Chapter 15: Diffusion and Reaction in Porous Catalysts

Professional Reference Shelf

Example CD12-3: Maximum Solids Holdup

    A pilot fluidized bed is to be used to test a chemical reaction. The bed diameter is 91.4 cm. You wish to process 28.3 x 10 3 cm 3 /s of gaseous material. The average particle diameter is 100 mum. The reactor height is 10 ft. Allowing for a disengaging height of 7 ft, this means that we have a maximum bed height of 91.4 cm. The distributor plate is a porous disk.

What is the maximum weight of solids (i.e., holdup) in the bed? Other data: 		 
       
   

Color of pellet: brown

image 12eq99.gif

 
       
    Solution:  
   

The amount of solids in the reactor is given by

image 12eq100.gif



(CD12-19)
       
    The two parameters that need to be found areimage 12eq11.gifandimage greekd.gif.  
       
    A. Calculation ofimage 12eq11.gif  
       
   

imag e 12eq101.gif

(CD12-29)
       
    1. Gravity term:  
       
   

image 12eq102.gif

 
       
    2. Cross-sectional area:  
       
   

image 12eq103.gif

 
       
    Superficial velocity:  
       
   

 
       
    Porosity at minimum fluidization [Equation (CD12-9)]:  
       
 

image 12eq105.gif

 
       
    B. Calculation of volume fraction of bubbles  
       
   

image 12eq106.gif

(CD12-46)
       
    Here we see that we must calculate u mf and u b .  
    Step 1. First the minimum fluidization velocity is obtained from Equation (CD12-25):  
       
 

image 12eq107.gif

(CD12-35)
       
    Step 2. To calculate u b we must know the size of the bubble d b , that is,
(CD12-36): 		 
       
   

image 12eq108.gif

(CD12-36)
       
    Step 3. The average size of the bubble, db , is determined by evaluating Equation (CD12-37) at h/2:  
       
   

image 12eq109.gif

(CD12-37)
       
    where d bm and d b0 are given in Equations (CD12-38) and (CD12-39), respectively  
       
    Maximum bubble diameter:  
       
 

(CD12-38)
       
    Minimum bubble diameter:  
     
   

image 12eq111.gif

(CD12-39)
       
    Solving for d b yields  
     
   

image 12eq112.gif

 
       
    At the top of the bed (h = 91.4 cm), d b = 8.86 cm. For purposes of the Kunii-Levenspiel model, we shall take the bubble diameter to be 5 cm  
       
    Step 4. We can now return to calculate the velocity of bubble rise and the fraction of bed occupied by bubbles from Equation (CD12-36). We have  
       
   

image 12eq113.gif

 
       
    From Figure CD12-6 we see that a 100-m particle corresponds to a value ofalphaof 0.5. Substituting this value into Equation (CD12-46), the fraction of the bed occupied by the bubble is  
       
   

image 12eq114.gif

 
       
    Thus 94% of the bed is in the emulsion phase plus the wakes.  
       
    C. Amount of solids holdup,  
       
image 12eq115.gif  
       
    or  
       
    W s = 678 lb of solid particles