Question

Please answer all parts

2. A total of 10000 L/h of metaxylene, C&H(CHs)2, is being isomerized to a mixture of orthoxylene, metaxylene, and paraxylene in a reactor with a volume of 1000 L. The isomerization reaction can be represented as: where A is the metaxylene being fed to the reactor, and B are the different isomers formed. The reaction is being carried out at 400°C and 20 bar. Under these conditions, 35% of the metaxylene fed to the reactor is isomerized. Using the same reactor as described above, at a flow rate of 6215 LI, 50% of the metaxylene fed is isomerized at the same temperature and pressure as in the previous case. In both cases, temperature and pressure changes in the reactor are negligible, and you can assume the reaction follows a first-order, irreversible kinetics a) (15 points) Determine if the reactor being used behaves as a CSTR or as a PFR? Hint: write down the mole balances for both CSTR and PFR; you will need to group some variables together and determine which reactor model matches the given data. b) (10 points) It is now proposed that a second plant be built to process 20000 Lh of metaxylene at the same temperature and pressure as described earlier. Determine the volume of the reactor required to achieve a conversion in the new plant of 46% instead of 35%? Use the same reactor type as determined in part a)

Answer 1

a) Testing with the design equation of each reactor, we can determine which satisfies this equation: then,

For CSTR:

Design equation: V = μo * X / k * (1-X)

We divide the expression for the flow case at 10000 L / h between the flow at 6215 L / h:

V1 / V2 = [10000 * 0.35 / k * (1-0.35)] / [6215 * 0.5 / k * (1-0.5)]

V1 / V2 must be equal to 1, since in both cases, the Volume is equal, if V1 / V2 is not equal to 1, the reactor is not CSTR.

simplifying we have:

V1 / V2 = 0.867 is different from 1, the reactor is not CSTR.

For PFR:

Integrated design equation: V = μo * Ln (1/1-X) / k

we divide the expressions again and solve to see if V1 / V2 is equal to 1:

V1 / V2 = [10000 * ln (1 / 1-0.35)] / [6215 * ln (1 / 1-0.5) = 1

This time V1 / V2 if it was equal to 1, that means that the reactor is a PFR.

b) We relate the integrated design equation of part a with part b, to each condition:

Vb / Va = [20000 * ln (1/1 - 0.46)] / [10000 * ln (1/1 - 0.35)] = 2.857

Vb = Va * 2,857 = 1000 L * 2,857 = 2,857 L.