Energy Procedia 28 ( 2012 ) 37 – 47

1876-6102 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Grove Steering Committee.

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Available online at www.sciencedirect.com

© 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Grove Steering Committee. Open access under CC BY-NC-ND license.

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38 Marius Dillig and Jürgen Karl / Energy Procedia 28 ( 2012 ) 37 – 47

to 75% can be assumed. Due to more favourable thermodynamic conditions of electrolysis at increased temperature levels ( G = 237 kJ/mol at ambient temperature compared to 183 kJ/mol at 900°C [2]), high temperature solid oxide cells present a possibility to considerably exceed the conversion efficiencies at low temperatures [3]. At high temperature part of the enthalpy of reaction can be supplied as heat either being entirely provided internally by non-reversible cell losses (mainly activation and ohmic losses) resulting in thermally neutral or exothermic operation. Even endothermic operation of the cell becomes possible in the case that an additional external heat source supplies the required heat.

A coupling of solid oxide electrolyser cells (SOECs) to volatile electricity sources implies strong load

gradients and thus strong changes in internal heat consumption/production rates, and consequently changing temperature profiles within the stacks. The resulting mechanical stress within the ceramic cell can induce micro-cracking and lead to a significant reduction in cell lifetime. Thus, the theoretically very fast electric load adaptation of SOECs is intensely restricted by inertial thermal adaptation of cell and stack and the need to prevent fracture of cell components [4]. Consequently, advanced temperature control strategies for combination of high temperature solid oxide systems and volatile electric power sources are mandatory. Commonly, the thermal management of solid oxide cells (fuel cells as well as electrolyser cells) is realized via adapting excessive air flow, i.e. air ratios, to cool/heat the cell in order to avoid high temperature differences (some 100K) between gas inlet and outlet. Typical values for air ratio of SOFC systems are 4–10, resulting in parasitic losses for blowers, large heat-exchanger surfaces and thermal energy losses [5]. In the same way, cooling/heating of exothermic/endothermic SOEC cells requires large air ratios to keep T reasonable, resulting in a dilution of the produced oxygen. Changes in load, i.e. current density, in certain operation modes can be followed by adapting air ratios [4], whereas changes in operation modes (exothermic–endothermic) cannot be equilibrated by simply adapting anode flow. Research on modelling thermal behaviour within solid electrolyser cells has been performed by several research groups, e.g. Udagawa et al., Laurencin et al. [6–9], showing a strong dependency of temperature distributions on operation conditions.

The aim of this study is to present the approach of integrating high temperature heat pipes to a solid

electrolyser cell stack. Heat pipes are tubes or other cavities filled with small amounts of heat transfer liquids (in this case sodium, Na); they provide very large heat transfer rates due to evaporation-transport-condensation processes of the liquid within the heat pipe. Because of these high heat transfer rates, only small differences between evaporation and condensation zones are formed (some K) [10], and the heat pipe can be assumed as almost isothermal. The concept of combining solid oxide cell systems and heat pipes has already been successfully tested within EU-research project Biocellus [11, 12]. Experimental results showed that internal cooling of stacks could be realized and temperature distributions were equilibrated. In this study a quasi-2D steady-state thermo-electrochemical modelling approach of an SOEC stack will be described, and first calculation results are presented. The potential of thermal management by integrated heat pipes is evaluated, and basic calculation results are shown.

