Elements of
Chemical Reaction Engineering
6th Edition



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Essentials of
Chemical Reaction Engineering
Second Edition

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Chapter 11: Nonisothermal Reactor Design: The Steady State Energy Balance and Adiabatic PFR Applications

Adiabatic Liquid Phase in A CSTR

   
Part A
Second Order Reaction Carried Out Adiabatically in a CSTR
 
       
   

(a) We will solve part (a) by using the non isothermal reactor design algorithm discussed in Chapter 8.  

1. CSTR Design Equation:

 

2. Rate Law:

 

3. Stoichiometry:

liquid,

 

4. Combine:

 

Given conversion (X), you must first determine the reaction temperature (T), and then you can calculate the reactor volume (V).  

5. Determine T:

From the adiabatic energy balance (as applied to CSTRs):

 

which reduces to:

 

Substituting for known values and solving for T:

 

6. Solve for the Rate Constant (k) at T = 380 K:

 

7. Calculate the CSTR Reactor Volume (V):

Recall that:

 

Substituting for known values and solving for V:

 
   
Part B
Second Order Reaction Carried Out Adiabatically in a CSTR
 
       
   

(b) For part (b) we will again use the non isothermal reactor design algorithm discussed in Chapter 8. The first four steps of the algorithm we used in part (a) apply to our solution to part (b). It is at step number 5, where the algorithm changes.  

1. CSTR Design Equation:

 

2. Rate Law:

 

3. Stoichiometry:

liquid,

 

4. Combine:

 

NOTE: We will find it more convenient to work with this equation in terms of space time, rather than volume:

 

Given reactor volume (V), you must solve the energy balance and the mole balance simultaneously for conversion (X), since it is a function of temperature (T).  

5. Solve the Energy Balance for X EB as a function of T:

From the adiabatic energy balance (as applied to CSTRs):

 

6. Solve the Mole Balance for X MB as a function of T:

We'll rearrange our combined equation from step 4 to give us:

 

Solving for X gives us:

 

Let's simplify a little more, by introducing the Damköhler Number, Da:

 

We then have:

 

7. Plot X EB and X MB :

You want to plot X EB and X MB on the same graph (as functions of T) to see where they intersect. This will tell you where your steady-state point is. To accomplish this, we will use Polymath (but you could use a spreadsheet).  

Plot of X EB and X MB versus T  

We see that our conversion would be about 0.87, at a temperature of 387 K.

 
   
Part C
Second Order Reaction Carried Out Adiabatically in a CSTR
 
       
   

(c) For part (c) we will simply modify the Polymath program we used in part (b), setting our initial temperature to 280 K. All other equations remain unchanged.  

1. CSTR Design Equation:

 

2. Rate Law:

 

3. Stoichiometry:

liquid,

 

4. Combine:

 

Given reactor volume (V), you must solve the energy balance and the mole balance simultaneously for conversion (X), since it is a function of temperature (T).  

5. Solve the Energy Balance for X EB as a function of T:

 

6. Solve the Mole Balance for X MB as a function of T:

 

7. Plot X EB and X MB :

You want to plot X EB and X MB on the same graph (as functions of T) to see where they intersect. This will tell you where your steady-state point is. To accomplish this, we will use Polymath (but you could use a spreadsheet).  

Plot of X EB and X MB versus T  

We see that our conversion would be about 0.75, at a temperature of 355 K.

 

Back to Problem Statement

Back to Chapter 10