Professional Reference Shelf

R12.2 Trickle Bed Reactors


and uses of a
trickle bed

  In a trickle bed reactor the gas and liquid flow (trickle) concurrently downward over a packed bed of catalyst particles. Industrial trickle beds are typically 3 to 6 m deep and up to 3 m in diameter and are filled with catalyst particles ranging fromtoin. in diameter. The pores of the catalyst are filled with liquid. In petroleum refining, pressures of 34 to 100 atm and temperatures of 350° to 425°C are not uncommon. A pilot-plant trickle bed reactor might be about 1 m deep and 4 cm in diameter. Trickle beds are used in such processes as the hydrodesulfurization of heavy oil stocks, the hydrotreating of lubricating oils, and reactions such as the production of butynediol from acetylene and aqueous formaldehyde over a copper acetylide catalyst. It is on this latter type of reaction,  

image 12eq18.gif

    that we focus in this section. In a few cases, such as the Fischer-Tropsch synthesis, the liquid is inert and acts as a heat transfer medium.  

CD12.1-A Fundamentals

    The basic reaction and transport steps in trickle bed reactors are similar to slurry reactors. The main differences are the correlations used to determine the mass transfer coefficients. In addition, if there is more than one component in the gas phase (e.g., liquid has a high vapor pressure or one of the entering gases is inert), there is one additional transport step in the gas phase. Figure R12.2-1 shows the various transport steps in trickle bed reactors. Following our analysis for slurry reactors we develop the equations for the rate of transport of each step.  
    1. Transport from the bulk gas phase to the gas-liquid interface. The rate of transport per mass of catalyst is  
image 12eq19.gif

Transport from bulk
gas to gas-liquid
interface to bulk liquid
to solid-liquid
Diffusion and
reaction in
catalyst pellet


Figure R12.2-1
(a) Trickle bed reactor; (b) reactant concentration profile.

    2. Equilibrium at gas-liquid interface:  

image 12eq20.gif

    C Ai = concentration of A in liquid at the interface
H = Henry's constant
    3. Transport from interface to bulk liquid:

  image 12eq21.gif (R12.2-4)
    k 1 = liquid-phase 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:  
  image 12eq22.gif (R12.2-5)
    5. Diffusion and reaction in the pellet. If we assume a first-order reaction in dissolved gas A and in liquid B, we have  
  image 12eq23.gif (R12.2-6)
    Combining Equations (R12.2-2) through (R12.2-6) and rearranging in a manner identical to that leading to the development of Equation (12-89) for slurry reactors, we have  

The overall rate equation for A

image 12eq24.gif (R12.2-7)
    that is,  

    whereis the overall transfer coefficient for the gas into the pellet (m 3 of gas/g cat.middots). A mole balance on species A gives  

image 12eq27.gif

    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:  

im age 12eq28.gif

    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:  

image 12eq29.gif

    Combining Equations (12-33) and (12-34) and rearranging, we have  

The overall rate
equation for B


image 12eq30.gif

    A mole balance on species B gives  

Mole balance on B


image 12eq31.gif

    One notes that the surface concentrations of A and B, CAs and C B s , appear in the denominator of the overall transport coefficientskvgandkvl.  
    Consequently, Equations (R12.2-7), (R12.2-9), (R12.2-12), and (R12.2-13) 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.  

R12.2-B 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 (R12.2-7) are dominant or that the liquid-phase concentration of species B does not vary significantly through the trickle bed. For these conditionskvg  
    is constant and we can integrate the mole balance. For negligible volume changexi= 0, then  

Catalyst weight
necessary to achieve a conversion X A of gas-phase reactant


image 12eq33.gif

    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 givekvgkvl.  

Catalyst weight
necessary to achieve
a conversion X B of gas-phase reactant



R12.2-C Evaluating the Transport Coefficients

The 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 R12.2-1. Note that the correlation for organic particles tends to under predict the transport coefficient.


Criterion for assuming
that plug flow
is valid

  The representative correlations given in Table R12.2-1 assume complete wetting of the catalyst particles. Corrections for incomplete wetting as flow regimes, pressure-drop equations, and other mass transfer correlations can be found in the reviews by Shah, Smith, and Satterfield. 3

The plug-flow design equation may be applied successfully provided that the ratio of reactor length L to particle diameter d p  satisfies the criterion (Satterfield, 1975)

image 12eq35.gif

    where Pe = Péclet number = d p U l /D AX
D AX = axial dispersion coefficient
n = reaction order

aAlso 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  

image 12eq37.gif

    Techniques for determining the single-phase axial dispersion coefficient are given in Chapter 14.  
    Example R12.2-1
Trickle Bed Reactor
    The material presented in this example is meant to serve as an introduction to trickle bed reactors. Other worked-out 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 Tarhan7.