A novel electrical energy storage system based on a reversible solid oxide fuel cell coupled with metal hydrides and waste steam

Applied Energy 262 (2020) 114522

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A novel electrical energy storage system based on a reversible solid oxide fuel cell coupled with metal hydrides and waste steam Van-Tien Giapa,b, Young Duk Leea,b, Young Sang Kima, Kook Young Ahna,b, a b

T

⁎

Environmental System Research Division, Korea Institute of Machinery & Materials (KIMM), 156 Gajeongbuk-ro, Yuseong-gu, Daejeon 34103, South Korea Department of Environment & Energy Mechanical Engineering, University of Science & Technology (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, South Korea

HIGHLIGHTS

RSOFC system coupled with a metal hydride (MH) and waste steam was investigated. • An MH (HTMH) and low-temperature MH (LTMH) materials were analysed. • High-temperature heat from the HTMH tank was used to produce steam during only 29% charge time. • The round-trip efficiencies of HTMH and LTMH were 45.6% and 48.1%, respectively. • Exergy • The HTMH has a potential function of both LTMH and external heat utilization. ARTICLE INFO

ABSTRACT

Keywords: Electrical energy storage Reversible solid oxide fuel cell Metal hydride Waste heat Off-design Exergy round-trip efficiency

Reversible solid oxide fuel cells (RSOFCs), with high energy densities, long operating times, and intermediate power ratings, have become promising devices for renewable energy storage. A metal hydride (MH) tank is a prospective thermochemical heat and hydrogen storage unit. External heat source such as waste steam is a wellknown efficiency booster for high temperature electrolysis system. Here, we propose a novel RSOFC system coupled with MH and waste steam. The MH materials of MgH2-5 at.% V and LaNi5 were used for high-temperature MH (HTMH) case and low-temperature MH (LTMH) case calculations, respectively. We found that, In HTMH case, the H2 compression power was low, but the MH tank produced steam only during the last 29% of the total absorption time. When the MH tank produced steam, the SOEC mode efficiency increased by 19.3% points. In the SOFC mode, the MH tank stored 76% of heat released from stack, and the system efficiency was lower than stack efficiency by 6% points. The system round trip efficiencies of HTMH system and LTMH system were 45.6% and 48.1%, respectively. For a specific HTMH material, there is an optimal current density in the SOEC mode where heat from MH tank can be used completely and the external heat source is minimal. By choosing appropriate operating strategy or MH material, the high temperature MH can result in a system roundtrip efficiency comparable to that of a low temperature MH combined with an external heat utilization system.

1. Introduction Renewable energy with intermittent nature has quickly penetrated the power sector, leading to the urgent demand for electrical energy storage (EES) technologies [1]. Reversible solid oxide fuel cells (RSOFCs) have become a promising technology for EES systems, because they are superior to other EES technologies in terms of energy density, power, and storage duration [2]. RSOFC is a high temperature electrochemical reactor, which generates electricity mainly from H2 and O2 reaction in fuel cell (SOFC) mode, and produces H2 and O2 from

electricity in electrolysis (SOEC) mode. RSOFCs have high efficiency, capability of hybrid power generation, and higher tolerance for fuel impurity than other fuel cell types. Moreover, SOEC stack can take advantage of external heat to increase hydrogen production efficiency. However, due to high temperature operation, RSOFCs show long startup time and fragile components, thus they are suitable for stationary application [3]. A demonstration system by FuelCell Energy and LG Fuel Cell System showed SOFC’s degradation rate of 0.9% per 1000 h [4]. In other study [5], the reversibly cycling between two modes of RSOFC completely eliminated the degradation caused by electrolysis-

⁎ Corresponding author at: Environmental System Research Division, Korea Institute of Machinery & Materials (KIMM), 156 Gajeongbuk-ro, Yuseong-gu, Daejeon 34103, South Korea. E-mail address: [email protected] (K.Y. Ahn).

https://doi.org/10.1016/j.apenergy.2020.114522 Received 16 September 2019; Received in revised form 5 January 2020; Accepted 11 January 2020 0306-2619/ © 2020 Elsevier Ltd. All rights reserved.

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Nomenclature

N p P Q s SC t T TR U UN y α σ0

Acronyms BLR EES HEX HRSG MH RSOFC SOEC SOFC

Blower electrical energy storage heat exchanger heat recovery steam generator metal hydride reversible solid oxide fuel cell solid oxide electrolysis cell solid oxide fuel cell

Variables C EA Eboil ech ED Eelec Eex EH2 EO2 eph G H j jo k l LHV m M n

reaction constant activation energy in absorption reaction (J/mol) boiling power (W) molar chemical exergy (J/mol) activation energy in desorption reaction (J/mol) electric power input (W) total exergy (W) activation energy of fuel electrode (kJ/mol) activation energy of air electrode (kJ/mol) molar physical exergy (J/mol) gravity of Earth (m/s2) specific enthalpy (J/kg) current density (A/m2) exchange current density of electrode exponential value exponential value low heating value (J/kg) mass flow rate (kg/s) mass fraction of hydrogen in metal hydride molar flow rate (mol/s)

γ η ηE ηF

molar ratio between hydrogen and metal partial pressure (bar) pressure (bar) heat of reaction (J/mol) specific entropy (J/molK) steam conversion ratio time (s) temperature (K) time ratio between stage 1 and stage 2 voltage (V) Nernst voltage (V) molar fraction exponential coefficient pre-exponential coefficient of electrolyte ionic conductivity pre-exponential kinetic parameter system round-trip efficiency SOEC system efficiency SOFC system efficiency

Subscripts a d elec eq ex H2 i in L O2 out S Up

mode operation. The switching between charge and discharge modes of RSOFC was tested by [6], it is proved that switching time of 6–10 min results in no degradation over 113 cycles. Theoretically, SOEC stack can have 100% H2 production efficiency, but the system round-trip efficiency of an RSOFC system still needs to be improved prior to realizing commercialization [2,7]. J. Mermelstein and O. Posdziech 2016 [7] reported a demonstration system using an RSOFC for energy storage. The developed RSOFC module exhibited a 50 kW power output in the SOFC mode and a 120 kW power input in the SOEC mode. The produced hydrogen was stored in gas storage tubes at 248 bars with a storage capacity of 12 h operation of fuel cell and electrolysis modes. The system was tested for approximately 1000 h over seven thermal cycles, and the round-trip efficiencies with and without considering the steam production power were 29.9% and 35.6%, respectively. Several methods have been proposed to improve the RSOFC system efficiency in each mode or both modes, such as heat storage [8], high operating pressure [9], partial oxidation [10], and external heat supplement methods [11]. Among these technologies, heat storage methods have been widely investigated by many researchers in both system and materials development [8,12–16]. The center idea of heat storage methods is using the heat generated in SOFC mode to support steam production and/or endothermic operation of SOEC mode. Perna A et al. [16] recently proposed an RSOFC system using Syltherm 800 liquid oil as a heat storage material. In the solid oxide electrolysis cell (SOEC) mode, the oil from the hot tank, which was used to heat the main streams and vaporize the water, flowed into the cold tank. In the SOFC mode, the cold oil passed through the oil network to

absorption desorption electricity equilibrium exergy hydrogen efficiency type index input lower limit value oxygen output saturated upper limit value

