Theoretical and experimental study of Reversible Solid Oxide Cell (r-SOC) systems for energy storage

Energy 141 (2017) 202e214

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Theoretical and experimental study of Reversible Solid Oxide Cell (rSOC) systems for energy storage S. Santhanam*, M.P. Heddrich, M. Riedel, K.A. Friedrich German Aerospace Center (DLR), Institute for Engineering Thermodynamics, Pfaffenwaldring 38-40, 70569, Stuttgart, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 January 2017 Received in revised form 19 July 2017 Accepted 18 September 2017 Available online 19 September 2017

A theoretical system model to study different system concepts is presented in this study. An SOC reactor model was developed based on the experimental analysis in pressurized SOFC and SOEC operation mode. An experimental analysis under pressurized conditions was performed on a commercially available Electrolyte Supported Cell (ESC) type 10 layer SOC stack. A simple system model analysis was performed based on this r-SOC reactor. The effect of different system operation parameters such as pressure, temperature, current density and utilization on system performance was analysed. Endothermic operation of an r-SOC stack in SOEC operation mode can lead to higher roundtrip efficiency. Endothermic operation in SOEC mode requires thermal energy supply. A thermal energy storage system to store high temperature heat released during the SOFC operation to supply heat with high exergy content for the endothermic SOEC process was investigated. A system roundtrip efficiency around 55%e60% is achievable with current ESC type r-SOC technology whereas the theoretical limit of roundtrip efficiency for an ideal reactor (no ohmic, activation and diffusion losses) is around 98% for the same operating conditions. Endothermic operation is beneficial and a heat storage concept is an attractive approach for a prototype system. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Keywords: Reversible Solid Oxide Cell Energy storage Heat storage Electrolysis Fuel cell Electrolyte supported SOC stack

1. Introduction New challenges arise with higher penetration of renewable energy sources in the energy mix. The intermittent nature of renewable energy sources on top of varying electrical energy demand pattern stresses a need for a grid stabilization system [1e4]. Additionally, by moving towards a decarbonized society driven by renewable energy where electrical energy becomes a prime mover, new pathways are needed to produce essential chemical energy and important industrial chemicals [5,6]. Different storage concepts and technologies exist, of which Power to X (PtX) is attractive. Storing electrical energy in form of chemical energy is beneficial due to high storage capacity [7,8]. An r-SOC energy system can meet the challenges mentioned above. Electrochemical systems especially fuel cells and electrolysis cells in combination can form effective energy storage systems [9e11]. With r-SOC systems electrical power and energy capacity can be decoupled and dimensioned individually. During the energy storage mode electricity is

* Corresponding author. E-mail address: [email protected] (S. Santhanam).

converted to fuel such as hydrogen or hydrocarbons (PtX) by means of electrolysis and during discharge mode the fuel can be used to produce power (XtP) via fuel cell operation. Solid Oxide Cell reactors, in theory can be operated as both fuel cell and electrolysis cells [12e14]. An SOC reactor can efficiently operate in PtX mode as an electrolyser and in XtP mode as a fuel cell. They have the potential to show significantly lower electrochemical losses than any other fuel cell/electrolysis technology [15e18]. Thermal management is essential for r-SOC systems. In the fuel cell mode, the r-SOC reactor is highly exothermic whereas in electrolysis mode it can be highly endothermic. Several possibilities for heat management have been proposed to fulfil the requirement of thermally selfsustained roundtrips including exothermic fuel cell mode and possible highly endothermic electrolysis. Bierschenk et al. showed that by coupling an exothermic chemical reaction such as methanation with endothermic electrolysis reaction inside SOC reactor a thermal balance can be achieved [19]. By this method, a thermoneutral or even exothermic operation of SOC reactor in electrolysis mode can be achieved. Similar strategy for thermal management has been proposed in other research works [20e22]. The proposed method poses certain challenges. Thermodynamically, exothermic reactions such as methanation require a combination of lower

https://doi.org/10.1016/j.energy.2017.09.081 0360-5442/© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

S. Santhanam et al. / Energy 141 (2017) 202e214

reaction temperatures in range of 400
Ce650
C and/or higher pressures up to 30 bar [23]. Hence, this requires development of SOC reactors with low electrochemical losses at those reaction temperatures capable of operating at high pressures. Low and intermediate temperature SOC reactors are in research and development phase [24], [25]. Commercially available r-SOC reactors are based on ESC design and operating at temperatures of 750
Ce900
C [26]. In this work, a novel method of thermal management strategy is proposed. In this method, high temperature heat storage is integrated. Integrating heat storage with r-SOC system will help store heat produced during the exothermic operation of r-SOC. This heat then can be used during the endothermic operation of r-SOC (during SOEC operation) or to supply heat to other interlinked processes. A high temperature heat source can be integrated for endothermic electrolysis operation enabling even higher roundtrip efficiencies [27,28]. In future one can envisage a heat storage integrated r-SOC energy system in industrial processes and chemical processes where high temperature heat is used or produced [29e31]. In this work, starting from a generalized formulation of an r-SOC system model, a heat storage integrated rSOC system for a simple hydrogen based energy storage system is considered. A commercially available r-SOC stack is experimentally characterized at pressurized conditions. Regimes for endothermic operation of a SOC reactor in the SOEC mode are investigated. Achievable roundtrip efficiencies are quantified. 2. Theory of SOC reactors and theoretical limit of roundtrip efficiency For SOC electrochemical reactors, the electrical energy produced during the exothermic electrochemical oxidation or electrical energy consumed for an endothermic electrochemical reduction process is given by solving the energy balance and entropy balance over the reactor. The irreversible entropy generation represents the internal losses. For an isothermal reactor, that corresponds to ideal work plus the electrical energy required to overcome the electrochemical losses. The ideal work of the SOC reactor is a function temperature, pressure and conversion ratio. The ideal SOC reactor would still incur losses due to unavoidable thermodynamic irreversibility resulting from change in composition, mixing of products and unconverted reactants in the fuel stream. This unavoidable loss can be termed as a thermodynamic loss and should be considered in evaluating the ideal work of the reactor [32], [33]. In literature, ideal voltage and ideal work of the SOC reactor is calculated by utilising the Nernst equation with either inlet or outlet compositions only. The use of inlet compositions in the Nernst equation does not take into account the effect of change in partial pressure of the components due to reactant conversion. Secondly, to compensate for the conversion effect, outlet compositions are often used to evaluate the ideal work by assuming the SOC reactor to behave like a continuously stirred reactor (CSTR) [34]. This assumption is not strictly correct, as the planar or tubular SOC reactors behave similarly to a plug flow reactor (PFR) and CSTR assumption is only valid when the gas hourly space velocity is very low or for low reactant conversion ratios. In this work, the ideal work of the r-SOC reactor is computed as the difference between the Gibbs function at the outlet of the reactor and Gibbs function at the inlet of the reactor as shown in equation (1). The Gibbs function at the inlet and outlet is a function of temperature, pressure and the gas compositions at the inlet and outlet of the r-SOC reactor respectively. This takes into account the effects of fuel/reactant conversion, air utilization and also change in temperature between inlet and outlet. Moreover, the Gibbs function being a thermodynamic state function depends only on initial and final states. A similar method is proposed by Gaggioli et al. [35,36] and Ratjke

203

P

et al. [37]. The term G0 in equation (1) is the sum of the Gibbs P 00 function of air and fuel streams at the inlet and the term G is the sum of Gibbs of product streams (air and fuel) at the reactor outlet. The equation for calculating the Gibbs function is provided in the Appendix (refer equations (A4eA7)).

