SOFC are devices characterised by many parallel phenomena occurring at different time and space scales. Multi-scale models come of aid to the increasing necessity for a correct and detailed representation of the micro-scale level, within a more complex channel or stack model, in order to capture the correct polarisation behaviour of the cells during normal steady state (i.e., design point, off-design), undesirable (i.e., local fuel starvation, coking) and transient (i.e., start-up, shut-down, load following) operation.

The present study aims at laying the theoretical basis for a multi-scale modelling approach applicable to state-of-the-art commercial SOFCs. The proposed multi-scale model is built with the main purpose to understand how micro-scale characteristics of the PEN structure and the thermo-chemical and electrochemical phenomena, which occur in the electrode and electrolyte assembly, may affect the overall performance of a complete cell and ultimately of the stack. The final goal is stack performance.

Modelling and Experimental Methodology

This study presents the integration of two dimensional finite volume models: a 1D micro-scale model and a 1D (or 2D) macro-scale (channel/cell) model. The former simulates the distributed mass and charge transport along the z direction through the thickness of the PEN structure; the mass transport is modelled with a reactive Dusty Gas Model whilst the charge transport with the combination of Ohm’s law and Butler-Volmer equations. The micro-scale model also solves the enthalpy balance through the PEN thickness. The micro structure characteristics of the electrodes and electrolyte structure are determined by means of the percolation theory.

The channel model sets the voltage of the equipotential plates and the thermodynamic and chemical inlet conditions of the cell. The macro-scale model simulates the gas diffusion from the electrodes surface to the gas bulk phase in each control volume; moreover, the mass and energy balance are solved. The heat exchange model includes axial and transversal (i.e., contact resistance) conduction, convection (laminar flow) and radiation. The energy balance considers also a heat loss proportional to the outer volume of the reactor. The channel model sets the geometry of the interconnect structure for current collection on each channel.

Polarisation experimental data measured on a SOLIDpower S.p.a short-stack test bench are presented, as reported in ¹. The short-stack has 6 cells in a co-flow arrangement. The cells are made up of a thin 8 mol% Y₂O₃ stabilised Zirconia (YSZ) electrolyte (8 ± 2 μm) supported on a conventional porous Ni/YSZ anode electrode (240 ± 20 μm). The cathode electrode (30 ± 2 μm) is constituted by a composite structure of metallic perovskite Sr-doped LaMnO₃ (LSM) and oxide-ion conductive electrolyte YSZ. The active area of each cell is 80 cm², equal to that of the cells employed in the 2.5 kW_el micro-CHP units of the manufacturer ².

Results and Discussion

The 2D+1D model is first calibrated using the polarisation curve obtained from the short-stack operating with pre-reformed natural gas, as reported in Figure 1. The results show high current density gradients along the channel, primarily due to the fuel flow-field layout and secondly due to the low thermal and composition contribution of the reforming reaction. Moreover, a high importance of thermal losses ( of inlet fuel LHV) is detected. The micro-scale model suggests the limited extent of the electrochemical active thickness on the fuel channel side ( of overall anode thickness), which remains approximately constant throughout the channel length; therefore, the anode structure behaves mainly as structural support as reported in Figure 2. The enthalpy balance within the PEN structure shows negligible temperature gradients (in z direction) along the whole channel length.

The optimisation of the stack should therefore focus on the micro-structure characteristics which should change along the channel (xdirection) in relation to the variation of temperature and composition in order to optimise the polarisation behaviour depending on the specific local conditions. A sensitivity analysis on the percolation parameters (thus the TPB length) is presented to support this conclusion.

Conclusions

Detailed multi-scale models are able to provide a comprehensive description of the phenomena occurring in a complete SOFC system. The model proposed here lays the basis for cell local optimisation and design-led techniques which are required for performance enhancement; the suggested design improvements affect both the micro-scale and the channel-scale levels, respectively in terms of PEN structural and electrochemical parameters and flow-field layout.

References

1. L. Mastropasqua, S. Campanari, J. Brouwer, SOFC Short Stack Performance Testing for Operation in Carbon Capture Applications (in submission to Journal of Power Sources)

2. L. Mastropasqua et al., in ASME 2016 14th International Conference on Fuel Cell Science, Engineering and Technology