Chapter 15: Diffusion and Reaction in Porous Catalysts
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R12.2 Trickle Bed Reactors
Transport from bulk 
Figure R12.21 

2. Equilibrium at gasliquid interface:  

(R12.23)  
C _{Ai} = concentration of
A in liquid at the interface H = Henry's constant 

3. Transport from interface to bulk liquid:


(R12.24)  
where  
k _{1}
= liquidphase mass transfer coefficient, m/s C _{Ai} = concentration of A in liquid at the interface, kmol/m ^{3} C _{Ab} = bulk liquid concentration of A, kmol/m ^{3} 

4. Transport from bulk liquid to external catalyst surface:  
(R12.25)  
5. Diffusion and reaction in the pellet. If we assume a firstorder reaction in dissolved gas A and in liquid B, we have  
(R12.26)  
Combining Equations (R12.22) through (R12.26) and rearranging in a manner identical to that leading to the development of Equation (1289) for slurry reactors, we have  
The overall rate equation for A 
(R12.27)  
that is,  

(R12.28)  
whereis the overall transfer coefficient for the gas into the pellet (m ^{3} of gas/g cat.s). A mole balance on species A gives  

(R12.29)  
We next consider the transport and reaction of species B, which does not leave the liquid phase.  
6. Transport of B from bulk liquid to solid catalyst interface:  

(R12.210)  
where C _{B} and C _{Bs} are the concentrations of B in the bulk fluid and at the solid interface, respectively.  
7. Diffusion and reaction of B inside the catalyst pellet:  

(R12.211)  
Combining Equations (1233) and (1234) and rearranging, we have  
The overall rate 

(R12.212)  
A mole balance on species B gives  
Mole balance on B 

(R12.213)  
One notes that the surface concentrations of A and B, C_{As} and C _{B s} , appear in the denominator of the overall transport coefficientsand.  
Consequently, Equations (R12.27), (R12.29), (R12.212), and (R12.213) must be solved simultaneously. In some cases analytical solutions are available, but for complex rate laws, one resorts to numerical solutions. ^{1} However, we shall consider some limiting situations.  
R12.2B Limiting Situations 

Mass Transfer of the Gaseous Reactant Limiting. For this situation we assume that either the first three terms in the denominator of Equation (R12.27) are dominant or that the liquidphase concentration of species B does not vary significantly through the trickle bed. For these conditions  
is constant and we can integrate the mole balance. For negligible volume change= 0, then  
Catalyst weight 

(R12.214)  
Mass Transfer and Reaction of Liquid Species Limiting. Here we assume that the liquid phase is entirely saturated with gas throughout the column. As a result, C _{As} is a constant. Consequently, we can integrate the combined mole balance and rate law to give.  
Catalyst weight 

(R12.215)  
R12.2C Evaluating the Transport CoefficientsThe mass transfer coefficients, k _{g} , k _{l} , and k _{c} depend on a number of variables, such as type of packing, flow rates, wetting of particle, and geometry of the column, and as a result the correlations vary significantly from system to system. Consequently, we will not give all the correlations here but instead will give correlations for particular systems and refer the reader to four specific references where other correlations for trickle bed reactors may be found. ^{2} Typical correlations are given in Table R12.21. Note that the correlation for organic particles tends to under predict the transport coefficient. 

Criterion for assuming 
The representative correlations given in Table R12.21 assume complete
wetting of the catalyst particles. Corrections for incomplete wetting as flow regimes,
pressuredrop equations, and other mass transfer correlations can be found in the
reviews by Shah, Smith, and Satterfield.
^{3} The plugflow design equation may be applied successfully provided that the ratio of reactor length L to particle diameter d _{p} satisfies the criterion (Satterfield, 1975) 


(R12.216)  
where Pe = Péclet number = d _{p U l /D AXD AX = axial dispersion coefficientn = reaction order } 
^{a}Also see N. Midoux, B. I. Morsi, M. Purwasasmita, A. Laurent, and J. C. Charpentier, Chem. Eng. Sci., 39, 781 (1984), for a comprehensive list of correlations. ^{b} In some cases this gives a low estimate of k _{l} a _{i} ; see M. Herskowitz and J. M. Smith, AIChE J., 29, 1983); F. Turek and R. Lange, Chem. Eng. Sci., 36 569 (1981) 
The CSTR design equations apply to the trickle bed when ^{4}  

(R12.217)  
Techniques for determining the singlephase axial dispersion coefficient are given in Chapter 14.  
Example R12.21 Trickle Bed Reactor 

The material presented in this example is meant to serve as an introduction to trickle bed reactors. Other workedout trickle bed example problems can be found in an article by Ramachandran and Chaudhari ^{6}. In addition, the hyrodesulfurication of a hydrocarbon in a trickle bed reactor is given in detail by Tarhan^{7}. 