 X   X 00   00 G0 T; p; x0i Wideal ¼  G T; p; xi 

(1)

The ideal voltage of the reactor is a derivative of the ideal work. The SOC ideal voltage is calculated using equation (2) when the SOC reactor is operating in either SOFC or SOEC mode.

Uideal

P 00 P 0  G  G Wideal  ¼ ¼ I I

(2)

Equation (2) cannot be used for calculating the open circuit voltage (OCV) at zero current since it results in an indeterminate as both numerator and denominator is zero. Hence, equation (3) is used to evaluate the OCV for a given reactant flows. equation (3) is the traditional Nernst equation for evaluating the electrochemical equilibrium potential.


UOCV ¼ U 

Y 1 RTln pyi i 2F

(3)

For electrochemical oxidation, the maximum conversion for a given inlet composition of reactants corresponds to the maximum current obtained for complete oxidation of the reactants. The actual conversion indicates the extent of fuel oxidation which, for solid oxide cell reactors can be indicated by the actual current produced in the system. This can also be indicated in terms of charge transferred as oxygen ions (from Faraday's law) as current is proportional to oxygen ions transferred through the electrolyte in a SOC reactor. The dimensionless extent of reaction or the utilization is given by the ratio of the actual current produced to the maximum current produced when complete oxidation occurs with the common SOFC gas components H2, CO and CH4 [34]. Likewise, the maximum extent of electrochemical reduction is given by the complete reduction of oxidized components (H2O and CO2, the latter reduced only as far as CO to avoid carbon formation and H2O to H2) in the reactants and actual extent of electrochemical reduction is proportional to actual current supplied to the SOC reactor. The conversion can be related to the charge transferred as oxygen ions through the electrolyte. Fuel cell mode:

  fc _ fc Imax ¼ 2F n_ fc þ n_ fc co þ 4nch4 h2 fc

I fc ¼ cfc Imax

(4) (5)

.

fc 2F xfc ¼ Dn_ fc o ¼I

.

fc _ fc xfc max ¼ Dno ¼ Imax 2F

(6) (7)

Electrolysis mode:

  ec _ ec Imax ¼ 2F n_ ec h2o þ nco2

(8)

ec I ec ¼ cec Imax

(9)

ec xec ¼ Dn_ ec o ¼ I =2F



ec _ ec xec max ¼ Dno ¼ Imax 2F

(10) (11)

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Here it is being assumed that the charge transferred (oxygen ions) from air to fuel side during SOFC operation be equal to the charge transferred (oxygen ions) from fuel to air side in SOEC mode. Further, for simplicity, it is assumed that the duration of charge and discharge is equal. This implies that the current obtained during electrochemical oxidation (extent of electrochemical oxidation) must be equal to the current supplied during electrochemical reduction (extent of electrochemical reduction). Note that for the system simulation in this work the fuel gas composition will be simplified to only H2 and H2O. The roundtrip efficiency of r-SOC is the ratio of energy obtained during discharge to energy supplied during the charging mode to obtain the same state of charge.



hrt ¼

W Tfc ; pfc ; x

 ideal;fc

 DUloss *Ifc *tfc

WðTec ; pec ; xÞideal;ec þ DUloss *Iec *tec

(12)

Due to these assumptions, the currents are identical; the roundtrip efficiency reduces to a ratio of SOC reactor voltage in fuel cell operation and its voltage in electrolysis operation [38,39].

hrt ¼

  U Tfc ; pec ; x

fc;ideal

 DUloss

UðTec ; pec ; xÞec;ideal þ DUloss

(13)

Consider a hypothetical ideal SOC reactor, which is assumed to have no electrochemical losses (ohmic, activation and diffusion). For an ideal SOC reactor with complete usage of reversible heat, the roundtrip efficiency is the theoretical maximum that can be attained for a set of thermodynamic condition of temperature, pressure and conversion ratio.



hrt;ideal ¼



U Tfc ; pfc ; x

fc;ideal

UðTec ; pec ; xÞec;ideal

(14)

The ideal voltage as a function of temperature, pressure and conversion ratio is calculated using equation (2). 3. Model development

Isothermal behaviour for the SOC reactor is assumed and all reactions within the reactor are assumed to occur at the isothermal reactor temperature. The reactions occurring within the reactor are assumed to reach chemical equilibrium at reactor temperature and pressure for a given extent of electrochemical reaction. The reactor voltage is given by

(15)

where i is the current density and ASR is the area specific resistance of the SOC reactor. In this paper, the following sign convention for current density is assumed. The current density is positive in the SOFC operation mode and is negative for the SOEC operation. The ideal voltage Uideal of the reactor for a specific operation point is calculated using equation (2). 3.1.1. Thermodynamic equilibrium model An equilibrium reactor model is used to calculate the reactions and outlet compositions. The following gas components are considered to be available in significant concentrations in the fuel gas stream; CH4, CO2, CO, H2O and H2 in the general model. No elemental carbon is considered, though the O/C ratio is checked externally to avoid carbon formation conditions. However for the current analysis the model is used for only H2-H2O system. For the

Dh ¼ 206 kJ=mol

CH4 þ H2 O#3H2 þ CO

Dh ¼ 41 kJ=mol

CO þ H2 O#H2 þ CO2

(16) (17)

Molar flows of C, H and O atoms in the gas streams at the inlet is given by

n_ 0C ¼ n_ 0CH4 þ n_ 0CO2 þ n_ 0CO

(18)

n_ 0H ¼ 4n_ 0CH4 þ 2n_ 0H2 O þ 2n_ 0H2

(19)

n_ 0O ¼ n_ 0H2 O þ 2n_ 0CO2 þ n_ 0CO

(20)

In SOC electrochemical reactor, the molar flows of H and C atoms remain constant between the inlet and outlet whereas the molar flow of O atoms increases at the outlet in fuel cell operation or reduces in electrolysis due to oxygen ion conduction principle of the electrolyte. The amount of oxygen atoms that are added to or removed from the fuel side gas streams is given by Faraday's law. The outlet molar flows of C, H, and O atoms are given by 00

00

00

00

n_ C ¼ n_ CH4 þ n_ CO2 þ n_ CO 00

00

00

(21) 00

n_ H ¼ 4n_ CH4 þ 2n_ H2 O þ 2n_ H2 00

00

00

00

n_ O ¼ n_ H2 O þ 2n_ CO2 þ n_ CO þ I=2F

(22) (23)

The equilibrium constant for reverse water gas shift (RWGS) and reverse steam methane reforming (RSMR) reactions are given by

Krwgs ¼

Krsmr ¼

3.1. SOC reactor model

U ¼ Uideal  i*ASR

above set of components in the gas streams, the equilibrium can be determined by a set of two independent reactions

pH2 pCO2 pCO pH2 O p3H2 pCO pCH4 pH2 O

(24)

(25)

The equilibrium constants are related to the Gibbs function through the change in Gibbs energy of reaction under standard pressure condition which can also be calculated as a function of temperature.

