Chapter 8 Self Test

Multiple Reactions in a PFR with Variable Coolant Temperature

The irreversible liquid phase reactions

Reaction (1)                                      

Reaction (2)                                     

                                                       

are carried out in a PFR with heat exchange. The following temperature profiles were obtained for the reaction mixture and the coolant stream.

 

The concentrations of A, B, C, and D were measured at the point down the reactor where the liquid temperature, T, reached a maximum of 516K at 54 dm3. The concentrations at the maximum  temperature were found to be CA = 0.05, CB = 0.22, CC = 0.245, and CD = 0.055 all in mol/dm3. The product of the overall heat transfer coefficient and the heat exchanger area per unit volume, Ua, is 5 cal/s•m3•K. The mole feed rate of A is 2 mol/s and the entering molar flow rate of B is 4 mol/s. The volumetric feed rate is 10 dm3/s which the molar flow rate of inerts is 0.5 mol/s. What is the activation energy for Reaction (1)? E1  =             

 

Additional Information

           

           

           

            Coolant flow rate = 25 g/s, and Coolant heat capacity = 20 cal/g•K

 

Hint 1: What is the energy balance?

Hint 2: What is Qr?

Hint 3: What are Qg1 and Qg2?

Full Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hint 1.  What is the energy balance?

                                               

The energy balance is

                                                 

For the two reactions given here the heat of reaction for reaction (1) is in terms of A and for reaction (2) it is in terms of B

 

                                     

At the maximum the derivative of T wrt V is zero.

                            

then

                                          

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Hint 2.  What is Qr?

                                          

            Qr

                                        

                                                              

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Hint 3.  What are Qg1 and Qg2

Note a quick check shows DCp = 0 for both reactions

            Reaction 1

                                  

            Reaction 2

                                  

            Therefore both heats of reaction are independent of temperature!!

            Qg1 = r1A DHRx1A

                               

                                                          

            Qg2 = r2B DHRx2B

                                                              

From the temperature dependence given in the problem statement we note at 516 K that

           

                                                             

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Full Solution

                                                             

                                                          

                                            

                                          

                                                                  

                                                              

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