Calculating the space time for parallel reactions. m-Xylene is reacted over a ZSM-5 zeolit...
Calculating the space time for parallel reactions. m-Xylene is reacted over a ZSM-5 zeolite catalyst. The following parallel elementary reactions were found to occur in excess H2 [Ind. Eng. Chem. Res., 27, 942 (1988)] :
(a) Calculate the PFR volume to achieve 85% conversion of m-xylene in packed-bed reactor. Plot the overall selectivity and yields as a function of τ. The specific reaction rates are k1 = 0.22 s-1 and k2 = 0.71 s-1 at 673°C.
A mixture of 75% m-xylene and 25% inerts is fed to a tubular reactor at a volumetric flow rate of 200 dm3/s and a total concentration of 0.05 mol/clm3 As a first approximation, neglect any other reactions such as
the reverse reactions and isomerization to o-xylene.
(b) Suppose that E1 = 20,000 cal/mol and E2 = 10,000 cal/mol, what temperature would you recommend to maximize the formation of p-xylene in a 2000-clm3 CSTR
Step-by-Step Solution
(a) The following parallel elementary reactions occur in excess of 
.
As the reactions occur in excess of 
, the rate of the each reaction depends on the concentration of 
. Rewrite the equivalent reactions as follows:
And
The following information is available for the above reactions occurring in PBR.
A mixture of 
and 
was fed to the PBR. Calculate the PFR volume:
Write the rate laws as follows:
The rate laws in terms of molar flow rate 
per volume 
are written as follows:
The mole balance can be written as follows:
Solve the differential equations using Polymath as follows:
The plot of conversion, overall selectivity and overall yield as a function of space time is as follows:
.
(b) If the activation energies are; 
, 
and 
. Calculate the temperature to maximize the formation of
.
Write the rate laws as follows:
Integrate the rate equations:
The Arrhenius equation is as follows:
Here, 
is the frequency factor and 
is the gas constant.
The mole balance for CSTR is written as follows:
Solve the integrated forms of the rate laws as follows:
Hence, the temperature is 
and the concentration of 
is 
.
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