DGorwgs ðTÞ ¼ RTlnKrwgs

(26)

DGorsmr ðTÞ ¼ RTlnKrsmr

(27)

Solving the equations from (18)e(27), the outlet mole compositions of the product stream can be determined.

3.1.2. Electrochemical model A simple electrochemical model was employed and the utilization dependent ideal voltage was determined using the Nernst equation and outlet composition. For the electrochemical model, a simple phenomenological model was developed based on pressurized SOC stack experiments in both SOFC and SOEC operation modes. The overpotential is calculated as a difference between the measured stack voltage and theoretically calculated utilization dependent ideal voltage at a given condition (temperature, pressure, extent of reactions etc.). The area specific resistance is then calculated from the DU as given in equation (28). The Uideal ðT; p; xÞ is calculated for each measurement point using equation (2).

S. Santhanam et al. / Energy 141 (2017) 202e214

DU ¼ Uideal ðT; p; xÞ  Uexp

(28)

    ASR ¼ DU=i

(29)

A commercial electrolyte supported cell (ESC) SOC stack was characterized under pressure. Experiments were performed in both SOEC and SOFC operation modes. Steady state U(i) characteristic curves were performed at different utilization values, current densities, temperatures and pressures. In steady state mode U(i) measurements, the reactant flow to the r-SOC reactor was set accordingly to maintain a constant reactant conversion at each current density. Whereas in dynamic U(i) measurements the reactant flow was constant and the current density was changed leading to varying reactant conversion values. The steady state measurements were performed at pressures of 1.4 bar, 3 bar, 6 and 8 bar; different furnace temperatures were 750
C, 800
C and 850
C. For each pressure and temperature, utilization values of 55%, 70% and 85% were maintained. The measurements were performed with a gas composition of 40% H2 and 60% N2 in the SOFC operation mode. The air flow rate was varied such that the air utilization was constant at 25% at all current densities in the SOFC mode. In the SOEC mode, the measurements were performed with gas compositions of 90% H2O and 10% H2. Electrochemical impedance spectroscopy (EIS) measurements were performed at different steady state conditions mentioned. The EIS measurements were performed in the galvanic mode and in the frequency range of 100 kHz to 10 mHz. An oscillation amplitude of 1 A was used for the measurements. EIS measurements were performed at OCV conditions at different temperatures from 700
C to 850
C. They were primarily performed to accurately quantify the ohmic resistance of the r-SOC reactor. The EIS measurements of the same r-SOC reactor measured at OCV conditions is reported by Marc Riedel et al. [40]. EIS measurements under steady state conditions were also performed at selected current densities at different pressures, conversion ratios and temperatures. The ASR from the EIS measurements is obtained from Nyquist plots [41]. A phenomenological semi empirical model for the ASR was established as a function of operating parameters based on the experimental results. The ASR was experimentally found to be a strong function of temperature and varied negligibly with pressure. The observed effect is in accordance with published results for an ESC stack, for which the ASR is largely dominated by the ohmic component owing to the thick electrolyte layer. It is well-known that, the ohmic resistance is a function of temperature [42e45]. The diffusion effect on the ASR is negligible in ESC stacks due to their thin electrode layers. Moreover, from a system perspective, the operational current densities are in a region where ohmic losses are dominant. Based on the above assumptions and experimental results a simplified temperature dependent semi empirical model is justified. The temperature dependence is described by an exponential function in equation (30).

ASR ¼ a1 þ a2*expða3*TÞ

205

3 Ratio of discharge period to charge period is set to 1 4 Charge transferred during the discharge mode is equal to the charge transferred during the charging mode 5 Due to assumptions 3 and 4, the current obtained from the SOC reactor in SOFC mode is equal in magnitude to the current supplied to the SOC reactor in SOEC mode. 6 Assumptions 3e5 ensure that the “state of charge” over one charge-discharge cycle remains the same. The fuel tank and exhaust tank in the system are brought to the same thermodynamic state before discharge. 7 Ideal heat transfer is assumed for heat recovery units. Due to this assumption, the effect on system performance is purely due to the reactor in the system. The effects especially of BoP components will be covered in future work. 8 Heat storage is assumed to take place at constant steady state temperature. 9 An ideal gas model is used throughout the study. Chemical energy in the form of fuel is stored in the fuel tank and the products of oxidation (oxidized fuel) are stored in the exhaust tank. The thermodynamic conditions for the tanks are chosen in order to avoid condensation of water and other components. 3.2.2. Process system In this study, a simple hydrogen-water system is considered. The schematic of the process system is shown in Figs. 1 and 2. The scheme shown in Fig. 1 corresponds to SOFC operation and Fig. 2 corresponds to SOEC operation. The fuel in the tank is assumed to be a reservoir with a composition of 90 mol% of hydrogen and 10 mol% of water. This corresponds to a fuel with LHV of 60.21 MJ/ kg. The process system comprises of an isothermal r-SOC reactor which depending on operation mode produces or consumes electrical power and or heat. The r-SOC reactor is modelled based on a commercially available ESC type r-SOC stack. The operational behaviour of the r-SOC reactor is described in section 2. A heat recovery unit is utilized to cool down the product gases of the reactor from reactor temperature to the storage tank temperature. The heat extracted from the product streams is used to heat reactant streams from storage tank temperatures to isothermal reactor temperature. A thermal energy storage system is considered to store the heat released by a r-SOC reactor during exothermic oxidation and supply stored heat to a r-SOC reactor during endothermic electrolysis operation. The heat recovery unit and heat storage systems are described in sections 3.2.3 and 3.2.4 respectively. In the fuel cell or in the discharge mode, the fuel reactants are preheated to the SOC reactor temperature using the product gases

(30)

3.2. System model 3.2.1. Assumptions and boundary conditions The following assumptions are made for modelling the system. 1 An isothermal SOC reactor model is used 2 All reactions occurring in the reactor take place at isothermal reactor temperature

Fig. 1. Schematic representation of process system in fuel cell mode, indicating directions of mass and energy flows (Fuel cell mode).

