Mathematical Modelling of an Innovative Solid Oxide Fuel Cell

A mathematical model of an innovative solid oxide fuel cell (IDEAL-Cell), made of the combining of the cathodic compartment of a conventional anionic-conducting SOFC with the anodic compartment of a protonic-conducting one (PCFC), is presented. The special feature of the cell is represented by the central membrane, i.e. the porous composite layer that joins cathodic and anodic compartments. The model describes transport phenomena and kinetics inside the central membrane in steady-state and transient conditions. A specific model to estimate morphological parameters, based on an extension of percolation theory and on 3D simulations of random packing of overlapping spheres, is also presented. The model is validated with first experimental results. Simulations show the effects of cell design, dimensions of powders, porosity, etc. on the global performances; a sensitivity analysis on unknown or uncertain parameters is presented too. At this state of the art, central membrane is in ohmic regime, improvements are required to reduce the thickness of layers and to increase effective conductivities. Specific experiments must be performed to obtain a stronger validation and to estimate unknown parameters. Model and submodels are valuable tools to interpret experimental data, to optimize the cell design and to predict future performances and developments

Physically-based Modelling to Unveil the Complex Interplay between Electrode Microstructure and Impedance Response

Solid oxide fuel cells (SOFCs) are promising systems which produce heat and power from the direct electrochemical conversion of a fuel, such as hydrogen, at high temperature. The cell performance and durability, which are typically assessed by using electrochemical impedance spectroscopy (EIS), are known to depend strongly on the microstructure of the porous electrodes. However, the complex interplay between electrode microstructure and EIS response is not well understood: very often spectra interpretation relies on phenomenological equivalent circuits and on empirical evaluations, thus making spectra deconvolution and the assessment of microstructure-performance correlation quite inaccurate. In this work, we describe how the use of physically-based models, based on the mechanistic description of electrochemical phenomena occurring within the electrode microstructure, provide an effective strategy to quantitatively assess the interplay between electrode microstructure and EIS response. Taking advantage of tomographic techniques, which allow for the three-dimensional reconstruction of the electrode microstructure, we show how the microstructure-performance correlation can be accurately described and predicted in a wide range of conditions [1,2]. Then, we show how modelling and EIS can be integrated to infer kinetic information [3] and to elucidate the degradation mechanisms which undermine the stability of SOFC electrodes [4], revealing that paradigms commonly accepted for charge-transfer phenomena in porous electrodes should be revisited [5]. Finally, we report how inhomogeneous microstructural properties may affect the EIS response of a porous electrode, providing ad-hoc modelling tools [6] to help researchers deconvolve real impedance spectra with more awareness

Multi-scale simulation of solid oxide fuel cell power units

A multi-scale physically-based model is presented in this study in order to quantitatively assess the effect of geometrical modifications and working conditions in an existing SOFC small power unit. The model, validated in different operating conditions, describes transport and reaction phenomena within the electrodes and the feeding channels through conservation equations, while the electrode microstructural properties are evaluated through the particle-based three-dimensional reconstruction of the microstructure. The model is able to capture the main chemical and physical phenomena occurring from the microscale to the macroscale, thus predicting the power output from the knowledge of the same input parameters available in reality, such as powder characteristics and operating conditions. The presented simulations rationalize how the power unit behaves upon a variation in flow configuration, operating temperature and cell geometry, thus providing a tool to predict how to optimize and control the operation of an SOFC system

