because of the low overpotential operating condition achieved at reasonable current density (ASR = 0.40 Ocm2) and has been explored in our previous work [12,51]. The energy density of the system increases by 120% if the tank pressure is increased to a nominal 50 bar, with an associated decrease in system efficiency of 2.9 percentage points. Comparing the stored vapor and water separation systems without a fuel expander, the water separation system has slightly lower roundtrip efficiency, but almost twice the energy storage capacity for a given size tank at 20 bar storage pressure. However, including a turbine in the water separation system does not have as much benefit as in the stored vapor system because less gas is expanded from the pressurized storage tank and the turbine is only used in SOFC mode in the water separation system. The water separation system with a turbine and an average 50 bar storage pressure achieves the highest energy density of 89.2 kWh/m3. In general, the stored vapor approach has higher roundtrip system efficiency, while the water separation approach has higher energy density. The system design challenges in the stored vapor case are focused on reducing the auxiliary power load of the fuel compressors by, for example, increasing fuel utilization or lowering the compression temperature. Utilizing a fuel expander in the stored vapor case is instrumental in maintaining high efficiency at elevated storage pressure. In contrast, the challenges in achieving high efficiency in the water separation system concept relate to operating the stack as efficiently as possible while still satisfying the preheating load (i.e. boiler load) in SOEC mode. Thus, configuration and operating condition modifications that increase heat generation in SOEC mode without lower stack efficiency are bene-

ficial, for example lowering stack temperature or increasing stack pressure which consequently increase the extent of internal methanation. These approaches to improving efficiency are important to make the ReSOC system competitive with other emerging and established distributed energy storage technologies, for example, lithium-ion batteries which can achieve >85% AC/AC roundtrip efficiency [53] and are experiencing rapid cost decline and economies of scale attributed to their use in electric vehicles [54]. High efficiency is especially critical for certain energy storage applications that rely on many charge/discharge cycles including area regulation and energy time shift (i.e., arbitrage). However, high efficiency is less important for certain long-duration applications that distributed ReSOC are well suited for including distribution upgrade deferral, micro-grid, and consumer power reliability [55]. The following cost results highlight the low marginal cost of energy capacity, making these systems attractive for long-duration (8 + hour) load balancing and backup applications. ReSOC system performance and operability at both design and off-design conditions is certainly dependent in part on the performance of BOP heat exchangers. Importantly, the total BOP cost is also related to heat exchanger sizing (UAs or NTUs). To get a sense of the change in the entire required heat exchanger size for the various concepts, Table 3 reports the total (i.e., sum of) system heat exchanger UA (‘HX UA’) values as determined from the log mean temperature difference and heat transfer rates within each heat exchanger. In general, the water separation systems have a UA value about 3 times greater than the stored vapor systems, indicating increased system cost. The difference is primarily attributed to the additional boiler and condenser in the water separation system. In fact, in the water separation systems, the condenser and boiler account for about 46% and 18%, respectively, of the total system UA. System UA increases when a fuel expander is included in the stored vapor system mostly because an additional heat exchanger is included to preheat fuel gases after turbine expansion using the hot air exhaust. Alternatively, the water separation system configuration has no additional heat exchangers when a fuel expander is included, and changes to the total UA are attributed to small variations in heat exchanger loads and approach temperature differences. The normalized energy storage cost reported in Table 3 represents the relative cost of energy storage as calculated by Eq. (8) for the different system configurations. A value of 1.0 is arbitrarily assigned to the basecase (stored vapor) system which has a capital cost of 317 $/kWh and energy storage cost of 8.8 ¢/kWh-cycle with expected accuracy of ±30% based on the bottom-up costing approach. The economic analysis reveals that cost of energy storage decreases substantially with increased energy density due to lower cost of tank storage, but the cost is also influenced by roundtrip efficiency, stack power density, and complexity of the heat exchanger network. For the stored vapor system, the cost of storage is reduced by 9% when a fuel expander is included because the increased roundtrip efficiency overcomes small capital cost increases from an additional heat exchanger and the cost of the fuel expander. Increasing the storage pressure to 50 bar further

Table 3 Summary of system configuration performance. Configuration Stored vapor Stored vapor + fuel expander Stored vapor + fuel expander Water separation Water separation + fuel expander) Water separation + fuel expander)

j (A/cm2)

ptank (bar)

gsystem (%)

gstack (%)

0.20 0.20 0.20 0.27 0.27 0.27

20 20 50 20 20 50

65.4 73.7 70.8 65.1 68.3 65.5

83.6 83.8 83.8 79.9 79.9 79.9

st

(kWh/m3) 18.9 20.1 44.2 36.8 38.4 89.2

HX UA (W/K)