206

S. Santhanam et al. / Energy 141 (2017) 202e214

account for non-ideal behaviour of heat recovery unit. The losses in the heat recovery unit and its impact on the system performance can be included by adapting corresponding exergy efficiencies for the heat pump and heat engine.

Fig. 2. Schematic representation of the process system in electrolysis mode, indicating directions of mass and energy flows (Electrolysis mode).

from the SOC reactor. Power and heat produced by the SOC reactor is calculated at the reactor pressure and temperature for given value of utilization. Heat produced by the SOC reactor in fuel cell mode is stored in a heat storage device at the melting point temperature of a phase change material. The product gases, which are mainly comprised of water, are stored in the exhaust tank. In the electrolysis or charging mode, the gases from the exhaust tank are preheated to SOC reactor temperature and fed to the SOC reactor. The discharge rate and capacity is the same as charge rate and capacity due to the assumptions 3 and 4. Accordingly, conversion ratio for electrochemical electrolysis reaction is calculated. The electrical power and heat required for electrolysis is calculated for SOC reactor conditions and reaction conversion. The heat for the electrolysis is obtained from the heat storage. A latent heat storage concept is considered for the system which also stores the heat produced in the FC mode. For heat transfer to take place, a plausible assumption for a temperature difference between the reactor and heat storage unit will be considered. This implies that SOC reactor temperature in SOFC mode should be higher than melting point temperature of the Phase Change Material (PCM) within the heat storage unit fc hs Tsoc > Tm

(31)

In the SOEC operation mode, the heat storage unit supplies the heat required by the SOC reactor when operated in endothermic region. This requires the SOC reactor temperature in SOEC mode to be lower than the isothermal heat storage temperature ec hs Tsoc < Tm

(32)

Therefore, this implies that the SOC reactor temperature in SOFC mode is higher than in SOEC mode. The temperature difference between the SOC reactor and heat storage is assumed to be equal in both operation modes. fc

hs hs ec Tsoc  Tm ¼ DT ¼ Tm  Tsoc

(33)

3.2.3. Heat recovery unit The ideal heat transfer is modelled using a system of ideal Carnot heat engine and heat pump network. Due to this modelling approach, the effect on the system performance at different operating parameters is only due to the behaviour of the SOC reactor. Since the aim of this study was to understand the behaviour of the SOC reactor in the context of an r-SOC system, the adopted modelling approach is beneficial. The model is still flexible to

3.2.4. Heat storage unit In this work, ideal heat storage without heat loss is considered. This approach is useful to provide an insight into realistic heat storage possibilities in this section. As mentioned before a latent heat storage concept using phase change materials (PCM) is considered. PCM based latent heat storage can facilitate storing large quantities of thermal energy at a constant temperature [46e48]. In this concept, the heat is stored in the material at the melting point temperature of the material. The material absorbs thermal energy corresponding to the heat of fusion at melting point temperature. The material phase changes during heat storage, as it absorbs the heat. The volume of the storage material can be dimensioned based on quantity of the thermal energy stored, heat of fusion of material and average density of the material. SOC reactor systems generally operate in the temperatures regions of 700
Ce900
C. Hence, the heat storage material should have high melting point temperatures. This requirement narrows down the list of possible candidate materials for heat storage. In literature, further requirements for heat storage materials are provided in detail. A detailed literature study was performed and materials with desired melting temperatures were identified. For the system considered, molten salts, salt ceramics and non-eutectic salt mixtures are viable candidate materials. A detailed list of possible materials is provided in the following literature [47,49e51]. 4. Results and discussions 4.1. Theoretical limit of roundtrip efficiency assuming an ideal reactor In this section, the limits of theoretically achievable efficiency for a system with a hypothetical ideal reactor as defined in section 2 is presented. The system behaviour was studied as a function of current density, extent of electrochemical reactions (conversion) and pressure. For each set of parameters, system performance as a function of different values of temperature difference between the SOC reactor and heat storage temperature was studied. For a defined system configuration, the maximum efficiency achievable, assuming an ideal SOC reactor, (no electrochemical losses present but thermodynamic losses still exist) is dependent on the temperature difference between the SOC reactor temperatures in SOFC and SOEC modes and on pressure. For a given electrochemical reaction conversion, the variation of theoretically achievable ideal roundtrip efficiency is plotted as a function of SOC reactor temperature in SOFC mode at different pressures and DT values in Fig. 3. At constant reactor temperature and pressure, the DT value between the reactor and heat storage has an effect on the system efficiency. But for a given reactor temperature in SOFC mode and DT, the pressure affects the theoretically achievable ideal round trip efficiency as shown in Fig. 3. The region of operational interest of the SOC reactors presented here is at around 800e850
C since the commercially available SOC stacks based on ESC technology are viable at these temperatures. Therefore, a reactor temperature of 850
C in FC mode and a system pressure of 1 bar is chosen as reference condition. From Fig. 3 it can be seen, that at this reference condition and varying DT, the theoretical limit of ideal round trip efficiency varies from 98.5% to 99.5%. By using heat storage to manage the thermal demands of SOEC operation, the upper limit for ideal round trip efficiency was increased close to 100%. The roundtrip efficiency decreases with

S. Santhanam et al. / Energy 141 (2017) 202e214

207

heat ratio indicates that the SOEC changed from endothermic to exothermic operation mode. The heat produced or consumed by an ideal SOC reactor is given by the net reversible heat of the reactions occurring within the reactor. For a real reactor it is the sum of reversible heat and the heat released in the reactor due to electrochemical losses. The reversible heat for an ideal reactor is given by the change in entropy due to the reaction. In this work, the reversible heat is calculated using the second law of thermodyP 00 namics as given in equation (35). The term S is the sum of entropy of fuel and air stream at the outlet of the reactor and the term P 0 S is the sum of entropy of fuel and air stream at the outlet of the reactor. The equation for calculating the entropy function is provided in the Appendix (refer equations (A1eA3)).

Qideal ¼ T

Fig. 3. Roundtrip efficiency of an ideal reactor as a function of temperature, pressure and temperature difference for a given conversion. Temperature of the SOC reactor in EC mode is Tsoec ¼ Tsofc  2DT. Conversion ratio (x/xmax) in FC mode is equal to 80% and in EC mode equal to 88%.

increasing DT between the reactor and heat storage. The operation temperature of the SOC reactor in SOEC mode is lower than that in SOFC mode. For a H2eH2O system, the change in Gibbs function increases with lowering temperatures. Hence the ideal work required in SOEC operation is higher than the ideal work produced during the SOFC operation. Therefore, the roundtrip efficiency decreases with increasing DT. The roundtrip efficiency approaches 100% as DT tends to zero. The efficiency increases with pressure by 0.5% on average between 1 and 15 bar. Further increase in pressure from 15 to 30 bar has marginal impact on efficiency. At reference temperature and DT of 25 K, varying the pressure from 1 bar at reference case to 30 bar increases efficiency from 98.3% to 98.8%. The behaviour of ideal roundtrip efficiency as a function of pressure can be explained due to the behaviour of Gibbs function with pressure. The Gibbs free energy is a logarithmic function of pressure. For both fuel cell mode and electrolysis mode, increasing pressure leads to an increase in ideal work for a given temperature and extent of electrochemical oxidation. This leads to increasing in roundtrip efficiency with increase in pressure from 1 to 15 bar. With further increase in pressure beyond 15 bar, the effect decreases significantly due to the logarithmic function of pressure. For the same system without thermal management and utilization of the reversible heat the roundtrip efficiency is limited to 73% at the reference condition since the heat required for endothermic operation has to be supplied by an external source. Hence, by utilising the reversible heat produced during SOFC operation in the SOEC operation, the theoretical limit for ideal roundtrip efficiency is increased to 98%. This highlights the advantage of incorporating a thermal management system for utilising the heat produced during SOFC operation for endothermic SOEC operation. The ratio of heat required for electrolysis to heat produced during fuel cell operation is defined as heat ratio (q).

