Question

Asked Oct 28, 2019

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**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 –r_{A}= kC_{A}C_{B}for all three cases, with k = 0.2 L/gr mole-min. The reactor feeds are F_{A0}= 3 gr mole/min and F_{B0}= 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 dX_{A}/dV for each case. Using the output of X_{A}versus V (the cumulative volume as one travels along the reaction length) for all three cases, **create a single plot of X _{A}(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?

Step 1

The given information are:

Case a: A+B→C

Case b: A+B→2C

Case c: A+B→4C

-r_{A} = kC_{A}C_{B} for all the cases and

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

F_{A0}= 3 g-mol/min

F_{B0}= 5 g-mol/min

v_{0} = 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:

Step 2

From the given data, calculate the values of C_{A0} and C_{B0} as:

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...

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