helpQUESTION

We are interested to lay out the mass balances involved in the synthesis of methanol in a workshop which is

constructed following the schematic drawn in the Figure $1.$ The operating pressure is $120$ atm and the operating

temperature is $553K.$

The methanol is produced as the outcome of the reactions of carbon monoxide $(CO),$ carbon dioxide $(C{O}_2)$

and hydrogen $(H_2)$ as follow:

$CO(g)+H_2(g)C{H}_{3}OH(g)$

$($Reaction $1)$

$C{O}_2(g)+H_2(g)C{H}_{3}OH(g)+H_{2}O(g)$

$($Reaction $2)$

The gases at the outlet of the reactor are directed to a condenser by$-$which the liquid mixture of methanol$/$water

is collected and the gases in excess are recycled. It has been confirmed that the condensation of methanol and

water is total which means that the recycle gas stream does not contain methanol and water.

Under steady state condition, the molar compositions of gas stream at the fresh feed $(A)$ and purge line $(P)$ are

as given:

Elsewhere, the composition of carbon monoxide in the gas stream at the outlet of the reactor $(C)$ is $2\mathrm{.}113\%.$

$($a$)$ Balance the Reaction $1$ and Reaction $2.$

$(0\mathrm{.}5$ mark$)$

$($b$)$ Fill up the information on the constituents in each stream in Figure I. Fill in the known molar

compositions where applicable.

Fill up progressively the process flow diagram as you progress through the questions.

$(0\mathrm{.}5$ mark$)$

$($c$)$ Determine the total molar flow rate of purge stream $(P).$

$($d$)$ Deduce on the molar flow rate of each gas constituent in the purge stream $($P$).$

$(1$ mark$)$

$($e$)$ Calculate the molar flow rates of liquid products in the liquid stream at point $($N$).$

$($Hint: methanol and woter are produced from Reaction I and Reaction $2).$

$\frac{2}{4}$

Conclude on the molar compositions of the mixture.

$(4$ marks$)$

$(1)$ Evaluale the percentage of the production of methanol coming from the Reaction $1$ as well as from the

Reaction $2.$

$(1$ marks$)$

$($g$)$ Determine the total molar flow rates of gas in the gas stream $(C)$ and $($D$).$

Therefore. deduce on the molar composition of gases in the gas stream $($D$).$

$(3$ marks$)$

$($b$)$ Calculate the molar flow rate of gases in the stream $($C$).$ Conclude on their molar composition within the

stream.

$($i$)$ Evaluate the molar flow rate of gas coustituents at the inlet of the reactor $($stream $($B$))$ and deduce on their

molar compositions.