Nomenclature

ci concentration of gas species i (mol/m³) Eelectrode activation energy for exchange current density calculation of anode or cathode (J/mol) e width of cell F Faraday’s constant (C/mol)

RG Gibbs free enthalpy of reaction (J/mol) RH enthalpy of reaction (J/mol)

enthalpy flow by gas flow (W)

Marius Dillig and Jürgen Karl / Energy Procedia 28 ( 2012 ) 37 – 47 39

hc i i0elektrankelecn ni pO2 R RohmRth,jr qs qtransc T UceUOC

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40 Marius Dillig and Jürgen Karl / Energy Procedia 28 ( 2012 ) 37 – 47

beiwitchaelethrocalflow

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Marius Dillig and Jürgen Karl / Energy Procedia 28 ( 2012 ) 37 – 47 41

(1)

The reversible potential of the cell can be calculated using the Nernst equation. With the use of thermochemical databases, in this case FactSage 6.2 [17], the equilibrium concentrations on each electrode can be calculated. The reversible potential can be converted to:

(2)

The total ohmic resistance of the solid structure of the cell is taken as a serial combination of the resistance of electrodes and electrolyte. Interconnects are assumed to be negligible:

+ (3)

The activation overpotential describes the voltage increase of an SOEC due to kinetic limitations of the electrode reactions. These losses can be described by applying the Butler-Volmer equation, which relates activation overpotentials to current densities with the help of the factors of exchange current density for cathode and anode, respectively. The Butler-Volmer equation can be converted by the use of a widely accepted simplifying approach [18]:

(4)

For the anode and cathode electrodes, the exchange current densities depend on temperatures and activation energies according to the Arrhenius law with a pre-exponential factor:

(5)

Further potential increases can occur during cell operation due to the restriction of mass transport by diffusion within the electrodes. The actual potentials to be used in the Nernst equation to determine the cell potential are those at the three-phase boundary (TPB) within the electrode. Since the Nernst potential is computed using the gas concentrations within the flow channel c , a correction has to be made by introducing the cathode concentration overpotential:

(6)

Concentration levels at the three-phase boundary can be obtained via the effective diffusion coefficients of the electrode [9]. The anode overpotential is neglected assuming the O2 pressure within the TPB is near the free flow concentration [8].

2.3. Mass transfer

In SOEC operation, at the anode oxygen ions are converted to molecular oxygen, thus the oxygen mass flow is increasing along the cell. Depending on additional air flow on the anode, oxygen

42 Marius Dillig and Jürgen Karl / Energy Procedia 28 ( 2012 ) 37 – 47

concentrations change. The gas composition at the cathode, with high H2O and low H2 concentrations at the cell inlet, changes depending on local current densities and thus conversion rates r(x). The finite volume model computes species concentrations for each volume dV:

(7)

2.4. Thermal balance

The steady-state thermal balance of the solid oxide cell considers internal heat sources/sinks due to electrochemical reactions, heat transfer between solid structures and gas streams, and thus gas enthalpy changes and heat conduction.

The energy balance of one volume dV for steady-state conditions is:

(8)

The heat sources are assumed within the solid cell structure, and they depend on local thermodynamic and electrochemical boundary conditions:

(9)

Assuming heat conduction in the cell structure in the flow direction is negligible in comparison to heat transport via gas streams, the first term of Eq. (8) can be approximated to 0. Due to small differences between the gas streams and solid structure (hcathode approx. 2000–3000 W/m²K [5]) the temperature of the solid structure and gas stream are assumed to be equal at position x.

In order to simulate the influence of heat pipe integration into the solid oxide cell stack, a transverse

heat flow perpendicular to cell planes has to be considered. For reasons of computability, transverse heat transfer depends on local temperatures in the cell structure, an isothermal heat pipe temperature and an equivalent heat transfer coefficient that describes the complex heat transfer regimes through the multi-cell layered stack towards the heat pipe:

(10)

The heat transfer coefficient through one cell layer can be obtained by considering parallel and serial heat flux pathways through the stack, represented by the thermal resistance circuit diagram (see Fig. 4):

(11)

Finally, the equivalent heat transfer coefficient through n cell layers between the considered cell and the heat pipe interconnect can be determined based on the following relation:

(12)

Marius Dillig and Jürgen Karl / Energy Procedia 28 ( 2012 ) 37 – 47 43

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Marius Dillig and Jürgen Karl / Energy Procedia 28 ( 2012 ) 37 – 47 47

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