The quench contents are fed to a $7-$stage distillation column above stage $2$ at $12$ atm $(T100$; stream $8)$ where $HCl$ is recovered at $97\%$ purity in the distillate $($stream $9)$ and the remainder of the pyrolysis products are fed in the bottoms stream to a second, similar, $9-$stage distillation column above stage $3$ at $4\mathrm{.}8$ atm $(T-101$; stream $10).$ This column yields a $97\mathrm{.}6\%$ pure vinyl chloride stream in the distillate $($stream $11)$ and the $1,2-$dichloroethane$-$rich bottoms stream is recycled ahead of the centrifugal pump $($stream $12).$ The energy flow framework diagram $($EFD$)$ and process flow diagram $($PFD$)$ for direct chlorination process are given in Figure $1$ and $2,$ respectively. Summaries data for all the processes is given in Table $1.$

Derive a differential balance on total mass and vinyl chloride if Stream $11$ is to be stored in a wellmixed tank. Provide your initial conditions. Predict the volume of the tank to be installed if the tank requires $10$ hours to be fully filled.

E$-100$CondenserE$-100$EthyleneChlorineP$-100$Reactor pumpR$-100$DirectchlorinationreactorR$-100$P$-101$Quench tankpumpE$-101$EvaporatorE$-101$E$-102$p$-100$T$-100$F$-100$HCI columnF$-100$PyrolysisfurnaceP$-101$V$-100$E$-10412$HCl columnreboilerV$-100$Quench tank$810$T$-101$E$-102$Quench coolerE$-106$VC columnE$-108$T$-100$Figure $1$: EFD for direct chlorination process.E$-104$E$-105$T$-101$E$-105$E$-108$HCI columncondenserVC columncondenserVCE$-106$VC columnreboiler