.

q ¼ Qec Q fc

X

00

S 

X  S0

(35)

For a real SOC reactor including the electrochemical losses within the reactor, the heat produced or consumed by the reactor is calculated using equation (36). The term I DU is the heat produced due to the electrochemical losses occurring within the reactor.

Qideal ¼ T

X

00

S 

X  S0 þ I DU

(36)

From Fig. 4 it can be seen, that at the reference condition (850
C and 1 bar) the heat ratio was 99%, meaning almost all the heat produced during the SOFC mode which is stored in the heat storage is consumed in the SOEC operation mode. The heat ratio is not equal to 100% because of the difference in reactor temperature in SOFC and SOEC mode. Since the reactor temperature in SOEC operation is lower than in SOFC operation, the reversible heat required for endothermic reaction is slightly lower than the reversible heat produced during the SOFC operation.

4.2. r-SOC system performance with a commercially available reactor 4.2.1. Performance of a commercially available r-SOC reactor A commercially available r-SOC reactor was characterized under pressurized conditions. The experimental analysis on the r-SOC reactor was performed using a pressurized stack testing facility.

(34)

By convention, the positive value for heat (Q) corresponds to exothermic heat production and negative value corresponds to endothermic heat consumption. Therefore a negative value for the heat ratio indicates that the SOC reactor is endothermic during SOEC process since SOFC process is always exothermic. A positive

Fig. 4. Variation of heat ratio for an r-SOC system with ideal reaction versus temperature for different conversion ratio, 50% (black) and 80% (blue). Temperature SOC reactor in EC mode is Tsoec ¼ Tsofc  2DT. For a conversion ratio (x/xmax) in FC mode equal to 50% the corresponding value in EC mode is equal to 81%. For a conversion ratio (x/xmax) in FC mode equal to 80% the corresponding value in EC mode is equal to 88%.

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With the test rig experiments in both SOFC and SOEC operation modes can be performed. It can reach a maximum pressure of 8 bar. A differential pressure of 10 mbare500 mbar between the fuel chamber and air chamber can be set and maintained. The furnace can reach a maximum temperature of 950
C while the minimum temperature is 700
C (details on the test rig were reported by Seidler et al. [52]). The utilized SOC reactor is based on ESC stack technology. It is a 10 cell stack with a closed fuel electrode, open air electrode stack design and with a maximum power of 300 W. The electrolyte is 90 mm thick made of 3 mol% Yttria Stabilized Zirconia (3YSZ). The air electrode is composed of LSCF with a GDC protective layer between air electrode and electrolyte. The total thickness of the air electrode amounts to 55 mm. The fuel electrode is a Ni-GDC matrix with a thickness of 30 mm. An analysis of the experiments performed in the SOFC operation mode is presented in this work. The analysis of the experimental results of the SOC reactor in the SOEC operation mode is presented by Riedel et al. [40]. Temperatures at the inlet, outlet and at the centre of the reactor were measured. The temperature of the cell measured at the centre of the reactor is representative of the reactor temperature. Hence the temperature measured at the centre of the reactor is referred to as the characteristic reactor temperature. The U(i) characterisation curves for the r-SOC reactor in SOFC mode measured under steady state conditions is shown in Fig. 5. The pressure effect can be observed in Fig. 5(top). The U(i) curves are plotted for a reactant conversion of 70% in SOFC mode is shown in Fig. 5(top left). The variation of characteristic reactor temperature for the corresponding points is shown in Fig. 5(top right). It can be seen that the pressure has a positive effect on the rSOC performance in SOFC mode and it is significant at lower pressures but diminishes at higher pressure. The effect of reactant conversion on the r-SOC performance in SOFC mode can be observed from Fig. 5(bottom). The U(i) curves for different conversion ratios at a pressure of 1.4 bar is shown in Fig. 5(bottom left). The corresponding variation of the characteristic reactor temperature with current density at 1.4 bar for different conversion ratio is shown in Fig. 5(bottom right). Higher reactant conversion has a negative on the SOFC voltage. As discussed in section 2 from thermodynamics, higher reactant conversion results in faster work

Fig. 5. Steady state U(i) characteristic curves of the r-SOC reactor in the FC mode. The top left figure shows the U(i) performance curve in FC mode at different pressures for furnace temperature of 750
C and conversion of 70%. Top right figure shows the variation of characteristic reactor temperature at different pressures for conversion of 70%. The bottom left figure describes the U(i) performance at different conversion rates in SOFC mode at 1.4 bar pressure and 750
C furnace temperature. In bottom right, variation of characteristic reactor temperature at different conversion rates is shown for pressure of 1.4 bar.

extraction thereby resulting in higher entropy generation. This is shown in the ideal voltage plot at 85% and 55%. The ASR calculated from the U(i) measurements is shown in Fig. 6. In this work, the ASR (indicated by red squares in Fig. 6) is calculated from the U(i) measurements using equations (28) and (29). The ideal voltage is calculated using equation (2). It can be observed from Fig. 6 that this method yields an accurate measure of ASR. The ASR calculated by the proposed method is closer to the ASR measured using EIS. Hence, this further validates the use of equation (2) for calculating the ideal voltage. A comparison of ASR calculated using other methods is also shown in Fig. 6. The blue cross in Fig. 6 indicates ASR calculated by using Nernst equation with outlet composition in equations (28) and (29) to calculate the 00 ideal voltage (Uideal ðT; p; x Þ). This yield an ASR considerably lower than the value measured using EIS and also lower than the ohmic component of ASR measured using EIS. Likewise, the purple stars in Fig. 6 indicate the ASR calculated with ideal voltage calculated using Nernst equation with inlet compositions (Uideal ðT; p; x0 Þ). This results in ASR values considerably higher than the values measured using EIS. Hence, this analysis further reaffirms the use of equation (2) to calculate the ideal voltage of an r-SOC reactor. The performance of the reactor is further examined to understand the behaviour and loss phenomena due to different operation parameters. The ohmic losses were characterized from EIS measurements performed at OCV conditions at different temperatures. These measurements act as a baseline for ohmic losses as a function of temperature. The ohmic loss at different temperatures for the same reactor obtained from EIS measurements is reported in Ref. [40]. A temperature dependant polynomial function was developed for the ohmic losses reported in Ref. [40]. The variation of the reactor temperature with different current densities at different pressures under steady state condition is shown Fig. 7(top). A trend of lower reactor temperature at higher pressure is observed. This can be due either due to test rig preheater limitation or due to air utilization rate used during experiments. At higher pressures, the r-SOC reactor has higher voltage leading to less heat generation. Hence, the high air flow rate is cooling the reactor thereby reducing the core reactor temperature at higher pressures. This temperature decrease leads to higher ohmic voltage losses with pressure seen from Fig. 7(bottom). The impact of pressure on polarisation losses can be observed in

