Answered: Calculating the space time for parallel…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Question

Calculating the space time for parallel reactions. m-Xylene is reacted over a ZSM-5 zeolite catalyst. The following elementary reactions are bellows:

m-Xylene ---> Benzene + Methane (arrow shows k1)

m-Xylene --> p-Xylene (arrow shows k2)

a) Calculate the PFR volume to achieve 85 % conversion of m-Xylene in a pack bed reactor. Plot the overall selectivity and yields as a function of τ. A mixture of 75 % m-Xylene and 25% inert is fed to tubular reactor at volumetric flow rate of 200 dm3 /s and a total concentration of 0.05 mol/dm3. As a first approximation, neglect any other reactions such as reverse reactions and isomerization to o-Xylene.

k1 = 0.22 (s^-1) at 673 C

k2 = 0.71 (s^-1) at 673 C

b) Suppose that E1 = 20000 cal/mole and E2 = 10000 cal/mole, what temperature would you recommend to maximize the formation of p-Xylene in a 2000-dm^3 CSTR?

Expert Solution

Step 1

Given reaction is-

$m - X y l e n e \overset{k_{1}}{\to} B e n z e n e + M e t h a n e m - X y l e n e \overset{k_{2}}{\to} p - X y l e n e$

Here the rate constants at 673⁰C are-

$k_{1} = 0.22 s^{- 1} k_{2} = 0.71 s^{- 1}$

Conversion, of m-xylene, X_A=85%=0.85

Mixture has, m-xylene, $ε$ _A= 75%=0.75 , inert=25%

Original volumetric flow rate, V₀=200 dm³/s

Total concentration= 0.05 mol/dm³

Now, if the reaction is elementary, then rate of recation is-

$\begin{array}{rcl} - \frac{d C_{m - x y l e n e}}{d t} & = & (k_{1} + k_{1}) C_{m - x y l e n e} \\ - \frac{d C_{A}}{d t} & = & (k_{1} + k_{2}) C_{A 0} \\ - \ln \frac{C_{A}}{C_{A 0}} & = & (k_{1} + k_{2}) t \\ C_{A} & = & C_{A 0} e^{- (k_{1} + k_{2}) t} \end{array}$