absorb available heat to be stored in the hot tank. The system round-trip efficiency was reported to be 60%. Other studies integrating heat storage units into an RSOFC system also showed a system round-trip efficiency of more than 70% [17,18]. Nevertheless, physical heat storage devices still exhibit several common problems, such as heat loss and a low storage capacity [19]. Moreover, if a portion of the hydrogen product is used somewhere far from SOEC system, it will be difficult to bring the heat generated from H2 reaction to the SOEC system. Storing heat by using a metal hydride (MH) material could be a promising option due to the high storage density, negligible heat loss, and low pressure requirement. MH materials store heat in chemical form via MH reactions; hence, they generally possess a high volumetric density and almost zero heat loss during storage. Unlike heat storage by phase change materials, MH tanks release the heat proportional to the amount of hydrogen stored, regardless of how and where hydrogen will be used. The concept of an RSOFC coupled with an MH was previously proposed as an electricity or a hydrogen storage system [20]. In the authors’ calculation, the heat of reaction in the MH tank was used to vaporize and heat the water in the SOEC mode. In the SOFC mode, the heat required in the MH tank was expected to be supplied by the surplus heat of the SOFC stack. However, the feasibility of detailed thermal management and kinetics of MH was not considered. Regarding the thermal management and implementation of an RSOFC/MH system, some studies have suggested direct integration by attaching an MH tank to the fuel cell stack. For example, in SOFC/MH systems, the heat of desorption in the MH tank was mainly supplied by radiation from the SOFC stack [21], or the SOEC and MH were integrated into a single electrolyzer tube [22]. The system designs were 2

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compact, but the strong thermal coupling of the solid oxide stack and MH requires strict system operation control and may lower the total system performance. For example, in the case of an SOEC/MH tube [22], even though both the H2 production and storage processes were exothermic, an external heat source was still needed to maintain the temperature difference between the SOEC and MH. In [23], the investigators found that an RSOFC system can be coupled with waste steam to realize higher efficiency and that the system efficiencies were almost unchanged over a wide range of waste steam temperatures. Thus, a storage system based on RSOFC might be coupled with the steam generated from MH tank that has low to medium temperature. Therefore, an EES system that takes advantage of the low charge pressure and high heat storage capacity of an MH is expected to have a high efficiency and a long-term storage capability. In the current study, we proposed a new EES system that integrates an RSOFC system and an MH tank and waste steam. This study will answer the following questions:

○ Conducted a parametric study on the nominal current density. ○ Analyzed cases with high- and low-temperature MH materials. 2. Proposed system The purpose of the system is to increase the RSOFC system roundtrip efficiency by using a low-pressure MH tank as a heat storage unit and taking advantage of external waste steam. In the SOFC mode, due to the endothermic reaction of the MH tank, some heat from the exhaust air was used for hydrogen gas desorption. In the SOEC mode, the charging process of the MH tank was exothermic; thus, the generated heat was used to produce additional steam. External waste steam was used as a supplementary source when the steam generated from the MH tank was insufficient. In addition, in the SOEC mode, several technologies, such as a fuel recirculation system and a heat recovery steam generator (HRSG), were applied to obtain high system efficiency. In the charge mode (SOEC), steam was provided from three sources: waste steam, an HRSG and MH cooling water, as shown in Fig. 1. On the fuel side, heat from the fuel electrode outlet (stream 11) was recovered by a fuel heat exchanger, namely F_HEX and an HRSG, and fuel recirculation (stream 13) was implemented by recycle blower 1 (R_BLR_1). On the air side, the heat from the air electrode outlet (stream 23) was recovered using two air heat exchangers, namely A_HEX and A_HEX_2 to heat the fresh incoming air (stream 19). The hydrogen-rich fuel product was cooled down by a heat exchanger and an HRSG and then (stream 14) passed through a three-stage reciprocating compressor with intercooling and water drainage. Then, pressurized hydrogen (stream 17) was absorbed in the MH tank. The heat released during the charge mode of the MH tank was used to produce additional water (stream 29). The drainage pipe (stream 30) at the outlet of the MH tank was used to drain the cooling water when it was in the liquid state. If

○ How is the RSOFC system integrated with the MH and waste steam from a thermal management viewpoint? ○ How much heat can be stored and reused with MH tank that has strong relationship between operating temperature, absorbed hydrogen, and reaction rate? Can steam from MH tank eliminate the need of external waste steam? ○ How do different MH materials affect the round-trip efficiencies of the system? In this study, we conducted the following tasks: ○ Proposed a new EES system using an RSOFC coupled with waste steam and an MH tank.

Fig. 1. System schematic of the RSOFC system in SOEC mode. 3

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the MH tank produces more steam than demand, the excess steam will be mixed with warm exhaust air (stream 27) and used for heating cold air inlet (stream 19). Fig. 2 shows a system schematic of the discharge mode (SOFC), in which the exhaust air from RSOFC stack comes through the first air heat exchanger (A_HEX) to heat up the fresh air. A portion of the exhaust air from the RSOFC stack was extracted at downstream (stream 24) of the A_HEX to provide heat for MH tank (stream 25). The hot air output from the MH tank was mixed with the remaining air from the stack (stream 27) prior to passing through the A_HEX_2. The steam content needed in the fuel mixture was only 3%; hence, the HRSG and fuel recirculation were not used in this mode. The product mixture (stream 11) passing through the fuel heat exchanger to heat the fresh mixture then proceeded to the first condenser and drain. After all the liquid water was drained, the product mixture (stream 15) was recirculated back by R_BLR_2 for mixing with stream 5 at the cold inlet of the F_HEX. Therefore, the system utilization of hydrogen was theoretically 100%, regardless of the stack utilization [24]. Most of the components had different loads in the two working modes; hence, to ensure the compatibility of the two modes, the fuel heat exchanger was equipped with bypass pipes to prevent overheating of the fresh fuel mixtures. Because of the large difference in the air mass flow rates, two blowers were used in the system, one for the SOFC mode and the other for the SOEC mode. Two heaters, namely F_HT and A_HT, were placed at the fuel inlet and the air inlet of the RSOFC stack to control the incoming flow temperatures. The heat exchanger in MH tank should be designed properly to use hot air in one mode and liquid water in other mode. There is not necessarily one single-channel heat exchanger, but a combination of two or more tubes, shell and/or plate as different channels, then each of them is for one fluid type (hot air, liquid water, and boiling water).

However, the design of the MH tank combined with heat exchanger is out of scope of the present paper, so we keep the lumped model simple and give the design freedom to the readers. 3. Mathematical modeling The proposed system was analyzed using lumped models. The RSOFC stack model and MH model were integrated as macro objects into EBSILON® Professional commercial software for system simulation. We assumed the following:

• No heat loss occurs in all components and pipes. • The system operates in a steady state. Due to high operating temperature, RSOFC systems in fact shows a certain amount of heat loss that varies according to thermal insulation types and hot box design. Thus, the heat loss analysis should be done as a separate study to optimize the systems setting and installation [25]. Consequently, at the analysis level of the present paper, introducing only heat loss to fuel cell might lead to misinterpret the whole system performance, so neglecting heat loss is common for this type of study [26–29]. However, the possible effects of heat loss in RSOFC stack will be discussed later in the results and discussion section. 3.1. RSOFC stack In modeling the RSOFC stack, some additional assumptions were made as follows:

• The working temperature of the RSOFC stack is the average of the inlet and outlet flow temperatures.