Fig. 6. Variation of ASR with characteristic reactor temperature. The ASR is calculated using equations (28) and (29) using equation (2) for computing Uideal . Red squares show the ASR computed by using equation (2) for calculating ideal voltage. Blue cross indicates ASR calculated using Nernst equation with outlet composition for computing ideal voltage. Green triangles indicate ASR measure with EIS at selected current densities. Purple stars indicate ASR computed using Nernst equation with inlet composition for calculating the ideal voltage.

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209

Fig. 7. Impact of pressure on the SOC reactor performance is shown. The top figure shows the variation of characteristic reactor temperature with current density at different pressures at a conversion ratio of 55%. Corresponding ohmic voltage loss vs. current density at different pressures is depicted in bottom figure.

Fig. 8(top). It can be seen from Fig. 8(bottom) that as the pressure increased, the characteristic reactor temperature decreases. The effects of pressure and temperature on activation losses due to the electrode reactions are not straightforward. Higher pressures can lead to higher partial pressures of reactants promoting adsorption of reactants on the reaction sites at triple phase boundaries leading to improved kinetics thereby decreasing activation losses. On the other hand, lower temperatures leads to sluggish reaction kinetics at the electrodes leading to higher activation losses [53e55]. From the detailed analysis of the experimental results, it was clear that the ohmic losses contributed close to 80% of the total electrochemical loss and also resulted in a higher ASR value. The higher ASR of the reactor is due to the thick electrolyte layer in the reactor. For an ESC reactor, the ohmic voltage losses dominate over other loss components. Ohmic loss is a function of temperature,

Fig. 8. Variation of polarisation losses with pressure for r-SOC reactor at different pressures for a conversion ratio of 55% is shown in the top figure. The bottom figure depicts the variation of characteristic reactor temperature with current density at different pressures for a conversion ratio of 55%.

hence the rSOC reactor showed a strongly temperature dependant performance. The effect of pressure on this ESC type SOC reactor was negligible and can be ignored for the current analysis. Hence, this substantiates the semi-empirical temperature dependant function for the electrochemical model used to evaluate the ASR. From the experimental results, the fitting parameters for the ASR model given in equation (30) are calculated using nonlinear curve fitting. The model is used to simulate the U(i) of the same reactor in SOEC operation mode. Though the ASR model was developed based on ASR obtained from SOFC experiments, it can be seen that the rSOC reactor can be described well in SOEC operation using a simple semi empirical model as shown in Fig. 9. The U(i) characteristic in SOEC mode measured and calculated by the model are shown in Fig. 9(Top). The empirical calculation is able to describe the loss behaviour of the stack. In Fig. 9(bottom), the variation of the characteristic reactor temperature with current density is shown. The core cell temperature is measured during the U(i) measurements. The temperature initially decreases due to endothermic water electrolysis until a current density of 0.3 A/cm2. At 0.3 A/cm2, the thermoneutral point is reached which corresponds to a cell voltage of 1.3 V. Further increase in current density increases the cell temperature and the r-SOC reactor moves towards exothermic operation in the SOEC mode. The behaviour of the modelled U(i) curve is not linear though the voltage is a linear function of current (equation (15)) because the semi-empirical electrochemical model of ASR (equation (30)) is an exponential function of temperature. Hence the non-linear behaviour of voltage with current is observed in Fig. 9. In Fig. 10 the roundtrip efficiency of an r-SOC system with a current SOC reactor concept is plotted against that of an r-SOC system with an ideal reactor. The stack ASR has a significant impact on the achievable roundtrip efficiency of a real system. At SOC reactor temperature of 850
C in FC mode and a DT of 25 K, the round-trip efficiency of 55% is achievable with current state of the art SOC reactor at 1 bar pressure and 80% conversion ratio in FC mode and 88% conversion ratio in EC mode. At similar conditions, the theoretical limit for an ideal system is at 98%. The theoretical

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Fig. 9. U(i) characteristic curve measured compared with the model calculations. (Top) Experimental values presented for r-SOC furnace temperature 800
C, pressure 1 bar (red) and 4 bar (blue). Inlet conditions of 90 mol% H2O and 10 mol% H2. Steam conversion ratio of 60% at maximum current density. (Bottom) Variation of the characteristic reactor temperature with current density during the U(i) measurements.

limit indicates the maximum roundtrip efficiency that can be achieved for the system for the given set of thermodynamic conditions. This comparison shows the variance of the current state-ofthe-art SOC reactor (with electrolyte supported cell (ESC)) available in the market to achieve efficiency close to the theoretical limit. With better SOC reactors with lower ASR values, achievable efficiencies can move towards the theoretical limit. For a real system, the roundtrip efficiency varies strongly with the reactor temperature. This is due to the strong inverse dependence of ASR with temperature. As the reactor temperature reduces, the ohmic resistance and in turn the ASR increases leading to efficiency as low as 35% at 750
C. In Fig. 11, the heat ratio of the r-SOC system with a currently available SOC reactor is plotted against the heat ratio of an r-SOC system with an ideal reactor. Negative values indicate endothermic

Fig. 10. Comparison of roundtrip efficiency of an r-SOC system with an ideal reactor and a currently available reactor. Temperature of the SOC reactor in EC mode is Tsoec ¼ Tsofc  2DT. Conversion ratio (x/xmax) in FC mode is equal to 80% and in EC mode equal to 88%.

