Steam reforming is a process to convert natural gas into synthetic gas containing CO and H$2.$ One of the problem is carbon deposit and to deal with it$,$ one of the solution is to increase the steam$-$to$-$carbon ratio $($S$/$C ratio$)$ or steam$-$to$-$gas ratio $($S$/$G ratio$).$ In ammonia plant, S$/$G ratio is maintained at $3\mathrm{.}1-3\mathrm{.}2($kg$/$kg$)$ and if the ratio drops to $2\mathrm{.}25($kg$/$kg$),$ the plant will be automatically shutdowned by the system

The reaction of steam reforming section is as follow:

CH$4($g$)+$ H$2$O$($g$)<->$ CO$($g$)+3$H$2($g$).....($A$)$

Nevertheless, this water$-$gas shift reaction also occurs at the same reactor:

CO$($g$)+$ H$2$O$($g$)<->$ CO$2($g$)+$ H$2($g$).....($B$)$

Problem Statement:

Its is supposed that the carbon deposit C$($s$)$ is produced according to these following reactions:

$2$CO$($g$)<->$ C$($s$)+$ CO$2($g$).....($C$)$

CH$4($g$)<->$ C$($s$)+2$H$2($g$).....($D$)$

Question $1-$ Determine the minimum S$/$C ratio $($mol$/$mol$)$ that can lead to carbon deposition from reaction C and$/$or D

Question $2-$ Determine which reaction from C or D that produces more carbon deposit, if any and if it happens

Assumptions:

a$.$ Reaction A and B always reach equilibrium

b$.$ The feed contains only methane and water vapor in gas phase

c$.$ Operating condition: $36\mathrm{.}5$ bar and $810$ C

For the first reaction, k$=181\mathrm{.}12$

For the second reaction, k$=1\mathrm{.}05$

For the third reaction, k$=0\mathrm{.}11$

For the fourth reaction, k$=20\mathrm{.}08$

Notes: Please show how to solve the problem using partial pressures, if you could screenshot the excel file it would be great, thanks $($manual calculation is also OK$)$