Fig. 2. System schematic of the RSOFC system in the SOFC mode. 4

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• All electrochemical reactions occur at the center of the stack.

For the purpose of validation, where PH2 and T are constants with time, by integrating (2) for absorption mode, we obtain:

The electrochemical reactions inside the RSOFC cell can be considered as an overall reversible reaction as follows:

1 O2 + H2 2

Na = NS

H2 O

hfi ) + mai (ha

hai ) + mfo (hfo

hf ) + mao (hao

Na =

ha)

where Q is the heat generated from RSOFC cells, which has a negative value in the endothermic mode; mf and ma are the mass flow rates of fuel and air flows, respectively; the subscripts i and o indicate input and output, respectively; and h is the specific enthalpy of the fluids. 3.2. MH tank The MH tank was modeled using the following additional assumptions:

• The mass average temperature of MH materials equals operating temperature of MH tank • The outlet flow temperature is equal to the operating temperature of the MH tank. • The ideal gas law is valid for the gas phase of hydrogen and air. • The reaction rate is limited by the temperature, pressure and hydrogen content in the MH tank. • The specific heat capacities of the materials inside the MH tank are

T¯ =

nd = Cd exp

ED RT

Peq

PH 2 Peq

Nal

(2)

Peq P0

=

H RT

S R

Peq

PH 2 Peq

t (1

l)

1 1 l

(6)

1 tend

tend

tstart

t start

T dt

(7)

h 0)fluid + msolid (h

h 0)solid + mH 2 (h

h 0)H 2 = Qreaction

(8)

3.3. The interplay between the two working modes

(3)

where NS and Na are the amounts of saturated and absorbed (mol/molmetal) hydrogen, respectively; na and nd are the reaction rates of hydrogen in the absorption and desorption processes, respectively; Ca and Cd are the reaction rate constants; k, l are fitting parameters. P0 and PH2 are reference pressure (1 bar by convention) and the MH tank pressure. The equilibrium pressure Peq was calculated from the Van’t Hoff equation as follows:

ln

Cd exp

ED RT

Here, fluid is liquid water in the absorption mode and hot air in the desorption mode. The parameter h is the specific enthalpy of the corresponding substance under the MH tank working conditions, and h0 is the specific enthalpy of the corresponding substance under the initial conditions. For the solid parts, the initial conditions were taken from the final state of the previous process. Qreaction is the average heat released in the MH reaction; thus, in the desorption mode, Qreaction < 0. Since in the desorption mode, the temperature at the H2 outlet was the same as the operating temperature, h0,H2 = hH2, where m is the amount of reactants per unit time. The solid parts in the MH tank were solid metal and solid MH; their different heat capacities were considered in the MH model, and they are given in Table 3.

According to Suda S. et al. [32] and [33], the rate of the hydride reaction for a specific MH material varies with the hydrogen concentration in the solid MH and the pressure and temperature in the MH tank as follows:

Na ) k

NUp1 l

mfluid (h

MHx

EA P ln H 2 (NS RT Peq

(5)

3.2.2. Energy conservation All heat generated or absorbed by reactions in the MH tank was considered a heat input or a heat output that heats up/cools down the flows and solid parts to the working temperature inside the MH tank. The energy conservation is illustrated in the following equation:

3.2.1. Hydride reaction kinetics The operation of a fixed capacity MH tank is naturally transient; thus, to simulate the RSOFC system in the steady state, we chose a timeaveraging approach for modeling the MH tank. The MH reactions that occur in the charge and discharge modes are as follows:

dNa = Ca exp dt

k)

During the desorption process, the working pressure PH2 was fixed at the pressure required for the hydrogen supplement in the system. During the absorption process, the operating pressure of the MH tank was fixed at the designed output pressure of the compressor.

constant over the investigated temperature range.

na =

Ca exp

1 1 k

To avoid a slow reaction near the end of the absorption/desorption process, the system mode was assumed to be switched before this point, which means that the system is switched at the upper limit of Na, NUp < Nsaturated, during the absorption process, and at the lower limit NL > 0 during the desorption process. Although the MH tank always works in a transient state, the tank pressure was chosen to be constant. Thus, the operating temperature of the MH tank was adjusted to control the hydrogen flow rate in both the absorption and desorption modes, by solving Eq. (2). In the SOFC mode, the operating temperature can be increased by introducing more hot air into the MH tank. In the SOEC mode, the working temperature can be decreased from Tmax to Tmin by increasing the cooling water mass flow rate. For a given operating time in each mode, the average operating temperature of MH tank was calculated by Eq. (7). Here, tstart and tend are the time when sorption process start and stop, respectively.

(1)

x H +M 2 2

NL

EA P ln H 2 t (1 RT Peq

And, by integrating Eq. (3), in the desorption process we have:

The voltage of the RSOFC stack was modeled followed [30] and [31], and it is shown in the Appendix A. The heat from electrochemical reactions was considered to increase the inlet flow temperature to the working temperature, and the new mixture flow temperature from the working temperature to the outlet temperature. The energy conservation can be given by the following equation:

Q = mfi (hf

(NS

)1 k

The RSOFC system components were designed based on the system working conditions in one mode; hence, in the other working mode, these components worked in off-design conditions. The working conditions of the components in the SOFC mode and SOEC mode could be completely different in terms of the temperature, mass flow rate of the working fluid, etc. Therefore, an interplay exists between the working conditions of the charge and discharge modes. This interplay was taken into account by using the off-design characteristics of the HRSG and heat exchangers. In the off-design conditions, the overall heat transfer coefficient and pressure drop of the heat exchanger vary with the flow

(4) 5

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rates [34,35]. The heat transfer coefficients of the heat exchanger in the off-design mode were calculated using the following formula [36]:

hHEX = hHEX _design ·

m mdesign

(9)

PHEX = PHEX _design

m

Vdesign

mdesign

2

(11)

The electrical round-trip efficiency considered waste steam to be a free-of-charge heat source. 2

=

EelecOut EelecIn

(12)

The exergy round-trip efficiency took into account the exergy content of the waste steam. Here, maximum power that can be extracted from waste steam is considered as one of the inputs of the system. Therefore, exergy round-trip efficiency represents the benefit of waste steam to the system efficiency. 3

=

EelecOut EelecIn + Exsteam

(13)

where E is the energy rate (W) and Ex is the exergy rate (W). The exergy of flows included chemical exergy and physical exergy, which have been sufficiently explained elsewhere [37–39]. To analyze the system performance in each working mode, the efficiencies of each working mode of the system were calculated. The output of the SOEC mode was the produced hydrogen, and the input of the SOFC mode was hydrogen from the MH tank. The system efficiencies in a single mode were defined as follows: For the charge mode (SOEC): 1E

=

mLHVH 2 Eboil + Eelec

3E

=

EexH 2out EexH 2in EexSteam + Eelec

(16)

1F

=

EelecOut Eboil + mLHVH 2

(17)

2F

=

EelecOut mLHVH 2

(18)

3F

=

EelecOut EexSteam + EexH 2in

EexH 2out

(19)

