Kinetic Model for Anode of a Direct Carbon Fuel Cell
Authors: Peng Feng , Li Yue , Parulekar Satish J. , Selman Jan Robert 
Published: February 2020

The Direct Carbon Fuel Cell (DCFC), which uses solid carbon as fuel and molten carbonate as electrolyte, has had resurgence of interest due to very high electrochemical conversion efficiency (nearly 100%), no requirement of fuel reforming, and potential for CO2 capture and sequestration. At the cathode, carbon dioxide is converted into carbonate ions. The main reaction at the anode is generation of carbon dioxide from carbon and carbonate, viz.,
(1) C + 2CO3
2- = 3CO2 + 4e-.
The net cell reaction is oxidation of carbon to carbon dioxide. Additional reactions that may occur at the anode are (i) a two-electron reaction resulting in co-generation of carbon dioxide and carbon monoxide, viz.,
(2) C + CO3
2- = CO2 + CO + 2e-,
and (ii) the Boudouard reaction leading to conversion of carbon and carbon dioxide to carbon monoxide, viz.,
(3) C + CO2 = 2CO2,
the so-called “carbon corrosion” reaction. The performance of DCFC can be appreciably limited by this reaction.
A one-dimensional macro-homogeneous kinetic model for a DCFC anode is developed in this study. We consider steady-state operation of a DCFC with uniform distribution of carbon and molten carbonate in the anode. The potential drop through the anode current collector, placed usually near the anode-electrolyte interface, is considered to be negligible. Given their small size, carbon particles are fully wetted in molten carbonate and the extent of the reverse Boudouard reaction is therefore negligible. For the characteristic pore diameters considered, there is substantial over-pressure in the thick slurry comprised of carbon particles and molten carbonate, permitting the reaction products to remain dissolved in the electrolyte. The reaction products are transported through the anode until they leave via gas channel at one end of the anode. In the thick slurry, the dominant mechanism for this transport is diffusion. The rates of reactions (1) and (2) are described by concentration- and temperature-dependent Butler-Volmer rate expressions. Each reaction is inhibited by its product(s).
The conservation equations for electronic and ionic potentials are related to each other due to electro-neutrality. This is also the case with the conservation equations for electronic and ionic currents. The conservation equations for carbon monoxide and carbon dioxide are based on Fick’s law of diffusion. Numerical effort in solution of the four conservation equations can be reduced considerably by recognizing that only two of these are independent, as there are only two independent reactions. One therefore needs to solve only two boundary-value problems to determine the profiles of electronic potential, ionic potential, electronic current, ionic current, and product concentrations. The boundary conditions for the four variables depend on the configuration of a DCFC and location of the current collector in the anode, its distance from the anode-electrolyte interface. The external current density I is specified. The base values of the system parameters were obtained using information available in the published literature.
Various microstructure and macrostructure parameters influence design and performance of a DCFC anode and these are considered in the model. Appropriate dimensionless parameters and variables are used to reduce the number of system parameters and variables via lumping. Five of the dimensionless parameters provide binary comparisons of resistances for reactions (1) and (2), ohmic resistance, and resistances for transport of the two reaction products. Various sets of the five dimensionless parameters are considered to examine the distribution of electronic and ionic potentials, electronic and ionic current densities, rates of reactions (1) and (2), and concentrations of carbon monoxide and carbon dioxide. Conditions under which reactions (1) and (2) occur throughout the anode, corresponding to a very effective anode, are identified. Conditions under which this is not the case are also investigated to see if there are specific benefits in constraining the two reactions to portion(s) of the anode. Besides generating spatial profiles of system variables for the anode, the kinetic model enables identification of polarization curves and power density versus current density plots. The optimum current density and the corresponding power density are influenced strongly by the relative importance of the five resistances. The effect of location of the anode current collector with respect to the anode-electrolyte interface is examined via few model simulations.