Chapter 4 Example

Batch Reactor Optimization

 

The following irreversible liquid phase reaction follows an elementary rate law
A+B → C
Determine the minimum number of batch reactors 1.0 cubic meter in size to produce 10,000 moles of C in a 300 day period. The processing time to fill, empty and clean the reactor between batches is 4.5 hours. The feed is equal molar in A and B and the initial concentration of A is 1.0 moles per cubic meter. In a trial run it was found that 50% conversion was achieved in 2 hours.

Solution
Part 1. Find X as a function of t and then find k.
Batch
A + B → C
Gas Phase
Equil Molar Feed
Mole Balance
(1)
Rate Law
(2)
Stoichiometry
Gas, but
(3)
(4)
The number of moles C formed in a batch is
(5)
Combine
(6)
(7)
(8)
          Integrating
(9)
          Evaluate k from information given
Evaluate
          At t = 2 hr then X = 0.5
          The conversion for a reaction time tR
 
Part 2. Find the minimum number of reactors
            The total time for carry out one batch t is the reaction time tR plus the processing time tP which is the sum of the times to empty, te, to clean, tclean, and to fill, tf
The total processing time, tP, between reactions is tP, = 4.5 hrs. How many 1 m3 reactors do you need to make 10,000 moles of C in 300 days? Consider a single reactor. The number of moles of C formed in one batch
Total number of C moles made in one reactor for a 24 hour work day over 300 days is
n = number of batches in 300 days
n = 300 days x no. of batch per day
n 
          Rearranging
For max production rate
Solving for tR
          The number of moles 1 reactor can make in 300 days is
          The number of reactors, m, to make 10,000 moles of C in 300 days is


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