Mathematical Modeling of Solid Oxide Fuel Cells

In this thesis, an integrated microstructural–electrochemical modeling framework for Solid Oxide Fuel Cells (SOFCs) is presented. At the microscale, the model numerically reconstructs the microstructure of the electrodes, which are random porous composite media wherein the electrochemical reactions occur. The effective properties of the electrodes are evaluated in the reconstructed microstructures and used, as input parameters, in physically–based electrochemical models, consisting of mass and charge balances written in continuum approach, which describe the transport and reaction phenomena at the mesoscale within the cell. Therefore, the strong coupling between microstructural characteristics and electrochemical processes can be conveniently taken into account by the integrated model. The presented modeling framework represents a tool to fulfill a from–powder–to–power approach: it is able to reproduce and predict the SOFC macroscopic response, such as the current–voltage relationship, knowing only the powder characteristics and the operating conditions, which are the same measurable and controllable parameters available in reality. As a consequence, empirical, fitted or adjustable parameters are not required, feature which makes the model fully predictive and widely applicable in a broad range of conditions and fuel cell configurations as an interpretative tool of experimental data and as a design tool to optimize the system performance

Effective transport properties in random packings of spheres and agglomerates

A modelling framework for the prediction of effective properties in random packings of particles is presented. Random packings of spheres and agglomerates of spheres are numerically generated by using packing algorithms. Effective properties of both the types of packings are evaluated through a Monte-Carlo random-walk (a.k.a. mean square displacement) method, which allows the calculation of both geometrical parameters (e.g., pore size distribution, specific surface area) and transport properties (e.g., effective gas diffusivity, permeability). The results are reported as a function of porosity in dimensionless form, in order to obtain scale-independent information. The effective properties obtained for random packings of spheres are compared with independent experimental data showing a satisfactory agreement. Effective properties of packings of agglomerates are also evaluated, showing that particle agglomeration significantly increases the mean pore size while reducing the effective gas diffusivity and the specific surface area. The results show that agglomerates can not be generally assimilated to spheres with an equivalent diameter. The modelling approach presented in this study may improve the quantitative characterization of porous media composed by aggregates of particles

Engineered electrode microstructure for optimization of solid oxide fuel cells

This paper presents a mathematical model for the description of transport and reaction phenomena in porous composite electrodes for solid oxide fuel cell (SOFC) applications. The model is based on charge and mass balances, describing transport of charged and gas species along with the electrochemical reaction occurring at the solid/gas phase interface. Effective properties of the porous media are evaluated on numerically reconstructed microstructures. The correlation between electrode microstructure and electrochemical performance is investigated. In particular, the study focuses on how a distribution of particle size within the thickness may improve the air-electrode efficiency. The results show that distributing smaller particles at the electrolyte interface reduces the sensitivity of the cathode efficiency to the electrode thickness, with clear advantages from the manufactory point of view. However, the conditions for which this advantage is relevant, that is, particle size smaller than 0.10 μm and porosity in the order of 15 %, are not technically achievable at the presen

Theory-based design of sintered granular composites triples three-phase boundary in fuel cells.

Solid-oxide fuel cells produce electric current from energy released by a spontaneous electrochemical reaction. The efficiency of these devices depends crucially on the microstructure of their electrodes and in particular on the three-phase boundary (TPB) length, along which the energy-producing reaction occurs. We present a systematic maximization of the TPB length as a function of four readily controllable microstructural parameters, for any given mean hydraulic radius, which is a conventional measure of the permeability to gas flow. We identify the maximizing parameters and show that the TPB length can be increased by a factor of over 300% compared to current common practices. We support this result by calculating the TPB of several numerically simulated structures. We also compare four models for a single intergranular contact in the sintered electrode and show that the model commonly used in the literature is oversimplified and unphysical. We then propose two alternatives

A comprehensive review and classification of unit operations with assessment of outputs quality in lithium-ion battery recycling

Lithium-ion batteries (LIBs) are the core component of the electrification transition, being used in portable electronics, electric vehicles, and stationary energy storage. The exponential growth of LIB use generates a large flow of spent batteries which must be recycled. This paper provides a comprehensive review of industrial realities of LIB recycling companies in Europe, North America, and Asia. An in-depth description of representative pyrometallurgy-based and hydrometallurgy-based processes is reported, providing classification of unit operations, their industrial readiness, and quality of output materials. The analysis shows that the pyrometallurgical route can treat different LIB chemistries without pre-sorting, but Li is not recovered unless the slag is refined. Hydrometallurgy-based processes are more chemistry-specific and in, although being affected by losses of electrode active materials during the mechanical pre-treatments for black mass separation. Efforts are required to promote in Europe the industrial capacity and readiness of hydrometallurgical processes by facilitating sorting and mechanical separations. There is also the need for harmonization of criteria for outputs definitions and rules for calculating recycling efficiency indicators. This represents an opportunity for modeling to support quantitative techno-economic and environmental assessments of the entire LIB recycling chain