The RSOFC stack working conditions were chosen as 750 °C and 1.1 bar in both modes. The working pressure of the RSOFC stack being near ambient conditions has many advantages in stack manufacturing and operation, such as a lower risk of leakage and crack control [40,41]. The operating temperature was chosen as an intermediate value to realize a lower degradation rate of the material while being high enough to reduce ohmic loss [42]. In the SOEC mode, the slightly endothermic mode was chosen due to the high stack efficiency and easy temperature control [43]. The hydrogen concentration at inlet of SOEC was chosen 40% at base case to recycle large amount of fuel off-gas thereby recovering much of heat and steam. A three-stage reciprocating compressor with intercooling and water drainage was used to compress hydrogen. The maximum compressor outlet temperature of the hydrogen at each stage in the compressor was 135 °C, in accordance with the API standard for a reciprocating compressor [44]. In the SOFC mode, the fuel utilization was set as 70% to lower the degradation rate [45,46]. The total discharge time and charge time were assumed to be equal; thus, the absolute current density of the RSOFC stack was the same in the two operating modes. According to L. Barelli et al. [47], the oxygen molar concentration in the sweep gas output can reach 50% with small impact on the SOEC voltage, which reduces the air flow demand. However, from the system point of view, if the mass flow rate of the sweep gas (air) is too low, the relative heat loss in the heat exchanger will be high because the air heat exchanger was designed based on the high air mass flow rate in the SOFC mode. Therefore, the air mass flow rate was calculated based on the condition that the molar fraction of oxygen in the sweep gas output equals 30%, i.e., the air utilization factor was fixed. Regarding the MH tank, in the desorption phase, the outlet temperature was calculated based on the desired pressure and hydrogen flow rate. In the absorption phase, the operating pressure was fixed at 4.5 bar for the MH material, considering that the starting absorption temperature was not lower than the ambient temperature, and the

To evaluate system performance in different perspectives, three types of round-trip efficiencies were used. Fig. 3 shows the system control volume for the efficiency calculation. The reference system round-trip efficiency considered the total heat needed for steam production, regardless of fuel type.

EelecOut EelecIn + Eboiler

(15)

4. System operating conditions

3.4. System efficiency definitions

=

mLHVH 2 Eelec

(10)

Here, V and m are the volume flow rate and mass flow rate of the working fluid, respectively.

1

=

For the discharge mode (SOFC):

where m is the mass flow rate of the working fluid and α is a coefficient set by the EBSILON® Professional program, which was 0.61, 0.697, and 0.784 for gases, phase change fluids and liquids, respectively [36]. The pressure drop was calculated as follows:

V

2E

(14)

Fig. 3. System control volume for the efficiency calculation. 6

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and the absorption rate requirement was 3.8 × 10−4 mol/(mol-metal·s). The operating temperature of MH tank was obtained by solving Eqs. (2) and (3) in absorption mode and desorption mode, respectively. The MH tank showed a low operating temperature most of charging time, which resulted in two operating stages of the system: the first stage, MH tank does not produce any steam; and the second stage, MH tank was hot enough and producing steam. The Van’t Hoff Eq. (4) shows that the equilibrium pressure Peq increases with increasing MH temperature (TMH) because ΔH is negative. Although an increase in Peq lowered the absorption rate, the reaction promotion effect of TMH was dominant in Eq. (2). Therefore, to keep the absorption rate fixed at 3.8 × 10−4 mol/(mol-metal·s), the temperature of the MH tank increased from 20 °C to 242 °C as the absorbed hydrogen content increased, as shown in Fig. 7. Accordingly, the MH could start producing steam during the last 140 min when the temperature was higher than the boiling temperature of 101 °C. Time-averaged temperature of the MH tank was estimated and used in system analysis for two stages of SOEC mode. In the first stage, TMH increased from the initial value to the boiling point (340 min), with an average temperature of 64 °C. Therefore, the cooling water from the MH tank was exhausted in the liquid state. In the second stage, TMH increased from the water boiling point to the final temperature of the absorption process, with a time-averaged temperature of 161 °C. Here, the cooling water was vaporized in the MH tank and then mixed with waste steam (stream 1). The desorption rate of the MH tank was very sensitive to the operating temperature. In the current study, the operating pressure of the MH tank was fixed at 1.1 bar, and the reaction rate was controlled only by the operating temperature. As shown in Fig. 8, the desorption process did not occur at 276.4 °C but did occur at 276.5 °C; the desorption rate was already higher than the required value of 3.8 × 10−4 (mol/ mol-s) in the entire discharge phase. However, the hydrogen desorption rate can be reduced even to zero by increasing the pressure of the MH

maximum Na value could reach 0.76 at the end of the process. The outlet temperature was calculated by the time-averaging method and depended on the absorption time, the hydrogen absorption rate, and the characteristics of the MH tank. MgH2-5 at.% V (5% of total atoms in the composite are Vanadium) was chosen for high temperature MH material as base case because it has fast kinetics and high heat of reaction. To compare the effects of a high-temperature MH material and a lowtemperature MH material, an AB5 material was also investigated. The system parameters are shown in Table 1. 5. Results and discussion 5.1. Components models validations 5.1.1. The RSOFC model Moyer et al. [48] and Zhu et al. 2005 [49] showed the complex mechanisms in electrolysis and fuel cell modes of a RSOFC stack that explain the difference in voltage loss in the two modes. An experiment study on Ni/YSZ electrode by Marina et al.[50] showed more than 40% difference in both exchange current density and activation energy between two modes. Therefore, to simulate the mechanisms of electrolysis and fuel cell, we chose separate parameters sets for activation loss in two modes, as shown in Table 2. Fig. 4 shows a validation of the RSOFC stack model with experimental data from a study of Jensen, S. H. et al. [51]. The characteristic curve of the experimental fuel cell stack showed good agreement with the present model. 5.1.2. The MH tank model Validation of the MH model was conducted by fitting four parameters (Ca, Cd, k, l) for the two working modes of the MH tank. Mechanically milled MgH2 with 5 at.% vanadium was used for validation and the base case calculation because of its fast absorption and desorption kinetics and its high availability [52]. The parameters of the MH model are shown in Table 3. The relation between the hydrogen fraction (N) and hydrogen content (M) in MH materials is:

Parameters

N=

mole of H2 absorbed total mol of metal

(20)

M=

mass of H2 mass of metal hydride

(21)

M=

NCM 1 + NCM

Table 1 System parameters of the base case and parametric study.

Inlet steam temperature Inlet air temperature (reference temperature) HRSG pinch temperature Inlet air pressure Electrical efficiency of the motors Waste steam boiler efficiency Heat exchanger Maximum effectiveness Pressure drop in hot and cold channels MH tank Absorption time −ΔH

(22)

with:

molar weight of H2 CM = molar weight of metal

(23)

In the absorption process, the kinetics model was in good agreement with the experimental data, as shown in Fig. 5. In the desorption phase, as observed in Fig. 6, the desorption mode model agreed well with the experimental data at operating temperatures above 523 K, which was also observed by Liang et al. [52]. It is noteworthy that, the reaction rate of both absorption and desorption processes increased with increasing operating temperature at a fixed pressure.

