Fundamental Balance Equations of Fixed Bed Reactors

let us inspect the basic equations of a fixed reactor for a single reaction of reactant A and steady state, if the so-called pseudo-homogeneous two-dimensional model in its most complex form is used (for simplification, all data on chemical media and also the fluid velocity are considered to be constant throughout the reactor, that is, only the values of Tand c change)  

Change of concentration Dispersion of mass in axial and radial direction in axial direction 

Equations (4.10.125) and (4.10.126) are extensions of the equations for an ideal plug flow reactor, Eqs. (4.10.69) and (4.10.70), to a tubular fixed bed reactor with radial gradients of temperature and concentration and hence include the factors considering the dispersion of mass and heat. (Note that we now use the term fm.effPb instead of ras used for homogeneous reactions.) 

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). 

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