Develop a block diagram showing all of the constituent process reactions $($one reaction or process per block$)$ required to produce common PET polyester $($polyethyleneterephthalate$)$ via the DMT Route starting from fundamental raw materials such as natural gas methane $($CH$4),$ natural gas condensate ethane $($C$2$H$6),$ crude oil naphtha $($assume normal octane, C$8$H$18)),$ air $($N$2$ and O$2),$ and water $($H$2$O$).$ Write balanced chemical equations for every reaction. Considering the overall supply chain and its component balances, comment on recycle possibilities among these constituent processes within the supply chain.

Intermediates you should consider include:

Ethylene, C$2$H$4$

Ethylene Oxide $($EO$),$ C$2$H$4$O $(3-$member ring$)$

Ethylene Glycol $($EG$),$ HOC$2$H$4$OH

Xylene $($mixed$),$ C$6$H$4($CH$3)2($three isomers$)$

Paraxylene $(1,4-$dimethylbenzene, pX$),$ CH$3$C$6$H$4$CH$3$

Terephthalic Acid $(1,4-$benzenedicarboxylic acid, TPA$),$ HOOCC$6$H$4$COOH

Carbon Dioxide, CO$2$

Carbon Monoxide, CO

Hydrogen, H$2$

Methanol $($MeOH$),$ CH$3$OH

Dimethylterephthalate $($DMT$),$ CH$3$OOCC$6$H$4$COOCH$3$

Bis$(2-$hydroxyethyl$)$terephthalate $($PET "monomer", BHET$),$ HOC$2$H$4$OOCC$6$H$4$COOC$2$H$4$OH

Polyethyleneterephthalate $($PET$),($C$2$H$4$OOCC$6$H$4$COO$)$n

Some chemistries:

Ethylene is made by steam cracking of ethane $($the steam keeps the system from coking$)$

Ethylene oxide is made by the air oxidation of ethylene

Ethylene glycol is made by ethylene oxide hydration

Xylene is made by the catalytic reforming of octane

Terephthalic acid is made by the air oxidation of paraxylene isomer

Carbon dioxide is made by the combustion of methane

Syngas $($hydrogen carbon monoxide mixture$)$ is made by the steam reforming of methane

Excess hydrogen in syngas can be reacted with carbon dioxide to produce carbon monoxide $($water gas shift reaction$)$

Methanol is made from an exactly $2$:$1($hydrogen : carbon monoxide$)$ ratio syngas

Dimethylterephthalate is made by the esterification of terephthalic acid with methanol

Bis$(2-$hydroxyethyl$)$terephthalate is made by the transesterification of DMT with EG

Polyethyleneterephthalate is made by the polycondensation of BHET splitting out EG

An appropriate basis for the overall supply chain component balances might be the final polymer repeat unit $-$C$2$H$4$OOC$6$H$4$COO$-.$