−ΔS CP,metal CP,hydride Pressure drop through the RSOFC (both channels) SOEC mode Stack fuel inlet temperature Stack air inlet temperature H2 concentration in the fuel Steam conversion ratio Temperature change through stack SOFC mode Stack fuel inlet temperature Stack air inlet temperature H2 concentration in the fuel Fuel utilization Temperature change through stack Stack power at base case

5.2. Analyses with system parameters 5.2.1. Base case a) The operation of MH tank in charge and discharge modes Based on hydrogen production rate at base case, we assumed the group of ten MH tanks, weights 10 kg each, [54] were used at the one time. Subsequently, we needs 16 groups for whole discharging process 7

Base value (range)

Units

400 (150–700) 25

°C °C

15 1.01325 85 80

°C bar % %

0.9 0.03

bar

8 74.3 (MgH2) and 31.8 (LaNi5) 0.136 (MgH2) and 0.11 (LaNi5) 25 (Mg-5 at.% V) 35 0.05

hours kJ/mol kJ/[mol·K] J/[mol·K] J/[mol·K] bar

775 775 40 (20–60) 50 50

°C °C % vol % °C

675 675 97 70 150 250

°C °C % vol % °C kW

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SOEC mode

SOFC mode

γa γf Ea (J/mol) Ef (J/mol) σ0 (S/m)

3.97E+07 1.93E+09 80,000 105,823

1.32E+12 2.40E+14 80,000 201,905

1.6

1.2 1

0.7

250

0.6 200

0.5

150

0.4 Tboil

100

0.3 0.2

50 no additional steam

950 °C sim 750 °C Jensen et al. 2007 750 °C sim 850 °C Jensen et al. 2007 850 °C sim 950 °C Jensen et al. 2007

1.4

Voltage (V)

4,238,843

MH operating temperature (°C)

Parameters

0.8

0

0

100

200 300 Absorption time (minutes)

steam added 400

0.1

Hydrogen to mdetal mol fraction

300

Table 2 Fitting parameters for RSOFC stack model.

0.0 500

Fig. 7. MH temperature and hydrogen-to-metal molar fraction as a function of the absorption time with the hydrogen reaction rate fixed at 3.8 × 10−4 mol/ (mol-metal·s).

0.8 Region of interest

0.6 0.4

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Current density (A/cm2) Fig. 4. Current density-voltage characteristic curve of the RSOFC stack model.

Fig. 8. Hydrogen desorption rate at constant pressure of 1.1 bar and different temperatures as a function of the hydrogen molar fraction in the MH tank.

tank, which can be accomplished by limiting the H2 output mass flow rate and fixing the operating temperature of the MH tank. The operating temperature of the SOFC mode was chosen as 277 °C to ensure that the MH tank is capable of discharging H2 at the required rate and pressure. In the current system design, the operating temperature of MH tank was varied to control hydrogen flowrate. Subsequently, the thermal inertia of the MH tank might limit the response speed of the EES system. In SOEC mode, a 2 °C drop in MH operating temperature can reduce hydrogen flow rate by at least 10%, as shown in Fig. 9. Depends on thermal properties of the MH materials and heat transfer area, the time for changing 2 °C of the MH material could range from seconds to minutes. Regarding switching process, the MH temperature increase 35 °C during a switch from SOEC mode to SOFC mode, while it decreased 213 °C in case of a switch from SOFC to SOEC mode. Therefore, the time for switching from SOFC mode to SOEC mode is expected to be much longer than the opposite case. A dynamic analysis should be conducted in a separate study to provide a transient characteristic of the system.

Fig. 5. Calculated hydrogen content as a function of time in the absorption mode at 10 bar along with experimental data from Liang et al. [52].

b) System performance In general, the benefit to system round-trip efficiency from waste steam utilization was dominant over the MH tank, because the MH tank produced additional steam in a short period of time during charge mode. The MH tank without waste steam utilization resulted in system round-trip efficiency of 39.5%, which is 9% higher than the recent demonstration RSOFC system by J. Mermelstein and O. Posdziech 2016 [7]. The combination of the waste steam utilization and the MH tank

Fig. 6. Calculated hydrogen content as a function of time in the desorption mode at 10 bar along with experimental data from Liang et al. [52]. 8

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A large amount of heat was stored by MH tank, and the air heater was needed for heating up the fresh cooling air to the required temperature. The heat for the MH desorption corresponded to approximately 31.4% of the total chemical energy of consumed hydrogen. The MH stored more heat than the case of phase change material in the study of Pegah Mottaghizadeh et al. [56], which was 28.7%. Subsequently, 1.9% stack power was used for the air heater to compensate for the heat reduction in the exhaust air; and the R_BLR_2 needed around 2.4% stack power to blow large amount of hot air, resulting in a SOFC system efficiency of 52.6%, as shown in Fig. 11. The stack efficiency was 58.9%, so the MH tank only stored 76% of the heat released from the stack. Therefore, with a better balance of plant, it is possible to eliminate the need of an air heater in the SOFC mode. For example, if the A_HEX_2 is designed with pinch temperature of 20 K that equals twice the value used in study of Pegah Mottaghizadeh et al. [56], the air heater can be turned off in SOFC mode, resulting in SOFC system efficiency of 53.7%. The heaters were used in SOFC mode because it was already there from SOEC mode. However, the heaters can be totally turned off and R_BLR_2 power can be reduced if MH tank is featured with additional heat source such as electric heater or furnace. Moreover, the high current density used in this study is one of the culprits for a low efficiency of the SOFC stack. The streams data for the SOFC mode are listed in Table 7 in Appendix B. In the SOFC mode, the heat loss in the stack will influence the system efficiency negatively. Generally, in a SOFC system that uses pure hydrogen as fuel, a certain amount of heat loss in the stack will reduce the cooling air flowrate and air blower power thereby increasing system efficiency. However, in the current system the heat absorbed by MH tank is proportional to the amount of hydrogen consumed. Subsequently, as the heat loss in the stack increases, although cooling air flow rate decreases, the BOP needs extra power to heat up the cooling air. As a result, the heat loss in SOFC stack will reduce the SOFC system efficiency. For example, in the current SOFC system, 2% heat loss in the stack results in 1.3% points reduction in the system efficiency. In case of phase change material, the heat loss in SOFC mode results in less heat stored, thus it might indirectly lower SOEC system efficiency.

Fig. 9. Hydrogen absorption rate as a function of temperature and H2 molar fraction in the MH tank at fixed pressure of 4.5 bar.

