Polyvinyl chloride $($PVC$)$ is one of the widely used polymers. It is obtained by polymerization of vinyl chloride monomer $($VCM$).$ This problem concerns process for VCM manufacturing. VCM can be produced from ethylene via a $2-$step process. In the first step, ethylene is converted into ethylene dichloride $($EDC$)$ by direct chlorination or oxychlorination. In direct chlorination, chlorine and ethylene react to form EDC.

C$2$H$4+$ Cl$2->$ C$2$H$4$Cl$2(29)$ In oxychlorination, ethylene reacts with hydrogen chloride, in the presence of oxygen, to

product EDC.

C$2$H$4+2$HCl $+21$O$2->$ C$2$H$4$Cl$2+$ H$2$O $(30)$ In the second step, the EDC is cracked to form vinyl chloride

C$2$H$4$Cl$2->$ C$2$H$3$Cl $+$ HCl $(31)9$

Feed gas Fresh benzene

Et$,$ Ey B

Et$,$ Ey$,$ B$,$ EB$,$ DEB

Et: Ethane

Ey: Ethylene B: Benzene EB: Ethylbenzene DEB: Diethyl benzene

Figure $3$: Ethylbenene process

Et$,$ Ey$,$ B

Et$,$ Ey$,$ B

B$,$ EB$,$ DEB

B$,$ EB$,$ DEB

RC

PC

Purge gas

Ethylbenzene

B$,$ EB$,$ DEB

Reactor

Et$,$ Ey$,$ B$,$ EB$,$ DEB

flash

Benzene

recycle

Et$,$ Ey$,$ B$,$ EB

DEB recycle

EB$,$ DEB

Q $12.$

A simplified process for VCM manufacturing plant is shown in figure $4.$ A part of the total ethylene feed is sent to direct chlorination reactor $($R$1).$ Ethylene is used in excess to force complete conversion of chlorine. The reactor outlet is sent to flash vessel $1.$ The vapor phase is recycled back to the reactor after taking out a small purge stream. The liquid phase is sent to the pyrolysis $($cracker$)$ reactor $($R$3).$ In order to maintain selectivity, reactor R$3$ conversion is kept to a low value. The outlet from R$3$ is sent to a recycle column, wherein HCl is separated from VCM and EDC. The bottom stream from the recycle column is sent to the product column wherein high purity VCM product is taken as distillate. The bottom stream containing predominantly EDC is recycled back to the pyrolysis reactor. In order to improve atom economy with respect to chlorine, the HCl generated is sent to oxychlorination reactor $($R$2).$ The remaining ethylene fresh feed is also sent to R$2,$ along with oxygen. In this reactor, excess ethylene is used to force complete conversion of HCl$.$ Due to the presence of oxygen, a small amount of ethylene also combusts to form CO$2.$

C$2$H$4+3$O$2->2$CO$2+2$H$2$O $(32)$

Accordingly, oxygen is also supplied in excess. The outlet from R$2$ is sent to flash vessel $2$ to remove light gases. The liquid from flash vessel $2$ is sent to the dewatering column to get dehydrated EDC, which is then sent to the pyrolysis reactor. The components present in each stream are indicated in the flowsheet.

Consider that the feed gas contains $99\%$ ethylene and rest ethane. Chlorine and Oxygen feed can be considered pure. Ethylene to Chlorine at R$1$ inlet is maintained at $2$:$1.$ Ethylene to HCl at R$2$ inlet is maintained at $0\mathrm{.}6$:$1.$ Oxygen to HCl at R$2$ inlet is maintained at $0\mathrm{.}5$:$1.$ Selectivity of EDC in R$2$ in terms of ethylene reacted is $0\mathrm{.}9.$ Conversion in R$3$ is $0\mathrm{.}4.$

You are required to compute the flow rate of feed gas required to produce VCM at $100$ kmol$/$h with $99\mathrm{.}5\%$ purity. You can select appropriate values of any other design variables, as required. Clearly state definition and selected value of any such design variable.