Continuum scale modelling and complementary experimentation of solid oxide cells

Solid oxide cells are an exciting technology for energy conversion. Fuel cells, based on solid oxide  technology, convert hydrogen or hydrogen-rich fuels into electrical energy, with potential applications in stationary power generation. Conversely, solid oxide electrolysers convert electricity into chemical energy, thereby offering the potential to store energy from transient resources, such as wind turbines and other renewable technologies. For solid oxide cells to displace conventional energy conversion devices in the marketplace, reliability must be improved, product lifecycles extended, and unit costs reduced. Mathematical models can provide qualitative and quantitative insight into physical phenomena and performance, over a range of length and time scales. The purpose of this paper is to provide the reader with a summary of the state-of-the art of solid oxide cell models. These range from: simple methods based on lumped parameters with little or no kinetics to detailed, time-dependent, three-dimensional solutions for electric field potentials, complex chemical kinetics and fully-comprehensive equations of motion based on effective transport properties. Many mathematical models have, in the past, been based on inaccurate property values obtained from the literature, as well as over-simplistic schemes to compute effective values. It is important to be aware of the underlying experimental methods available to parameterise mathematical models, as well as validate results. In this article, state-of-the-art techniques for measuring kinetic, electric and transport properties are also described. Methods such as electrochemical impedance spectroscopy allow for fundamental physicochemical parameters to be obtained. In addition, effective properties may be obtained using micro-scale computer simulations based on digital reconstruction obtained from X-ray tomography/focussed ion beam scanning electron microscopy, as well as percolation theory. The cornerstone of model validation, namely the polarisation or current-voltage diagram, provides necessary, but insufficient information to substantiate the reliability of detailed model calculations. The results of physical experiments which precisely mimic the details of model conditions are scarce, and it is fair to say there is a gap between the two activities. The purpose of this review is to introduce the reader to the current state-of-the art of solid oxide analysis techniques, in a tutorial fashion, not only numerical and but also experimental, and to emphasise the cross-linkages between techniques.