Chapter 4 Self Test

Pressure Drop in a Packed Bed Reactor

The elementary isomerization

A --> B

is carried out at 20 atm in a fluidized CSTR containing 100 kg of catalyst where 50% conversion is achieved

It is proposed to replace the CSTR with a packed bed reactor

The entering pressure was 20 atm and the exit pressure was found to be 10 atm.

• What would be the conversion if No pressure drop?

  Hint 1. What information can you obtain from the CSTR?

  Solution Part A
  
  

• What will be the conversion in the new PBR with pressure drop?

  Hint 2.  How do you calculate the pressure drop parameter?

  Solution Part B
  
  

• Plot the conversion as a function of particle diameter assume everything else is unchanged.

  

  Why does the X-d_p curve look the way it does?

  Solution Part C
  
  

• Suppose you could choose another pipe diameter to hold the same amount of catalyst. Would you choose a larger or smaller pipe diameter, or would you use the current pipe diameter? Explain.

  Solution Part D

Hint for A

     CSTR                  

     Solving for F_A0/(kC_A0)

                                                                        kg

Solution for A

            PFR                                               

            For no pressure drop P=P₀ and y = 1

                                                           Integrating with W = 0: X=0

Hint for B

            d = 0

Solution for B

            M.B.                         

            R.L.                         

            Stoichiometry       

            Combine                         

            For ε = 0; y = (1-αW)^1/2

            Seperating Variables         

            Integrating

            we note

            Compared with ΔP = 0 where X = 0.632

Solution for C

A plot of conversion vs. particle diameter is as follows

c)   As the particle diameter decreases, the pressure drop increases, so the concentration decreases as does the reaction rate. Consequently when the reaction rate is small the conversion will be small. As the particle size increases the pressure drop decreases and conversion increases. As the particle size increases the pressure drop decreases and  the concentration increases. however, for large particles, it takes a long time for the reactants to diffuse in and out of the catalyst particle. (I.e. -r_A ∼ 1/d_p therefore k ∼ 1/d_p, see p.829, last equation on the page where R = d_p/2 .)

Solution for D

d)   You would like to have the biggest pipe diameter possible because the bigger the pipe diameter, the less the pressure drop, and thus the conversion.

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