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[Dumpmeadrenaline]

Consider a tubular reactor of circular cross sectional area through which fluid is flowing. There is a catalyst coating on the wall and there is no homogeneous reaction.

 

The reaction rate is given by: -rA=kCA mol/m^2*s

 

How would we develop the mole balance equation in the case of a high fluid velocity and small rate constant and in the second case where the fluid velocity is low and the reaction rate is extremely fast. 

 

I am not sure if my approach and choice of model are correct

 

In the first case, where the fluid velocity is high and the reaction rate is small, we consider modelling the packed bed reactor using pseudo-homogeneous 1D model. I think the choice is reasonable because there are no significant temperature and concentration gradients due to the slow conversion of reactant to products  The process is reaction limited.

 

To develop a mole balance assuming steady-state conditions, we can consider the following equation for an incremental volume ΔV:

Molar Flow rate in- Molar Flow rate out - Rate of disappearance of A by catalytic reaction=0 

-ΔFA-Sa*ρb*(-rA)*ΔV where Sa is the surface area per unit mass of catalyst and ρb is the bed density.

 

In the first case, how are we maintaining a steady-state process when the rate of mass transfer of reactant molecules diffusing through the boundary layer and adsorbing onto the catalyst surface is much faster than the rate of reactant molecules on the catalyst surface reacting?

 

In the second case, assuming steady-state conditions, I would consider a heterogeneous 1D model and treat each phase separately. This is because the high reaction rate would induce temperature and concentration gradients between fluid and solid.

The mole balance equation for the fluid phase over an incremental volume ΔV can be written as:

-ΔFA-km*am*(CAf-CAs) where km- is the mass transfer coefficient, am- is the effective area of mass transfer CAf is the bulk fluid concentration and CAs is the surface concentration 

 

The mole balance equation for the solid phase: 

km*am*(CAf-CAs)-Sa*ρb*(-rA)*ΔV=0