Ethylene oxide $(C_2{H}_{4}O)$ is used primarily as a sterilizing agent for medical equipment and supplies, and as a chemical intermediate in the production of ethylene glycol and other chemicals. It is produced by the catalytic oxidation of ethylene $(C_2{H}_4)$ :

$2C_2{H}_4+O_{2}2C_2{H}_{4}O$

The feed to the reactor $($R$1)($not the fresh feed to the process$)$ contains $75$ mol $\%$ of ethylene and the balance oxygen $(O_2).$ The production is designed for $30\%$ of single pass conversion. Product stream exit at R$1$ enters a two$-$stage separator unit. The two$-$stage separator unit is functioned to separate the ethylene oxide $($stream exit the R$1)$ from other components. The product stream exit R$1$ enters the first$-$stage separator $($S$1).$ The S$1$ top product contains ethylene and oxygen only. while the $S1$ bottom product consists of ethylene and ethylene oxide only. The top product of $S$ is recycled to the reactor. The bottom product of $S1$ enters second$-$stage separator $($S$2).$ At separator $S2,95\%$ of ethylene fed to the $S2$ will exit the $S2$ as top product. Only ethylene present at $S2$ top product. Meanwhile, S$2$ bottom product contains $97\mathrm{.}7$mol$\%$ of ethylene oxide and the balance ethylene. It is noted that the production rate is refer to the molar flowrate of $S2$ bottom product.

The basic process flow diagram is presented in Figure $1.$

YOUR TASK

The production rate of ethylene oxide is in range between $100$kmo$\frac{l}{h}r$ to $150$kmo$\frac{l}{h}r.$ As a group of engineers in the company, you are assigned to evaluate the plant design in producing ethylene oxide. Your task is to cover three $(3)$ case study, case $($a$),$ case $($b$)$ and case $($c$)$ as listed below:

a$)$ By choosing one $(1)$ basis of production rate, evaluate the molar flowrate of stream $F,n_1,n_2,n_3,n_4,$ and $T$ and the molar composition of stream $F,n_2,n_3,$ and $n_4.$

Hint: The chosen value musf be in the range of currenf production rate $(100$ kmo$\frac{l}{h}r$ to $150$ kmolhry.

b$)$ Evaluate the molar flowrate and composition of stream $F$ if top product of $S2($Stream $T)$ in case $($a$)$ is recycle to the reactor at the mixing point. Give your opinion about the difference between value of $F$ in case $($a$)$ and case $($b$).$

c$)$ If the manager of the company proposes to maximize ethylene oxide production by considering ALL factors including:

To increase the production rate about $10\%$ from the value as chosen in case $($a$)$

To achieve a composition of $99$ mol$\%$ ethylene oxide at production stream $($Stream P$)$

To recycle the top product of $S2($Stream T$)$ to the reactor at the mixing point

Evaluate the molar flowrate of stream $F,n_1,n_2,n_3,n_4,$ and $T$ and molar composition of stream $F,n_2,n_3,$ and $n_4.$ Give your opinion about the difference between molar flowrate and composition of streams in case $($a$),$ case $($b$)$ and case $($c$)$ including advantages and constraints for these three cases.

Hint: The composition of stream $n$ is the same as case $($a$)$ and case $($b$).$ Similarly to case $($a$)$ and case $($b$),95\%$ of ethylene fed to the $S2$ will exit the $S2$ as top product.

d$)$ Draw and label the flowchart for case $($a$),$ case $($b$)$ and case $($c$)$ completely with molar flawrate and composition for each stream.