Effect of ε value on conversion in PFR reactor: Consider the following similar reaction stoichiometries (assume gas phase reaction):Case a:  A +  B  →  CCase b:  A +  B  →  2CCase c:  A +  B  →  4CUse the same reaction rate law of –rA= kCACBfor all three cases, with k = 0.2 L/gr mole-min.  The reactor feeds are FA0= 3 gr mole/min and FB0= 5 gr mole/min; volumetric flow rate is 5 L/min.  Also, there are no inerts present, and there is no C in the feed.  Using a single-tube plug flow reactor of dimensions length L = 6 m and ID = 0.1 m, prepare the integral form of the PFR reactor design equation(with rate law and constants substituted into the equation) for each case.  Then, use your calculator, numerical integration, or MATLAB to solve the differential equation dXA/dV for each case.  Using the output of XAversus V (the cumulative volume as one travels along the reaction length) for all three cases, create a single plot of XA(y-axis) versus V (X-axis), and label each of the three curves on the plot with its respective value of ε. Which value of ε (which case) gives the highest value of conversion?

Question
Asked Oct 28, 2019
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  1. Effect of ε value on conversion in PFR reactor: Consider the following similar reaction stoichiometries (assume gas phase reaction):

Case a:  A +  B  →  C

Case b:  A +  B  →  2C

Case c:  A +  B  →  4C

Use the same reaction rate law of –rA= kCACBfor all three cases, with k = 0.2 L/gr mole-min.  The reactor feeds are FA0= 3 gr mole/min and FB0= 5 gr mole/min; volumetric flow rate is 5 L/min.  Also, there are no inerts present, and there is no C in the feed.  Using a single-tube plug flow reactor of dimensions length L = 6 m and ID = 0.1 m, prepare the integral form of the PFR reactor design equation(with rate law and constants substituted into the equation) for each case.  Then, use your calculator, numerical integration, or MATLAB to solve the differential equation dXA/dV for each case.  Using the output of XAversus V (the cumulative volume as one travels along the reaction length) for all three cases, create a single plot of XA(y-axis) versus V (X-axis), and label each of the three curves on the plot with its respective value of ε. Which value of ε (which case) gives the highest value of conversion?

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Expert Answer

Step 1

The given information are:

 

Case a: A+B→C

Case b: A+B→2C

Case c: A+B→4C

 

-rA = kCACB for all the cases and

k = 0.2 L/(g.mol-min)

FA0= 3 g-mol/min

FB0= 5 g-mol/min

v0 = 5 L/min

 

For single-tube plug flow reactor,

L = 6m

ID = 0.1 m

 

No inerts or C is present in the feed.

 

Initial volume of the reactor is calculated as:

ID
0.1
=3.14x
2
x6
0.0471 m
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Image Transcriptionclose

ID 0.1 =3.14x 2 x6 0.0471 m

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Step 2

From the given data, calculate the values of CA0 and CB0 as:

3 g moles/min
5 L/min
F40
CA0
g moles/L
= 0.6
5 g-moles/min
5 L/min
F30
C50
-moles/L
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3 g moles/min 5 L/min F40 CA0 g moles/L = 0.6 5 g-moles/min 5 L/min F30 C50 -moles/L

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Step 3

In this rate law, CA and CB can be written in terms of XA, fractional conversion, initial concentration of reactants, CA0 and CB0, and &e...

(C40-C40X) (C0-C40-X)
0.2
Vo(1+EX) (1+6X)
(1-X,)(Cso/C40-X,
V(1+6X
0.2
40
Let, Cg0/C0M
(1-X) (M-X
V(1+EX
0.2
(1)
40
help_outline

Image Transcriptionclose

(C40-C40X) (C0-C40-X) 0.2 Vo(1+EX) (1+6X) (1-X,)(Cso/C40-X, V(1+6X 0.2 40 Let, Cg0/C0M (1-X) (M-X V(1+EX 0.2 (1) 40

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