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3.6 T w ed Beds o-Phase Fix 141

a filtering catalyst make the close control of temperature and the maintaining of optimum
temperature conditions rather impossible.

3.6.2 Modeling of fixed beds

wing,
In the follo the one-dimensional model will be presented. The basic ideal models
assume that concentration and temperature gradients occur in the axial direction (Froment
and Bischoff, 1990). The model for a fed-bed reactor consists of three equations, which ix
will be presented in the following sections and are

• material balance equation
• energy balance equation
• pressure drop equation

Material balance equation
Consider a solution of concentration of C (mol/vol of fluid) entering at W in a control
W
volume of length z and efe cross-sectional area v fecti A , with a volumetric flow rate Q
(Figure 3.34). The reaction takes place with rate (– R ) in (mol dissappearing/time v ol of the
reactor) and the exit concentration is C E (mol/vol of fluid).
Under the assumption of complete mixing in the radial direction, the material balance is

 rate of change 
 in the direction  rate   rate of 
     
 of flow due to   of   accumulation  (3.272)
a

 flow and axial     
 dispersionn   consumption   of moles 


The terms in this material balance are in moles per unit time.
In the follo wing analysis, is the volume occupied by the fluid phase per unit v olume
of the control element. Then, the corresponding volume fraction for the solid phase is (1 – ).
The first term in eq. (3.272) is

 rate of c ha nge 
 in the dir e tion c  axial  
    flow   
 of flow due to  dispersion     (3.273)


flow a a nd  xia l   term    term 
 
 dispersion n 

W E

Q A

Figure 3.34 Control volume in a f ed bed. ix