Problem

# 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

Solution 1

(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:

Hence, the PFR volume to achieve 85% conversion is.

(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 .