Recycling of Lithium-Ion Batteries: Overview of Existing Processes, Analysis and Performance

Lithium-ion batteries (LIBs) have become a widespread technology for electrochemical energy storage in the current era of digitalization and transport electrification, being used as electric stationary storage as well as for powering electric vehicles, e-bikes and portable electronic devices such as smartphones and laptops. However, LIBs contain valuable materials, such as cobalt, nickel, lithium and graphite, whose supply has become critical to meet the increasing demand of batteries. Therefore, proper recycling processes are required in order to recover these materials from spent batteries and re-use them to produce new batteries in a sustainable cycle. This contribution provides an extensive survey of the main recycling routes available today, focusing specifically on pyrometallurgical and hydrometallurgical processes based in Europe, North America and Asia. Attention is also devoted to the recycling behaviour of individuals and companies and to the possible ways to increase their recycling rate. The comparison of different processes allows for the ranking of best practices as well as the drawbacks of different process units, with identification of which materials can be recovered, their recovery rate, and an assessment of the overall recycling efficiency of the process for different battery sizes (small and large, for portable electronics and electric vehicles, respectively). The analysis reveals that pyrometallurgical processes can flexibly treat different LIB chemistries but, since the electrolyte and graphite are burnt in the process, the global recycling efficiency cannot compete with hydrometallurgical processes, especially for small format batteries. Nevertheless, hydrometallurgical processes typically require preliminary mechanical separation treatments to separate the black mass, which contains valuable electrodic materials, as well as complex precipitation steps, which eventually reduce the material recovery rate and the applicability to diverse LIB chemistries. Finally, the study reports an analysis of the electrochemical performance of a battery made with recycled materials, showing that even if recycled cathodic materials had a lower gravimetric capacity and solid-state diffusivity, the performance of a recycled battery could be compensated by simple minor changes to the cell design which would ultimately decrease the specific energy density by a few percent compared to a LIB made with virgin materials

Experimental approach for the study of SOFC cathodes

The suitability of impedance measurements in Solid Oxide Fuel Cells (SOFCs) is an important concern, especially in case of measuring separately the behaviour of one of the electrode when an overvoltage is applied. In this case a thin electrolyte-supported cell with the RE (Reference Electrode) coplanar with the WE (Working Electrode) is experimentally convenient, but many authors highlighted that incorrect results can be obtained if an inappropriate geometric configuration is used. In this work LSM cathodes ((La0.8Sr0.2)MnO3-x) were investigated in a Yttria-stabilised Zirconia (YSZ) electrolyte-supported cell, using an electrolyte 3 mm thick. Two types of cells were prepared: the first (Cell1) according to the geometric requirements suggested in literature: little WE (diameter 3 mm) aligned to the CE (Counter Electrode) and with equal Rpol(polarisation resistance) and time constant; RE co-planar around the WE and placed at a distance greater than three-electrolyte thicknesses from the WE; the second one (Cell2) equal to Cell1 but with a bigger WE (diameter 8 mm). Impedance measurements were carried out both in two- and three- electrode configuration, at OCV (Open Circuit Voltage) and under applied overpotentials. A preliminary comparison between the results extracted from Cell2 at two- and three- electrodes confirms that a thick electrolyte allows extracting suitable three-electrode impedance results in case of OCV and small overpotentials. On the other side, when an overpotential over 0.2 V is applied, a comparison between Cell1 and Cell2 gives quite different results. The investigation here presented considers also an experimental approach useful for the comprehension of the main phenomena governing the kinetic of the process