Chapter 6: Isothermal Reactor Design: Molar Flow Rates

Chapter 6 Self Test

What four things are wrong with this membrane reactor solution?

The gas phase elementary reaction

2A → B + 2C

Diagram of a plug flow reactor with an inlet concentration of Ct0 = 0.4 mol/dm³ and a molar flow rate FA0 = 10 mol/s. The product B is formed and exits the reactor.

is carried out in a membrane reactor in which there is pressure drop with α = 0.019 kg-1. An equal molar feed of A and inerts, I, enter the reactor and only species B can exit the membrane. Plot the conversion of A down the membrane reactor containing 50 kg of catalyst. The specific reaction rate is kA = 2.5 dm6/mol/kg/s, and the mass transfer coefficient kC = 1.5 dm3/kg•s

Proposed Solution

List of differential and explicit equations for a chemical reaction system. Differential equations include d(Fa)/d(W) = ra, d(Fb)/d(W) = rb - Rb, and d(Fc)/d(W) = rc. Explicit equations define various terms such as Ft, ka, Cto, alpha, y, Ca, Cb, rb, ra, rc, kc, and Rb.

Identify 4 things that are incorrect

Solution 1

Solution 2

Solution 3

Solution 4

Go to Actual Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

First Incorrect Thing

rB = -kCA  should be  rA = -kCA2

Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Second Incorrect Thing

rA = -rB/2  should be  rB = -rA/2

Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Third Incorrect Thing

FT = FA + FB + FC  should be  FT = FA + FB + FC + FI

Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fourth Incorrect Thing

y = (1 - αW)1/2  should be \( \frac{dy}{dW} = - \frac{\alpha F_T}{2y F_{T0}} \)

Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Actual Solution

rB = -kCA  should be  rA = -kCA2

rA = -rB/2  should be  rB = -rA/2

FT = FA + FB + FC  should be  FT = FA + FB + FC + FI

y = (1 - αW)1/2  should be \( \frac{dy}{dW} = - \frac{\alpha F_T}{2y F_{T0}} \)

FT0 = FA0 + FI

FI = FA0

POLYMATH Report: Calculated values of DEQ variables. A table lists variables including alpha, Ca, Cb, Cto, Fa, Fb, Fc, Ft, ka, kc, ra, rb, and more, showing their initial, minimal, maximal, and final values. The table displays numerical data for each variable across these categories.

List of differential and explicit equations for a chemical reaction system. Differential equations include d(Fa)/d(W) = ra, d(Fb)/d(W) = rb - Rb, and d(Fc)/d(W) = rc. Explicit equations define various terms such as Ft, ka, Cto, alpha, y, Ca, Cb, rb, ra, rc, kc, and Rb. Graph showing molar flow rates F_A, F_B, and F_C versus catalyst weight W. The graph highlights a potential issue with the solution in a mixed reactor system, with F_A decreasing and F_B and F_C increasing as W increases.


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