operation of SOEC mode, and heat is supplied to the r-SOC reactor from heat storage. Positive values indicate that the SOC reactor entered exothermic region during SOEC operation mode. The internal losses in the SOC reactor produce more heat than required for the endothermic reaction. At the same conditions of 850
C reactor temperature in FC mode, 1 bar pressure and DT of 25 K, the heat ratio for a real system is just around 5% whereas for an ideal system the heat ratio in similar condition is as high as 99%. At these conditions, the SOC reactor is still endothermic in EC mode. But the majority of the heat required for the endothermic electrochemical reduction is now supplied by the heat generated internally due to electrochemical losses. At lower reactor temperatures, the SOC reactor becomes very exothermic in both FC and EC mode. In the EC mode, the heat generated due to the electrochemical losses is higher than the heat required for endothermic electrochemical reduction. This heat is generated due to the electrical energy overcoming the losses. As the SOC reactor turns exothermic in EC mode, the heat generated is unutilized and wasted. This in turn accounts for the loss and hence leading to lower roundtrip efficiencies. In general, as the EC operation goes more exothermic, the roundtrip efficiency reduces. The effect of temperature difference between the SOC reactor and heat storage and in turn between the two operations modes was studied. The effect of the same on roundtrip efficiency is shown in Fig. 12. As in the case of an ideal system, DT has a smaller effect on the roundtrip efficiency of the system. By varying the DT from 5 K to 25 K, the round trip efficiency decreased from 58% to 56% at 850
C reactor temperature in FC mode and 1 bar pressure. On average, the decrease in roundtrip efficiency by increasing DT is about 2%. The effect of pressure on the roundtrip efficiency of the real system remained similar to that of an ideal system. Since the ASR varies negligibly with pressure for an ESC stack, the effect on real system performance is insignificant. At given conditions of reactor temperature and extent of reaction, an increase in pressure leads to an increase in roundtrip efficiency for all values of DT. The effect of temperature difference between SOEC and SOFC operation mode for an r-SOC system with a current reactor concept is shown in Fig. 13. At 850
C in FC mode and 1 bar pressure, the heat ratio varied from 15% to 5% when DT is increased from 10 K to 25 K. At DT of 10 K, the SOC operates at 830
C in EC mode and heat required for the endothermic electrochemical reduction reaction is

Fig. 11. Comparison of the heat ratio of an r-SOC system with a current reactor to that of an ideal reactor system. Temperature SOC reactor in EC mode is Tsoec ¼ Tsofc  2DT. Conversion ratio (x/xmax) in FC mode is equal to 80% and in EC mode equal to 88%.

S. Santhanam et al. / Energy 141 (2017) 202e214

211

increases. Hence, the roundtrip efficiency decreases. 4.3. Summary

Fig. 12. Impact of temperature difference on roundtrip efficiency of an r-SOC system with a currently available reactor. Temperature of SOC reactor in EC mode is Tsoec ¼ Tsofc  2DT. Conversion ratio (x/xmax) in FC mode is equal to 80% and in EC mode equal to 88%.

greater than with DT 25 K, where the SOC operates at 800
C. This is due the fact that at 830
C, the ASR is lower than at 800
C and hence heat produced due to the losses is lower. Secondly, the thermodynamic heat required for the SOEC process at 840
C is higher than at 800
C for a given reaction conversion. Therefore due to the combined effect, the net heat required is higher when the DT is lower. The behaviour of an r-SOC system operated at different current densities is shown in Fig. 14. System performance is inversely impacted by current density. As the current density is reduced from 2500 Am2 to 1500 Am2 the efficiency increases for all conditions of pressure, temperature and reaction conversion. The electrochemical loss is a product of current density and area specific resistance. For a given temperature and pressure the ASR is constant, as the current density is increased, the electrochemical losses increases. Due to this, the work obtained from an SOC reactor in FC mode reduces and the work supplied to the SOC reactor in EC mode

Fig. 13. Impact of temperature difference between the two operation modes on heat ratio. Temperature of SOC reactor in EC mode is Tsoec ¼ Tsofc  2DT. Conversion ratio (x/ xmax) in FC mode is equal to 80% and in EC mode equal to 88%.

A simple process model was employed to quantify achievable roundtrip efficiencies for r-SOC systems at the ideal thermodynamic limit and for commercially available r-SOC reactors. Using the simple model, theoretical limits of achievable roundtrip efficiencies were quantified. The theoretical limits depend only on the thermodynamic operation conditions or thermodynamic states such as pressure, temperature and extent of electrochemical reaction. The thermodynamic efficiency limit is a function of reactor temperature and pressure. Under the operating conditions considered in this work, for a reactor temperature of 850
C in SOFC mode and 800
C in SOEC, 1 bar operating pressure and 80% fuel utilization in SOFC mode (corresponds to 88% utilization in SOEC mode for equal charge transfer and extent of reaction) the thermodynamic limit for roundtrip efficiency is 98%. The thermodynamic limit for roundtrip efficiency must be treated akin to the Carnot efficiency limit for thermal energy conversion systems. In this case, the thermodynamic limit represents the maximum achievable roundtrip efficiency for SOC electrochemical reactor systems. With the commercial r-SOC technology available in the market, a roundtrip efficiency as high as 60% is achievable at reactor operating temperatures of 800e850
C and an operation pressure of 30 bar. Under nominal operating conditions, 1 bar pressure and a reactor temperature of 850
C, a roundtrip efficiency of 55% is achievable. The difference between the efficiency achievable with current commercial reactor technology and the thermodynamic limit is purely due the reactor performance. With better reactor technology, real roundtrip efficiencies will move towards the thermodynamic limits. This would require improvements in materials of the functional layers and reactor design. There are of course obvious limitations in achieving real round-trip efficiencies very close to the thermodynamic limit which are dependent on the material properties. Further, the advantage of operating electrolysis in endothermic mode is highlighted. Achievable roundtrip efficiencies are higher as operation moves into stronger endothermic behaviour of SOEC operation mode. Integration of high temperature heat storage systems is found to be a viable alternative for thermal management and supplying the heat required for endothermic SOEC operation

Fig. 14. Impact of current density on the performance of an r-SOC system. Temperature of SOC reactor in EC mode is Tsoec ¼ Tsofc  2DT. Conversion ratio (x/xmax) in FC mode is equal to 80% and in EC mode equal to 88%.