resulted in higher system round-trip efficiency of 47.4% (η2) and 45.6% (η3). If the MH tank can produce steam in whole charge mode, the system round-trip efficiency can reach 47.0% without utilizing external heat source (η1). This can be achieved by whether using the MH tank with H2 content starting from 71% or using other catalyst materials for MgH2. In the latter method, the absorption pressure of MH tank might vary, so it needs to be considered to minimize compression work in SOEC mode. Despite the significant benefits of MH tank and waste steam utilization in SOEC mode, the low efficiency of SOFC mode made the system round-trip efficiencies below 50%. The system efficiencies in each operating stage and the system round-trip efficiencies are shown in Table 4. In SOEC mode The two operation stages of SOEC mode reveals that, the MH tank required a low compression work and when it was hot enough to produce steam, it boosted the system efficiency more than waste steam did. In the both stages, the hydrogen compression power was less than 3% of LHV of produced hydrogen, while in the system using 350 bar tank it generally is higher than 9% [55]. Table 4 shows that, the three types of efficiencies were significantly different in stage 1, while they were similar in stage 2. In stage 1, the MH tank did not produce any steam; thus, the effect of waste steam on the system round-trip efficiency was significant. Due to the low exergy value of waste steam, the use of waste steam resulted in η3E values that were 15.1% points higher than the η1E values. In stage 2, the steam production in the MH tank was high enough to completely eliminate the need for waste steam, which resulted in around 19.3% points increase in system efficiency and very similar values between three types of efficiencies. As shown in Fig. 10, the boiler heat consumption was 22.2% of total heat and power input in stage 1, while it was 0.0% in stage 2. Due to the relatively low-temperature steam (stream 31) produced by the MH tank, the fuel heater power in the second stage was higher than that in the first stage. Therefore, the steam from MH tank resulted in a significant increase of power share for SOEC stack that was from 68.4% in the first stage to 87.2% in the second stage, as shown in Fig. 10. Because the stack worked at nearly thermal neutral conditions, the stack power share can approximately represent the hydrogen production efficiency. The stream data of SOEC mode is provided in Table 6 in Appendix B. To estimate the possible effects of heat loss in the SOEC stack, a calculation with heat loss in the stack was conducted. Due to endothermic operating condition of SOEC mode, the heat loss in the stack is compensated by electric power. Therefore, the heat loss directly affects hydrogen production efficiency of the SOEC stack. For example, if the heat loss in the SOEC stack equals 2% of total stack power, the SOEC system efficiency will reduce by 1.4% points. In the SOFC mode

5.2.2. Effects of the current density The three round-trip efficiencies decreased with increasing current density, but the rates of changes were different, as shown in Fig. 12. The electrical round-trip efficiency, η2 slightly decreased with increasing current density, while the others remarkably decreased. Moreover, the round-trip efficiencies η1 and η3 that consider heat of steam production and exergy of waste steam, decreased faster at current density above 0.476 A/cm2. However, the round-trip efficiencies slopes of below 28%/[A/cm2] are not so steep as that in others studies of EES with RSOFC which were 80%/[A/cm2][56] and 40%/[A/cm2][28]. Since both modes operate at the same absolute current density, namely nominal current density, the changes in the system round-trip Table 3 MH tank parameters for validation. Parameters Material ΔH ΔS EA = ED Ni Nf NS Ca Cd k l

9

Value Mechanically milled MgH2 - 5 at.% V −74.3 [53] −0.136 [53] 62.3 0.06 0.76 0.90 4.48⋅106 3253 6.70 0.46

Units kJ/mol kJ/[mol·K] kJ/mol mol-H2/mol-metal mol-H2/mol-metal mol-H2/mol-metal 1/s 1/s

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6.26 kJ/gH2. As a result, system efficiency η1E-2 increased with current density and reached maximum value of 89.5% at 0.476 A/cm2 and then quickly dropped. The other efficiencies in stage 2 were slightly affected by current density, which had similar reason with those in the stage 1, as shown in the Fig. 13. In the SOFC mode, as the current density increased, the system efficiency decreased three time slower than the stack efficiency. Because, more chemical energy was converted to thermal energy due to high voltage losses, the cooling air mass flow rate increased with current density. Because the relative heat required per gH2 released in the MH tank was constant, more hot air was available for preheating the incoming fresh air. Thus, the relative power consumption per gH2 in the blower slightly increased, but the air heater power decreased with increasing the current density. For example, as the current density increased from 0.380 A/cm2 to 0.516 A/cm2, the air blower power increased from 4.24 kJ/gH2 to 4.83 kJ/gH2 but the air heater power decreased from 5.66 kJ/gH2 to 0.35 kJ/gH2, as shown in Fig. 14. As a result, SOFC system efficiency decreased by only 1.2% points, although the RSOFC stack efficiency decreased by 4.4% points. As a prediction, from the point that the air heater power becomes zero, further increasing of current density will lead to the system efficiency decrease with the similar rate as the decrease of the SOFC stack efficiency.

Table 4 System efficiencies of the base case. Parameters η1 η2 η3 time EelecIn EelecOut Eboil ExSteam

SOEC 1st stage

SOEC 2nd stage

70.2 90.2 85.3 340.00 457.92

89.5 89.5 89.5 140.00 461.33

130.34 26.14

0.00 0.00

SOFC 52.4 52.6 52.6 480.00 217.60 1.33 0.27

Round-trip 39.5 47.4 45.6

Units % % % minutes kW kW kW kW

efficiencies were contributed by efficiencies variations in both SOEC and SOFC modes. Before going to more detail explanation of each operating mode, for convenience we introduced a power unit that will be used in the next parts of this paper. Because the parametric study was conducted with a fixed RSOFC cell number, for convenient comparison and explanation, the unit of energy per gram hydrogen produced or consumed (kJ/gH2) was used instead of power in kW. In the SOEC mode, as the nominal current density increased, the system efficiencies decreased in different rates, due to the changes in steam recovery, as shown in Fig. 13. The hydrogen content in the inlet of the fuel electrode was decreased with increasing current density to maintain the SOEC stack endothermic working conditions and the oxygen level in the exhaust air. For example, as the nominal current density increased from 0.380 A/cm2 to 0.516 A/cm2, the hydrogen concentration in the fuel decreased from 60% to 20%, as shown in Fig. 13. As hydrogen concentration decreased, the fuel recirculation rate decreased, thus less steam was recovered by recycle blower and HRSG. Consequently, the system needed more steam from external source or MH tank, as current density increased. In the stage 1, the MH tank did not produce any steam, thus external waste steam increased with increasing current density. For example, as absolute current density increased from 0.380 A/cm2 to 0.516 A/cm2, the relative heat for steam production increased from 29.6 kJ/gH2 to 46.4 kJ/gH2, simultaneously η1E-1 decreased from 72.6% to 67.4%. The η3E-1 was slightly affected by steam production change, because of low exergy value of waste steam. Owing to the reduction in flowrate of hydrogen-water mixture, the fuel heater power decreased, resulting in slightly increase of η2E-1 with increasing current density. In the stage 2, as current density increased, the MH tank produced enough steam until current density reached 0.476 A/cm2, at hydrogen concentration of 40%. As current density increased further than 0.476 A/cm2, the external steam was needed and rapidly increased. For example, as current density increased from 0.476 A/cm2 to 0.516 A/ cm2 the heat for waste steam production increased from 0 kJ/gH2 to

5.3. Low-temperature metal hydride materials (AB5) case Low-temperature MH materials, such as AB5, have several advantages, such as a low heat of desorption and a low operating pressure. However, due to the low absorption temperature (below 100 °C), they cannot produce additional steam in the SOEC mode. In this section, the system using LaNi5 in the MH tank was investigated and compared to the base case, namely, the high-temperature MH. For convenience, the MH working conditions were derived from the existing validated model [57] and experimental data [58] for LaNi5. The properties and parameters of the MH tank are shown in Table 5. Accordingly, the operating pressure and temperature of AB5 tank were calculated to be 6.8 bar and 26 °C in absorption mode; and 1.1 bar and 25 °C in desorption mode. The detail derivation of AB5 tank operating condition is shown in the Appendix C. To avoid overheating of the LaNi5 material, the warm exhaust air was supplied to the MH tank from the output of the air heat exchanger (A_HEX) instead of utilizing the hot air at the outlet of the SOFC stack. The results showed that the system round-trip efficiencies, η1, η2, and η3 were 39.6%, 50.9%, and 48.1%, respectively, which were higher than those in the high-temperature MH case (MgH2). This difference occurred for two main reasons: 1) The temperature and heat requirement in the MH tank in the SOFC mode were low in the case of LaNi5, so the efficiency of the SOFC mode was not affected by the MH tank. For

Fig. 10. Power distribution in the first and second stages of the SOEC mode. In the case of the boiler, the chart shows the share of heat for steam production. 10

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Fig. 11. (a) Distribution of the chemical energy in fuel to others forms and (b) distribution of stack-generated electricity in the SOFC mode.

