Finite-additive distributions, reaction

Some research groups working on the modeling of MCFC include the reforming reactions in their process models in different ways. He and Chen [1] and Yoshiba et al. [2] only consider the water-gas shift reaction in a spatially distributed anode channel. Due to its high rate, they assume the shift reaction to be in chemical equilibrium. Lukas and Lee [3] and Park et al. [4] also describe the water-gas shift reaction in equilibrium, but in addition they include the steam reforming reaction of methane as an irreversible reaction with a finite reaction rate. In particular, Park... 

The Arrhenius form of the reaction results from the Maxwell speed distribution and the rate at which molecular bonds in gas-phase species are broken [44], In full-scale fire modeling, the finite reaction rates must be considered if one attempts to model things such as CO and soot production and oxidation, or ignition and extinction. However, then the simple mixture fraction formulation must be supplemented by additional variables keeping track of the reaction progress. 

It should be mentioned that even in the absence of dipolar, polarizable, or ionic reaction partners, high electric fields may cause shifts in chemical distributions. Such a field effect requires, however, that the solvent phase has a finite temperature coefficient of the dielectric permittivity or a finite coefficient of electrostriction an additional condition is that the chemical reactions proceed with a finite reaction enthalpy (AH) or a finite partial volume change (A V). Electric field induced temperature and pressure effects of this type are usually very small they may, however, gain importance for isochoric reactions in the membrane phase. 

The relevance of interphase gradients distinguishes between two different classes of problems, and this is reflected on the type of boundary condition at the pellet s surface. It is known that specifying the value of the concentration (or temperature) at the surfece (Dirichlet boundary condition) may not be realistic, and thus finite external transfer effects have to be considered (in a Robin-type boundary condition) [72]. Apart from these, a large number of additional effects have also been considered. Some examples include the nonuniformity of the porous pellet structure (distribution of pore sizes [102], bidisperse particles [103], etc.), nonuniformity of catalytic activity [104], deactivation by poisoning [105], presence of multiple reactions [106], and incorporation of additional transport mechanisms such as Soret diffusion [107] or intraparticular convection [108]. 

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