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Energies 2020, 13, 5043 4 of 20 2.1.2. Flame-Assisted Fuel Cells This section provides a theoretical model of the FFC, in which performance depends on the fuel-rich equivalence ratio (Φ), defined in Equation (2), as the independent variable. A more detailed FFC model is given in [42]. Here, nCH4 and no2 are molar flow rates of methane and oxygen, respectively. The superscript ‘S’ denotes rates required for stoichiometric reaction. Thus, combustion is fuel-rich for Φ > 1, fuel-lean for Φ < 1, and stoichiometric for Φ = 1. nCH4 Φ= no2 (2) Figure 2 shows a schematic of a FFC with various reaction zones. The SOFC in the FFC configuration consists of a porous anode and cathode separated by a dense electrolyte layer. Partial oxidation of the fuel (i.e., methane in this study) and oxygen mixture sent to the fuel-rich pre-burner results in the generation of syngas (H2 + CO). The syngas then diffuses into the anode where it reacts with the oxygen ions diffusing from the cathode side through the electrolyte to form CO2 and water. After the fuel cell, remaining syngas combusts with oxygen, in the fuel-lean (excess oxygen reactant) after-burner and generates heat. The after-burner exhaust exits the fuel cell subsystem. The overall FFC subsystem generates heat during fuel-rich combustion, fuel cell electrochemical oxidation, and fuel-lean combustion. Figure 2. Schematic of a flame-assisted fuel cell (FFC). The first reaction is the fuel-rich combustion of methane in oxygen. Equation (3) shows this reaction. Chemical equilibrium from a Gibbs minimization constrained by conservation of the elements determines the stoichiometry of the products for fuel-rich combustion, i.e., a, b, c, and d, for CO, H2, CO2, and H2O, respectively. ΦCH4 + 2(O2) → aCO + b H2 + c CO2 + d H2O (3) The enthalpy released by the fuel-rich combustion reaction (∆HRC) can be calculated as shown in Equation (4), where m. is the mass flow rate for species i and h is the species specific enthalpy ii (i.e., per unit mass). ∆H =m. h +m. h +m. h +m. h −m. h (4) RC COCO CO2 CO2 H2OH2O H2 H2 CH4 CH4 ns CH4 ns o2PDF Image | Hybrid Fuel Cell Supercritical CO2 Brayton Cycle CO2 Storage
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