Methanol is a promising liquid fuel for solid oxide fuel cells (SOFCs), but Ni-based anodes risk carbon deposition (coking). The first thermo-electrochemical model of a methanol-fuelled SOFC (Xu et al. 2021) coupled methanol decomposition, water-gas shift chemistry, electrochemical kinetics, and heat/mass transport, yet omitted carbon formation chemistry entirely — although the added steam was motivated by coking suppression — and used a 2D geometry without the interconnect rib. A 2024 follow-up resolved the 3D rib geometry and thermal-stress coupling but still omitted carbon chemistry, and multiphysics models that include carbon-deposition chemistry exist for methane-, biogas-, and syngas-fuelled SOFCs and related hydrocarbon-fuelled cells. The open problem is to couple carbon-forming reaction chemistry (Boudouard, methanation/methane cracking, and pyrolysis routes) to the thermo-electrochemical model of a methanol/steam-fuelled SOFC: to predict whether, where, and how fast carbon deposits across the operating envelope (steam-to-carbon ratio, inlet temperature, operating voltage including open-circuit conditions, flow rates), to map carbon-safe operating windows, and to quantify the feedback of deposits on transport, performance, and long-term durability, validated against experimental performance and coking observations.

Background

A solid oxide fuel cell (SOFC) is a high-temperature (typically 873–1173 K) electrochemical converter in which a gas-tight oxide-ion-conducting electrolyte — commonly yttria-stabilized zirconia (YSZ), i.e. zirconia doped with yttria to create oxygen-vacancy ionic conductivity — separates a porous nickel–YSZ (Ni/YSZ) composite anode from a porous cathode (e.g. strontium-doped lanthanum manganite, LSM). Electrochemical charge transfer occurs only where gas, electronic conductor, and ionic conductor meet, the so-called three-phase boundary (TPB). Because of the high operating temperature, SOFCs can internally reform hydrocarbon and alcohol fuels inside the anode: methanol decomposes to carbon monoxide and hydrogen (CH3OH → CO + 2H2), the water–gas shift reaction (CO + H2O ⇌ CO2 + H2) adjusts the syngas composition, and H2 and CO are electrochemically oxidized at the TPB with kinetics commonly described by the Butler–Volmer equation (the standard exponential relation between current density and activation overpotential). Methanol is an attractive SOFC fuel because it is a liquid at ambient conditions (far easier to store and transport than hydrogen), can be synthesized carbon-neutrally from renewable or biomass feedstocks, and suits portable, marine, and auxiliary power applications.

The central complication on Ni-based anodes is carbon deposition ("coking"): solid carbon formed via the Boudouard reaction (2CO ⇌ CO2 + C), methanation followed by methane cracking (CO + 3H2 ⇌ CH4 + H2O, then CH4 → C + 2H2), or direct fuel pyrolysis encapsulates nickel particles, blocks pores, and can delaminate the anode from the electrolyte. Carbon was observed on a Ni/YSZ anode after 12 hours of pure-methanol operation at open-circuit voltage (OCV, i.e. no current drawn), leading to severe electrode delamination, whereas high-current operation suppresses carbon thermodynamically because the electrochemical products steam and CO2 are generated in situ. Adding steam to the fuel — quantified by the steam-to-carbon ratio (S/C), the molar ratio of steam to carbon in the fuel — is the standard thermodynamic countermeasure, but it dilutes the fuel and lowers power density. Experiments have established the coking phenomenology for methanol, and thermodynamic equilibrium carbon-boundary maps for methanol-fuelled SOFCs exist (Cimenti and Hill 2009), but equilibrium maps cannot resolve where inside an operating cell carbon forms, because local temperature and composition vary strongly along the cell.

Xu, Xia, He, Guo, and Ni (2021) built the first thermo-electrochemical model of a methanol-fuelled SOFC: a two-dimensional, anode-supported tubular cell model coupling methanol decomposition, the water–gas shift reaction, Butler–Volmer electrochemical kinetics, Stefan–Maxwell multicomponent diffusion (a formulation of species diffusion driven by chemical-potential gradients in gas mixtures), and momentum and energy transport, validated against the direct-alcohol SOFC experiments of Jiang and Virkar (2001). It predicted a peak power density of about 10220 W/m² at 0.55 V and 1073 K with S/C = 1, an inlet–outlet temperature variation of nearly 180 K driven by the coupling of endothermic reforming with exothermic electrochemistry and overpotential losses, and quantified the trade-offs of S/C ratio (1–8), inlet temperature (898–1173 K), and fuel/air flow rates. Crucially, the model omitted carbon formation entirely — the authors state the cell is described "without considering the carbon formation", even though the motivation for adding steam is coking suppression — and the 2D geometry omitted the interconnect rib (the current-collecting spacer between adjacent channels, which shades part of the electrode and reshapes gas transport and reactions), which the authors explicitly flagged for future three-dimensional work.

Two later developments frame what remains open. First, Li, Liao, Cheng, Huo, and Xu (2024) resolved the geometric part with a three-dimensional methanol-SOFC model that "sufficiently considers the rib structure", coupling electrochemistry, mass transport, heat transfer, and thermal stress — but still without any carbon chemistry. Second, multiphysics models that include carbon-deposition chemistry and its feedback on porosity and performance are well established for other fuels: methane (Wang, Jiang, and Lin 2015), transient biomass-syngas operation (Zhu et al. 2022), dynamic syngas operation (Zeng et al. 2025), coke-tolerant electrode design (Huang et al. 2025), and carbon-induced degradation (Song, Dang, and Xi 2026). The methanol case is the gap: no published model couples carbon-forming chemistry to the thermo-electrochemical fields of a methanol-fuelled SOFC, so the carbon-safe operating envelope of such cells is still unknown from theory, and the steam-dilution penalty cannot currently be traded off against quantitatively predicted coking risk.

Problem Statement

Construct and validate a thermo-electrochemical model of a methanol-fuelled (with steam) solid oxide fuel cell that includes carbon-forming chemistry and its consequences, within the framework established by Xu et al. (2021) and its rib-including 3D extension (Li et al. 2024). The single scientific objective is to predict whether, where, how fast, and with what consequences carbon deposits in an operating methanol-fuelled SOFC. Concretely, the answer should: (1) add the gas-phase and surface reactions that form solid carbon in this system — at minimum the Boudouard reaction (2CO ⇌ CO2 + C), with methanation/methane cracking and methanol pyrolysis routes as indicated by the kinetic literature — with defensible kinetic parameters, to the coupled conservation equations for momentum, species, energy, and charge; (2) compute, over the operating envelope of the source study (steam-to-carbon ratio 1–8, inlet temperature 898–1173 K, operating voltage including open-circuit and low-current conditions, and fuel/air flow rates; in 2D or 3D geometry, rib optional but stated), the spatial and temporal distribution of carbon formation rate and cumulative deposit, and identify carbon-deposition thresholds or carbon-safe operating windows; (3) quantify the feedback of deposited carbon on porous transport (porosity, tortuosity, active three-phase-boundary length), current density, temperature distribution, and performance degradation over operating timescales; and (4) validate against available experimental data — at least one cell performance dataset (e.g. the direct-alcohol SOFC data used by the source) and at least one reported coking observation (e.g. carbon deposition and anode delamination under open-circuit methanol operation). Deliverables (1)–(4) jointly serve this one objective: a study delivering only equilibrium carbon maps without transport and electrochemical coupling, or only performance simulation with carbon chemistry excluded, does not answer the question.

References

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