Question

Methanol (CH3OH) is produced via the partial oxidization of methane (CH4). The fresh feed contains methane and oxygen that have been mixed in stoichiometric proportions. This feed is mixed with recycle gases. The single-pass conversion of methane is 10.0%. The stream leaving the reactor is passed into a separation process where the entire methanol, and none of the other materials, is removed. All of the remaining materials are recycled to be mixed with the fresh feed. Determine the feed rate of the stream entering the reactor required to produce 1000.0 mol/h of methanol. The following reaction is taking place.

Answer 1

Let us take the basis as 100 mol/h of feed. We will the answer for 1000 mol/h of methanol by correlation at the end.

Reaction:

CH4 + (1/2)O2 ---> CH3OH

Feed composition is stoichiometric.

From reaction, mole fraction CH4 = 1 / (1+0.5) = 0.6667

mole fraction O2 = 0.5 / (1+0.5) = 0.3333

As there is no loss of CH4 and O2 from the process, therefore, overall conversion is 100%

In 100 mol/h of fresh feed,

CH4 = 0.6667 x 100 = 66.67 mol/h

O2 = 0.3333 x 100 = 33.33 mol/h

1 mol of CH4 gives 1 mole of CH3OH from the stoichiometry of the reaction.

.: CH4OH produced = 66.67 mol/h

100 mole fresh feed gives 66.67 mol/h of methanol in the final product.

Now, the per pass conversion = 10%

10 % per pass conversion of the feed to the reactor gives 66.67 mol/h of methanol in the final product.

Let M mol/h be the mixed feed to the reactor.

.: 10 % conversion of methane in M gives 66.67 mol/h of methanol

.: 0.1 x methane in M = 66.67 mol/h

.: methane in M = 666.7 mol/h

the mole fraction of methane in M = mole fraction of methane in F

( as the feed is in the stoichiometric quantity, the mole fraction remains same in F,M and R)

mole fraction of methane in M = 0.6667

methane in M = 0.6667 x M = 666.7

.: M = 1000 mol/h

Now,

1000 mol/h of M gives 66.67 mol/h of methanol

x mol/h of M gives 1000 mol/h of methanol.

By cross multiplication,

x = (1000 x 1000) / 66.67 = 15000 mol/h

Answer: feed rate of the stream entering the reactor to produce 1000 mol/h of methanol = 15000 mol/h