Dispersion reactor models heterogeneous

LPCVD Reactor Models. First-Order Surface Reaction. The traditional horizontal-wafer-in-tube LPCVD reactor resembles a fixed-bed reactor, and recent models are very similar to heterogeneous-dispersion models for fixed-bed reactors (21,167,213). To illustrate CVD reactor modeling, this correspondence can be exploited by first considering a simple first-order surface reaction in the LPCVD reactor and then discussing complications such as complex reaction schemes, multicomponent diffusion effects, and entrance phenomena. 

If the catalyst is dispersed throughout the pellet, then internal diffusion of the species within the pores of the pellet, along with simultaneous reaction(s) must be accounted for if the prevailing Thiele modulus > 1. This aspect gives rise to the effectiveness factor" problem, to which a significant amount of effort, summarized by Aris ( ), has been devoted in the literature. It is important to realize that if the catalyst pellet effectiveness factor is different from unity, then the packed-bed reactor model must be a heterogeneous model it cannot be a pseudohomogeneous model. 

The developed dynamic reactor model for the simulation studies of the unsteady-state-operated trickle-flow reactor is based on an extended axial dispersion model to predict the overall reactor performance incorporating partial wetting. This heterogeneous model consists of unsteady-state mass and enthalpy balances of the reaction components within the gas, liquid and catalyst phase. The individual mass-transfer steps at a partially wetted catalyst particle are shown in Fig. 4.5. 

Under these circumstances, a general stationary heterogeneous dispersion (PD-)model for an irreversible catalytic second order reaction between a gaseous and a liquid reactant in dimensionless form consists of the balance equations shown in Fig. 18. In this model the whole fluiddynamics are lumped into a single parameter, i.e. the Bodenstein number, here based on the reactor length. 

Fig, 18 A general steady state isothermal heterogeneous dispersion (PD-)model for multiphase catalytic reactors... 

The collocation methods can be shown to give rise to symmetric, positive definite coefficient matrices that is characterized with a acceptable condition number for diffusion dominated problems or other higher order even derivative terms. For convection dominated problems the collocation method produces non-symmetric coefficient matrices that are not positive definite and characterized with a large condition number. This method is thus frequently employed in reactor engineering solving problems containing second order derivatives of smooth functions. A t3q)ical example is the pellet equations in heterogeneous dispersion models. 

The simplest heterogeneous model is that with plug flow in the fluid phase and only external mass and heat transfer resistances between the bulk fluid and the catalyst surface. More complex fluid phase behaviour can be accommodated by including axial and radial dispersion mechanisms into the mode). If tJie reactor is non-adiabatic, radial dispersion is usually more important. 

By neglecting intraparticle thermal gradients and both axial and radial dispersion phenomena, a fixed - bed catalytic reactor can be simulated by a heterogeneous one - dimensional plug-flow model. This provides a picture, at least from a qualitative point of view, reasonably close to the real one [cf. Carberry, 1975 Pereira et al., 1979]. Let us introduce new dimensionless temperatures ... 

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