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compared to the coupling of an exothermic chemical reaction (such as methanation) within the SOC reactor as proposed by Bierschenk et al. For the operating regions considered, heat required for endothermic SOEC operation is only 10% of the heat produced during the SOFC mode. Hence the heat storage system can be dimensioned according to requirements. If heat storage is only used for SOEC operation a smaller system can be employed. If heat storage is planned to be integrated with other coupled processes, a bigger heat storage system can be designed. An examination using a detailed process system model is advised and is being worked on by the authors to provide a better understanding of thermal management requirements considering the balance of plant components and heat transfer losses in the heat exchangers. 5. Conclusions and outlook A theoretical study of r-SOC energy systems was performed based on the experimental analysis of an r-SOC reactor under pressurized conditions. The r-SOC reactor was experimentally characterized under pressurized conditions in both SOFC and SOEC operation modes. A simple analytical process system was modelled based on the experimentally characterized r-SOC reactor. Using the simple model the thermodynamic limits for ideal round-trip efficiency were quantified as function thermodynamic states for electrochemical reactor systems (temperature, pressure and difference in temperature between SOFC and SOEC operation) based on a hypothetical ideal reactor with no electrochemical losses (ohmic, activation and diffusion). The thermodynamic limit for roundtrip efficiency represents the maximum that can be reached for a given set of thermodynamic states. The difference between the achievable round-trip efficiency of a real SOC reactor and the thermodynamic limit indicates the state of the SOC reactor. The closer the real round-trip efficiencies to the thermodynamic limit, the better the state of the r-SOC reactor. To conclude:  A roundtrip efficiency of 55% is achievable for a r-SOC system based on a commercially available r-SOC reactor based on electrolyte supported cells operating at 850
C in SOFC mode and 800
C in SOEC mode, reactant utilization of 80% and 88% in SOFC and SOEC mode respectively, current density of 2500 A/m2 and pressure of 1 bar. Increasing pressure to 30 bar, increases the round-trip efficiency to 60%.  For the above conditions, the maximum theoretical limit for roundtrip efficiency was determined to be 98% at 1 bar and 99% at 30 bar.  Contrary to the common assumption that the theoretical maximum roundtrip efficiency is equal to 100%, it has been shown that the theoretical roundtrip efficiency limit is slightly lower than 100%. This is due to the difference in operation temperatures of the r-SOC reactor in SOFC and SOEC mode. The theoretical thermodynamic limit or ideal roundtrip efficiency will move closer to 100% as temperature difference between two operation modes tends to zero.  It has been theoretically and experimentally shown that the accurate estimation of ideal work of an r-SOC reactor is the difference between Gibbs function at the outlet and inlet of the reactor. The ideal voltage is a derivative of the ideal work with respect to the extent of electrochemical reaction. Use of inlet compositions or outlet composition in the Nernst equation as often done in literature is not accurate for calculating the ideal or reversible potential.  Improvement in r-SOC reactor technology with thinner electrolytes and better performing materials will result in lower electrochemical losses. This can lead to roundtrip efficiencies closer to theoretical limits predicted by reaction

thermodynamics. But thinner electrolytes and materials will need to have same stability against long term degradation, redox operation etc.  Endothermic operation of SOEC mode is shown to be generally beneficial and leads to higher roundtrip efficiency values.  A thermal energy storage system is an attractive option for thermal management between the SOFC and SOEC mode. For operating conditions considered, the heat requirement of the SOEC process accounts for less than 10% of heat produced in SOFC mode. This value will be higher for r-SOCs with lower ASRs since heat produced due to losses will be lower in both SOFC and SOEC mode. Thereby, the SOFC mode becomes less exothermic. More heat is required from heat storage for the SOEC process, since less heat is produced internally due to a lower ASR which is not sufficient anymore to compensate the thermal requirements of the endothermic SOEC process. The work presented in this paper will be used as a basis to select system operation parameters for an r-SOC prototype system. Detailed process modelling and engineering for the selected system operating parameters will follow taking into account the balance of plant effects and thermal management in detail. Different scenarios and system architectures will be investigated and component requirements will be identified using commercial chemical process engineering software. Appendix The entropy function of the fuel and air flows at the inlet and outlet of the reactor is calculated using the following equations

_ S ¼ ns

(A 1)

In the above equation, s_ is the specific entropy in J/(mol K). The specific entropy of the gas mixture, assuming ideal gas, is given by equation (A2).

s¼

X

x j sj

j2H2 ; N2 ; CH4 ; O2 ; H2 O; CO2 ; CO

(A 2)

j

The specific entropy of a gas species is calculated using equation
(A3). The term sj is the entropy of gas species at standard pressure (1 bar) and temperature (25
C). The term cp is the specific heat capacity at constant pressure.


sj ¼ sj þ cp ln

pj T  R ln T
p


(A 3)

The Gibbs function of the fuel and air streams at the inlet and outlet of the r-SOC reactor is calculated using equations A4eA7.

_ G ¼ ng

(A 4)

In equation (A4), g is the specific Gibbs function of the fuel and air streams in J/mol. The specific Gibbs function is calculated using equation (A5).

g¼

X

xj gj

j2H2 ; N2 ; CH4 ; O2 ; H2 O; CO2 ; CO

(A 5)

j

The specific Gibbs function for the gas species is calculated using equation (A6).

gj ¼ hj  Tsj

(A 6)

The term sj is equation (A6) is calculated using equation (A3) and term hj in equation (A6) represents the enthalpy of the gas species. The enthalpy of gas species is calculated by equation (A7).

S. Santhanam et al. / Energy 141 (2017) 202e214

hj ¼

f hj

y

ZT þ cp

dT

(A 7)

T


The term hfj is the enthalpy of formation of the gas species at

standard conditions of 1 bar and temperature of 25
C. Nomenclature and abbreviations

Abbreviations SOFC Solid Oxide Fuel Cell SOEC Solid Oxide Electrolysis cell r-SOC Reversible Solid Oxide Cell PtX Power to Chemicals XtP Chemicals to Power FC Fuel Cell EC Electrolysis Cell ESC Electrolyte Supported Cell OCV Open Circuit Voltage YSZ Yttria stabilized zirconia LSCF Lanthanum-Strontium-Cobalt Ferrate GDC Gadolinia-doped ceria PCM Phase Change Material Chemical H2 CO CO2 H2O C H O O2

compounds Hydrogen Carbon monoxide Carbon dioxide Water Carbon atom Hydrogen atom Oxygen atom Oxygen

Stoichiometric coefficient of gas components in a reaction, positive for products, negative for reactants, Ratio of heat produced or consumed in electrolysis mode to ratio of heat produced in fuel cell mode, -

Subscripts rxn Reaction e variation of thermodynamic quantity due to reaction fc Fuel Cell mode ec Electrolysis mode tn Thermoneutral mode ideal Ideal conditions of reactor with no electrochemical losses rt Round trip e consists of one charge-discharge cycle max Maximum value rwgs Reversible water gas shift reaction rsmr Reversible steam methane reforming reaction soc Solid Oxide Cell m Melting point temperature of phase change material Superscripts o Represents standard pressure conditions, pressure ¼ 101.3 kPa 0 Represents a quantity at inlet 00 Represents a quantity at outlet fc Fuel cell mode ec Electrolysis mode hs Heat storage References

Latin letters T Temperature, K p Pressure, Pa I Current, is negative for SOEC operation and positive for SOFC operation, A F Faraday's constant ¼ 96485.332, C/mol n_ Molar flow rate, mol/s U Voltage, V G Gibbs Function, J S Entropy, J/K t Time, s ASR Area specific Resistance, U m2 i Current density; positive for SOFC operation and negative for SOEC operation, A/m2 K Equilibrium constant, R Gas constant, J/mol K h molar Enthalpy, J/mol z Moles of electron produced per mole of fuel, x Mole fraction of the gas component, Q Thermal power, W Greek letters x Reaction conversion rate or extent of reaction, mol/s c Utilization or conversion ratio ¼ x= ,-

h D

q

213

xmax

Efficiency, Operator indicating difference in quantities between two state points, -

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