Fig. 12. System round-trip efficiencies and hydrogen concentration vs. nominal current density.

Fig. 14. System efficiency, stack efficiency, and air heater power as functions of current density. Table 5 Specifications of the AB5 tank. Parameters Material ΔH ΔS Ed Molar weight LaNi5 CpLaNi5 CpLaNi5H6 NL NUp

Value

Units

Milled LaNi5 −31.8[59] −0.110[59] 16.42 432.4 0.419 0.535* 0.45 2.64

kJ/mol kJ/[mol·K] kJ/molH2 g/mol kJ/[kg·K] kJ/[kg·K] mol H2/mol LaNi5 mol H2/mol LaNi5

* Based on Neumann-Kopp’s law, the effect of the H atom was fitted with CpLaNi5H6.39 [60].

Fig. 13. SOEC system efficiencies in stage 1 and stage 2 as a function of the current density.

MgH2 tank can produce steam during the entire absorption process at temperatures and pressures similar to those in stage 2, the η1 of MgH2 case will reach 47.0%.

example, the LaNi5 tank required only 15.5 kJ/gH2 for hydrogen desorption, while 37 kJ/gH2 was required for the MgH2 tank, hence the air heater was turned off in SOFC mode, as shown in Fig. 15. Consequently, in the SOFC mode, the system efficiencies η2F of the LaNi5 and MgH2 systems were 56.7% and 52.6%, respectively. 2) The contribution of additional steam from the MgH2 tank in the SOEC mode was small due to the low absorption temperature in the first long stage. Therefore, in the SOEC mode, the η3E of the LaNi5 system was 85.2%, while the timeaveraged value of η3E for the MgH2 system was 86.6%. In terms of the reference system round-trip efficiency, the LaNi5 tank with a simple system configuration showed an η1 of 39.6%, which was very close to that in the MgH2 case (η1 = 39.5%). However, if the

6. Conclusions A novel electricity storage system based on reversible solid oxide fuel cell stacks coupled with waste steam and a metal hydride tank was proposed. A system analysis was conducted using 0-D models. The reversible solid oxide fuel cell stack was operated at 1.1 bar and 750 °C. In the base case, the waste steam temperature was 400 °C, and the metal hydride materials of MgH2-5 at.% V and LaNi5 were investigated. The time-averaged temperature of the metal hydride tank was calculated and used as the operating temperature of the metal hydride tank, with a 11

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Fig. 15. (a) Distribution of the total energy input and (b) distribution of stack-generated electricity in the SOFC mode when AB5 tank is used.

• The LaNi

total absorption/desorption time of 8 h. The parametric study investigated the effects of the nominal current density on the system round-trip efficiencies. From analyses with MgH2-5 at.% V we found the following:

•

• Despite the high enthalpy of reaction of MgH , the metal hydride 2

•

•

•

•

tank with 5 at.% V started absorbing at ambient temperature and 4.5 bar, resulting in less than 3% power share for compression work. However, the low starting absorption temperature makes the stored heat unusable in 71% of the charging time. The MgH2-5 at.% V tank with two stages of operation in electrolysis mode, showed a small heat storage function of the metal hydride tank, resulting in η1 of 39.5%. In the stage 2, when the metal hydride tank produced steam, it increased the electrolysis system efficiency by 19.3% points, eliminating external heat source demand. For the current metal hydride material and system configuration, the waste steam showed the dominant benefit to the system roundtrip efficiency, i.e. η3 was 45.6%. The heat stored by MgH2 tank was high, i.e. 31.4% of total chemical energy input in fuel cell mode, so the air electric heater was needed to heat up the cooling air. The fuel cell mode efficiency was 52.6%, which is 6.3% lower than stack efficiency. Balance of plant improvement in fuel cell mode could eliminate the need of the air heater. By choosing proper catalyst for MgH2, its absorption temperature can be high and the metal hydride tank can work as an effective heat storage unit. However, the absorption pressure and desorption temperature of metal hydride tank should be taken into account to minimize balance of plant power consumption in charge and discharge modes. A specific material of metal hydride tank can store and release a fixed relative amount of heat, for example MgH2 can only store and release 37 kJ/gH2. Therefore, there is an optimal current density for each metal hydride material, where the heat released from metal hydride tank can be used completely in electrolysis mode without the need of an external heat source. In fuel cell mode, the air heater power could be minimized by choosing the current density that separates from electrolysis mode.

In the future, an economic analysis of the system is needed to evaluate its feasibility as well as its competitiveness with other electrical energy storage technologies. Additionally, the metal hydride material needs to be optimized and selected in terms of the working temperature, pressure, and enthalpy of formation. CRediT authorship contribution statement Van-Tien Giap: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Writing - original draft, Data curation. Young Duk Lee: Writing - review & editing, Funding acquisition. Young Sang Kim: Writing - review & editing. Kook Young Ahn: Funding acquisition, Supervision, Resources, Conceptualization, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This study has been financially supported by the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea: (Project No. 20163010140530, KETEP, Engineering technology for renewable energy hybrid system with reversible SOFC/SOEC and waste steam) and (Project No. 2019281010007A, KETEP, Development of 2MW-class hybrid electrolysis for green hydrogen production and storage technologies to maximize renewable energy utilization).

From the comparison between low and high temperature metal hydride materials, we found that: Appendix A. RSOFC voltage model The RSOFC stack voltage was modeled as follows:

U = Urev

Uact

Uohm

5 tank showed round-trip efficiencies η1 and η3 of 39.6% and 48.1%, which were higher than those in the MgH2 case. Because the heat requirement in fuel cell mode of LaNi5 was lower than that of MgH2 case. If the hot metal hydride tank produces steam during entire the absorption process, then the MgH2 alone will have an efficiency comparable to that of the combination of LaNi5 and waste steam case in terms of the exergy system round-trip efficiency η3. Therefore, the metal hydride material should be properly chosen to improve system efficiency.

