Boundary conditions pseudo homogeneous model

The effective reaction rate tm eff (related to the mass of catalyst/solid) already considers all extra- and intraparticle mass and heat transfer effects (Sections 4.5-4.7). Thus the pseudo-homogeneous model does not distinguish between the conditions in the fluid and in the sohd phase, as more sophisticated heterogeneous models do, as discussed, for example, in Baerns ef al. (2006), Froment and Bischoff (1990), and Westerterp, van Swaaij, and Beenackers (1998). Thus, gradients of temperature and concentration within the particle and in the thermal and diffusive boundary layers are combined by the use of an overall effectiveness factor that enables the system of four equations (mass and heat balances for solid and fluid phase) to be replaced by just two equations, Eqs. (4.10.125) and (4.10.126). 

Heterogeneous reactions. Components of water or air pollution are usually in the fluid phase. Hence we may write equations such as equations 6.2, 6.6, 6.8, and 6.12 for the fluid. The fluid may have non-permeable boundaries (the reactor walls) and permeable boundaries (entrances and exits of the system as well as catalytic surfaces where mass fluxes must be equal to the superficial reaction rates). Usually, these reaction rates are modeled as pseudo-homogeneous and, moreover, concentration measurements are almost always made in the fluid phase. Heterogeneous reactions are the result of a process that occurs at phase interfaces. This means that for the differential equation written for the fluid phase, heterogeneous reactions (surface reactions, for example) are just boundary conditions. The problem is very simple to formulate at steady state and at the boundary of an active surface, the normal mass or molar fluxes must be made equal to the heterogeneous, superficial reaction rate. Then,... 

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