Modeling and analysis of hydrogen permeation in mixed proton-electronic conductors

A rigorous model for hydrogen permeation through dense mixed conductors was derived using the formalism of non-equilibrium thermodynamics for various operating modes and process conditions. The concentrations of charge carriers were rigorously included in this model through defect equilibria with the chemical environment at each membrane surface and through balance equations and a virtual pressure formalism within the membrane. Hydrogen permeation rates through proton–electron–hole mixed conductors were simulated using this framework under open-circuit, short-circuited, and applied potential operating modes. The sensitivity of H2 permeation rates to the reduction–oxidation potentials at each side of the membrane and to the membrane properties (e.g. electron/hole di4usivity, oxygen binding energy) was examined in terms of the mobility and concentration of each charge carrier in order to identify rate-limiting steps for H2 transport. These simulations showed that electronic transport controls H2 permeation rates in proton–electron–hole mixed conductors typically used for H2 permeation, especially when hydrogen chemical potentials are signi5cantly di4erent in the two sides of the membrane. These electronic conduction limitations arise from a region of very low electronic conductivity within the membrane, caused by a shift in the predominant charge carriers from electron to holes with decreasing hydrogen chemical potential. Under these asymmetrical conditions, H2 permeation rates increase more markedly when an external electron-conducting path is introduced than at lower chemical potential gradients. Such interplay between rate-controlling variables leads to complex e4ects of H2 chemical potential gradients on permeation rates. The e4ects of intrinsic membrane properties on H2 permeation were examined by systematic changes in the defect equilibrium constants. A decrease in oxygen binding energy, manifested in a stronger tendency for reduction of the oxide membrane material, leads to higher electron concentrations and to higher rates for open-circuit operation, during which electron conduction limits H2 transport rates. ? 2003 Elsevier Science Ltd. All rights reserved.