## PFR/CSTR Example

Example Algorithm for Steps in Solving Closed-Ended Problems
1. Statement

The elementary, liquid-phase, irreversible reaction is to be carried out in a flow reactor. Two reactors are available, an 800 dm3 PFR that can only be operated at 300 K and a 200 dm3 CSTR that can be operated at 350 K. The two feed streams to the reactor mix to form a single fee d stream that is equal molar in A and B, with a total volumetric flowrate of 10 dm3/min. Which of the two reactors will give us the highest conversion?

 Additional Information: at 300 K, k = 0.07 dm3/mol-min E = 85000 J/mol-K CA0B = CB0B = 2 mol/dm 3 vA0 = vB0 = 0.5*v0 = 5 dm3/min
2. Real Problem

We have two choices, a PFR operated at 300 K and a CSTR operated at 350 K. Which one do we choose?

3. Sketch  4. Identify and Name

1. Relevant Theories and Equations
 Arrhenius Equation: The higher the temperature, the faster the reaction rate.

 Rate Law: Mole Balances:  2. Systems

Volume of CSTR
Volume of PFR

3. Dependent and Independent Variables

Independent: V, FA0, T
Dependent: X

4. Knowns and Unknowns

Knowns: k0, E, V, n0, CA0B, CB0B
Unknowns: X

5. Inputs and Outputs

In: FA0 = FB0, so QB = 1
Out: FA = FA0(1-X), FB = FA0(1-X), FC = FA0X

6. What color should we paint the reactor?

Not an issue.

5. Assumptions

Isothermal, no pressure drop. The CSTR is well mixed. There are no radial variations in the PFR.

6. Specifications

There is neither too much redundant information, nor is there too little information given. Therefore, the problem is neither over-specified, nor under-specified.

7. Similar or Related Example Problems

This problem has a solution procedure in common with Examples 4-2 and 4-4 in the text.

8. Algorithm

 CSTR PFR

1. Mole Balance  2. Rate Law 3. Stoichiometry - liquid, v = vo; equal molar \ QB = 1 CA = CA0(1-X)

CB = CA0(1-X)

4. Combine (eqn 1) (eqn 2)

5. Evaluate
v A0 = 5 dm3/min
Before mixing
CA0B = 2 mol/dm3
FA0 = CA0B* vA0
FA0 = (5 dm3/min)(2 mol/dm3) = 10 mol/min
After mixing
v0 = vA0 + vB0 = 5 dm3/min + 5 dm3/min = 10 dm3/min
CA0 = 1 mol/dm3 at 350 K, k = 8.447 dm3/mol-min

9. Manipulate

1. CSTR @ 350 K

the combined CSTR equation (eqn 1) can be arranged as      2. PFR @ 300 K   Choose the CSTR, because it gives the highest conversion.

10. Units Check

X is dimensionless

11. Is it reasonable?

This is a reasonable conversion.

This the end of the PFR/CSTR example. A sample registration exam problem is also available.