Normalized energy storage cost

439 589 594 1443 1475 1428

1.00 0.91 0.77 0.84 0.80 0.74

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reduces system cost because of the smaller tanks required for equivalent energy capacity. The baseline water separation system has 16% lower cost than the baseline stored vapor system, indicating that the increased complexity and size of the heat exchangers and lower roundtrip efficiency are overcome by reduced capital investment in large storage tanks and reduced stack cost due to increased power density. Similar to the stored vapor systems, the cost of the water separation system decreases with inclusion of a turbine and increased tank pressure. Ultimately the lowest cost system is that with water separation and high tank pressure, which has a comparatively low roundtrip efficiency of 65.5%. The component capital costs are given in Table 4 for the highest and lowest cost systems. The annualized component cost breakdown for the highest and lowest cost systems is given in Fig. 10. The annualized cost reflects the shorter lifetime of the ReSOC stack compared to other system components. The majority costs in the baseline stored vapor case are the ReSOC stack (46.1%) and gaseous storage tanks (34.9%) with smaller contributions from the relatively simple BOP. The lowest cost system (water separation + fuel expander, 50 bar nominal storage) has substantially lower tank cost due to the reduced volume. The system BOP cost is a larger share of total system cost because of increased heat exchanger area, particularly from the air-cooled condenser. The results in Table 3 report system performance at high roundtrip efficiency. However, the economic results indicate that the higher stack power density and smaller tanks required in the water separation systems lead to lower cost of energy storage. This suggests that the operating conditions to achieve optimal efficiency may be distinct from the lowest cost system. Previously reported large-scale systems achieve roundtrip system efficiency >70% for the water separation system with pressurized ReSOC stacks [11]. The lower efficiency reported here is attributed to both differences in system configuration and operating conditions. The pressurized stack allows more carbonaceous fuel mixtures to be used without depositing carbon, such that a higher rate of in-situ methanation occurs in the SOEC stack. Furthermore, additional turbomachinery including an air turbine at the pressurized stack exhaust recuperates compression energy and results in net energy generation from the BOP, allowing system efficiency to exceed stack efficiency by efficiently expanding air exhaust.

5.2. Influence of lower stack ASR on system performance Improvements in cell-stack performance by lowering the effective stack ASR can affect the system in a number of ways. The

Table 4 Component capital cost for the stored vapor (20 bar) and water separation + fuel expander (50 bar) systems (1000$). Component ReSOC stack Balance of stack Fuel tanks Exhaust tanks Gas compressors Air blower Expander Heat exchangers Air cooled condenser Boiler Miscellaneous Total

Stored vapor (20 bar)

Water separation + fuel expander (50 bar)

46.7 2.9 43.3 64.9 18.6 7.8 – 23.9 – – 7.4

35.2 2.2 13.2 12.1 18.2 7.5 12.3 26.6 20.8 14.6 8.6

215.6

171.4

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calibrated cell model used in the simulations has an ASR of about 0.40 Ocm2 at 600°C, and the resistance decreases to about 0.20 Ocm2 at 650°C. Improving the cell performance at 600°C will allow the stack to operate at a higher power density while still achieving the system efficiencies reported in Table 3. The previous system results show that system efficiency is limited by energetic preheating requirements, meaning that improving the cell performance will not enable roundtrip efficiencies higher than those already presented. However, system cost will certainly be affected by ASR improvements. Fig. 11 shows the SOFC mode power density vs. ASR for the stored vapor + fuel expander configuration. For the conditions considered in this study at a current density of 0.20 A/cm2, present day button-cell performance achieves a power density of 0.19 W/cm2 when operating on carbonaceous reactants. The power density increases to 0.38 W/cm2 at 0.40 A/cm2 for an improved ASR of 0.20 Ocm2. Economically viable current densities for full-scale ReSOC systems will likely require stack-level ASRs very near these performance levels. Normalized annual cost is also given in Fig. 11, indicating a 20% reduction if the target ASR is achieved. 5.3. Implications of tanked storage The steady state results presented herein reveal useful tradeoffs between efficiency and energy density within different system configurations. However, energy storage is inherently a dynamic process and the implications of tanked storage must be considered in system design and analysis. This sub-section discusses some implications of tank property variation during filling and evacuating, the interdependency of thermal management and compression, and elevated temperature storage for the stored vapor system. For rigid tanks, temperature variation associated with pressure change during filling and evacuation will change system performance by influencing BOP operation and tank conditions. As the tank is discharged, temperature and pressure decrease, increasing the preheating load to achieve a given stack inlet temperature and eventually condensing the water vapor present in the gas mixture. Satisfying the increased thermal load may require a lower stack efficiency to increase stack waste heat generation. Alternatively, the opposite tank (i.e., that being filled) will increase in temperature, so thermally integrating the two storage tanks may mitigate the temperature variations. The tank property variations are particularly impactful in the stored vapor system approach where pressure variations affect dewpoint temperature. For the water separation systems, heat exchange with the environment may stabilize tank temperatures and declaring tank geometry and material properties is necessary to inform this design. Another potential challenge for the systems considered in this study is that they utilize compression heat to preheat reactant streams. Under transient operation, the compression heat will vary with tank pressure. For example, when the system is initially discharging from a fully-charged state, the exhaust tank will have low pressure and little compression heat is available for preheating. The deficit heat may require lower efficiency stack operation. The auxiliary power from compressors and turbines will also vary with state of charge. Preliminary analysis indicates that the roundtrip efficiency of systems with turbine expansion improves slightly when considered over a full charge/discharge cycle compared to the steady state efficiency at nominal storage pressures as presented here. However, the integration of preheating with compression heat and tank pressure variation indicates that the roundtrip efficiency will depend on system state of charge and depth of discharge. A variable volume storage tank will solve many of the issues discussed in this section by maintaining a more constant tank

