Here, we present a methodology for the generalized quantification of the carbon (C)-formation risk in hydrocarbon mixtures based on the normalized chemical activity. An open-source computational thermodynamics tool is coupled to a solid oxide fuel cell (SOFC) stack model to apply and validate this approach with literature data based on methane-fueled SOFC systems with anode off-gas recirculation. Two- and three-dimensional C-formation risk maps valid for all C-H-O mixtures are proposed for a practical, accurate, and meaningful assessment of the trade-off between C-deposition risk and SOFC performance. Compared to conventional risk evaluation methods such as steam-to-carbon ratio (SCR), oxygen-to-carbon ratio (OCR), or C-H-O ternary-phase diagrams, this approach allows a system-agnostic evaluation of different designs operated at varying conditions at a constant C-formation risk margin. The generalized formulation allows integration into process optimization workflows to obtain high-performance system designs with extended stack operating windows.

With a growing energy demand in a carbon-constrained society, fuels cells powered by renewable fuels, and specifically solid waste, are seen as interesting contributors to the energy portfolio. The alternative energy industry needs to reduce costs, enhance efficiency, and demonstrate durability and reliability to be economically feasible and attractive. This paper addresses biomass waste gasification in distributed energy systems, using a solid oxide fuel cell (SOFC) to produce electricity and heat. The potential and optimal plant efficiency and layout (i.e., anode off-gas (AOG) recirculation point via small-scale turbomachinery and heat exchanger network) are analyzed through a multi-stage approach that includes scenario evaluation and multi-objective optimization via a hybrid optimization strategy with heuristics and mathematical programming. The results in this paper summarize the most convenient operating conditions and provide an optimized heat exchanger network (HEN). The AOG recirculation toward the gasifier combustor is the preferred option; the electrical and thermal efficiencies can separately go up to 49 and 47%, respectively. The combined total efficiency ranges between 76 and 82%, and the area of heat exchange, which corresponds to an amount of heat exchanged between 91 and 117 kW, is within 6–14 m ².

By means of this corrigendum, the authors would like to include relevant information regarding the validation of the meanline turbine model employed in the original article. The improvement regarding the validation of the model was made possible thanks to the contribution of Prof. Jürg Schiffmann. The additional results documented here provide more confidence on the reliability of the model when it applied to mini-ORC turbines. Therefore, we kindly ask the Editor to add his name to the authors list. The following paragraph extends the one that discusses the meanline validation located in Section 2. The turbine preliminary design is performed by means of a meanline code, which is based on the loss models listed in Ref. [1]. These models have been developed for conventional turbomachinery operating with fluids in the ideal gas state, featuring subsonic flows and large Reynolds numbers. The meanline code has been validated with the results of literature test cases presenting these characteristics [2]. It has been also compared against an experimentally validated turbine model for mORC machines operating in the subsonic regime [3]. Table 1 shows the information of the machine geometry for which results of the two codes were compared, while Fig. 1 presents the meridional channel of the turbine. Table 2 shows the corresponding operating conditions. The results of the total-to-static efficiency computation are presented in Fig. 2. It can be observed that the efficiency trend obtained with zTurbo is similar to that computed with the validated EPFL code. The comparison between the two models suggests a deviation lower than 2.5% for all the tested operating conditions. This deviation occurs because each model uses a different set of loss correlations. These correlations are described in Refs. [1,3].