Ucon

Nernst voltage: 12

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G RT yH 2 pO2 + ln yH 2o 2F 2F

Urev =

Here ΔG, F, R, T are Gibbs free energy change of reaction, Faraday constant, universal gas constant and cell temperature, respectively; p and y are partial pressure and molar concentration. Activation loss

Uact = sign (j )

2RT sinh nF

jo_air =

0.25 EO2/ RT a yO2tpb e

jofuel =

f yH 2tpb yH 2Otpb e

1

|j| , n = 2(for H2), 4(for O2) 2jo

EO2/ RT

Here j and j0 are current density and exchange current density of electrode. γ is the pre-exponential coefficient. EO2 and EH2 are activation energies of air and fuel electrodes, respectively. Ohmic loss

jde

Uohm =

e

80000 RT

0

Here we assume ohmic loss in electrolyte is dominant over ohmic loss in the electrode and interconnector. de and σ0 are electrolyte thickness and preexponential coefficient of electrolyte ionic conductivity. Concentration loss

Ucon =

y RT RT yH 2 yH 2Otpb ln O2 + ln 4F yO2tpb 2F yH 2tpb yH 2O

Here, yH2tpb and yO2tpb are concentration of hydrogen and oxygen at triple phase boundary:

yO2tpb =

1

1

O2

O2

yH 2tpb = yH 2

O2

=

yO2 exp

RT j O2 da 4F PDeffO2

RT jdf 2F PDeffH 2

DeffO2 DeffO2 + DeffO2N 2

Here da and df are thickness of air electrode and fuel electrode, respectively. DeffA and DeffAB are effective diffusion coefficient of A and binary mixture of A and B which were well explained in the works of [61]. Appendix B. Streams data at base case (See Tables 6 and 7)

Table 6 Stream data for the SOEC mode. Stream

p (bar)

T (°C)

m (g/s)

Molar fraction O2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

H2

1st stg

2nd stg

1st stg

2nd stg

1st stg

2nd stg

1st stg

2nd stg

1st stg

2nd stg

1.08 1.08 1.08 1.08 1.08 1.05 1.08 1.08 1.05 1.05 1.02 0.99 1.08 0.86 1.08 4.50

– – – – – – – – – – – – – 0.87 – –

400 400 362 64 362 64 362 245 649 775 725 294 142 113 64 91

– 168 173 161 173 161 173 151 636 – – 210 132 105 63 –

32.86 32.86 44.02 0.00 44.02 0.00 44.02 66.22 66.22 66.22 38.86 38.86 22.20 16.65 0.00 4.47

0.00 37.35 – – – – – – – – – – – – – –

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

– – – – – – – – – – – – – – – –

0.00 0.00 0.00 1.00 0.00 1.00 0.00 0.40 0.40 0.40 0.70 0.70 0.70 0.70 0.91 0.97

– – – – – – – – – – – – – – – –

(continued on next page) 13

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Table 6 (continued) Stream

p (bar)

T (°C)

m (g/s)

Molar fraction O2

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

H2

1st stg

2nd stg

1st stg

2nd stg

1st stg

2nd stg

1st stg

2nd stg

1st stg

2nd stg

4.50 1.01 1.05 1.05 1.05 1.05 1.04 1.04 1.04 1.04 1.04 1.04 1.01 1.01 1.08 1.15 1.08

– – – – – – – – – – – – – – – 1.10 –

91 25 29 708 724 775 725 711 25 118 711 711 64 64 64 25 248

– – – 660 721 – – 671 – 121 671 662 161 161 168 – 199

3.45 191.49 191.49 191.49 191.49 191.49 218.85 218.85 901.32 218.85 218.85 218.85 901.32 901.32 0.00 11.16 11.16

– – – – – – – – 39.56 221.05 – 221.05 39.56 0.00 37.35 6.66 6.66

0.00 0.21 0.21 0.21 0.21 0.21 0.30 0.30 0.00 0.30 0.30 0.30 0.00 0.00 0.00 0.00 0.00

– – – – – – – – – – – – – – – – –

1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

– – – – – – – – – – – – – – – – –

“–”: indicates the same value as in the first stage.

Table 7 Stream data for the SOFC mode. Stream

1 2 4 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Descriptions

p (bar)

Steam from waste boiler Mixture of stream 1 and steam from MH tank Hydrogen flow from MH tank Bypass stream from stream 4 Mixture of all recirculated fuel off-gas and fresh fuel Mixture of bypass flow and outlet of F_HEX H2/H2O mixture inlet to RSOFC H2/H2O mixture outlet of RSOFC Hot outlet of F_HEX Recycled fuel off-gas Remaining fuel off-gas output from HRSG Recycled hydrogen-rich flow outlet of H2 compressor High purity hydrogen flow Air input Cold fresh inlet air to A_HEX_2 Hot fresh outlet air from A_HEX_2 Hot fresh air from A_HEX Hot air inlet to RSOFC Hot exhaust air from RSOFC Exhaust air from A_HEX Hot air/liquid water to MH heat exchanger Air exhaust to surrounding Remaining exhaust air from A_HEX Mixture of cooling air/water vapor outlet from MH and stream 27 Cooling air/water outlet of MH tank liquid water exhaust duct steam produced through MH tank liquid water fed to HRSG Steam produced from HRSG

1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.09 1.10 1.02 1.10 4.50 4.50 1.01 1.16 1.13 1.10 1.10 1.07 1.04 1.04 1.01 1.04 1.04 1.01 1.01 1.10 1.10 1.10

T (°C)

400 400 277 277 179 675 675 825 449 464 449 48 66 0 25 39 253 669 675 825 410 410 64 410 282 277 277 282 25 102

m (g/s)

0.33 0.33 3.45 1.42 4.86 6.29 6.29 33.65 33.65 0.00 33.65 2.50 0.00 0.00 951.22 951.22 951.22 951.22 951.22 923.85 923.85 923.66 923.85 0.19 923.85 923.66 0.00 0.00 0.00 0.00

Molar fraction O2

H2

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.21 0.21 0.21 0.21 0.21 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.00 0.00

0.00 0.00 1.00 1.00 0.96 0.97 0.97 0.29 0.29 0.29 0.29 0.93 0.93 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Appendix C. AB5 metal hydride operating condition determination In our calculation, the LaNi5 tank was assumed to be that used in the experiment of N. Endo et al. [58]. The experimental study of N. Endo et al. [58] showed that the MH reaction in the LaNi5 tank was so fast that the working temperature and reaction rate were maintained throughout the desorption and absorption processes with little change in pressure. For the SOEC mode, we chose the working temperature of the LaNi5 tank and the molar fraction range of hydrogen in the metal to be the same as those in the experiment, i.e., 26 °C and 0.45 ≤ N ≤ 2.64, respectively. Our system operating time was 8 h for each mode, while it was 9 h in the experiment of N. Endo et al. Therefore, the operating pressure of the LaNi5 tank in the SOEC mode was calculated based on the relation in U. Mayer 14

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et al. [57]:

na ln

Pa Peqa

Pa = Paexp + Peqa e

na naexp

Here:

Peqa = P0exp

{ RTH

S R

} = 1.56bar

and:

na 9 = = 1.125 naexp 8 We obtained an absorption pressure for our system of 6.8 bar. In the desorption mode, the MH tank pressure was fixed at 1.1 bar, so the desorption temperature was calculated based on the reaction rate model validated in the study of U. Mayer et al. [57] as follows:

n d = Cd exp

Ed P Peqd Na RT Peqd

The equilibrium pressure Peqd was calculated as a function of T using the relation of H. Dhaou et al. [62]. In the study of N. Endo, the average pressure was measured at the middle point Na = 1.5. Therefore, the following equation was solved for the working temperature T:

n d15Nl/min 15 = = exp n d16.875Nl/min 16.875

Ed 1 R 331

1 T

5.1 1.15

Peqd 6.0 × Peqd 6

We obtained a desorption temperature of 25 °C.

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