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Fig. 10. Annualized component cost contributions for the highest (basecase stored vapor) and lowest (water separation + fuel expander systems) cost systems.

Fig. 11. Power density and normalized annual cost vs. ASR for projected improvements in ReSOC cell-stack performance at constant efficiency of 73.7% for the ‘‘stored vapor + fuel expander” configuration at nominal stack temperature of 600°C.

68.3% in the water separation case. The water separation case is limited by the thermal load required to re-boil water in SOEC mode. A fuel expander is necessary to achieve high roundtrip efficiency, particularly at elevated storage pressure in the stored vapor system. The energy density is higher in the water separation system as a result of the lower quantity of stored gas and lower storage temperature. Energy density of 89.2 kWh/m3 is achieved in the water separation case for a storage pressure of 50 bar compared to 44.2 kWh/m3 at the same storage pressure for the stored vapor case. The preliminary system capital costs are estimated to be 233–317 $/kWh. The cost of energy storage is strongly influenced by stack power density and energy density because storage tanks and ReSOC stack comprise a majority of the system cost. The water separation systems show lower cost of energy storage compared to the stored vapor systems, and increased storage pressure lowers system cost in both cases. The effects of improvement in ReSOC cell-stack performance and transient tanked storage on system efficiency are also discussed. Improved cell performance does not allow increased roundtrip system efficiency because roundtrip efficiency is limited by energetic preheating loads. However, reducing present day cell resistance from about 0.40 to 0.20 Ocm2 at 600°C will increase power density from 0.19 to 0.38 W/cm2 and reduce annualized system cost by about 20% for fixed system efficiency. System simulations during transient charge/discharge operation must be explored to address unresolved design decisions related to the variation in tank properties during filling and evacuation. The tank design will affect system efficiency because of the interdependence with preheating and turbomachinery loads. Furthermore, operation under off-design conditions is an important area of future study to demonstrate the capabilities and potential limitations of ReSOC systems targeted for distributed energy storage applications. Acknowledgements

pressure during operation. One considered approach to variable volume tanking is a ‘‘floating piston” tank where a rigid vessel is separated into two compartments by a movable partition, creating distinct fuel and exhaust chambers. This arrangement mitigates many problems associated with individual rigid tanks and also increases energy density by reducing the total tank volume [56,57]. Comparatively, the volumetric energy density of these early ReSOC system concepts appear to be about half that sodium-sulfur batteries (90 vs. 150–200 kWh/m3) and more than double vanadium redox flow batteries (90 vs. 16–35 kWh/m3) [47,53]. Strategies for improving ReSOC system energy storage density are explored further by the authors in Ref. [58]. 6. Conclusions Stand-alone energy storage systems utilizing ReSOCs are conceptualized and analyzed for 100 kW-scale distributed applications. These systems use carbonaceous reactants and promote heterogeneous reforming and fuel synthesis reactions to achieve higher efficiency compared to low temperature reversible fuel cells, or those operated only on steam–hydrogen reactants. System modeling is used to calculate efficiency and energy density metrics using a calibrated ReSOC model based on intermediate temperature LSGM-electrolyte data at 600°C. The system results compare ‘‘stored vapor” and ‘‘water separation” strategies, which are distinguished by the phase of the H2O constituent during tanked storage. The stored vapor system achieves higher roundtrip system efficiency of 73.7% compared to

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